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Two pole compensation frequency responses

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northumber82

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Two pole compensation frequency response

Hello, I'm building a low distortion amplifier. Until now, I've used only the Miller compensation (or one-pole). Now I'm trying to use the two-pole compensation. Is this the correct frequency response? Or for stability it must be flat?

Immagine.png
 

Re: Two pole compensation frequency response

You seemingly have plotted the curves for the open-loop system, which is not enlightening at all, moreover, even if you ploted for the closed-loop system, it would be expected to position the cursor on the point of interest, the phase approximately at 45deg, not there where you placed it, 120deg. Anyway, AFAIK, one do not make a pole compensation without adding a zero as well, therefore unless you are aware of what exactly are doing, all this will turn into an endless process of trial and error.
 

Re: Two pole compensation frequency response

This is the plot of the closed-loop gain. I've read on the Cordell's book that more pole added means more phase degree, Miller is equal to 90°, two o three pole means more. But I'm not sure about the frequency peaking.
 

Re: Two pole compensation frequency response

It is not clear exactly what you want to accomplish, such as the cutoff frequency, the circuit used (ie the poles and zeros currently present), the selectivity, minimum allowed gain, etc .... In other words, you seem to be developing something backwards. I presume you have some of these requirements and constraints already defined.
 

Re: Two pole compensation frequency response

Is this amplifier, with this frequency response, stable? Is the peaking normal for the two-pole compensation?
 

Re: Two pole compensation frequency response

Is this amplifier, with this frequency response, stable?
Is the peaking normal for the two-pole compensation?

No, not stable (read post #2).
No, since it is not stable, there is no compensation effectivelly made.
 

Re: Two pole compensation frequency response

@northumber82

Check the Fig. 1.25 and 1.26 from this position: https://payhip.com/b/5Srt (please click the Preview button). Hope that would clarify you how a typical AC response should look like. Of course, opamp's AC responses varies a lot, but I think you have problem with basics and hope that this will help.
 

Re: Two pole compensation frequency response

If you compensate you should know that the stable system is when for your gain equal to 0 dB the phase is still above 0 degrees (assuming that the phase starts from 180 degrees). You may use any compensation. The point is the system is stable. And not only Miller changes by "only" 90 degrees. Every pole changes by 90 degrees.
 

Re: Two pole compensation frequency response

Why do you want two-pole compensation?

Much less THD to high frequencies.

If you compensate you should know that the stable system is when for your gain equal to 0 dB the phase is still above 0 degrees (assuming that the phase starts from 180 degrees). You may use any compensation. The point is the system is stable. And not only Miller changes by "only" 90 degrees. Every pole changes by 90 degrees.

Yes, with the Miller compensation the amplifier is stable, but a lot of THD going towards the high frequencies.

Now, I have this two-pole compensation:

Closed loop:
Immagine.png

Open loop:
Immagine2.png

Can this be declared stable?
 

Re: Two pole compensation frequency response

Now, I have this two-pole compensation:

Can this be declared stable?

You keep insisting on this approach of repeatedly designing without doing this check by yourself. A simple and well-known metric to know whether the system will be stable or not is to verify that in phase -180 if the gain is greater than 0dB. It was at this point where we expected the cursor to be positioned. By the way, adding poles will not stabilize your system, as opposed to adding zeros as well. A good way to do this would be to use the Lead compensator, which by having a zero dominant to the pole, would be pulling the phase up, thus giving a larger working margin for the gain.
 

Re: Two pole compensation frequency response

You keep insisting on this approach of repeatedly designing without doing this check by yourself. A simple and well-known metric to know whether the system will be stable or not is to verify that in phase -180 if the gain is greater than 0dB. It was at this point where we expected the cursor to be positioned. By the way, adding poles will not stabilize your system, as opposed to adding zeros as well. A good way to do this would be to use the Lead compensator, which by having a zero dominant to the pole, would be pulling the phase up, thus giving a larger working margin for the gain.

Sorry for misunderstanding, let me understand well:

In the closed loop (follow the red line), 180° of phase is upper to the 0dB, located at 12dB. Is this that I have to verify? Or I was even wrong to understand?
Immagine.png
 

Re: Two pole compensation frequency response

That is the classic criterion for the margin gain, which we would agree would give a strongly ringing response (not exactly oscillating), and so the phase module should actually be well below -180 for a 0dB gain. If this phase is only slightly below that, technically it can be considered stable, because the output will converge to the value of the input. Anyway, why not make experiments by yourself, applying a step input to see what happens?
 

Re: Two pole compensation frequency response

The stability criterion has to be checked for the loop gain, not the closed loop gain. Getting a flat closed loop gain without any peaking suggests that the loop gain phase margin is more than sufficient. In this case you can usually skip further stability checks.

To get the actual loop gain, you need to multiply the open loop gain with the feedback factor, I guess (-)0.05.

- - - Updated - - -

Estimating the phase margin from your open loop plot gives >60°.

phase margin.png
 

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