Help understanding remarkable Voltage Controlled Filter
Here's the internal schematic of the uA776 opamp, pulled from the datasheet:



Note that Iset (pin 8) is connected to a group of high-side current mirrors (Q12, Q13, Q16) that set the bias current for a bunch of the middle stages of the opamp (and also Q19, Q20 on the low side).

Note also C1, which is added to provide negative feedback at high frequencies in order to make the opamp stable under a wider range of operating conditions. This capacitor creates a "dominant pole" in the overall response of the opamp, which has the general form of a low-pass filter.

C1 charges and discharges more slowly when the bias currents in the circuit around it are lower, reducing the frequency of this dominant pole. Pulling more current from the Iset pin increases the bias currents, raising the frequency of the pole.

This effect is what the VCF design is taking advantage of.



In the surrounding circuit, A1 is effectively inverting the control current (on X1 pin 1, with some bias current provided by R1) and drawing it through the parallel combination of R2 and the B-E junction of VT1 (note that its base is held at "virtual ground" by the negative feedback). With the component values given, most of this current flows through R2, applying a voltage that varies between 0 and about 0.24 V to the B-E junction as the input current varies between 0 and 80 &micro;A.

Therefore, the base current is an exponential function of the input current, and so is the collector current. The collector current is divided evenly between the Iset pins of A2 and A3, where it causes the cutoff frequency to vary exponentially with respect to the original control current.



And yes, it is the combination of A2 and A3 in series that gives you the 12 dB/octave rolloff.