Open loop stability: Bode - Pole zero plot mismatch

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Wyatt - 2020-12-21T10:43:28+00:00
Question: Open loop stability: Bode - Pole zero plot mismatch

I'm analyzing open loop stability of an amplifier. Plotting the bode diagram I can see a negative phase margin (PM) indicating the system is not stable. When I plot the pole/zero plot however all the poles still remain on the left half plane. See attached figure. Note that instability results due to the 3rd zero crossing where the PM is negative. I do not understand why the complex poles have not shifted to right half plane (RHP). Using SPICE however I can observe these poles locating to RHP. How come this cannot be observed in matlab? While this is very likely because the model in Matlab is just a simplification, I do not understand how the bode plot can show a negative PM while the poles reside within LHP. Any thoughts?

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    • Expert Answer

    Profile picture of Prashant Kumar Prashant Kumar answered . 2025-11-20

    You did not post your system, so it is a bit hard to figure out what is going on, especially when you say that you see poles moving to RHP in Spice.
    Going purely on the plots you provided (poe zero map primarily) I tried to construct a model that would create similar plots.
     
    sys=zpk([2.4*10^9*j -2.4*10^9*j], [-0.0000001 -11.5*10^7+1.2*10^9*j  -11.5*10^7-1.2*10^9*j],-100000000);
subplot(121);bode(sys);grid;
subplot(122);pzmap(sys);
xlim([-1.5e+8 2e+7]);

    The first subplot shows full bode plot. If you focus on the region you are looking at, you will see similar plot to what you show:

     

    subplot(121); bode(sys, {1e+9*0.1034 1e+9*2.8278}); grid;
    Now if you zoom in bode plot magnitude that looks similar to your plot.
    If you do
     
    allmargin(sys)
    you will see phase margins at first two crossovers are negative and phase margin at 3rd crossover is positive.
    If you do
     
    isstable(sys)
    you will see the system is stable because all poles are in the left half plane, even though one of them is essentially at the origin.
    Bottom line: even though you see negative phase margins, this system is stable, as all poles lie in the LHP. Hope this helps.


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