Analog Modular Synthesizer 6.101 Final Project

Dominik Martinez

May 20, 2017 Introduction

The modular synthesizer is a musical instrument that produces sound from electronic systems rather than mechanical as with traditional musical in- struments. Synthesizers first were developed in the late 18th century and have since been under the development from the musical and engineering communities for over a century. This report explores the design and construction of an analog modular synthesizer. Modular synthesizers are unique because each stage of the sound processing chain is a separate module (i.e. the oscillator, the filter, the amplifier). The sound signal can be routed in different ways through the synthesizer, with older modular synths actually using patch cables to manually route the signal through different modules. This provides musicians an intuitive way to produce unique sounds. The modular synthesizer is one of the most pervasive type of synths to this day due to its ease of use. Figure 1 shows a very general overview of how the analog modular synthesizer is designed to work. Generally speaking, there is a power supply, a keyboard for physically playing the notes, an amplifier, and speaker. Figure 2 shows the sound processing system in more detail. The keyboard sends a voltage to the voltage controlled oscillator (VCO) which produces the initial sound wave. In general the wave can be any shape, but for this project the VCO produces a triangle, sine, and ramp wave. This waveform is then propagated through the voltage controlled filter (VCF), which acts as a either a low-pass, high-pass, or band-pass filter depending on user set parameters, and the voltage controlled amplifier (VCA), which controls the gain of the signal before it is sent to the amplifier. While the VCO is controlled from the keyboard’s linear 1V/octave signal, the VCF and the VCA are controlled by the Attack-Decay-Sustain-Release (ADSR) module. The ADSR module is an envelope generator that is set to the parameters of the user and triggered by the keyboard receiving input (the ADSR module

1 Power Supply

Keyboard Sound Processing Ampliﬁer

Figure 1: Very general block diagram will be explored in more detail later in this report). The scope of the project includes the design and contructing of the amplifier, keyboard, VCO, VCA, and ADSR modules. This report will explore these modules. The justification for these modules is that they are the most critical components for a fully functioning synthesizer. The power supply used is from the 6.101 lab kit, providing 15V rails. The VCF was completely left out of the sound chain. While this means that the synth does have a bit less flexibility in terms of the different musical timbres it can produce, the synth is still, by definition, a fully function analog modular synthesizer.

2 VCO1 VCF VCA

VCO2 ADSR ADSR

Keyboard

Figure 2: Detailed sound processing block diagram

3 Ampliﬁer

The audio amplifier circuit (seen in Figure 3) is a 3-stage power amplifier. Its design is inspired by the work presented in Douglas Self’s textbook Audio Power Amplifier Design. The 3 stages in this amplifier are the input stage, the voltage-amplifier stage, and the output stage. The output of the amplifier is then fed back into the input of the amplifier in the form of negative feedback. Notice that since the amount of feedback is very large, this amplifier only has a gain of 6 dB. This amount of gain is intentional, since during testing the sound signal voltage from the sound processing module was already found to be very large (on the scale of 10V peak to peak), so further voltage gain was not necessary.

Input Stage

The role of the input stage is to take the input signal and the feedback signal and subtract the latter from the former. It accomplishes this in the form of a long-tailed pair differential amplifier. The design used for the synthesizer in this project uses Q3 to create a tail current-source to provide more stability. In practice this worked reasonably well, but there was a slight misbalance between the two ends which caused the output of the amplifier to sit at 50 mV. Potential improvements that would have minimized this issue would have been to put a potentiometer across the -15V ends of the amplifier and use that to fine tune the balance to manually minimize DC offset. The superior method for controlling the balance would be to install a current mirror at the base of this amplifier. A current mirror, seen in Figure 4 would be a near perfect method of eliminating any DC offset since the circuit mirror forces the current at the tails to be equal.

4 Voltage-Ampliﬁer Stage

This stage takes the current output of the input stage, converts it to a voltage, and ampliﬁes it. This stage is in the form of a common emitter ampliﬁer with a current source as its load. Optimally there would be voltage biasing between the amplifying transistor and the current transistor to remove crossover distortion. This would generally be in the form of a rubber diode. Practically I found that crossover distortion was not an issue with negative feedback, so I left the biasing out.

Output Stage

The output stage implemented here is a unity gain voltage follower stage, a topology that Self claims is one of the most commonly used circuits in power ampliﬁers. In the implementation here, a complementary feedback pair (CFP) topology is used for current gain. The CFP topology generally shows better thermal stability than a plain emitter follower topology. Because each CFP is only conducting for half the input signal, this is a Class B power ampliﬁer. The output from here is then fed back into the negative input on the input stage.

5 Figure 3: Schematic for the 3-stage ampliﬁer

Figure 4: Generic current mirror

6 Attack-Decay-Sustain-Release

The Attack-Decay-Sustain-Release (ADSR) module is a envelope generator that is triggered by the keyboard, has four user controllable parameters, and produces a voltage envelope which is then used as a control voltage for the VCA and VCF. A graph of the envelope produced by the ADSR and how the parameters control it can be seen in Figure 5. Attack controls the time for the voltage to reach the maximum voltage, decay controls how long it takes for the voltage to reach the sustain voltage. Sustain controls the voltage that the envelope will remain at while the user holds down the key. Release controls how long it takes for the voltage to return to 0 after the release of the key. Figure 6 shows the implementation of the ADSR module for this project. The trigger voltage is a pulse of about 10 V, with it normally being held at around -10 V. In the untriggered state, Q1 is off, which causes Q2 to be on. With Q2 turned on, the 555 reset pin is held to ground, which keeps the circuit’s output at 0V. When the trigger voltage comes, Q1 turns on, which turns off Q2 and turns on Q3. This causes the trigger voltage to be grounded which causes the output voltage of the 555 to go high. R10 controls how quickly C3 charges which controls the length of the attack. Eventually the 555 threshold goes high which causes discharge to be grounded. The topology with U3, R13, and U2 controls how quickly the circuit sustains and on what voltage it sustains on by shunting some of the voltage away from the output to ground. Finally, when the key trigger is returned to its initial state, Q1 is off, Q2 is on, and C3 begins to discharge through R8, which controls the release. This design worked very well in practice, requiring no debugging or alterations.

7 Figure 5: The ADSR envelope

8 Figure 6: Schematic for the ADSR envelope generator

9 Voltage Controlled Oscillator (VCO)

The VCO has the role of taking in a linear voltage input, converting that input to an exponential signal, and converting that signal into several types of waveforms. The reason for the conversion between the linear input and exponential conversion is because music is exponential. On a standard piano for example, the frequency from middle C to the next C an octave up is doubled. And from that C to the next C it is doubled again. The schematic presented here drew heavy inspirations from Thomas Henry’s book An Analog Synthesizer for the 21st Century. The first stage in the VCO is running the linear input through an adder. R2 is a high value so that the input from the tuning pot has a much smaller effect on the frequency than the actual keyboard input. The output of the adder is then ran to a dual BJT circuit where the exponential relationship between the base voltage and the collector current of a BJT is used to convert that linear voltage input to an exponential voltage output. The dual transistor topology is use so that the output of the exponential convert is independent of variations in temperature of the transistors. U3 provides Q2 a reference current, which is then modified depending on the voltage at the base of Q1. The output of the linear to exponential convert is then ran to a transconductance amplifier, so that the circuit can convert the current into a voltage. This dual transconductance amplifier produces a triangle wave, with its base frequency being controlled by C3. This signal is ran to U6 which amplifies the wave. The output of U4 and U5 produces a square wave which is used later on in the circuit. This triangle wave is then ran into a long tailed pair amplifier and amplified into its nonlinear region. This is a easy trick to force a triangle wave to look like a sine wave, obviously it’s not a true sine wave, but practically speaking

10 for music it is close enough. The first few terms of the sine wave’s Taylor x3 x5 series is x − 3! + 5! and for the wave produced by this circuit the Taylor x3 2x5 series is x − 3 + 15 . Both waves are linear to the first order so the circuit’s sine wave is nearly indistinguishable from a true sine wave. For the ramp wave, the triangle wave is first ran through U9, which allows us to control the gain of the wave, then it is ran to U11, which in conjunction with J1 acts as either a voltage follower or an inverter. Since the square wave from the transconductance amplifier is at the same frequency as the triangle wave, this allows U11 to flip about half of the triangle wave to produce a ramp wave. This can be fined tuned with pot U10. The output impedance of every waveform used for sound is 1k. This value was chosen experimentally, and produced the best results when amplified.

11 12

Figure 7: Schematic for the VCO Figure 8: Schematic for the VCO cont.

13 Voltage Controlled Ampliﬁer (VCA)

The VCA is a long tail pair with the tail current being controlled by the control voltage (the output of the ADSR envelope generator). The schematic can be seen in Figure 9. U3, U4, and U6 are used to fine tune the effects of the CV on the output. Q1 controls the current of the tail which in turn controls the amplification of this circuit. This module is particularly important since the VCO is always producing a waveform, the only way to control when a note is sounding or not is through this module. In practice this circuit worked extremely well and required practically no debugging.

14 Figure 9: Schematic for the VCA

15 Keyboard

The physical keyboard is 62 resistors in series with 5V applied across them as seen in Figure 10; this is 1V/Octave. When a key is played, a connector connects at the junction of one of the resistors which creates a large voltage divider. As diﬀerent junctions are selected, a linear voltage change can be seen. This linear change is then fed to the circuit seen in Figure 11. This is a simple comparator circuit that simply checks if a nonnegative voltage is being applied (a negative voltage is the default state when no key is pressed). If there is an input, the comparator outputs a +V signal for use in the ADSR module. If there is no input signal (i.e. no key is pressed), then the comparator holds the output at ground.

16 Figure 10: The voltage divider that creates the keyboard

Figure 11: Schematic for the keyboard

17 Results

With all of the modules connected together, the synthesizer proved to be quite successful. The musical notes were very clear and undistorted even at very loud volumes, and after properly adjusting the pots on the VCO for the 1 V/octave control, the synthesizer was very well tuned and stayed in tune for the entire 5 octave range of the keyboard. The final checkoffs and test were done running on the 6.101 lab kit’s current limited power supply. I found that for a computer speaker 500 mA was plenty to power both the amplifier and the sound circuitry. Although not tested, it is safe to assume that to power a larger speaker a higher current power supply would have been required. There is a severe issue with this design that was not addressed during the construction of the synth. With the keyboard schematic, when a key is no longer pressed, the input being fed to the VCO is floating. The VCO still generates waveforms even though there is a voltage input of around 0V. Remembering back to the ADSR module as seen in Figure 5, when the key is lifted, the sound from that note should not disappear. This issue is apparent when the ADSR’s release is set to a long time, then when the key is lifted, instead of hearing the same note, one could hear the note switch to a different note and then fade out when the key was lifted. The solution to this would be to design a keyboard circuit that could essentially “save” the voltage of the last key that had been pressed even after the key was lifted. While this is certainly possible with analog circuity, it was a significantly more challenging design project than the author had time to deal with, so it was ignored. Assuming the release on the ADSR module is small, this issue was not noticeable. Practically speaking, this is not an actual solution to the problem.

18 Conclusion

While I set out to design and construct every module that were presented in Figures 1 and 2, due to time constraints this was not reasonably possible. Because of this, I had to shrink the scope of the project to what you see reported here. Overall, I was very happy with the result even if I didn’t accomplish all I set out to build. In the future I plan on ﬁnishing the VCF and power supply and printing a PCB so that I can use the synthesizer for casual music playing. I am very thankful for the help of the instructors Gim, Yanni, and the CI-M instructor Dave.