# What does the LOOP GAIN's phase and gain margin say about the CLOSED LOOP response?

1. ## What does the LOOP GAIN's phase and gain margin say about the CLOSED LOOP response?

Starting with an open loop system, you specific frequency gain and phase response plots. If you provide negative feedback, then that plot then gets split in half. The top portion is the loop gain and the bottom portion is the closed loop system response. When you do stability analysis, it is optimizing the phase and gain margin of the loop gain response, but what does that do to the closed loop response plot? At the end of the you excite the input of the closed loop system and measure an output from the closed loop system, but the phase and gain margin of the LOOP bode plots effect how good that response will be. So it seems like the loop phase and gain margin have some sort of the meaning for the closed loop response bode plots.

Thanks

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2. ## Re: What does the LOOP GAIN's phase and gain margin say about the CLOSED LOOP respons

Gain and phase margin are quantities defined for the loop gain. In a negative feedback system you want to keep away from the point where the feedback becomes positive - that is your loop gain has a value of 1 or 0dB and your excess phase is 180deg. Since it is a negative feedback, you already have an inversion for the loop gain even at DC. With frequency, the loop adds extra delay and shifts the phase. If you accumulate more phase compared to the initial 180deg you start running into troubles. That additional phase accumulation is the excess phase. If it becomes 180deg, then your total phase shift along the loop becomes 360deg and your feedback becomes positive. If at that frequency you also have loop gain of 0dB, then you meet the conditions for oscillation.
So, you look at the frequency where the loop gain crosses 0db and check the phase for that same frequency. The phase margin is a measure of how far the phase is from the 360deg (or 0deg as some simulators show it). If PM is for example 90deg, then your closed loop amplifier behaves like a 1st order system with nice exp settling to a step. The lower you go with the PM, the more ringing you see in the step response. As a rule of thumb people take 45deg as min. PM, but you already have quite a bit of ringing for it. Now it depends on your application. For switch cap circuits you generally shoot for about PM=75deg. If you process sine signals, it is customary to aim at 60deg. For LDO, you may go to 45deg perhaps.

Gain margin is another metric of goodness for your loop.It says how much your loop gain has fallen below 0dB when the PM=0deg - in other words how far you are from the dangerous point of 0dB. Usually you want to have double digits GM.

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3. ## Re: What does the LOOP GAIN's phase and gain margin say about the CLOSED LOOP respons

In general you study the bode plots of the open loop system, follow certain guidelines (gain and phase margin) and it tells you the closed loop system will be stable.

It also tells you a little about the closed loop response but this relationship complicates quickly and to be clear, the closed loop response is different.

The best way to learn this is in a simulator. I highly recommend ltspice and Psim.

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4. ## Re: What does the LOOP GAIN's phase and gain margin say about the CLOSED LOOP respons

Loop gain is the product of the gains of all the components of a feedback path. The loop gain phase margin and gain margin are basically expectations that when you meet them, your closed loop system is supposed to be stable (except in some exceptional cases of course).

So when you analyze the open loop system, you obtain gain and phase asymptotes (and of course frequency response plots). So when you multiply the gains of all the other components in the feedback path and set the gain of the compensator to 1, you obtain the gain of an uncompensated loop. When you analyze the gain and phase of this uncompensated loop gain asymptotes (or actual plots), you get to know the actual situation of things. It gives you an idea how to compensate the loop to meet the expectations.

5. ## How does gain margin affect transient response?

The phase margin of a negative feedback amplifier affects the overshoot, so what does the gain margin affect? Does it affect the settling time? Thanks

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6. ## Re: What does the LOOP GAIN's phase and gain margin say about the CLOSED LOOP respons

No. GM holds more or less the same information as PM. See previous answer by sutapanaki.

For simple amplifier characteristics, e.g. integrator with additional poles, relation between PM, GM and e.g. overshoot can be calculated. Rule-of-thumbs are describing this relation, e.g. no overshoot if PM > 57°.

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