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I am using LTPowerCAD to help design a buck converter circuit using the LT8645S. I would like to add a second stage LC filter at the output to achieve lower output ripple, but when I add the second stage, the bode plot of the loop compensation shows 3 gain crossover frequencies. The software uses the last crossover to measure the phase margin, but I don't know if I should trust this.

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My question is, when there are multiple gain crossovers in a control system, which crossover do you use to determine the phase margin? Does it depend on the details of the system, or is it always the same?

Note: Unfortunately I am unable to provide more details about the design, but I'd like to ask this question generally and not tailored toward any specific application, although the answer may be that it really depends on the application and system details which is ok with me.

imnotarobot
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  • Are you sure you have selected a crossover frequency at least 3-4 times the resonant frequency of your LC filter, assuming this is voltage-mode control of course? – Verbal Kint Sep 30 '21 at 19:12
  • It is a current-mode controlled regulator. I redesigned the filter to get rid of the multiple crossings, but I'm still puzzled by the frequency response of the original loop. The block diagram of the regulator in the datasheet shows an internal RC network on the output of the error amplifier that adds a zero (probably to boost the phase). I'm guessing that zero is right around where I placed a zero in my compensation which caused the big phase hump and change in slope for the gain. I moved my filter poles to a lower frequency and that fixed the problem. – imnotarobot Oct 01 '21 at 14:34
  • I see, for a current-mode-controlled buck converter, pole-zero placement using the k factor usually gives good result (which is not the case for a voltage-mode type). But I agree that the manufacturer may have added several filters in the signal path which may adversely affect the loop gain in the end. Glad if your new compensation strategy has fixed the issue. – Verbal Kint Oct 02 '21 at 09:47

2 Answers2

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I found the answer in "Fundamentals of Power Electronics" by Robert W. Erickson and Dragan Maksimovic (Pages 365-367). The book works through an example of testing the stability of a system with three crossover frequencies and states the following.

Hence the simple phase margin test is ambiguous, and it is necessary to sketch the Nyquist plot to correctly determine whether this loop gain leads to a stable system.

So the answer is that it depends on the system details. It may be that for buck converters it's always the last one that counts, but you're always going to be safest by testing for absolute stability with the Nyquist stability criterion as was mentioned in some of the comments.

imnotarobot
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If the gain crosses zero db multiple times, it's the last (highest frequency) crossing that counts for stability purposes.

John D
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  • Hi John, thanks for your answer, +1. Could you elaborate on why it is the last crossing that counts and/or refer me to any resources that discuss the reasoning? – imnotarobot Sep 30 '21 at 18:58
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    I think what matters is the distance to the -1 point in all cases. With Bode, I would consider PM at all crossover points: if you have a first crossover at 1 kHz with a 10° PM and another at 10 kHz with a PM at 70°, would you trust this control system? – Verbal Kint Sep 30 '21 at 19:14
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    No I don't trust it, that's why I'm asking. – imnotarobot Sep 30 '21 at 19:44
  • My source is here: https://www.ridleyengineering.com/hardware/ap310-analyzer/ap300-application/loop-stability-requirements.html which has proved to be true in my experience. – John D Sep 30 '21 at 20:14
  • @JohnD in my experience, the full Nyquist criterion of _counting the encirclements_ has to be used rather than just the last one. – AJN Oct 01 '21 at 08:58
  • I do not know about the reliability of the linked site, but it is possible that they deal with systems which always satisfy some assumption; e.g. minimum phase system or open loop stable system or system with low pass characteristic etc. It may be one such assumption which may be leading to the _highest-frequency-phase-margin_ criteria. – AJN Oct 01 '21 at 09:05
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    @AJN Dr. Ridley's site is mainly focused on SMPS, and the OP's question was about a buck converter so I believe the statement to be correct for power converters. However, I have no proof of the assertion. One could plot a Nyquist plot and see if the system encircles -1 counterclockwise the same number of times as the number of poles. I think that would be definitive. – John D Oct 01 '21 at 15:20
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    Here's a reference that seems to reinforce the last crossing assertion, see Fig. 4 and text: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1183681 – John D Oct 01 '21 at 15:40
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    @JohnD The abstract looks promising. I will read it later as I don't have full access at the moment. I think that both links (particularly the first one for which a sign-in is not required) can be added to the body of the answer as references. – AJN Oct 01 '21 at 17:01
  • @JohnD According to the paper you referenced, the author used the system's root locus to determine which crossover to use which tells me that it depends on the details of the system. – imnotarobot Oct 01 '21 at 17:32
  • @imnotarobot This seems like a question that needs more research. I agree that it could apply only to certain systems, but my experience says that switchmode power supplies fall in that category. However, untill we have definitive proof I can't say with 100% certainty. – John D Oct 01 '21 at 18:34