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tenso

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Phase margin in closed loop
Sep 02^nd, 2016, 4:55pm

I had a question about Phase margin measurement in the unity gain feedback configuration for an op-amp.

I get about 83 degrees PM ( 180 + -96) in the open loop analysis.

I then connected the op-amp as a voltage follower. The gain drops to 0 dB as expected and the UGF frequency is about the -3dB frequency in this configuration.
But measuring the phase at this frequency I get a PM of about 130 degrees ( 180 + -50).
Shouldn't it be same as the open loop condition? ( or is PM measured only for open loop ?)

So in voltage follower, does the phase margin actually improve? If I want to ensure that my op-amp is stable in unity gain feedback, at what frequency should I look at the PM?

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buddypoor Community Fellow Offline Posts: 529 Bremen, Germany	Re: Phase margin in closed loop Reply #1 - Sep 3^rd, 2016, 2:11am Stability margins (GM and PM) are to be determined under open loop conditions only. Closing the loop changes gain magnitude and phase, of course. But the closed-loop phase must not be used to find the phase margin.
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vroy_92 Junior Member Offline Posts: 30 Leuven, Belgium	Re: Phase margin in closed loop Reply #2 - Sep 3^rd, 2016, 8:04am In closed loop, phase margin really gives you no idea about stability and thus there is really no value to the meaning of phase margin in closed loop. But generally, an op-amp will have poorer stability margins in unity gain. You can refer to Grey and Meyer for this.
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tenso

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Re: Phase margin in closed loop
Reply #3 - Sep 3^rd, 2016, 8:56am

buddypoor wrote on Sep 3^rd, 2016, 2:11am:

Stability margins (GM and PM) are to be determined under open loop conditions only.
Closing the loop changes gain magnitude and phase, of course.
But the closed-loop phase must not be used to find the phase margin.

vroy_92 wrote on Sep 3^rd, 2016, 8:04am:

In closed loop, phase margin really gives you no idea about stability and thus there is really no value to the meaning of phase margin in closed loop.

But generally, an op-amp will have poorer stability margins in unity gain. You can refer to Grey and Meyer for this.

Thanks you guys your answers help a lot. I will check out Gray-Meyer.

I had a follow up question about .stb analysis. stb analysis gives you the loop gain.

Now in most books open loop gain and loop gain is defined as follows.
Ao = open loop gain
Ao*β = loop gain
α*Ao/(1+Ao*β) = closed loop gain (operational gain of the amplifier with feedback)

I ran a stb analysis using only the iprobe element in feedback. The stb simulation then gave me the loop gain equal to Ao. If I had passive elements in my feedback path would it actually give me Beta * Ao and not Ao?

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tenso

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Re: Phase margin in closed loop
Reply #4 - Sep 4^th, 2016, 7:18pm

just a follow up with numbers.

my open loop gain Ao = 70 dB
connected the opamp in non-inverting configuration with β = 0.33
so closed loop gain ao = 9.5 dB
calculated loop gain ≈ 61 dB

measured loop gain with stb analysis in spectre ≈ 36 dB.
stb says it measures loop gain but I get nowhere near my calculated value. I put iprobe in the feed back path before the feedback resistors. What am I doing wrong in loop gain measurement?

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buddypoor Community Fellow Offline Posts: 529 Bremen, Germany	Re: Phase margin in closed loop Reply #5 - Sep 5^th, 2016, 1:50am I don`t know how stb analysis works. Why not simply open the loop and using a test ac voltage source for finding loop gain and phase? The loop gain magnitude maximum must be app. 70-9.5=60.5 dB.
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Ken Kundert

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Re: Phase margin in closed loop
Reply #6 - Sep 5^th, 2016, 10:28am

Gain and phase margin only make sense when applied to the loop gain of a feedback system. And loop gain is a characteristic of the loop. It can, and should, be measured when the loop is intact. You can estimate loop gain by opening the loop, but you should not, because the estimate can become quite inaccurate as the gain approaches unity.

The basic issue with trying to measure loop gain by opening the loop is that you have changed the circuit. So the answer to the question "Why the gain and phase margin results different between when I measure them with the loop open and closed?" the answer is always "You changed the circuit when you opened the loop."

Measuring the loop gain even when the loop is closed is tricky. To do it simply you would need to identify an ideal controlled source in your circuit and use it to measure the return ratio (the return ratio is the same as loop gain, but it is only defined when there is an ideal controlled source in the loop that, when removed, breaks the loop). You generally do not have such a source. In that case the measurement becomes complicated. Several measurements must be made in order to compensate for the fact that the signal injection point is not ideal. The process and the corrections are tedious, but fortunately, they have been automated in Spectre.

When you compare your open loop estimates of the loop gain with the loop gain computed by Spectre's stb analysis, they should generally agree at low frequencies, but you can expect them to deviate near and beyond the unity gain frequency. Thus, your comment that Spectre's stb analysis is not getting the expected loop gain at DC seems to suggest a problem somewhere.

-Ken

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tenso

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Re: Phase margin in closed loop
Reply #7 - Sep 5^th, 2016, 11:41am

Ken Kundert wrote on Sep 5^th, 2016, 10:28am:

Gain and phase margin only make sense when applied to the loop gain of a feedback system. And loop gain is a characteristic of the loop. It can, and should, be measured when the loop is intact. You can estimate loop gain by opening the loop, but you should not, because the estimate can become quite inaccurate as the gain approaches unity.

The basic issue with trying to measure loop gain by opening the loop is that you have changed the circuit. So the answer to the question "Why the gain and phase margin results different between when I measure them with the loop open and closed?" the answer is always "You changed the circuit when you opened the loop."

Measuring the loop gain even when the loop is closed is tricky. To do it simply you would need to identify an ideal controlled source in your circuit and use it to measure the return ratio (the return ratio is the same as loop gain, but it is only defined when there is an ideal controlled source in the loop that, when removed, breaks the loop). You generally do not have such a source. In that case the measurement becomes complicated. Several measurements must be made in order to compensate for the fact that the signal injection point is not ideal. The process and the corrections are tedious, but fortunately, they have been automated in Spectre.

Thanks for taking the time to answer Ken. Yes, I have read earlier threads discussing stb analysis on this forum where you have said that breaking the loop is not the right way to go about things. Good to know. I think the technique to measure loop gain I have seen most people use is where they insert a LC network and an AC source into the broken loop. I will use lstb in HSPICE and STB in spectre going forward.

Ken Kundert wrote on Sep 5^th, 2016, 10:28am:

When you compare your open loop estimates of the loop gain with the loop gain computed by Spectre's stb analysis, they should generally agree at low frequencies, but you can expect them to deviate near and beyond the unity gain frequency. Thus, your comment that Spectre's stb analysis is not getting the expected loop gain at DC seems to suggest a problem somewhere.

-Ken

The loop gain I calculated when I connected the opamp in non-inverting configuration with a β of 0.33 was around 60 dB (open loop gain was 70 dB and closed loop as expected of around 10 dB). When I use the iprobe element connected in the feedback path, between the output node and the feedback network, and run stb I get a loop gain magnitude of about 36 dB. As you said, this should agree with my calculated value, at least for lower frequencies. Maybe I am connecting something wrong. I will try to post a screenshot of my setup soon.

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Ken Kundert Global Moderator Offline Posts: 2384 Silicon Valley	Re: Phase margin in closed loop Reply #8 - Sep 5^th, 2016, 3:44pm There is a good chance that by opening the loop you are changing the low frequency open loop gain as well. In fact, I would say that is the most likely explanation. -Ken
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tenso

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Re: Phase margin in closed loop
Reply #9 - Sep 5^th, 2016, 6:23pm

Ken Kundert wrote on Sep 5^th, 2016, 3:44pm:

There is a good chance that by opening the loop you are changing the low frequency open loop gain as well. In fact, I would say that is the most likely explanation.

-Ken

I didn't open the loop when measuring the loop gain of the non-inverting amplifier using stb analysis. Just connected iprobe in series with feedback resistors.

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Ken Kundert Global Moderator Offline Posts: 2384 Silicon Valley	Re: Phase margin in closed loop Reply #10 - Sep 5^th, 2016, 8:09pm You must have opened the loop to measure open loop gain. I suspect that is where the error lies. -Ken
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tenso Junior Member Offline Posts: 30 USA	Re: Phase margin in closed loop Reply #11 - Sep 6^th, 2016, 6:05pm I actually used a close loop to measure my open loop gain (about 70 dB). Used both a large RC network to set the DC bias and stb to measure it. �I just connected iprobe in the feedback path. Here is the frequency response plots.
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tenso Junior Member Offline Posts: 30 USA	Re: Phase margin in closed loop Reply #12 - Sep 6^th, 2016, 6:11pm Here is the setup for measuring the loop gain with stb including the feedback network. I get a loop gain of 36 dB using this setup. When I replace it with LC network and AC source in feedback path and do a transient analysis, I get the expected loop gain of 61dB.
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Ken Kundert

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Re: Phase margin in closed loop
Reply #13 - Sep 6^th, 2016, 6:45pm

I am just going to keep saying the same thing. When you opened the loop you modified the circuit, which changed the open loop gain. You have no output stage, so the output impedance of the amplifier is very high and as a result the effective open loop gain is a strong function of the load, including the load provided by the feedback circuit. Any change to the feedback circuit can strongly affect the open loop gain.

For example, in the circuit shown the output is loaded with the attenuator that is the feedback circuit. This presents a DC resistive load to the amplifier, which dramatically lowers its DC gain. When you measured the open loop gain you had an RC circuit as the feedback network. This presents an infinite impedance at DC, which means that your DC gain will be much higher. Thus, you changing the feedback circuit is dramatically affecting all of the gain characteristics of your circuit.

The lesson to learn here is that when you changed the feedback circuit, you completely changed all of the characteristics you were trying to measure. You must not do that. Instead, you should simply forget the open loop gain, it is a meaningless number, focus on the loop gain, and measure it without modifying the circuit at all (inserting an iprobe in series with a wire does not count as a change to the circuit).

-Ken

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tenso

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Re: Phase margin in closed loop
Reply #14 - Sep 6^th, 2016, 7:08pm

Ken Kundert wrote on Sep 6^th, 2016, 6:45pm:

The lesson to learn here is that when you changed the feedback circuit, you completely changed all of the characteristics you were trying to measure. You must not do that. Instead, you should simply forget the open loop gain, it is a meaningless number, focus on the loop gain, and measure it without modifying the circuit at all (inserting an iprobe in series with a wire does not count as a change to the circuit).

-Ken

Thanks for the patient responses Ken. If I understand you right my feedback network reduces my open loop DC gain by a lot. So my loop gain value of 36 dB is a reflection of that, right?

Just some �more questions

1) does my setup for measuring loop gain with iprobe look right to you?

2) I have seen a lot of people use the LC network setup with AC souce above to measure loop gains of LDOs, bandgap references etc. Am I right in saying that you don't recommend it and stb is the right way to go about things?

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