Sizing capacitor across op amp inputs

Question

I'm studying the constant current portion of the schematic for the Agilent E3610A DC Lab Power Supply, redrawn below for reference.

The current reference supply develops a negative voltage \$V_{CREF}\$, adjustable using the ten-turn pot VR19. \$V_{CREF}\$ represents the constant current setpoint, with the value -2mV/mA of the current limit. This feeds a 20-to-1 resistive summing point connected on its other end to the current sample voltage of 0.1mV/mA of output current. The resulting error signal is fed into the current error amplifier to control the pass device as necessary.

My question has to do with the capacitor C20 across the input terminals to U4A, the inverting op amp circuit that generates \$V_{CREF}\$.

I'm assuming, based on the answer to an earlier question of mine about this sort of capacitor placement, that C20 is there to reduce high-frequency noise that might either produce drift in the setpoint, introduce noise into the power supply output, or both.

My question is "How would I go about sizing this capacitor?". I'd like to understand the design steps rather than just plop in an 18pF cap whenever I design a similar circuit :)

The current state of my transfer function derivation skills is to start with the characteristic gain formula for the op amp circuit, e.g. \$G(s) = -Z_f/Z_g\$, replace the impedances with \$R\$, \$1/sC\$, etc., and crank through the algebra. But unfortunately in this case C20 doesn't fit into the classic gain formula.

I can see it forms a low-pass filter with R28, with a breakpoint at about 100kHz. But I'm not sure how the value of VR19 might fit in, if at all, and I'm not sure how to arrive at 100kHz as an appropriate breakpoint in this case.

What would be the analysis/design steps for a thoughtful selection of the value for C20?

Answer 1

I agree with Andy. although there is a clue in the schematic.

Note the 18pF capacitor (which partly forms the internal compensation pole, amongst other things). It is possible that the original design had some instabilities due to ripple / noise on the 5V input and this capacitor was added. The actual external pole is going to be quite a high frequency (as it is dominated by VR19, when looking at the resistance seen at the inverting input, VR19 || R28).

Using the same value across the inputs as the internal compensation capacitor is stretching the limits of coincidence, so it was probably chosen for this reason.

Just why is very likely lost in the mists of time.

I used the answer box so I could add the image.