I'm trying to get a better understanding of frequency compensation for op-amps. I'll start off with a very specific questions and then get into the context. For a certain op-amp, open loop gain is 90dB and GBWP is 10MHz, so the first pole in open-loop mode is at about 300Hz. With a nominal closed-loop gain of 1, the closed loop gain won't start to roll off until 10MHz. Does this mean that the first pole of the system has been moved to 10MHz, or is it still down at 300Hz? The important consideration is the phase - is there a pole in the amplifier that will cause 90 degree phase shift by shortly after 300Hz, or will the phase be about 0 out into the MHz?
This plays into dominant-pole compensation. If the pole is at 10MHz, I could have a low-pass filter at about 100Hz to cause around 100dB of attenuation, or less than 1 loop gain, by the time the 10MHz pole brings the total phase shift to 180 degrees. But if the first pole of the system is still at 300Hz, the phase shift from that plus the new "dominant" pole will cause 180 degrees phase shift when the loop gain is still far too high and cause instability.
I assume the pole does move, or else dominant-pole compensation would be pretty useless for anything outside of DC. But I was talking to someone who insists that the pole is still down at 300Hz causing significant phase shift before we even get into the kHz.