Synth Thoughts: Multiple VCAs

This post got motivated by a twitter discussion some time ago:

So that’s the question: why would I want to use more than one VCA in a standard (think Oscillator->Filter->Amplifier) kind of synth voice?

A Basic Patch

Using the Patch Designer from modulargrid, I painted up a truly basic patch:

VCA Basic.png

I’m using Doepfer modules all the way. First because I like them, second because their design philosophy stays true to the “one module, one function” approach.

However, you’re free to use any modules you will have for your experiments. Results may be almost identical, slightly different, or radically over the place. Which is a good thing.

We assume we control this thing by MIDI, and signals go from the MIDI interface to the oscillator pitch CV and to the ADSR for triggering. The audio signal flow is then oscillator into filter into VCA, while the VCA is controlled by the only envelope in this setup, an amplitude envelope. Finally, the audio signal goes out to the right (that open cable end).

We’ll stick with a one-envelope setup for now, so every time I say “envelope” it refers to that one envelope used as an amplitude envelope.

What does the VCA even do?

Rather than just say “it’s a voltage controlled amplifier, so it amplifies controlled by voltage”, let’s have a more detailed look at it.

A standard (linear) amplifier is mathematically speaking something that does this: It has an input signal i(t) (it changes over time, which we describe by the “(t)”) and an output signal o(t). These are related by

o(t) = a*i(t)

The factor a here is what we call our gain, i.e. how much the signal will be amplified. If a is 2, it will be doubled, if it’s 4 it will be quadrupled etc. If it’s 1, then the amplifier doesn’t do anything, the equation becomes o(t) = i(t) – this is called unity gain. On the other hand, if a is smaller than one, e.g. if it’s 0.5, then the signal will be attenuated to half its amount. If a is zero, the signal will become zero (“off”).

Now another case (which we’ll come back to later) is if a is -1 (or any negative value). For a = -1, the equation becomes o(t) = – i(t), that means it inverts the polarity.

The VCA

Now let’s apply what we discussed before to a (standard) VCA. There’s two important things.

  1. The gain a does not remain constant. Rather, we control it from the outside and thus, it becomes a function of time. So our equation ends up being o(t) = a(t)*i(t).
  2. Our “a” cannot have negative values. Modules which allow for negative values are often called “four-quadrant multiplier” or “polarizer“.

We already learned that a cannot go below zero. In typical applications, it will also not go above one, i.e. unity gain. So our VCA becomes more of a voltage-controlled attenuator.

How do we then change that a over time? Simple – we patch something to the corresponding input, usually called “CV”. Coming back to our example above, the “a” is controlled by the envelope, and so once the envelope receives a trigger, it changes the level of the output signal according to its ADSR shape. When the envelope is “off”, it will set a to zero, i.e. no signal (and that’s a good thing, otherwise all of our synths’ voices would drone all the time. Well, maybe that would be considered a good thing by some).

I’d like to further direct your attention to a rather obvious detail: looking at our equations above, what the VCA does is that it multiplies the input signal with the CV signal to generate the output signal.

Why a second VCA?

Picking up with what we’ve just said: we need it if we want to multiply our signal with another CV signal.

Velocity

The most obvious use of a second VCA is velocity control, which started to happen in the synth world for real around the 80s. Many synths from that era simply put a second VCA in series with the first one, controlled one with velocity and the other with the envelope.

VCA Velocity.png

This is the typical way to design a synth with velocity control. A similar approach was done in the CEM 3396 (used in e.g. Oberheim’s Matrix 6 and Matrix 1000), and it’s also used in the A-132-8 OctaVCA by Doepfer which (as you might have guessed) is four pairs of two VCAs in series.

Tremolo

For the electric guitar makers here: “tremolo” refers to a modulation of the amplitude, not of pitch. With that being said: a simple idea would be to patch a LFO to the second VCA, and be happy with it.

However, that wouldn’t work: as we’ve discussed before a VCA does not work for negative CV signals. For that reason, we simply add an offset to the signal.

VCA Tremolo.png

The signal from the LFO goes into input 2 of the A-138c polarizing mixer. On this device, channel 1 i normalled so if nothing is connected, you can set an offset with the In1 knob. So by using sensible settings for In1 and In2, you can add a decent tremolo.

Further Ideas

Different Positions for Velocity Control

We stuck with the usual synth-maker approach to put the envelope-controlled and velocity-controlled VCAs right behind each other. This means that if they’re at the end of the signal chain, the behavior is linear, in layman’s terms “if you hit the key harder, the sound will become louder but not change otherwise”.

If you’ve ever played a (non-synth) instrument, you’re used to something different. Instruments sound radically different if you hit them hard.

One very easy way to replicate this in our setup is to place the velocity-controlled VCA somewhere where it does change the sound. A good spot (especially when using the wonderful A-108 filter) is right before the filter.

VCA vel before filter.png

This gives you a patch where the harder you hit your keys, the louder but also angrier your sound gets. Essentially just what you’d want from a real instrument.

Tremolo is a Form of AM, after all

Coming back to the patch from above, note that the A-145 LFO we used here has a frequency range from 0.005Hz (ca. 3.5 minutes for one period) to 4.5kHz. Which means if we turn the frequency up, we perceive the effect not as a variation in amplitude, but as the generation of additional frequencies. Try that patch with the In1 knob set to zero (center) and high LFO frequencies for some radical metallic sounds!

Now I already hear you exclaim “the CV signal must nut go below zero”! Following the usual approach for modular synths, what will happen then is not that the system will blow up in a cloud of smoke, rather it will do something you may or may not have wanted:

Here, the VCA will change the gain following the LFO’s wave (e.g.the triangle) for the positive part of the waveform and “do nothing” (i.e. remain at a=0) for the negative part. If you use the square out of the LFO, you can easily realize a stutter effect that way. And in general, what happens is that you do amplitude modulation with infinite modulation index with a modulating waveform that has its bottom half cut away, i.e. which has a more interesting harmonic spectrum. “Interesting” if you look for ugly, industrial sounds that is.

Summary

This post will end with the usual anti-caveat regarding modular synths: I just showed a few ideas, there’s no-one keeping you from trying different things. Reading up on signal and systems theory can help, just randomly connecting cables and twisting knobs will work, too. The sky’s the limit! Enjoy!

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