# Gain and phase margin of multiple feedback bandpass filter

I designed a multiple feedback bandpass filter using the Analog filter wizard. The design is purely education therefore I used ideal op-amp. Fc = 50KHz; DC gain = 6dB; Q = 5; I followed the instructions included in the AD tutorial “Stability of Op-Amp Circuits” and simulated the circuit in the same fashion. LTspice: Stability of Op Amp Circuits | Analog Devices

My recollection from control systems is that the negative feedback circuit is stable as long as we do not invert the signal by 180° with a magnitude equal to or greater than 0dB to prevent oscillation. If correct my 0dB point is at 10Mhz and I have 93° of phase margin. Which is sufficient. Additional circuit never reaches the -180° phase shift. However, at 90KHz the phase shift equals 164° with 22.7 dB of gain. I would imagine that it is a very low phase margin of only 26° with 22.7dB of gain. I vaguely remember the “rule of thumb” for phase margin as 45° and gain margin as 20dB.

If the above statements are correct are they applicable for filters?

If yes how can I improve the phase margin? Would the introduction of a delay in order to shift the phase response be a good idea?

• The gain is not zero at that point. As for the improvement in the phase response (in case it's needed), why not follow the advice in the video you linked? If you're worried about a "wobbly" initial transient, that's the inherent impulse response. Apr 4, 2022 at 13:56
• @aconcernedcitizen Thank you for your reply. "The gain is not zero at that point." are you referring to the point where the phase shift is equal to 164°? Isn't that worse as we get nearly 180° of phase shift with loads of gain? Regarding the video, I was not sure if this solution is specific to the problem presented which is driving a large capacitance at the output of the op-amp. I will give it a go and experiment. Apr 4, 2022 at 14:07
• Since you already have enough phase margin, there's nothing to correct for. That the phase goes as low as it does, that's a direct consequence of the response of the transfer function -- it's a sharp bandpass. Making the phase smoother will result in a wider transition width for the filter. Think of it this way: if that would have been an inverse filter (inverse Pascal, inverse Chebyshev, Cauer/elliptic), you would have had zeroes, and the phase would have jumped 180 degrees. Would you have considered that to be unstable? Apr 4, 2022 at 14:15
• As to your last sentence - the phase margin of app 90 deg (see my detailed answer) is caused by the opamp only (opamp phase shift at very large frequencies) and not by the frequency-dependent filter circuitry. Shifting the phase response in negative direction would be the worst solution.
– LvW
Apr 4, 2022 at 15:35