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# Frequency Response of Bandgap Loop

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#### pseudockb

##### Member level 5
Hi, I am designing a bandgap reference as shown below and I am measuring the loop gain of the circuit of (Vob-Voa)/(Via-Vib). By changing the size of the cascode transistor that is circled, I could get two different frequency response of the loop gain. The graph on the left is obtained when the cascode transistor is small. Is the graph obtained on the right showing a stable loop? I am not able to explain the change in phase plot in different cases. All the transistors are in saturation in both cases. Please explain to me. Thanks.

How does your AC analysis circuit look like ? Where did you cut the loop ?

For me the most convinient is to cut at the output of the OTA (so between M14 and M7), inject a signal there and see what's coming back from the ota.

I think you will have a hard time getting this design stable : you apply self biasing (which is one loop), you have a feedback loop trying to equalize the bandgap nodes (which is in fact a combination of feedback and feedforward) , and there's a feedback loop (probably not very high gain) setting the cascodes.

Anyway, a good check for stability is step response in transient.

My AC analysis circuit is as shown below and I am breaking the two cascode loops at points A and B respectively. How would you bias the cascode transistors M2,M3,M12 and M13 if not applying self biasing? I am also puzzled as to why did you choose to break the loop at the output of the OTA? How about the stablility analysis of other loops as well?

I have tried transient analysis by applying a ramp input to the Vdd and the circuit seems to be functioning well and stable even though I got a strange frequency response curve. Is the frequency response curve on the right stable as it has a positive phase margin but the starting phase seems wrong. Thanks for the help.

Well, the easiest to check AC stability is to cut the circuit at a point where you have all the feedback loops included, and this is at the output of the OTA.

Concerning the biasing, I would use a simple current mirror biased with a resistor to bias the cascodes and/or current sources.

I remember I had a hard time getting a similar circuit stable in the past, but I don't say it can't work.

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