Gain and phase margin of multiple feedback bandpass filter

Question

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?

Answer 1

The simulation results as shown in your problem description look weird (rising phase characteristics). I suppose, it is your intention to produce a Bode diagram for the loop gain, correct? Your ac source (input signal at the inv. node) has an inverting polarity (causing the rising phase) - nevertheless, you can perform a stability check.

However - your interpretation of the results is wrong. The stability check requires to verify the phase response relativ to 360 deg (0 deg) and NOT to 180 deg. Note that the correct definition for the loop gain contains the signal inversion at the "-" opamp input. And the loop gain as simulated by you does, of course, include this signal inversion.

Remember: The oscillation condition (stability limit) is defined for zero phase shift of the loop gain function.

(In some documentation - in particular in control theory papers - the loop gain is used without the phase inversion at the summing junction, which gives rise to some confusion, as we can see here)

Therefore - the magnitude crosses the 0dB axis at app. 10 MHz with a phase shift of app. 90deg. Hence, the phase margin is 90 deg.