We generally say 60 degree of phase margin at 0db gain is stable. But what if the phase drops to say 45 degrees at 10db gain, then comes back up to 60 by the time we get to 0db gain? Is it less stable at that 10db 45 degree frequency, or the 0db 60 degree frequency?

 

Yes the stability is determined by the worst phase-gain margin. When folk mention "at 0dB" they usually show a monotonically reducing gain from the lower frequencies. With a dip, it is worse at the dip.

 

I don't know all the Math involved,
but from past apparent successes,
I've found that using an Op-Amp with a very high Slew-Rate,
and then limiting the Slew-Rate with a Feedback-Capacitor,
down to a Frequency-Response that is adequate for the application,
has always been a successful strategy for me,
but, I don't attempt anything much over Audio-Frequencies,
except when using a specialized-Chip specifically designed to operate at higher Frequencies.

Never directly Load the Output of an Op-Amp with a Capacitor,
there must always be some Resistance before or after the Capacitor,
or You will instantly create an Oscillator.

Don't use ~0.35 cent Op-Amps designed in the '70's,
more expensive Op-Amps are more expensive for a reason, usually multiple reasons.
.
.
.

 

We generally say 60 degree of phase margin at 0db gain is stable. But what if the phase drops to say 45 degrees at 10db gain, then comes back up to 60 by the time we get to 0db gain? Is it less stable at that 10db 45 degree frequency, or the 0db 60 degree frequency?

I think, something should be corrected:
* When the phase margin (determined at the 0dB-crossing) is 60 deg, the closed-loop sysytem will not only be stable - it will have sufficient margin for a "good" step response (only minor or no overshoot).

* A closed-loop system will be stable even for a phase margin of 5 deg only - however, the step response will show severe ringing.

* For an existing system there is nothing like a "worst case phase margin". There is only one single margin which is defined at the 0dB-crossing.

* "If the phase drops to say 45 degrees at 10db gain, then comes back up to 60 by the time we get to 0db gain?"
In this case, the phase margin still is 60 deg. However, the step response will be affected (overshoot).

* The slew rate is a large-signal parameter and, thus, has no relation to stability properties of the sysytem-

 

"worst case phase margin" is not a correct description. But any amplifier which shows an overshoot is not ideal. If the phase drops before rising again that is a worse case than if the phase falls monotonically before reaching 0dB.