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Design >> Analog Design >> Loop gain analysis for feedforward compensated opamp
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Message started by ULPAnalog on Dec 19^th, 2015, 5:20pm

Title: Loop gain analysis for feedforward compensated opamp
Post by ULPAnalog on Dec 19^th, 2015, 5:20pm

Dear experts

I have the following question about feedforward compensated opamp. Referring to the attached figure, the usual implementation has Vb connected to the inverting input of Gm3. In such case, the output is only a function of Va-Vb and the loop gain is computed by injecting a current (shown in blue) and measuring the return ratio for unity feedback (shown in dashed line). Now, I consider the possibility of having the inverting terminal of Gm3 at incremental ground. Output voltage is now function of both Va-Vb and Va+Vb. My question is, does the process of computing return ratio by injecting the current still hold good and if yes, what does it convey, given the presence of both common mode and differential mode gains. If stability analysis were to be performed in spectre, does having iprobe in the feedback path ensure the correct evaluation of loop gain?

Thanks and regards

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by raja.cedt on Dec 20^th, 2015, 5:31am

hi--didn't the following from your post.

Now, I consider the possibility of having the inverting terminal of Gm3 at incremental ground. Output voltage is now function of both Va-Vb and Va+Vb.

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by ULPAnalog on Dec 20^th, 2015, 11:54am

Hi Raja

Thank you for the response. The actual textbook implementation of feedforward compensated opamp has the structure shown the attached figure (in red). Input signal is differentially applied to Gm3 (Va-Vb). The modified version of it, that is of interest to me is, when inverting terminal of Gm3 is incrementally grounded (AC ground) instead of being driven by Vb (which is shown in Fig in the initial post). The textbook structure has output voltage as function of input differential voltage only (Va-Vb), while the modified version has contributions to the output from both differential and common mode input (Va-Vb and Va+Vb respectively). My question is then, how to evaluate the loop gain for the modified opamp? Does the method of injecting the test current source (shown in blue) by breaking the loop at the point shown in blue wiggle work and if it does, what is the interpretation for that quantity and finally if stability analysis were to be performed in spectre, does having iprobe in the feedback path ensure the correct evaluation of loop gain?

Thanks and regards

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by DanielLam on Dec 22^nd, 2015, 9:18am

I think there is only an open loop gain here because it is feedforward. Probably can do an AC test. Furthermore, there should no stability problems because the circuit is feedforward. No negative feedback, no stability problems.

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by nrk1 on Dec 28^th, 2015, 10:42pm

Gm3 appears in the loop gain expression only if there is some feedback to the positive terminal of the opamp as well. Otherwise(e.g. if used as a voltage follower), it is just a feedforward path.

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by ULPAnalog on Jan 10^th, 2016, 12:23pm

Hello nrk1

Thank you for the response.
Gm3 appears in the loop gain expression only if there is some feedback to the positive terminal of the opamp as well. Otherwise(e.g. if used as a voltage follower), it is just a feedforward path.

I believe this statement is made in reference to the schematic in the first post. My understanding is that gm3 appears in loop gain for schematic shown in post 3 (Gm stages hooked up in red). Isn't that correct?

I probably did not make myself clear, but the question that I have in mind is the following. Consider an opamp with has differential gain and a significant common mode gain. One is interested in assessing its stability under unity gain feedback. One way in which I have seen it being measured is to excite the amplifier differentially and check the frequency response to get an idea of stability margins. The other way (which I usually do) is to insert iprobe in the feedback path and check for the stability margins. My understanding is that both the methods give different results as the former method fails to account for the common mode gain, but I am not quite sure if my understanding is indeed correct. Any thoughts on it would be appreciated.

Thanks and regards

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by DanielLam on Jan 11^th, 2016, 7:57pm

So you want to check stability of the opamp in unity gain under differential and common mode inputs. The easiest way is to just run two tests.

1) Do an AC test with differential input
2) Do an AC test with a common mode input

I believe Ken Kundert wrote a guide for an all-in-one testbench
http://www.designers-guide.org/analysis/diff.pdf

Unfortunately, I have not tried the guide yet.

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by ULPAnalog on Jan 11^th, 2016, 9:48pm

Hello Daniel

Thank you for the reply. That was not exactly what I was looking for. Let us say we have a single ended opamp with both differential and common mode gains. Exciting the opamp with differential and common mode signals in open loop gives respective frequency response plots. What I have seen some people do is that they derive stability margins from the differential response. My understanding if that it should be done by connecting the opamp in unity gain configuration and perform stb analysis. In this gain, loop gain happens to be a weighted sum on both differential and common mode gains and it is from this plot, I believe stability margins should be derived. I wanted to confirm if my understanding is correct.

For a fully differential amplifier, I usually use differential stability probe from analogLib to arrive at stability margins.

Thanks and regards

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by DanielLam on Jan 12^th, 2016, 9:45am

Yes, that method will work. It tells you if the circuit is stable or not (make sure the loading is correct). But you will not know what is causing the instability. So I personally also run separate differential and common input tests.

Most of the time the instability arises from a differential input because it has gain > 1, and the common mode gain is < 1. But if you have a common mode gain > 1, I am pretty sure it could go unstable.

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by ULPAnalog on Jan 12^th, 2016, 7:00pm

Yes. I agree. I was wondering if it is possible to have a case where both common mode and differential mode frequency responses show adequate stability margins and yet the unity gain feedback configuration is unstable (Since loop gain in unity gain feedback is going to be a weighted sum of differential and common mode gains).

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by ULPAnalog on Jan 17^th, 2016, 4:02pm

Sorry. I realized that as long as the the poles of both common mode and differential mode gains are in LHP, any linear combination of those would also have poles in LHP and hence stable.
(Could not find time to post at an earlier date)

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by deltasigmaADC on Feb 1^st, 2016, 12:18am

Loop is analyzed for unity feedback configuration when you have done frequency compensation by miller compensation. Because for a miller compensated feedback loop UGB(unity gain bandwidth) is the worst freq which could make the loop unstable. For a feed-forward configuration any freq can be bad, because your system has multiple poles inside UGB which is compensated by zeros. This is why feed-forward is used in application specific opamps and not on general purpose opamps. So analyze stability for the loop that you are going to use the opamp in.

Injecting current into a node and measuring voltage for the transfer function will only for a passive network, or when you are finding the output impedance, in which case you short/open the input. When you have control sources in a network you need to use the adjoint network. You can get it using Tellegen't theorem. For a passive network the adjoint network is the same. That is why it will work in that case.

Also opening the loop for finding won't give u an accurate loopgain. Use diffstb probe and analyze the stability of common mode and differential loop gain separately. Like you have told, if both are stable loops, their linear combination has to be a stable network.

Title: Re: Loop gain analysis for feedforward compensated opamp
Post by ULPAnalog on Feb 6^th, 2016, 5:47pm

Hello deltasigmaADC

You made some very interesting comments. Isnt it always the case that the loop gain needs to be simulated with the configuration in which opamp is supposed to be used for? For instance when an opamp is used as transimpedance amplifier for a photodiode readout, with a large reverse bias junction capacitor of photodiode at inverting input of opamp, degrading its stability. Why would you say it is specific only for a feed forward compensated OTA?

I did not mean opening the loop in the sense of what some books refer to (large inductors and capacitors and what not). I meant insertion of iprobe. By the way, when one has access to the control voltage/current source, isnt correct loop gain obtained by opening/shorting the controlled source and injecting voltage/current signals and going around the loop to find the return ratio? (Gray Meyer does similar thing, AFAIR). Here in the example, I have assumed availability of such access point.