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Signal Chain Basics

# The basics of op amp loop-stability analysis: A tale of twin loop-gains

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ritesh1347
9/15/2018 5:47:04 PM
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Newbie
Re: Feedback Analysis Problems
Hi Feucht,

I really like your point 3. That's really new way to think of it. Similarly we can say that increasing R is providing enough damping.(which is making it stable).

But I agree with Collin on point 2. Mostly while working with opamps, in case of unstability, we feel that our root cause of unstability is Beta path and we don't even think about Aol.

Sometimes, we put our opamp in undesired conditions (as in circuit 2) and we still  consider that Aol is going to be same as given in datasheet. But, may be in that condition, our Aol is changing its behaviour as shown in figure and then , your loop gain is going to  get change because of 'Aol' which you may not find or guess if you are only checking loop gain. In that case, it's good practice to check Aol, beta and Aol*beta as well. This will also give you an idea about your loading condition.

And also truly speaking, you can analyse the circuit in so many ways. If I consider output impedance as a part of Beta path , then in that case Aol is going to be same as in normal load conditon and then in that case its your Beta path (which is now going to include your load , feedback path and output impedance)  which has an issue.

But, I really feel that it's a good practice to break your loop gain to get better understanding of real issue.(even you can break it into so many smaller blocks).

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D Feucht
9/8/2018 12:50:09 AM
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Re: Feedback Analysis Problems
Collin (with both "l"s this time!),

re: your #3: That's true too, but beginners might become confused into thinking that it is the same effect as the closed-loop resonance caused by impedance gyration of the open-loop output resistance into an inductance in the frequency region between loop-bandwidth and its unity-gain bandwidth. (Maybe I am anticipating your next article with this?)

And by the way, for closed loops with two-pole rolloff (or -40 db/dec unity-gain crossover), I am still interested in doing a joint article with you on this, but I must confess that I haven't worked out the considerably harder impedance-gyrated equivalent circuits at the ouput yet. Maybe you will! It would be a significant feat.

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CollinWells
9/6/2018 10:10:17 PM
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Re: Feedback Analysis Problems
Hi Dennis!  Thanks for reading and posting.

#1:  Glad you agree with the analysis.  I used "problem" in my responses to 2/3 :)

#2:  No controversy here. We can definitively conclude that both loop-gain responses (GH) in Figure 3 are unstable based on both the slope at the cross-over frequency (40dB/decade) as well as the phase-margin (8 degrees).  The main point of the article and analysis method is that by loop-gain alone you can't determine where to apply compensation unless you have inside knowledge about capacitive loading, input impedance interactions, and why they're causing stability problems in the circuit.  Experts such as you will be able to quickly identify the root cause of the problem but beginners don't always know where to apply compensation once they've discovered they have a loop-gain problem.  Analyzing if problem is from Aol (G) or 1/Beta (H) helps target the compensation methods to apply to fix the problem.

#3:  Agreed.  Another way I commonly describe this is that the open-loop output resistance of the op amp and capacitive load form an RC network which results in an additional pole in the loop-gain response, degrading the circuit phase margin.

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D Feucht
9/6/2018 8:28:00 PM
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Blogger
Feedback Analysis Problems
Colin,

1. There is nothing controversial about feeedback analysis as applied here. Thus, there are no issues. They are problems instead. The word issues is being widely misapplied nowadays; let's try to correct that.

2. I find it easier to do feedback analysis using the loop gain, GH, (or A*beta in the old nomenclature). Then the slope of GH as it crosses a gain of one tells much about stability. Separate G and H are not needed to determine stability.

3. The output-node impedance transformation that occurs above the open-loop bandwidth of GH can introduce additional poles or zeros that affect stability. This  is why capacitive loading of amplifiers can cause them to oscillate. The amplifier  output resistance increases with frequency from the closed-loop value as loop gain decreases with frequency, causing the amplifier output to appear inductive. This inductance resonates with the external load capacitance.

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