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# [SOLVED]Confusion about the phase margin of this system

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#### merenguelee

##### Newbie level 4
Hello everyone

When I did analog design recently, I got a frequency response of a system like this(I have slightly simplified the plot):

The phase margin and gain margin printed by the Virtuoso are 80 degrees and 10 dB.

What I'm confused is:
- based on the theory I have learnt, the phase has shifted 80 degrees at UGB frequency compared with low frequency, so the phase margin should be 100 degrees rather than 80 degrees, right?
- also, the point we get the gain margin should be the frequency when the phase crosses -180 degrees or 180 degrees, but it seems that Virtuoso considered the frequency at which the phase crosses 0 degree as that frequency and then got a 10-degree gain margin.

Now, I doubt myself a little bit, so I post these to confirm with you guys.

Phase shift shown was normalized to the inversion of 180 so started at 0. It then rose to 90 ( by partial differentiation) then falls to 80 deg at 0dB.

The initial conditions of the plot are just different to show margin rather than absolute phase in both cases.

Phase shift shown was normalized to the inversion of 180 so started at 0. It then rose to 90 ( by partial differentiation) then falls to 80 deg at 0dB.

The initial conditions of the plot are just different to show margin rather than absolute phase in both cases.
Hi Tony

I got this plot from Virtuoso, and the phase at low frequency is not exactly 0 degree because I simplified it to make the plot clear.

Apart from that, I suppose no matter what this waveform stands for(actually I plotted it by stb. sim and got the phase), we should focus on the phase change compared with low frequency. Also, if the plot shows the phase margin, the low frequency should be absolutely unstable because of the very high gain.

Phase shift shown was normalized to the inversion of 180 so started at 0. It then rose to 90 ( by partial differentiation) then falls to 80 deg at 0dB.
Unlikely that a system with shown gain characteristic has a rising phase. I guess something is sketched wrongly.

Hi, Tony, thanks for your reply so far and I finally figured out the reason why I got this plot. It may be caused by the simulator (Spectre) or the PDK I used rather than the circuit design.

The simulation I did these days is measuring the common-mode feedback performance of an Op-amp in a modulator. Normally, its frequency response should be something similar to that of an OTA, i.e. the dominant pole is an LHP rather than an RHP I showed you before.

This has troubled me a lot recently and when I made a small change to the Op-amp I measured, which technically shouldn't have any significant impact on the frequency response, something magical happened: the phase starts from 180 degrees and coincides with the previous curve at high frequency (the purple curve shown below). That matches our theory.

As for the change I made, I just changed the connection of the bulk of the input differential pair. Before, I connected it to the source, and when I changed it to the power rail, the simulation plot was normal.

Unlikely that a system with shown gain characteristic has a rising phase. I guess something is sketched wrongly.
Thank you FvM, I just replied to Tony about the phenomenon I have seen and the root cause I suppose.

Aha, Bias bliss.

Aha, Bias bliss.
Oh, you have met this kind of phenomenon? so that's a common issue?

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