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Everything I read on the web, concerning this question, says that in order to measure or set the phase margin of an amplifier the loop must be opened and the phase lag around the loop measured when the gain around the loop equals -1 (unity loop gain).

This seems to be almost universal advice with its resulting practical problems such as DC offset across the break and creating the correct load for the output of the opened loop.

My question - Can the phase margin be measured in a closed loop setup, why is an open loop always recommended for this?

Classical amplifier theory says that for an amplifier to be stable the loop phase must be less than 180 degrees lag by the time the loop gain gets down to 1 (unity). To give sufficient phase margin the value of the compensation capacitor is often set to give a loop phase of, say, 135 degrees at unity loop gain (phase margin = 45 degrees).

Consider the following amplifier:-

schematic

simulate this circuit – Schematic created using CircuitLab

Loop Gain = BAol

where:-

Aol = Vout/Vdiff

and

B = Vfeedback/Vout

Therefore loop gain = Vfeedback/Vdiff (using pk to pk values).

Loop phase is the phase of Vfeedback to Vdiff.

It appears that I can measure both loop gain and loop phase in a closed loop configuration.

Why can't I just increase the input signal frequency until Vdiff = Vfeedback (unity loop gain) and then measure the loop phase with a 2 channel oscilloscope (phase of Vfeedback to Vdiff) to determine or set the phase margin? (How short of 180 degrees the loop phase is).

Is there anything with this apparently very practical closed loop method of determining (or setting) phase margin. Why is such a much more practically difficult open loop technique so commonly recommended?

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  • \$\begingroup\$ Measure the loop frequency response, \$\frac{output}{error}\$, with the loop closed. \$\endgroup\$ – Chu May 25 at 18:08
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Vd isn't possible to be measured easily, because it's not against GND. Differential mode oscilloscope is a must. Of course you in theory can calculate Vd=V1-Vf, if you store simultaneously measured V1 and Vf. Waveform math shouldn't be a big deal if you have that capable oscilloscope.

But that math has a problem: The accuracy. Vf and V1 can both be acceptably accurate alone, but their calculated difference can have so high error percentage that it's useless. Think, if V1 and Vf both have 1% error, but to different directions and Vd is only about 2% of V1.

Another problem: An oscilloscope in the -input of the opamp is a capacitive load. One must be well aware how to be sure that it doesn't cause substantial phase shift.

Conclusion: Not theoretically impossible, but needs some work and good enough equipment. I guess a creative enough person can find a way around the accuracy limitations of ordinary tools. He for example swaps channels and compensates errors with more math and introduces a calibration method.

Why this isn't recommended? I guess measuring A and B separately is easier. At least at high frequencies where the absolute value of A isn't especially high. At DC it can be several decades higher.

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