A linear VCA is one of the simplest synth modules. It uses an OTA (Operational Transconductance Amplifier, which is a type of opamp that takes a differential input voltage and produces an output current. See Also.
This output current is given by
    Eq 1)  Iout = gm*Vin.
gm is the transconductance, given by
    Eq 2)  gm = kT/2q * Iabc.
Iabc is an addition pin the OTA has for a control current which flows into the OTA. The simplified equation is to use Iout = 19.2*Vin*Iabc at room temperature.

The reason the OTA is such a useful device for analog synths is because is behaves as a two quadrant multiplier, multiplying the input voltage Vin times the control current Iabc. This lends itself to be an excellent voltage control element.

Linear VCA

Referring to the VCA2 schematic, pin 6 of U11:B is at virtual ground, so a control voltage applied to J5 is converted to a current I = Vcv/R88. This flows into the emitter of pnp transistor Q7, and most of it flows out the collector to become the control current for OTA U10. Thus the control current is linearly proportional to the control voltage.

The input signal is applied at point 1B, and reduced by the voltage divider formed by R84 and R86. This is because the OTA can only handle 20mV - 30mV p-p at its input without distorting. The input voltage is mutiplied by the control current in the OTA according to Eq. 1. Opamp U11:A converts the current back into a voltage. Thus the amplitude of the output varies with the control voltage: a Voltage Controlled Amplifier.

RV14 acts as a control voltage rejection trim. Ground the input signal. then apply a large signal to the control voltage. Adjust RV14 for minimum output on U11:A.

Linear/Exponential VCA

A variation of the VCA with both linear and exponential control inputs is shown here. It uses an exponential current generator similar to the one used in the VCO. However, instead of a fixed reference voltage VREF which is converted to the exponential generator's reference current, the reference current is derived from a control voltage applied at point 1V. This voltage is inverted then converted to a current by R47.

The reference current is multiplied by an exponential term. At 0v at the output of U4:C, the Vbe's of the two transistors are equal to the reference current. As positive voltages are applied to the exponential control input at 5V, the reference current is multiplied exponentially (doubles every 1v applied to the exponential input). Thus the exponential input acts as a "master gain" control.

We take advantage of this by applying an ADSR waveform to the linear input to determine the amplitude shape (envelope), and the MIDI Velocity voltage at the exponential input to determine the peak amplitude. This produces touch sensitivity.