I'm designing a noisy power circuit. V1 and V2 signals are coming from a long path, and they are likely to contain some noise. What happens if I connect the Cn capacitor as in the schematics above? Would the opamp output stay stable?
V1 and V2 signals are coming from some mechanical systems, and they are changing very slowly in time; maximum rate of change is around 0.1 V/s. And it is not necessary to have a fast response at the the oamp output. In short words, it is OK as long as I get the nominal summing amplifier output at steady state.
Can I place the Cn capacitor there under these conditions?
I agree with the previous posts. Capacitance at the summing node will cause a large peak in the response and possibly oscillations. Connect the capacitor across Rf to create a first-order low pass filter. If response time is an issue than you could go to a higher order active filter (2nd order or higher).