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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.

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  • \$\begingroup\$ 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? \$\endgroup\$ Sep 30, 2021 at 19:12
  • \$\begingroup\$ 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. \$\endgroup\$ Oct 1, 2021 at 14:34
  • \$\begingroup\$ 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. \$\endgroup\$ Oct 2, 2021 at 9:47

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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.

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

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    \$\begingroup\$ 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? \$\endgroup\$ Sep 30, 2021 at 19:14
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    \$\begingroup\$ No I don't trust it, that's why I'm asking. \$\endgroup\$ Sep 30, 2021 at 19:44
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    \$\begingroup\$ @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. \$\endgroup\$
    – John D
    Oct 1, 2021 at 15:20
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    \$\begingroup\$ Here's a reference that seems to reinforce the last crossing assertion, see Fig. 4 and text: ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1183681 \$\endgroup\$
    – John D
    Oct 1, 2021 at 15:40
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    \$\begingroup\$ @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. \$\endgroup\$
    – AJN
    Oct 1, 2021 at 17:01

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