(1730,2,'2012-11-06 17:21:12','2012-11-06 22:21:12','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Sectio</span></strong></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">n 3. Drivers and Mixers </span>*incomplete*</strong></a>\r\n<ul>\r\n	<li><a href=\"#led\"> LED driver</a></li>\r\n	<li><a href=\"#mixer\">Signal mixer</a><strong></strong></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignleft\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div></div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 an\r\n\r\nd\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>                                           comparator also functions as a pulse width modulation processor.\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Mixer</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is calculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-25','','','2012-11-06 17:21:12','2012-11-06 22:21:12','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-25/',0,'revision','',0);
INSERT INTO `wp_posts` VALUES (1731,2,'2012-11-06 17:21:58','2012-11-06 22:21:58','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Sectio</span></strong></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">n 3. Drivers and Mixers </span>*incomplete*</strong></a>\r\n<ul>\r\n	<li><a href=\"#led\"> LED driver</a></li>\r\n	<li><a href=\"#mixer\">Signal mixer</a><strong></strong></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 an\r\n\r\nd\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>                                           comparator also functions as a pulse width modulation processor.\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Mixer</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is calculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-26','','','2012-11-06 17:21:58','2012-11-06 22:21:58','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-26/',0,'revision','',0),(1737,2,'2012-11-06 19:33:09','2012-11-07 00:33:09','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><span style=\"color: #0000ff;\"><a href=\"#sec3\"><span style=\"color: #0000ff;\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mixer\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-31','','','2012-11-06 19:33:09','2012-11-07 00:33:09','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-31/',0,'revision','',0),(1734,2,'2012-11-06 19:20:50','2012-11-07 00:20:50','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Sectio</span></strong></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">n 3. Drivers and Mixers </span>*incomplete*</strong></a>\r\n<ul>\r\n	<li><a href=\"#led\"> LED driver</a></li>\r\n	<li><a href=\"#mixer\">Signal mixer</a><strong></strong></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n<a name=\"sec3\">\r\n<h3><span style=\"color: #3366ff;\"><strong><a href=\"#sec3\"><span style=\"color: #3366ff;\"><strong>Sectio</strong></span></a><strong><a href=\"#sec3\"><span style=\"color: #3366ff;\">n 3. Drivers and Mixers</span></a></strong></strong></span></h3>\r\n<ul><a name=\"mix\">\r\n	<li><strong style=\"color: #3366ff;\">Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is calculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n\r\n<hr />\r\n<a name=\"led\">\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-28','','','2012-11-06 19:20:50','2012-11-07 00:20:50','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-28/',0,'revision','',0),(1733,2,'2012-11-06 17:25:03','2012-11-06 22:25:03','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Sectio</span></strong></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">n 3. Drivers and Mixers </span>*incomplete*</strong></a>\r\n<ul>\r\n	<li><a href=\"#led\"> LED driver</a></li>\r\n	<li><a href=\"#mixer\">Signal mixer</a><strong></strong></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Mixer</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is calculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-27','','','2012-11-06 17:25:03','2012-11-06 22:25:03','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-27/',0,'revision','',0),(1738,2,'2012-11-06 19:36:56','2012-11-07 00:36:56','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mixer\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-32','','','2012-11-06 19:36:56','2012-11-07 00:36:56','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-32/',0,'revision','',0),(1736,2,'2012-11-06 19:28:52','2012-11-07 00:28:52','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><span style=\"color: #0000ff;\"><a href=\"#sec3\"><span style=\"color: #0000ff;\"><strong><span style=\"text-decoration: underline;\">Sectio</span></strong></span></a><strong><span style=\"text-decoration: underline;\"><a href=\"#sec3\"><span style=\"color: #0000ff; text-decoration: underline;\">n 3. </span></a>Sound and Light</span></strong></span>\r\n<ul>\r\n	<li><a href=\"#led\"> LED driver</a></li>\r\n	<li><a href=\"#mixer\">Signal mixer</a><strong></strong></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-30','','','2012-11-06 19:28:52','2012-11-07 00:28:52','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-30/',0,'revision','',0),(1735,2,'2012-11-06 19:23:58','2012-11-07 00:23:58','Throughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Sectio</span></strong></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">n 3. Drivers and Mixers </span>*incomplete*</strong></a>\r\n<ul>\r\n	<li><a href=\"#led\"> LED driver</a></li>\r\n	<li><a href=\"#mixer\">Signal mixer</a><strong></strong></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n<hr />\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. Drivers and Mixers</span></span><strong style=\"color: #3366ff;\">Mixer</strong></h3>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','NovaDrone Tech Manual',0,'','inherit','open','closed','','1704-revision-29','','','2012-11-06 19:23:58','2012-11-07 00:23:58','',1704,'http://casperelectronics.com/2012/11/06/1704-revision-29/',0,'revision','',0),(1741,2,'2012-11-09 07:48:34','2012-11-09 12:48:34','The NovaDrone was designed (and continues to evolve) in collaboration with experimental musician and epic visionary G. Lucas Crane aka <a href=\"http://nonhorse.com/\">Nonhorse</a> and with support from <a href=\"http://perte-de-signal.org/\">Perte De Signal</a> in Montreal. \r\nI\'d like to send a big <strong>thanks</strong> to <a href=\"http://www.darsha.org/\">Darsha</a> and Robin at PDS for all their help. And I\'ll be hi-fiving Lucas for the rest of my life for all the amazing work he\'s done so far. \r\n<hr />\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublefinished.better.jpg\"><img class=\"alignleft size-medium wp-image-1229\" title=\"doublefinished.better\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublefinished.better-273x300.jpg\" alt=\"\" width=\"253\" height=\"300\" /></a><img class=\"alignleft size-medium wp-image-1231\" title=\"singlefinished.better2\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/singlefinished.better2-191x300.jpg\" alt=\"\" width=\"191\" height=\"300\" /></a>\r\n<h1>Please send all questions to Novaworldorders@gmail.com.</h1>\r\n<iframe src=\"http://www.youtube.com/embed/kpwnVEOsOrA?rel=0\" frameborder=\"0\" width=\"460\" height=\"235\"></iframe>\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublePCB.lone_.better.jpg\"><img class=\"aligncenter size-full wp-image-1226\" title=\"doublePCB.lone.better\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublePCB.lone_.better.jpg\" alt=\"\" width=\"460\" height=\"436\" /></a>\r\n\r\n<hr />\r\n<h1>What is it?</h1>\r\nThe Nova Drone is an open source, analog experimental sound and light synth.\r\nIt it can be used to create effects ranging from slowly fading drones to chaotic harmonic sequences. It also functions as a complex visual pattern generator when combined with a digital/phone video camera. See the video below for an example of the color patterns generated by holding a camera up to the LED.\r\n<iframe width=\"460\" height=\"235\" src=\"http://www.youtube.com/embed/8V4F9szooI8?rel=0\" frameborder=\"0\" allowfullscreen></iframe>\r\n<iframe src=\"http://www.youtube.com/embed/i0o9QEYpCIs?rel=0\" frameborder=\"0\" width=\"450\" height=\"315\"></iframe>\r\n\r\nThe Nova Drones offers 12 potentiometers, 10 switches, 6 oscillators, 9 oscillator sync inputs, 6 frequency modulation inputs and an epic 15 voltage outputs as well as 3 high current outputs for controlling external LEDs. All of the ins and outs have been routed to a prototyping breadboard at the bottom of the unit which allows for liberal experimentation and development of custom circuits. The prototyping area is especially useful for syncing the oscillators of 2 or more Nova Drones together.\r\n\r\n<hr />\r\n\r\n<iframe src=\"http://www.youtube.com/embed/lxDt0-l2eH4?rel=0\" frameborder=\"0\" width=\"450\" height=\"315\"></iframe>\r\n\r\n<hr />\r\n\r\n<h2>The NovaDrone Stacks!</h2>\r\nPlug 2 or more NovaDrones together to share power and audio and get super drones.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/stackin.jpg\"><img class=\"alignnone size-medium wp-image-1250\" title=\"boardIllustrationPLAIN\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/stackin-300x186.jpg\" alt=\"\" width=\"400\" height=\"266\" /></a>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-medium wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1-300x6.jpg\" alt=\"\" width=\"300\" height=\"6\" /></a>\r\n<iframe src=\"http://www.youtube.com/embed/lO6QA9Tyn3E?rel=0\" frameborder=\"0\" width=\"420\" height=\"315\"></iframe>\r\n\r\n<hr />\r\n\r\n<strong>HARDWARE</strong>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/boardIllustrationCONTROLS.jpg\"><img class=\"alignleft size-medium wp-image-1251\" title=\"boardIllustrationCONTROLS\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/boardIllustrationCONTROLS-176x300.jpg\" alt=\"\" width=\"176\" height=\"300\" /></a>\r\nThe NovaDrone offers 3 channels of sound and light. <strong>Each channel</strong> has the following features:\r\n<strong>ADJUSTABLE CONTROLS</strong>\r\n-volume\r\n-TONE pitch coarse tune 24Hz to 750Hz\r\n-TONE pitch fine tune\r\n-LFO rate .008 Hz (around 1 cycle every 2 minutes) to 750Hz\r\n<strong>SWITCHES</strong>\r\n-sync 1\r\n-sync 2\r\n<strong>INPUTS</strong>\r\n- ext sync 3\r\n-PITCH modulation\r\n-LFO rate modulation\r\n<strong>OUTPUTS</strong>\r\n-TONE square wave\r\n-TONE triangle wave\r\n-LFO square wave\r\n-LFO triangle wave\r\n-PWM square wave\r\n-High current LED out for off board LEDs.\r\n\r\n<hr />\r\n\r\n<strong>SCHEMATIC:</strong>\r\nV1.2 fixed virtual ground error\r\n5/1/2012\r\nV1.3 fixed signal path errors\r\n5/16/2012\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/HomePage/NovaDroneV1.3_schematic.png\"><img class=\"alignnone size-medium wp-image-1046\" title=\"NovaDroneV1.3_schematic\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/HomePage/NovaDroneV1.3_schematic-225x300.png\" alt=\"\" width=\"225\" height=\"300\" /></a>\r\n\r\n<hr />\r\n<strong>Links:</strong>\r\n<h2><span style=\"color: #33cccc;\"><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/novadrone-sales-page/\"><span style=\"color: #33cccc;\">Store</span></a></span></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/users-manual/\">User\'s Manual</a></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/assembly-manual/\">Assembly Manual</a></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/theory/\">Circuit Theory</a></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/parts/\">Parts List</a></h2>\r\n<hr/>\r\n<h3><strong>Version 1.2</strong></h3>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/V1.2/IMG_2655.jpg\"><img class=\"alignnone size-large wp-image-1129\" title=\"IMG_2655\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/V1.2/IMG_2655-1024x682.jpg\" alt=\"\" width=\"450\" height=\"280\" /></a>\r\n\r\n<iframe src=\"http://www.youtube.com/embed/QHB4rVwSh8Y?rel=0\" frameborder=\"0\" width=\"450\" height=\"280\"></iframe>\r\n\r\n<iframe src=\"http://www.youtube.com/embed/d5PooXdGQzU?rel=0\" frameborder=\"0\" width=\"450\" height=\"255\"></iframe>\r\n\r\n<hr />\r\n\r\n<h3><strong>PROTOTYPING:</strong></h3>\r\n<iframe src=\"http://www.youtube.com/embed/XYliYHHihzU?rel=0\" frameborder=\"0\" width=\"400\" height=\"275\"></iframe>','Nova Drone',0,'','inherit','open','closed','','1028-revision-60','','','2012-11-09 07:48:34','2012-11-09 12:48:34','',1028,'http://casperelectronics.com/2012/11/09/1028-revision-60/',0,'revision','',0),(1742,2,'2012-11-09 07:49:37','2012-11-09 12:49:37','The NovaDrone was designed (and continues to evolve) in collaboration with experimental musician and epic visionary G. Lucas Crane aka <a href=\"http://nonhorse.com/\">Nonhorse</a> and with support from <a href=\"http://perte-de-signal.org/\">Perte De Signal</a> in Montreal. \r\nI\'d like to send a big <strong>thanks</strong> to <a href=\"http://www.darsha.org/\">Darsha</a> and Robin at PDS for all their help. And I\'ll be hi-fiving Lucas for the rest of my life for all the amazing work he\'s done so far. \r\n<hr />\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublefinished.better.jpg\"><img class=\"alignleft size-medium wp-image-1229\" title=\"doublefinished.better\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublefinished.better-273x300.jpg\" alt=\"\" width=\"253\" height=\"300\" /></a>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/singlefinished.better2.jpg\">\r\n<img class=\"alignleft size-medium wp-image-1231\" title=\"singlefinished.better2\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/singlefinished.better2-191x300.jpg\" alt=\"\" width=\"191\" height=\"300\" /></a>\r\n<h1>Please send all questions to Novaworldorders@gmail.com.</h1>\r\n<iframe src=\"http://www.youtube.com/embed/kpwnVEOsOrA?rel=0\" frameborder=\"0\" width=\"460\" height=\"235\"></iframe>\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublePCB.lone_.better.jpg\"><img class=\"aligncenter size-full wp-image-1226\" title=\"doublePCB.lone.better\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublePCB.lone_.better.jpg\" alt=\"\" width=\"460\" height=\"436\" /></a>\r\n\r\n<hr />\r\n<h1>What is it?</h1>\r\nThe Nova Drone is an open source, analog experimental sound and light synth.\r\nIt it can be used to create effects ranging from slowly fading drones to chaotic harmonic sequences. It also functions as a complex visual pattern generator when combined with a digital/phone video camera. See the video below for an example of the color patterns generated by holding a camera up to the LED.\r\n<iframe width=\"460\" height=\"235\" src=\"http://www.youtube.com/embed/8V4F9szooI8?rel=0\" frameborder=\"0\" allowfullscreen></iframe>\r\n<iframe src=\"http://www.youtube.com/embed/i0o9QEYpCIs?rel=0\" frameborder=\"0\" width=\"450\" height=\"315\"></iframe>\r\n\r\nThe Nova Drones offers 12 potentiometers, 10 switches, 6 oscillators, 9 oscillator sync inputs, 6 frequency modulation inputs and an epic 15 voltage outputs as well as 3 high current outputs for controlling external LEDs. All of the ins and outs have been routed to a prototyping breadboard at the bottom of the unit which allows for liberal experimentation and development of custom circuits. The prototyping area is especially useful for syncing the oscillators of 2 or more Nova Drones together.\r\n\r\n<hr />\r\n\r\n<iframe src=\"http://www.youtube.com/embed/lxDt0-l2eH4?rel=0\" frameborder=\"0\" width=\"450\" height=\"315\"></iframe>\r\n\r\n<hr />\r\n\r\n<h2>The NovaDrone Stacks!</h2>\r\nPlug 2 or more NovaDrones together to share power and audio and get super drones.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/stackin.jpg\"><img class=\"alignnone size-medium wp-image-1250\" title=\"boardIllustrationPLAIN\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/stackin-300x186.jpg\" alt=\"\" width=\"400\" height=\"266\" /></a>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-medium wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1-300x6.jpg\" alt=\"\" width=\"300\" height=\"6\" /></a>\r\n<iframe src=\"http://www.youtube.com/embed/lO6QA9Tyn3E?rel=0\" frameborder=\"0\" width=\"420\" height=\"315\"></iframe>\r\n\r\n<hr />\r\n\r\n<strong>HARDWARE</strong>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/boardIllustrationCONTROLS.jpg\"><img class=\"alignleft size-medium wp-image-1251\" title=\"boardIllustrationCONTROLS\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/boardIllustrationCONTROLS-176x300.jpg\" alt=\"\" width=\"176\" height=\"300\" /></a>\r\nThe NovaDrone offers 3 channels of sound and light. <strong>Each channel</strong> has the following features:\r\n<strong>ADJUSTABLE CONTROLS</strong>\r\n-volume\r\n-TONE pitch coarse tune 24Hz to 750Hz\r\n-TONE pitch fine tune\r\n-LFO rate .008 Hz (around 1 cycle every 2 minutes) to 750Hz\r\n<strong>SWITCHES</strong>\r\n-sync 1\r\n-sync 2\r\n<strong>INPUTS</strong>\r\n- ext sync 3\r\n-PITCH modulation\r\n-LFO rate modulation\r\n<strong>OUTPUTS</strong>\r\n-TONE square wave\r\n-TONE triangle wave\r\n-LFO square wave\r\n-LFO triangle wave\r\n-PWM square wave\r\n-High current LED out for off board LEDs.\r\n\r\n<hr />\r\n\r\n<strong>SCHEMATIC:</strong>\r\nV1.2 fixed virtual ground error\r\n5/1/2012\r\nV1.3 fixed signal path errors\r\n5/16/2012\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/HomePage/NovaDroneV1.3_schematic.png\"><img class=\"alignnone size-medium wp-image-1046\" title=\"NovaDroneV1.3_schematic\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/HomePage/NovaDroneV1.3_schematic-225x300.png\" alt=\"\" width=\"225\" height=\"300\" /></a>\r\n\r\n<hr />\r\n<strong>Links:</strong>\r\n<h2><span style=\"color: #33cccc;\"><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/novadrone-sales-page/\"><span style=\"color: #33cccc;\">Store</span></a></span></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/users-manual/\">User\'s Manual</a></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/assembly-manual/\">Assembly Manual</a></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/theory/\">Circuit Theory</a></h2>\r\n<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/parts/\">Parts List</a></h2>\r\n<hr/>\r\n<h3><strong>Version 1.2</strong></h3>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/V1.2/IMG_2655.jpg\"><img class=\"alignnone size-large wp-image-1129\" title=\"IMG_2655\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/V1.2/IMG_2655-1024x682.jpg\" alt=\"\" width=\"450\" height=\"280\" /></a>\r\n\r\n<iframe src=\"http://www.youtube.com/embed/QHB4rVwSh8Y?rel=0\" frameborder=\"0\" width=\"450\" height=\"280\"></iframe>\r\n\r\n<iframe src=\"http://www.youtube.com/embed/d5PooXdGQzU?rel=0\" frameborder=\"0\" width=\"450\" height=\"255\"></iframe>\r\n\r\n<hr />\r\n\r\n<h3><strong>PROTOTYPING:</strong></h3>\r\n<iframe src=\"http://www.youtube.com/embed/XYliYHHihzU?rel=0\" frameborder=\"0\" width=\"400\" height=\"275\"></iframe>','Nova Drone',0,'','inherit','open','closed','','1028-revision-61','','','2012-11-09 07:49:37','2012-11-09 12:49:37','',1028,'http://casperelectronics.com/2012/11/09/1028-revision-61/',0,'revision','',0),(1743,2,'2012-10-10 11:35:54','2012-10-10 16:35:54','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\n\n<hr />\n\nOn this page you will find the circuit theory PDF along with some comments as the document is updated. Feel free to post questions. \nThe manual is under construction (october 10, 2012) Please check back soon!\n<a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/phase-copy-copy.jpg\"><img class=\"alignnone size-large wp-image-1392\" title=\"phase copy copy\" src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/phase-copy-copy-1024x451.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-10-10 11:35:54','2012-10-10 16:35:54','',1369,'http://casperelectronics.com/2012/10/10/1369-revision-9/',0,'revision','',0),(1744,2,'2012-10-21 20:34:24','2012-10-22 01:34:24','<a href=\"http://casperelectronics.com/wp-content/uploads/Convergence.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/Convergence-200x149.jpg\" alt=\"\" title=\"Convergence\" width=\"200\" height=\"149\" class=\"alignleft size-medium wp-image-1566\" /></a>\r\n\r\n<h1>Convergence is an interactive installation that invites the audience to create music and colorful visuals by manipulating a few <a href=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/HomePage/NovaDroneV1.3_schematic.png\">simple electronic oscillators</a>.</h1>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"1\" class=\"size-full wp-image-1300\" /></a>\r\n<hr>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pedestal.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/pedestal-200x200.jpg\" alt=\"\" title=\"Pedestal\" width=\"200\" height=\"200\" class=\"alignright size-medium wp-image-1602\" /></a>\r\nThe installation is made up of a circular control station monitored by a small camera hanging directly above it. Manipulating the controls on the control station triggers oscillators which are represented as sound from within the station and light from the light fixture on top of the station. The light is then captured by the camera and projected on the screen. See the second video below (the horizontal color bars) for an example of the video output of the camera.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"1\" class=\"size-full wp-image-1300\" /></a>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/sketch.jpg\"><img class=\"alignnone size-large wp-image-1568\" title=\"Sketch\" src=\"http://casperelectronics.com/wp-content/uploads/sketch-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a>\r\n<hr>\r\n\r\n&nbsp;\r\n\r\n<strong>Background:</strong>\r\nThis piece is an evolved version of a musical instrument I have recently designed called the <a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\">NovaDrone</a>. There is extensive documentation of this project <a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\">here</a>.\r\n\r\nThe NovaDrone is a sound and light synthesizer which uses analog oscillators and pulse width modulation to create interlink sound and light.\r\nThis technology will be implemented in Convergence to achieve lighting effects similar to the video below. \r\n<iframe src=\"http://www.youtube.com/embed/QHB4rVwSh8Y?rel=0\" frameborder=\"0\" width=\"450\" height=\"280\"></iframe>\r\nThe video below shows a complex visual display which is created by holding a digital camera up to the light source. This effect will be utilized to create the projected visuals for Convergence.\r\n<iframe width=\"450\" height=\"230\" src=\"http://www.youtube.com/embed/8V4F9szooI8?rel=0\" frameborder=\"0\" allowfullscreen></iframe>\r\n<iframe src=\"http://www.youtube.com/embed/i0o9QEYpCIs?rel=0\" frameborder=\"0\" width=\"450\" height=\"315\"></iframe>\r\n\r\n\r\n\r\n\r\n<strong>History / other sound&Light installations:</strong>\r\nThe projects below deal with similar topics of interlinked sound and light and public engagement. \r\n<a href=\"http://casperelectronics.com/art/kosmos/\">Kosmos.</a> Outdoor installation. Reacts to environmental stimulation.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/Kosmos1.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/Kosmos1-200x132.jpg\" alt=\"\" title=\"Kosmos1\" width=\"200\" height=\"132\" class=\"alignnone size-medium wp-image-1577\" /></a>\r\n\r\n<a href=\"http://casperelectronics.com/art/specter/\">Specter.</a> Installation in elevator. Glow in response to environmental sounds.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/acapela.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/acapela-200x133.jpg\" alt=\"\" title=\"Acapela\" width=\"200\" height=\"133\" class=\"alignnone size-medium wp-image-1578\" /></a>\r\n\r\n\r\n<a href=\"http://casperelectronics.com/art/bit-bender/\">BitBender.</a> Video game with custom joysticks. Allows viewers to play game while creating complex sounds and graphics manipulations.<a href=\"http://casperelectronics.com/wp-content/uploads/BitBender/IMG_2184.jpg\">\r\n<img src=\"http://casperelectronics.com/wp-content/uploads/BitBender/IMG_2184-300x200.jpg\" alt=\"\" title=\"IMG_2184\" width=\"200\" height=\"133\" class=\"alignnone size-medium wp-image-874\" /></a>\r\n\r\n<a href=\"http://casperelectronics.com/art/white-light-2/\">\r\nWhite Light.</a> Interlinked sound and light performance interface.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/WhiteLightEnsemble.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/WhiteLightEnsemble-200x132.jpg\" alt=\"\" title=\"WhiteLightEnsemble\" width=\"200\" height=\"132\" class=\"alignnone size-medium wp-image-1579\" /></a>\r\n','Convergence',0,'','inherit','open','closed','','1564-revision-29','','','2012-10-21 20:34:24','2012-10-22 01:34:24','',1564,'http://casperelectronics.com/2012/10/21/1564-revision-29/',0,'revision','',0),(1745,2,'2012-11-09 07:54:28','2012-11-09 12:54:28','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\n\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>When this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until that vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-09 07:54:28','2012-11-09 12:54:28','',1369,'http://casperelectronics.com/2012/11/09/1369-revision-10/',0,'revision','',0),(1807,2,'2013-02-25 11:07:09','2013-02-25 16:07:09','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\nIn this document I will explain the basic operation of the NovaDrone.\n\nThis guide is intended to serve as a list of suggestions and inspiration. I encourage users to explore and find new ways to use the NovaDrone.  I also encourage those interested in how the NovaDrone works to read through the <a href=\"http://casperelectronics.com/finished-pieces/nova-drone/theory/\">NovaDrone theory page</a>.\nIf you want to get right to it you can jump ahead to the illustrated <a href=\"#tutorials\">tutorial section</a>.\n\n<hr />\n\n<b>Table of contents</b>\n\n<a name=\"power\"></a>\n<ol>\n	<li><a href=\"#power\">Power</a></li>\n	<li><a href=\"#stacking\">Stacking</a></li>\n	<li><a href=\"#controls\">Controls</a></li>\n	<li><a href=\"#syncing\">Syncing</a></li>\n	<li><a href=\"#IO\">Inputs&amp;Outputs</a></li>\n	<li><a href=\"#adventure\">The adventure board</a></li>\n	<li><a href=\"#tutorials\">Tutorials</a></li>\n</ol>\n\n<hr />\n\n<b><b> </b></b>\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>POWER</strong></span></h2>\nThe NovaDrone requires a power adapter in order to operate.\n\nA suitable power adapter is sold in the Casperelectronics store.\n\nYou are welcome to source your own power supply as long as it matches the parameters listed below:\n\n<b>12-24 Volts DC. </b>\n\n<b>300mA (or more).</b>\n\n<b>negative ring, positive tip.</b>\n\n<b>inner dimension of 2.5mm. </b>\n<a name=\"stacking\"></a>\n\nThe power input is diode protected so plugging in a supply of the wrong polarity will have no negative effect (it just won’t work). The power input is also regulated which means that any voltage between 10 and 30 volts DC will be regulated down to a smooth 9 volts.\n\n&nbsp;\n\n<hr />\n\n<b><b> </b></b>\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>STACKING</strong></span></h2>\nThe NovaDrone has two <b>link ports</b>, an <i>input</i> on the right and an <i>output</i> on the left. This allows multiple units to be plugged together. Linked units share power and a common audio bus. This means that all of the units operate on one power supply plugged into the <b>left most power jack</b> and all audio is bussed to the <b>left most audio output jack</b>.\n\nThe audio chain can be broken by plugging a guitar cable into any one of the output jacks in the chain as shown in fig. 1.\n<a name=\"controls\"></a>\n<a href=\"http://casperelectronics.com/wp-content/uploads/boardIllustrationSTACKING.jpg\"><img class=\"alignnone size-large wp-image-1812\" alt=\"BoardIllustrationSTACKING\" src=\"http://casperelectronics.com/wp-content/uploads/boardIllustrationSTACKING-460x96.jpg\" width=\"460\" height=\"96\" /></a>\n\n<hr />\n\n<b><b> </b></b>\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>CONTROLS</strong></span></h2>\n<a href=\"http://casperelectronics.com/wp-content/uploads/CONTROLS.jpg\"><img class=\"alignnone size-large wp-image-1816\" alt=\"CONTROLS\" src=\"http://casperelectronics.com/wp-content/uploads/CONTROLS-460x1020.jpg\" width=\"460\" height=\"1020\" /></a>\nThe NovaDrone has three voices labeled RED, GREEN and BLUE. These voices combine to create a single audio output and light display.\nEach voice has the following controls:\n-<strong>LFO mode</strong>. Set the range of the LFO from very slow (once per 2-3 minutes) to very fast (30Hz).\n-<strong>SYNC mode 1 and 2</strong>. Create harmonic links between oscillators.\n-<strong>VOLUME</strong>. Control the audio amplitude and LED brightness.<a name=\"sync\"></a>\n-<strong>COARSE PITCH</strong>. Control the pitch of the audio oscillator.\n-<strong>FINE PITCH</strong>. Make fine adjustments to the pitch.\n-<strong>LFO RATE</strong>. Control the rate of the LFO which modulates the pulse width of the audio oscillator.\n\n<hr />\n\n<b><b> </b></b>\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SYNC</strong></span></h2>\n<a href=\"http://casperelectronics.com/wp-content/uploads/SYNC.jpg\"><img class=\"alignnone size-large wp-image-1821\" alt=\"CONTROLS\" src=\"http://casperelectronics.com/wp-content/uploads/SYNC-460x147.jpg\" width=\"460\" height=\"147\" /></a>\nEach channel has two sync switches. These are used to harmonically link two voices together. This can be used to create dense harmonic drones and other strange and noisy effects.\nEach switch has three settings. RED sync switch 1 (the left most switch) is labeled PWG/SQG/OFF. This means <strong>P</strong>ulse <strong>W</strong>idth <strong>G</strong>reen/ <strong>SQ</strong>uare wave <strong>G</strong>reen / off (no syncing).\n<ul>\n	<li>\n<h1>SQUARE WAVE SYNC</h1>\n</li>\n</ul>\nEach voice has a few different outputs. You can read about these below in the <a href=\"#IO\">inputs and outputs</a> section. The SYNC feature uses two of the waveforms from each voice, the audio oscillator square wave and the PWM wave.\nWhen Red Sync 1 is set to SQG (middle position) that means that the RED voice is synced to the GREEN audio oscillator square wave. Give it a try. Make sure all other SYNC switches are OFF first. Adjusting the pitch of the RED oscillator will result in harmonic jumps relative to the pitch of the GREEN voice.\nYou can set up interesting relationships between the voices by making <strong>SYNC loops</strong>. For instance SYNC the RED voice to SQG, the GREEN voice to SQB and the BLUE voice to SQR.\n<strong>PULSE WIDTH SYNC:</strong>\nThe next setting on RED SYNC 1 is PWG. This setting is similar to the SQG setting but the pitch will modulate across a harmonic scale at a rate determined by the GREEN LFO.\n<ul>\n	<li>\n<h1>COMPOUND SYNCING</h1>\n</li>\n</ul>\n<a name=\"IO\"></a>\nEach voice has two switches. Therefore it is possible to sync to multiple oscillators. The effects of compound syncing is often discordant but interesting effects can be achieved, especially when combined with <a href=\"adventure\">adventure board</a> hacks and tweaks.\n\n<hr />\n\n<b><b> </b></b>\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>INPUT AND OUTPUTS</strong></span></h2>\n<a href=\"http://casperelectronics.com/wp-content/uploads/IO.jpg\"><img class=\"alignnone size-large wp-image-1824\" alt=\"CONTROLS\" src=\"http://casperelectronics.com/wp-content/uploads/IO-460x325.jpg\" width=\"460\" height=\"325\" /></a>\nThe NovaDrone offers 15 outputs and 15 input points which can be used to access and manipulate the various features of the circuit.\n<ul>\n	<li>\n<h1>OUTPUTS</h1>\n</li>\n</ul>\nEach voice of the NovaDrone is made up of two triangle/square wave oscillators. What you here when you turn up the volume of one voice is actually a third wave form created by combining the two oscillators. This is a PWM (pulse width modulation) wave form. The pitch of this wave is controlled by the audio oscillator, the pulse width is controlled by the LFO. The effect is an audio wave with a phaser/tremolo effect.\nThat makes 5 outputs per voice, 15 outputs total.\nAll of these wave forms are available at the Signal I/O Header at the bottom of the board.\nThese wave forms can be used as control voltages for other analog gear, can be sent to a mixer as discreet audio signals and can be used with the adventure board to generate strange cross mod effects. I often use them as utility oscillators when I am developing new circuits and need a stock oscillator to play with.\n<ul>\n	<li>\n<h1>INPUTS</h1>\n</li>\n</ul>\n............\n<ul>\n	<li>MOD INPUTS</li>\n</ul>\n&nbsp;\n\nEach of the six oscillators has a mod input header. This header allows you to control the pitch of the oscillator by varying the resistance between the two points of each header. Light sensitive resistors (LDR) work especially well as a source of changing resistance. Simply pug an LDR into one of the mod headers and change the pitch by waving your hand over the sensor.\nIt is also possible to control the pitch by applying a voltage to the top point of each header. The modulation curve is non-linear and will give you some strange but effective results as you apply a varying voltage to the modulation point.\n...........\n<ul>\n	<li>SYNC INPUTS<a name=\"adventure\"></a></li>\n</ul>\n&nbsp;\n\nEach voice has a sync input jack available on the Signal I/O Header. These work like the sync switch and are especially useful for syncing across multiple NovaDrones. When an external oscillator is plugged into the RED sync input jack, the RED voice will sync to the external oscillator.\n\n<hr />\n\n<b><b> </b></b>\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>ADVENTURE BOARD</strong></span></h2>\n<a href=\"http://casperelectronics.com/wp-content/uploads/ADVENTURE.jpg\"><img class=\"alignnone size-large wp-image-1831\" alt=\"CONTROLS\" src=\"http://casperelectronics.com/wp-content/uploads/ADVENTURE-460x250.jpg\" width=\"460\" height=\"250\" /></a>\nThe Adventure Board is a bread board which is connected to the Signal I/O header. All of the output wave forms and 3 sync inputs are connected to the adventure board and are available for cross modulation and tweaking.\nA bread board is a simple piece of hardware used for rapid circuit prototyping. In the image above you can see several columns of connection points. Each column is surrounded by a grey box. This indicates points which are connected together. Each point in each column is connected by a shared bus. The horizontal space across the middle of the board separates the top bunch of columns from the bottom.\n\nNOW WHAT? The pink section (see the above drawing) is where all the outputs and sync inputs are available for patching. Try connecting electrical components like LEDs and capacitors between these points. We have found especially interesting effects by plugging a large polarized capacitor between the PWM output of one voice and the SQ1 of the same voice.\n\n<strong>No harm will come to the NovaDrone by interconnecting points on your adventure board.</strong> Connecting external signals from other synths may lead to unexpected behavior and may damage something, but that\'s half the fun. AND if something does break it will be one of the OP AMP chips which are cheap and easy to replace. SO rather than making a design which is closed off but likely to never break, I have opted for a design which invites hacking and is exceedingly easy to repair. Simply pop the questionable op amp out of the socket and put in a new one. Be adventurous! Try new stuff, connect other circuits and see what happens.\n\n&nbsp;\n<ul>\n	<li>SUGGESTIONS</li>\n</ul>\n&nbsp;\n\n<a name=\"tutorials\"></a>\n-Plug LOTS of LEDs between points in the pink zone (see above image) of the adventure board.\n-Plug capacitors between points in the pink zone of the adventure board.\n-Connect points from the pink zone to the MOD Input headers in the middle of the circuit board.\n-Connect points from the pink zone to a potentiometer placed elsewhere on the board. Connect the output of the pot back into another point in the pink zone.\n\n<hr />\n\n<b><b> </b></b>\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>TUTORIALS</strong></span></h2>\nThis section is under construction (as of February 24, 2013). I will soon post a series of illustrations which walk you through the process of generating drones and exploring the Adventure Board.','User\'s Manual',0,'','inherit','open','closed','','1379-autosave','','','2013-02-25 11:07:09','2013-02-25 16:07:09','',1379,'http://casperelectronics.com/2013/02/23/1379-autosave/',0,'revision','',0),(1752,2,'2012-11-13 17:31:50','2012-11-13 22:31:50','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n&nbsp;\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"10\" class=\"alignnone size-full wp-image-1302\" /></a>\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\n\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are Sine, ramp, triangle and square.Sine, triangle and square are symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\n\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators.\r\n Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts which means the green wave sweeps from +2.5 to -2.5 and is 5 Vpk-pk.\r\n\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is <em>relative to the difference in phase</em> of the two source waves.\r\n\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is <strong>phase controlled amplitude modulation</strong> and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\nOscillator 1 and 2 combine to make a square wave oscillator with a frequency controlled by oscillator 1 and pulse width modulation controlled by oscillator 2. \r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 17:31:50','2012-11-13 22:31:50','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-17/',0,'revision','',0),(1746,2,'2012-11-13 12:48:58','2012-11-13 17:48:58','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 12:48:58','2012-11-13 17:48:58','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-11/',0,'revision','',0),(1753,2,'2012-11-13 17:34:37','2012-11-13 22:34:37','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n	<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>What we are most interested in is the oscillation (or modulating amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are Sine, ramp, triangle and square.Sine, triangle and square are symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\n\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators.\r\nLet’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts which means the green wave sweeps from +2.5 to -2.5 and is 5 Vpk-pk.\r\n\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is <em>relative to the difference in phase</em> of the two source waves.\r\n\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is <strong>phase controlled amplitude modulation</strong> and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators are simple and robust. Each oscillator is built around 2 <strong>op amps</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\nOscillator 1 and 2 combine to make a square wave oscillator with a frequency controlled by oscillator 1 and pulse width modulation controlled by oscillator 2.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 17:34:37','2012-11-13 22:34:37','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-18/',0,'revision','',0),(1747,2,'2012-11-13 12:54:32','2012-11-13 17:54:32','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n&nbsp;\r\n\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"10\" class=\"alignnone size-full wp-image-1302\" /></a>\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\n\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 12:54:32','2012-11-13 17:54:32','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-12/',0,'revision','',0),(1748,2,'2012-11-13 12:55:20','2012-11-13 17:55:20','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n&nbsp;\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"10\" class=\"alignnone size-full wp-image-1302\" /></a>\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\n\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are: Sine, ramp, triangle and square.Sine, triangle and square are the most common and are all symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 12:55:20','2012-11-13 17:55:20','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-13/',0,'revision','',0),(1750,2,'2012-11-13 13:08:13','2012-11-13 18:08:13','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n&nbsp;\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"10\" class=\"alignnone size-full wp-image-1302\" /></a>\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\n\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are Sine, ramp, triangle and square.Sine, triangle and square are symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\n\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators.\r\n Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts which means the green wave sweeps from +2.5 to -2.5 and is 5 Vpk-pk.\r\n\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is <em>relative to the difference in phase</em> of the two source waves.\r\n\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is <strong>phase controlled amplitude modulation</strong> and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n\r\nThis phenomenon of phase controlled amplitude is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.The beating is the phase of two detuned strings aligning and diverging.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 13:08:13','2012-11-13 18:08:13','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-15/',0,'revision','',0),(1749,2,'2012-11-13 12:57:48','2012-11-13 17:57:48','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n&nbsp;\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"10\" class=\"alignnone size-full wp-image-1302\" /></a>\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\n\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are Sine, ramp, triangle and square.Sine, triangle and square are symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators. Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts.\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is relative to the difference in phase of the two source waves.\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is phase controlled amplitude modulation and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nThis phenomenon of phase controlled amplitude is something many musicians use without even realizing it. This is the vary trick one uses when tuning a guitar. You tune one string to the other until the “beatingâ€ effect slows and eventually disappears.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 12:57:48','2012-11-13 17:57:48','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-14/',0,'revision','',0),(1751,2,'2012-11-13 13:12:40','2012-11-13 18:12:40','<h2><a href=\"http://casperelectronics.com/finished-pieces/nova-drone/\"> Back to the NovaDrone HOME page</a></h2>\r\n\r\nThroughout this guide I will attempt to give you some insight into the circuit theory and scientific principles at play in the NovaDrone. That said I will be giving little more than an intro to each topic and strongly encourage you to do further reading on topics you find interesting.\r\n<ul>\r\n	<li>This is a beta version of the <strong>NovaDrone Technical Guide</strong>. I expect to make revisions over time and eagerly encourage readers to send me feedback, questions, suggestions and especially corrections. Comments should be addressed to <a href=\"mailto:pete@casperelectronics.com\"><strong>pete@casperelectronics.com</strong></a>.</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h3 style=\"text-align: center;\"><span style=\"color: #000000;\"><strong>TABLE OF CONTENTS:</strong></span></h3>\r\n<a href=\"#sec1\"><strong><span style=\"text-decoration: underline;\">Section 1. Oscillator Primer</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#1.1\"><strong>1.1 Frequency, amplitude &amp; wave shape</strong></a>\r\n<ul>\r\n	<li><a href=\"#frequency\">Frequency</a></li>\r\n	<li><a href=\"#amplitude\">Amplitude</a></li>\r\n	<li><a href=\"#waveshape\"> Wave shape</a></li>\r\n	<li><a href=\"#review\"> Review<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#1.2\"><strong>1.2 Phase</strong></a>\r\n<ul>\r\n	<li><a href=\"#phase\"> Phase controlled amplitude modulation</a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a href=\"#sec2\"><strong><span style=\"text-decoration: underline;\">Section 2. NovaDrone Oscillators</span></strong></a>\r\n<ul>\r\n	<li><a href=\"#2.1\"><strong>2.1 The Circuit</strong></a>\r\n<ul>\r\n	<li><a href=\"#feedbackloops\"> Feedback loops</a></li>\r\n	<li><a href=\"#schematic\"> Schematic</a></li>\r\n	<li><a href=\"#rctimeconstant\"> RC time constant</a></li>\r\n	<li><a href=\"#howitworks\"> How it works<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n	<li><a href=\"#2.2\"><strong>2.2 Pulse Width Modulation</strong></a>\r\n<ul>\r\n	<li><a href=\"#comparator\">The comparator<strong></strong></a></li>\r\n</ul>\r\n</li>\r\n</ul>\r\n<a name=\"sec1\"></a><a name=\"1.1\"></a><a href=\"#sec3\"><strong><span style=\"text-decoration: underline;\">Section 3. Sound and Light</span></a></strong></span>\r\n<ul>\r\n	<li><a href=\"#mix\">audio mixer</a><strong></strong></li>\r\n<li><a href=\"#led\">LED driver</a></li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 1. OSCILLATOR PRIMER</strong></span></h2>\r\n<h2><span style=\"color: #3366ff;\"><strong style=\"text-align: center;\"><strong>◊ 1.1 Frequency, amplitude and wave shape◊</strong></strong></span></h2>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/ampandfreq.jpg\"><img class=\"alignleft size-medium wp-image-1636\" title=\"Figure 1. A triangle wave oscillator\" src=\"http://casperelectronics.com/wp-content/uploads/ampandfreq-200x242.jpg\" alt=\"\" width=\"200\" height=\"242\" /></a>\r\n<div>\r\n\r\nThe heart of the NovaDrone is a bank of six independent oscillators.\r\n\r\n</div>\r\nAn oscillator is simply a pattern which repeats indefinitely. This can be a pattern of light, movement, electricity, even life cycles of organisms. The <a href=\"http://en.wikipedia.org/wiki/Oscillation\">wikipedia entry</a> gives dozens of examples of different kinds of oscillation.\r\n&nbsp;\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" title=\"spacer\" width=\"460\" height=\"10\" class=\"alignnone size-full wp-image-1302\" /></a>\r\n<address> </address><address><em><span style=\"color: #33cccc;\">Figure 1. triangle oscillator</span></em></address>\r\n\r\nWhat we are most interested in is the modulation (changing amplitude) of electricity. All of the electrically produced sound we hear is a repeating pattern of fluctuating electrical current.\r\nWhen this is applied to a speaker, the current activates a coil in the speaker which pushes the cone of the speaker away from or towards a fixed magnet. This action vibrates the air in front of the speaker which in turn vibrates the air in front of that and so on until those vibrations hit our ear drums and are perceived as sound. The sounds we hear around us are all incredibly complex patterns of air pressure modulation.\r\n<div>\r\n<ul>\r\n	<li><strong>The red line in fig 1 represents a voltage which goes up and down over a period of time. This is an oscillator.</strong></li>\r\n</ul>\r\n\r\nThere are three basic factors that make up all oscillators: <a name=\"frequency\"></a><strong>frequency</strong>, <strong>amplitude</strong> and <strong>wave shape</strong>. In musical terms we would call these <strong>pitch</strong>, <strong>volume</strong> and <strong>timbre</strong>. I will also talk a fair amount about <strong>phase </strong>which is relevant when working with multiple oscillators and plays an important role in creating drones.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Frequency</strong></span></h3>\r\n</li>\r\n</ul>\r\nOne complete sweep up and down is called a <strong>cycle</strong>. The number of cycles per second is your <strong>Frequency</strong> or <strong>Pitch</strong>.<strong></strong>\r\n<strong>Frequency</strong> is commonly measured in <strong>Hertz</strong>, which is the number of cycles per second.\r\n<a name=\"amplitude\"></a><strong>Pitch</strong> is another term for frequency which is used <span style=\"text-decoration: underline;\">only</span> when referring to the frequency of an audio signal.\r\nFigure 1 shows a triangle wave with a cycle length of .5 seconds. The frequency of this wave would be determined by seeing how many cycles will occur in 1 second. In this case there are 2 complete cycles in 1 second. That means the wave has a frequency of 2 Hertz. This is well below the hearing range. Humans can hear oscillators between 20Hz and 20,000 Hz.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Amplitude</strong></span></h3>\r\n</li>\r\n</ul>\r\nAmplitude refers to the magnitude of voltage change across one cycle of an oscillation.\r\n<a name=\"waveshape\"></a>This in turn impacts the volume of the signal if it is sent to a speaker.\r\nThe image above shows a triangle wave with a positive peak of +5 volts and a negative peak of -5 volts. The amplitude is determined by figuring the absolute difference between these peaks. In this case that difference is 10 volts. This is commonly referred to as 10 Vpk-pk (10 volts peak to peak). There are many different ways to measure amplitude (pk-pk, RMS, Vp, etc…) but we’ll just be talking about Vpk-pk.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Wave shape</strong></span><a href=\"http://casperelectronics.com/wp-content/uploads/waveshapes.png\"><img class=\"alignright\" title=\"Waveshapes\" src=\"http://casperelectronics.com/wp-content/uploads/waveshapes-200x160.png\" alt=\"\" width=\"292\" height=\"233\" /></a></h3>\r\n</li>\r\n</ul>\r\nThe wave shape is the pattern of amplitude modulation over the course of a cycle. The waveforms in fig 2 are Sine, ramp, triangle and square.Sine, triangle and square are symmetrical waves. That means the positive and negative portions of each cycle are of the same duration. Many musical synthesizers offer other wave forms which are asymmetrical versions of these common waves such as ramp, saw and pulse waves.\r\n<p style=\"text-align: right;\"><span style=\"color: #33cccc;\"> Figure 2. Waveshapes  </span></p>\r\nThe importance and impact of wave shape depends on its application. Many audio effects such as <strong>tremolo</strong> or <strong>phaser</strong> use low frequency oscillators (LFOs) to modulate certain parameters of the sound. It is commonly more desirable to use a sine or triangle wave for many of these effects such as the tremolo which\r\n<a name=\"review\"></a>fades the volume in and out. Using a square wave for this would create dramatic shifts in volume which can be unpleasant.\r\nMany natural sounds are synthesized using overlapping wave forms like those shown above. For instance a flute can be synthesized using several octaves of a sine wave. A horn on the other hand will use more square waves and maybe a triangle or saw wave. More advanced wave and synthesis theory sites the sine wave as the basis of all wave forms. It is shown how even square waves can be created by combining several sine waves.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><strong>Review</strong></h3>\r\n</li>\r\n</ul>\r\nThe basic components of an oscillator are:\r\n<h3><a name=\"1.2\"></a></h3>\r\n<ul>\r\n	<li><strong>Frequency</strong>. The number of oscillation cycles that occur in one second. Measured in Hz</li>\r\n	<li><strong>Amplitude</strong>. Magnitude of voltage sweep in one cycle of an oscillator. Measured in Volts or Vpk-pk (volts peak to peak)</li>\r\n	<li><strong>Wave shape</strong>. Sine, triangle, square</li>\r\n</ul>\r\n\r\n<hr />\r\n\r\n<div></div>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊1.2 Phase◊</strong></span></h2>\r\nPhase is a bit more complicated than the other terms but plays an important role in audio circuitry and especially in making drones. Phase refers to a particular position in a <span style=\"text-decoration: underline;\">single cycle</span> of a wave (such as the positive or negative peak) and is measured in degrees. It is most commonly used to describe the relationship between multiple waves.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phasedegrees.jpg\"><img class=\"alignnone size-large wp-image-1643\" title=\"Phasedegrees\" src=\"http://casperelectronics.com/wp-content/uploads/phasedegrees-460x236.jpg\" alt=\"\" width=\"460\" height=\"236\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 3. Phase</span>\r\nFig. 3 shows two sine waves (red &amp; blue) of identical amplitude and frequency. The green oscillator is the mix or <em>average</em> of the red and blue oscillators.\r\nPhase is measured in degrees with 360 degrees being one complete cycle. 180 degrees is exactly ½ of a cycle.\r\nIn fig. 3 the phase of the blue oscillator is offset at 45 degree increments from the red oscillator from left to right. With each step you’ll notice that the waves get farther apart and that the amplitude of the green (average) oscillator decreases.\r\n\r\nThis may seem confusing at first but it’s really quite simple. The green oscillator is the average of the red and blue oscillators.\r\n Let’s say the red and blue oscillators sweep from -5 to +5VDC (10Vp-p). Now look at the right most illustration of the 2 waves out of phase by 180 degrees. When the blue wave is at its positive peak (90 degrees) of +5 volts, the red wave is at it’s negative peak (270 degrees) of -5 volts.\r\nWhat is the average of -5 and +5? Zero. They are always going to be the opposites of each other so the average will always be zero. Now look at the 90 degree image. When Blue is at +5 volts/90 degrees, red is at 0 volts/zero degrees. The average of +5 and zero is 2.5 volts which means the green wave sweeps from +2.5 to -2.5 and is 5 Vpk-pk.\r\n\r\nThe important thing to take away from the info above is that the amplitude of an oscillator created by mixing two similar oscillators is <em>relative to the difference in phase</em> of the two source waves.\r\n\r\nIn fig. 3 the oscillators have identical frequencies. This means that the phase relationship once established will remain the same and the resulting averaged amplitude of the two waves will also remain the same.\r\n<strong>Q: What will happen if the frequencies of your two waves are NOT identical? </strong>\r\nWe established above that the amplitude of the averaged waveform is relative to the phase difference of the two wave forms, therefore as the phase difference of two waves increases and decreases so too will the averaged waveforms’ amplitude. What we have here is <strong>phase controlled amplitude modulation</strong> and the rate of phase modulation is controlled by the frequency difference between your two oscillators.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/phaseModulation.jpg\"><img class=\"alignnone size-large wp-image-1644\" title=\"PhaseModulation\" src=\"http://casperelectronics.com/wp-content/uploads/phaseModulation-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a><a href=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2.jpg\"><img class=\"alignnone size-large wp-image-1645\" title=\"Phase Modulation2\" src=\"http://casperelectronics.com/wp-content/uploads/phase_modulation2-460x220.jpg\" alt=\"\" width=\"460\" height=\"220\" /></a><a name=\"sec2\"></a><span style=\"color: #33cccc;\">Figure 4. Phase controlled amplitude</span>\r\n<h3><a name=\"2.1\"></a></h3>\r\nIn fig. 4 the blue oscillator has a frequency of 10 Hz, the red is 11Hz. That means that it takes the red wave 1/10<sup>th</sup> of a second longer to complete a cycle than the blue wave. You can see that with each cycle the red wave lags a little bit further behind the blue wave which increases the phase difference between the two. As a result, the amplitude of the averaged wave (green) decreases as the phase offset approaches 180 degrees and then increases as it continues past 180 to 360 degrees.\r\n\r\n<hr />\r\n\r\n&nbsp;\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>SECTION 2. NOVADRONE OSCILLATORS</strong></span></h2>\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊ 2.1 The circuit ◊</strong></span></h2>\r\nThe NovaDrone contains 6 oscillators. Each oscillator outputs a square wave and a triangle wave.\r\n<span style=\"text-decoration: underline;\"><a name=\"schematic\"></a></span>The circuit which generates the oscillators is clean, simple and robust. They are generated using a remarkable device called an <strong>op amp</strong>. If you are interested in building synthesizers and don’t know where to start, read up on <strong>op amps</strong>. They are the key elements of most oscillators, filters, envelope generators, mixers and amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>Schematic</strong></span></h3>\r\n</li>\r\n</ul>\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/OSC2rc.jpg\"><img class=\"alignleft\" title=\"OSC2rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC2rc-200x163.jpg\" alt=\"\" width=\"200\" height=\"163\" /></a><img class=\"alignleft\" title=\"OSC1rc\" src=\"http://casperelectronics.com/wp-content/uploads/OSC1rc-200x170.jpg\" alt=\"\" width=\"200\" height=\"163\" />\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"size-full wp-image-1302 alignnone\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" />\r\n\r\n</div>\r\n<div><span style=\"color: #33cccc;\">Figure 5. LFO                                    Figure 6. Audio oscillator</span></div>\r\n<div>\r\n\r\nEach channel of the NovaDrone (Red, green and blue) has 2 oscillators. These are shown in fig. 5 and fig. 6.\r\n\r\n<a name=\"feedbackloops\"></a> They are very similar to one another but have been calibrated for different purposes.\r\n<strong>Osc 1</strong> is an audio frequency oscillator. It has a coarse and fine tune adjustment and only operates at audible frequencies (20Hz-20kHz).\r\n<strong>Osc 2</strong> is calibrated as a low frequency oscillator (LFO) with cycles as long as 2 minutes. It has a range switch and a single adjustment knob.\r\nOscillator 1 and 2 combine to make a square wave oscillator with a frequency controlled by oscillator 1 and pulse width modulation controlled by oscillator 2. \r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3> <span style=\"color: #3366ff;\"><strong style=\"color: #3366ff;\">Feedback loops</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe oscillator circuit is a feedback loop between two op amps that are configured as a <strong>schmitt trigger</strong> and an <strong>inverting integrator</strong>.\r\nBasically an <em>integrator</em> turns square waves into triangle waves.\r\nA <em>Schmitt trigger</em> is a kind of comparator that turns modulating signals (like triangle waves) into square waves.\r\nThe key elements of the relationship between these two circuits is that they form a loop (Schmitt &gt; integrator &gt;Schmitt&gt;integrator&gt; etc…) and that the integrator is also an <strong>inverter</strong>. This creates a continuous cycle of modulation:\r\n1) Schmitt output goes HI.\r\n2) Integrator inverts Schmitt signal and outputs slope going down (LOW).\r\n3) When slope is near zero volts, Schmitt trigger is thrown and its’ output goes LOW.\r\n4) Integrator inverts and generates upward slope (HI).\r\n5) When integrator slope reaches peak, Schmitt trigger is thrown and output goes HI.\r\n<a name=\"rctimeconstant\"></a>6) etc……\r\nThis is an overly simplified explanation but enough for our purposes. Do more research on these valuable circuits once you are familiar with some of the basics of op-amps.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>RC (resistor capacitor)time constant</strong></span></h3>\r\n</li>\r\n</ul>\r\nIn both oscillators (fig. 5 and 6) the primary element which defines frequency is the <strong>RC time constant</strong>. This relationship is a core component of most oscillators and is worth reading up on.\r\n\r\nThe RC time constant is a period of time defined by the relationship between a resistor and a capacitor.\r\nThe equation for this is simply <strong>t =</strong> <strong>R*C</strong>. In the case of the oscillators above it would be <strong>t=R1*C1</strong>.\r\nUnfortunately calculating the frequency of an oscillator is more complicated than just calculating your RC constant.\r\nIn many oscillators (including this one) there is a schmitt trigger component which watches the rising or sinking voltage from the integrator. The Schmitt trigger activates when the slope reaches predefined upper and lower limits. In order to determine the frequency of an oscillator we need to know what our upper and lower limits are and then calculate how long it takes our wave (the output of the integrator) to travel from one limit to the other.\r\nThese limits are determined by the relationship of 2 resistors in the schmitt stage. In fig 5 and 6 these are R2 and R3.\r\nThe equation for determining the duration of one cycle is\r\n(1/4R1C1)*(R3/R4)\r\nIn Oscillator 2 <strong>R</strong><strong>1</strong> is a 500k potentiometer in series with a 4.7k resistor between pins 8 and 13 of the two op amps. <strong>C</strong><strong>1</strong> is one of the three capacitors between pins 13 and 14 of the rightmost op amp. One of these caps is selected using a three way switch on the NovaDrone circuit board. This controls the frequency range of the LFO.\r\nLet’s say the pot is all the way up (full resistance) and the middle cap has been selected. The equations for RC and subsequently the frequency is:\r\n<strong>R1=504,700 Ohms</strong>\r\n<a name=\"howitworks\"></a><strong>C1= .000022 Farads</strong>\r\n<strong>R2 = 8,300 Ohms</strong>\r\n<strong>R3 = 10,000 Ohms</strong>\r\n<strong>Frequency in Hz = (1 / 4*R</strong><strong>1C</strong><strong>1) * (R</strong><strong>3/R</strong><strong>2)</strong>\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>How it works</strong></span></h3>\r\n</li>\r\n</ul>\r\nResistors limit the flow of current and capacitors store current. Current flows through the resistor and is stored in the capacitor. The resistor controls how much current flows into the capacitor per second. Therefore the size of capacitor and the amount of resistance will determine how long it takes to fill the capacitor. A common analogy is to think about current flow as water, the resistor as a spigot\r\n<h3><a name=\"2.2\"></a></h3>\r\nand the capacitor as a cup. The more you open the spigot (reduce resistance), the more water (electrical current) will flow and the faster the cup will fill (capacitor will charge). The oscillator circuit is configured in a special way which causes the capacitor to continuously charge and discharge. It is looking for two states from the cap, fully charged or fully discharged. When the cap reaches either of these states, the whole circuit reverses polarity and the capacitors charge status begins moving toward the opposite state. The amount of time it takes to charge and discharge is your cycle duration.\r\n\r\n<hr />\r\n\r\n<h2 style=\"text-align: left;\"><span style=\"color: #3366ff;\"><strong>◊2.2 pulse width modulation (pwm)◊</strong></span></h2>\r\nPWM is exciting stuff….really! It is essentially a <strong>1 bit digital</strong> representation of an <strong>analog</strong> wave form.\r\nDigital wave forms only have 2 states, <strong>high</strong> and <strong>low</strong>. <strong>High</strong> is a voltage <em>at</em> or very close to the positive supply voltage. <strong>Low</strong> is a voltage <em>at</em> or very close to the negative supply voltage. It is basically just a square wave. Analog on the other hand is infinitely variable. Think about it like the difference between a light switch (digital) and a light dimmer (analog). PWM is a wave form that bridges the gap between these two formats. It can be used to make sound, control the brightness of an LED, control the speed of high torque motors and speak to microprocessors. It is also the language that a microprocessor will use to speak with the analog world.\r\nPulse Width (PW) refers to the relative durations of high and low voltage in a single <strong>cycle</strong> of a square wave.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/pulsewidth.jpg\"><img class=\"alignnone size-large wp-image-1648\" title=\"Pulsewidth\" src=\"http://casperelectronics.com/wp-content/uploads/pulsewidth-460x214.jpg\" alt=\"\" width=\"460\" height=\"214\" /></a><span style=\"color: #33cccc;\">Figure 7. Pulse width</span>\r\nFig. 7 shows three square wave oscillators of the same amplitude and frequency but with differing <strong>pulse width</strong>. The red oscillator has a 10% pulse width. That means the wave goes high for 10 % of the duration of one cycle. The green wave is 50% and the purple wave is 90%. What is important to note is that pulse width has nothing to do with frequency and only refers to the relationship between the high and low swing of the wave.\r\n\r\n<hr />\r\n\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>The Comparator</strong></span></h3>\r\n</li>\r\n</ul>\r\nThe job of a comparator is simple. Two signals are fed into the “+â€ and “-“ inputs (labeled 10 and 9 in fig. 8 respectively). If the voltage at the “+â€ input is <em>higher</em> than the “-“ input the output of the comparator goes <strong>high</strong>.<strong> </strong>If the “+â€ input drops below the “-“ input the output goes <strong>low</strong>.\r\nIn the NovaDrone t<a href=\"http://casperelectronics.com/wp-content/uploads/comparator.jpg\"><img class=\"alignleft\" title=\"Comparator\" src=\"http://casperelectronics.com/wp-content/uploads/comparator-200x76.jpg\" alt=\"\" width=\"200\" height=\"76\" /></a>he triangle output of Osc 1 and Osc 2 combine through a simple comparator (fig. 8) to make a single square wave with a modulating pulse width. In this way, the comparator also functions as a pulse width modulation processor.\r\n\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\"><img class=\"alignnone size-full wp-image-1302\" title=\"spacer\" src=\"http://casperelectronics.com/wp-content/uploads/casper/spacer1.jpg\" alt=\"\" width=\"460\" height=\"10\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">Figure 8.</span>\r\n\r\nFig. 9 below shows how two triangle waves are transformed through the comparator into a square wave with a modulating pulse width.\r\nThe blue triangle wave in fig. 9 is oscillator 1. The red triangle is osc 2. The green line is the combined PWM output.\r\nAny time the blue line (osc 1) is above the red line (osc 2), the green line (pwm) goes high. As the red line rises the percentage of each cycle that the blue line is above the red line decreases. This changing percentage is what makes our modulating pulse width effect.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy.jpg\"><img class=\"alignnone size-large wp-image-1647\" title=\"PWM3 Copy\" src=\"http://casperelectronics.com/wp-content/uploads/PWM3-copy-460x202.jpg\" alt=\"\" width=\"460\" height=\"202\" /></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"sec3\"></a>\r\n\r\n<span style=\"color: #33cccc;\">\r\n</span>\r\n\r\n<a name=\"mix\"></a><span style=\"color: #33cccc;\">Figure 9. Pulse width modulation detail</span>\r\n\r\n<hr />\r\n\r\n<h3><span style=\"color: #3366ff;\"><span style=\"color: #3366ff;\">Section 3. SOUND &amp; LIGHT</span></span></h3>\r\n<ul>\r\n	<li><strong style=\"color: #3366ff;\">Audio Mixer</strong></li>\r\n</ul>\r\nThe audio signals from each of the three channels of the NovaDrone are mixed using the circuit in fig. 10.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/mixer.jpg\"><img class=\"alignleft\" title=\"Mixer\" src=\"http://casperelectronics.com/wp-content/uploads/mixer-200x135.jpg\" alt=\"\" width=\"200\" height=\"135\" /></a>This mixer is nice and simple and uses just one <strong>op amp</strong> and a few other components. This circuit is configured as an inverting mixer with an amplitude controlled by the <strong>feedback resistor</strong> and <strong>input resistors</strong>. The amplitude is c\r\n\r\n<a name=\"led\"></a>\r\n\r\nalculated as RF/RI. In this case RF = 10,000 and RI = 100,000. That means the output signal is 1/10<sup>th</sup> the amplitude of the input signal.\r\n<strong><span style=\"text-decoration: underline;\">\r\n</span></strong>\r\n<ul>\r\n	<li>\r\n<h3><span style=\"color: #3366ff;\"><strong>LED drivers</strong></span></h3>\r\n</li>\r\n</ul>\r\n(3) 2N3904 NPN transistors are used to make 3 LED drivers.\r\n<a href=\"http://casperelectronics.com/wp-content/uploads/LEDdriver.jpg\"><img class=\"alignleft\" title=\"LEDdriver\" src=\"http://casperelectronics.com/wp-content/uploads/LEDdriver-200x108.jpg\" alt=\"\" width=\"200\" height=\"108\" /></a>A driver is a simple but important circuit which isolates elements which use lots of current (like LEDs) from sensitive circuits (like the oscillators in the NovaDrone). Failure to use a driver can result in something called a <strong>loading effect</strong> which basically means that the device being driven will affect the behavior of the rest of the circuit in bad ways, like the pitch changing when the lights turn on. The LED in the NovaDrone uses a lot of current relative to the rest of the circuit (90mA vs around 30mA for the rest of the circuit) therefore a driver is necessary. The key component of a driver is the <strong>transistor</strong>. This is another topic worth reading a lot about\r\n.\r\n\r\n</div>','Theory',0,'','inherit','open','closed','','1369-revision-v1','','','2012-11-13 13:12:40','2012-11-13 18:12:40','',1369,'http://casperelectronics.com/2012/11/13/1369-revision-16/',0,'revision','',0),(1754,2,'2012-11-13 18:10:41','2012-11-13 23:10:41','','Casperhousing',0,'','inherit','open','closed','','casperhousing','','','2012-11-13 18:10:41','2012-11-13 23:10:41','',1739,'http://casperelectronics.com/wp-content/uploads/casperhousing.jpg',0,'attachment','image/jpeg',0),(1755,2,'2012-11-09 07:47:16','2012-11-09 12:47:16','','Auto Draft',0,'','inherit','open','closed','','1739-revision','','','2012-11-09 07:47:16','2012-11-09 12:47:16','',1739,'http://casperelectronics.com/2012/11/09/1739-revision/',0,'revision','',0),(1757,2,'2012-10-07 16:09:03','2012-10-07 21:09:03','<hr><h2> The NovaDrone</h2>\r\n<a href=\"http://casperelectronics.com/finished-pieces/nova-drone/novadrone-sales-page/\"><img src=\"http://casperelectronics.com/wp-content/uploads/NovaDrone/store/doublefinished.better-934x1024.jpg\" alt=\"\" title=\"doublefinished.better\" width=\"450\" height=\"500\" class=\"alignnone size-large wp-image-1229\" /></a>\r\n<h2>Here\'s the <a href=\"http://casperelectronics.com/finished-pieces/nova-drone/novadrone-sales-page/\">order page.</a></h2>\r\n\r\n</hr><hr></hr>\r\n<h2>The Drone Lab</h2><br>\r\nThe Drone Lab is a 4 voice analog drone synth, rhythm generator and FX processor. <br>\r\n<strong>You can buy the Drone Lab as a kit, a fully assembled unit or you can buy just the PCB. Ordering info below</strong><p>\r\n-More info on the Drone Lab <a href=\"http://casperelectronics.com/finished-pieces/drone-lab/drone-lab-v2/\">here</a>.<br>\r\n-Builders forum <a href=\"http://www.ghostwizard.com/\">here</a>.<br>\r\n-Listen to music from the Drone Lab community <a href=\"http://soundcloud.com/groups/drone-lab-music/\">here</a>.</p>\r\n\r\n<img src=\"http://casperelectronics.com/images/finishedpieces/droner/V2/housing/_blackpic2.jpg\" width=\"400\" height=\"311\" alt=\"\" title=\"\" /><br>\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"encrypted\" value=\"-----BEGIN PKCS7-----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-----END PKCS7-----\r\n\">\r\n<input type=\"image\" src=\"https://www.paypal.com/en_US/i/btn/btn_viewcart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypal.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n</hr><hr>\r\n<h2>NOTE TO BUYERS:<br></h2>\r\n<h3> Kits and assembled units are IN stock.  Orders are shipped twice a week. If you have any special instructions please include them with your payment. All questions should be emailed to support(at)ghostwizard(dot)com.</h3><br>\r\n</hr>\r\n\r\n<hr><h2>Shipping:</h2><br>\r\nShipping is included in the price of your order. Make sure you select the appropriate shipping (international or domestic) frm the drop down menu for the item you are ordering. <br><strong>Shipping discounts ARE available on orders of multiple units. Please contact us for details at support[at]ghostwizard[dot]com.</strong></hr>\r\n<hr><h2> Housing Kit:</h2><br>\r\n<strong>BACK IN STOCK!</strong><br>\r\n<img src=\"http://casperelectronics.com/images/finishedpieces/droner/V2/housing/_Faceplate.JPG\" width=\"400\" height=\"266\" alt=\"\" title=\"\" />\r\nFaceplates come with protective paper backing shown above. The picture below shows the housing kit fully assembled. Faceplates have laser etched labeling. click on the image below for a detail shot.\r\n<a href=\"http://casperelectronics.com/images/finishedpieces/droner/V2/housing/Faceplate_Applied.JPG\"><img src=\"http://casperelectronics.com/images/finishedpieces/droner/V2/housing/_Faceplate_Applied.JPG\" width=\"400\" height=\"300\" alt=\"\" title=\"\"  /></a>\r\n-We have two styles of faceplate that comply with the two versions of the PCB we have sold. The first 100 PCBs we sold are labeled V2 on the back. All PCBs after the first 100 are labeled V2.1. If you are ordering a new PCB it is a V2.1. If you have an old PCB and are unsure of what version it is, you can find the version number marked on the back.<p>\r\nShipping is included in the price below. If you order several units you only need to pay shipping once. Contact us for ordering details for multiple units. If you have already paid for multiple units you will receive a refund for the double shipping. support[at]ghostwizard[dot]com.\r\n\r\n\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"hosted_button_id\" value=\"HQRG7JGT64Y82\">\r\n<table>\r\n<tr><td><input type=\"hidden\" name=\"on0\" value=\"Housing Kit V2\">Housing Kit V2</td></tr><tr><td><select name=\"os0\">\r\n	<option value=\"International\">International$30.00 USD</option>\r\n	<option value=\"Domestic\">Domestic$25.00 USD</option>\r\n</select> </td></tr>\r\n</table>\r\n<input type=\"hidden\" name=\"currency_code\" value=\"USD\">\r\n<input type=\"image\" src=\"https://www.paypalobjects.com/en_US/i/btn/btn_cart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypalobjects.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n\r\n\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"hosted_button_id\" value=\"NEPMMTY35YRQ8\">\r\n<table>\r\n<tr><td><input type=\"hidden\" name=\"on0\" value=\"Housing Kit V2.1\">Housing Kit V2.1</td></tr><tr><td><select name=\"os0\">\r\n	<option value=\"International\">International$30.00 USD</option>\r\n	<option value=\"Domestic\">Domestic$25.00 USD</option>\r\n</select> </td></tr>\r\n</table>\r\n<input type=\"hidden\" name=\"currency_code\" value=\"USD\">\r\n<input type=\"image\" src=\"https://www.paypalobjects.com/en_US/i/btn/btn_cart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypalobjects.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n\r\n\r\n</hr>\r\n<hr><h2>Printed Circuit Board:</h2><br>\r\nThis is just the PCB. a materials list and build guide are available <a href=\"http://casperelectronics.com/finished-pieces/drone-lab/drone-lab-v2/\">here</a>. Also be sure to check out the <a href=\"http://www.ghostwizard.com\">forum</a> for discussions on building and modding.\r\n\r\n\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"hosted_button_id\" value=\"D3EZMENGQU9RS\">\r\n<table>\r\n<tr><td><input type=\"hidden\" name=\"on0\" value=\"PCB\">PCB</td></tr><tr><td><select name=\"os0\">\r\n	<option value=\"International\">International$60.00 USD</option>\r\n	<option value=\"Domestic\">Domestic$55.00 USD</option>\r\n</select> </td></tr>\r\n</table>\r\n<input type=\"hidden\" name=\"currency_code\" value=\"USD\">\r\n<input type=\"image\" src=\"https://www.paypalobjects.com/en_US/i/btn/btn_cart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypalobjects.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n\r\n\r\n\r\n\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"hosted_button_id\" value=\"GJ4CF2GYX7UUS\">\r\n<table>\r\n<tr><td><input type=\"hidden\" name=\"on0\" value=\"PCB + Housing Kit\">PCB + Housing Kit</td></tr><tr><td><select name=\"os0\">\r\n	<option value=\"International\">International$80.00 USD</option>\r\n	<option value=\"Domestic\">Domestic$75.00 USD</option>\r\n</select> </td></tr>\r\n</table>\r\n<input type=\"hidden\" name=\"currency_code\" value=\"USD\">\r\n<input type=\"image\" src=\"https://www.paypalobjects.com/en_US/i/btn/btn_cart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypalobjects.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n\r\n\r\n\r\n\r\n\r\n\r\n</hr><hr><h2>Complete parts kit & PCB:</h2><br>\r\nThe parts kit includes the PCB and all the components you will need to build the Drone Lab. Includes resistors and capacitors, ICs, sockets, LEDs, special board mount potentiometers, color coded knobs, switches, jacks....everything. I encourage anyone who feels up to it to buy the parts on their own. A parts list has been added to the <a href=\"http://casperelectronics.com/finished-pieces/drone-lab/drone-lab-v2/\">Drone Lab</a> page.<br>\r\n<a href=\"http://casperelectronics.com/images/finishedpieces/droner/V2/kit/DroneKit.jpg\"><img src=\"http://casperelectronics.com/images/finishedpieces/droner/V2/kit/_DroneKit.jpg\" width=\"400\" height=\"266\" alt=\"\" title=\"\"  /></a>\r\n\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"hosted_button_id\" value=\"CJ4UDY2PDST3S\">\r\n<table>\r\n<tr><td><input type=\"hidden\" name=\"on0\" value=\"KIT\">KIT</td></tr><tr><td><select name=\"os0\">\r\n	<option value=\"International\">International$220.00 USD</option>\r\n	<option value=\"Domestic\">Domestic$210.00 USD</option>\r\n</select> </td></tr>\r\n</table>\r\n<input type=\"hidden\" name=\"currency_code\" value=\"USD\">\r\n<input type=\"image\" src=\"https://www.paypalobjects.com/en_US/i/btn/btn_cart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypalobjects.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n\r\n\r\n\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"hosted_button_id\" value=\"MBEHZVKWCYF4Q\">\r\n<table>\r\n<tr><td><input type=\"hidden\" name=\"on0\" value=\"KIT + Housing\">KIT + Housing</td></tr><tr><td><select name=\"os0\">\r\n	<option value=\"International\">International$240.00 USD</option>\r\n	<option value=\"Domestic\">Domestic$230.00 USD</option>\r\n</select> </td></tr>\r\n</table>\r\n<input type=\"hidden\" name=\"currency_code\" value=\"USD\">\r\n<input type=\"image\" src=\"https://www.paypalobjects.com/en_US/i/btn/btn_cart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypalobjects.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n\r\n\r\n\r\n</hr><hr><h2>Assembled and tested units:</h2><br>\r\nWant a Drone Lab but don\'t have the time or experience to make your own? Order a finished model and we\'ll do all of the work for you! On top of that, our work is covered with a 1 year limited warranty.<br>\r\n<a href=\"http://casperelectronics.com/images/finishedpieces/droner/V2/housing/angle.JPG\"><img src=\"http://casperelectronics.com/images/finishedpieces/droner/V2/housing/_angle.JPG\" width=\"400\" height=\"278\" alt=\"\" title=\"\"  /></a>\r\n<form target=\"paypal\" action=\"https://www.paypal.com/cgi-bin/webscr\" method=\"post\">\r\n<input type=\"hidden\" name=\"cmd\" value=\"_s-xclick\">\r\n<input type=\"hidden\" name=\"hosted_button_id\" value=\"AZAAMNNZ44F7U\">\r\n<table>\r\n<tr><td><input type=\"hidden\" name=\"on0\" value=\"Assembled + Tested Unit\">Assembled + Tested Unit</td></tr><tr><td><select name=\"os0\">\r\n	<option value=\"International\">International$370.00 USD</option>\r\n	<option value=\"Domestic\">Domestic$360.00 USD</option>\r\n</select> </td></tr>\r\n</table>\r\n<input type=\"hidden\" name=\"currency_code\" value=\"USD\">\r\n<input type=\"image\" src=\"https://www.paypalobjects.com/en_US/i/btn/btn_cart_LG.gif\" border=\"0\" name=\"submit\" alt=\"PayPal - 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The safer, easier way to pay online!\">\r\n<img alt=\"\" border=\"0\" src=\"https://www.paypal.com/en_US/i/scr/pixel.gif\" width=\"1\" height=\"1\">\r\n</form>\r\n\r\n<object height=\"360\" width=\"100%\"><param name=\"movie\" value=\"http://player.soundcloud.com/player.swf?url=http%3A%2F%2Fapi.soundcloud.com%2Fgroups%2F5034&height=377&color=3b5998&show_artwork=false&width=460\"></param><param name=\"allowscriptaccess\" value=\"always\"></param><embed allowscriptaccess=\"always\" height=\"360\" src=\"http://player.soundcloud.com/player.swf?url=http%3A%2F%2Fapi.soundcloud.com%2Fgroups%2F5034&height=377&color=3b5998&show_artwork=false&width=460\" type=\"application/x-shockwave-flash\" width=\"100%\"></embed></object><span><a href=\"http://soundcloud.com/groups/drone-lab-music\">Drone Lab V2</a></span>','For Sale',0,'','inherit','open','closed','','137-revision-v1','','','2012-10-07 16:09:03','2012-10-07 21:09:03','',137,'http://casperelectronics.com/2012/10/07/137-revision-16/',0,'revision','',0),