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I've a 3 stage closed loop amplifier with many loops inside of which some loops cannot be broken, to analyze the loop gain, as the parasitic capacitors are intrinsic to the device. What is the method to analyze the stability of this amplifier and ensure a good phase margin?

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    \$\begingroup\$ This is a very nontrivial problem, and as you probably already know, standard linear stability analysis using Rollet's stability criterion is not sufficient with multi stage amplifiers. There are a number of methods that have been developed for multi stage amplifiers, with a number of a papers available on IEEE Xplore. Here's one for example: ieeexplore.ieee.org/document/7540305 \$\endgroup\$ Apr 8, 2021 at 3:02
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    \$\begingroup\$ The general idea is that you need to measure the impedances at intermediate nodes, in addition to the port impedances, at all relevant frequencies. \$\endgroup\$ Apr 8, 2021 at 3:05

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In many cases, the inner loops have smaller time constants (reaction time) and the stability properties of the whole circuit (closed-loop) are determind primarily by the outer (overall) loop which is the slowest one.

When you cannot open the inner loops you have to live with this situation....unless the circuit is unstable when the outer main loop is open. In this case, you must use the complete Nyquist criterion for the special case "unstable loop gain" for finding some methods to stabilize the closed loop.

With other words: Treat the closed-loop circuit as it would have no inner loops.

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