0

I'm studying Chapter 8.6 of Razavi's Analog IC Design textbook (Bode's Analysis of Feedback Circuits).

Bode's method provides a way of simplifying feedback analysis by replacing one dependent source (for example a MOSFET) with an independent source and computing the simpler transfer functions for when the source is disabled or the input is shorted.

enter image description here

How can this method can be extended for multiple non-trivial feedback loops?

Can it be applied recursively, eliminating sources one-by-one? (I don't think so --- once you've eliminated one source, the circuit is already broken...)

Razavi seems to think this method is applicable to any number of feedback loops, but the only multi-loop examples he gives are ones where one of the loops is trivial (like a source-degenerated CS) and can be solved by inspection.

Null
  • 7,448
  • 17
  • 36
  • 48
Adam Q
  • 557
  • 2
  • 9
  • I assume you have the 2nd edition of the book. In the first edition from 2001 there is no chapter 8.6. I am talking about "Design of Analog CMOS Integrated Circuits". In case of textbooks it is worth stating the exact title and edition, because many could have it on their shelves, making it easier for them to quickly look into the context. – Horror Vacui Sep 03 '22 at 08:47

2 Answers2

1

Yes, Bode showed how it can be applied to multiple loops.

He brokes all active elements and makes one after another active. The product of the return differences is the total return difference.

If, like in your case, you broke any active element and the whole circuit is broken, this is an easy special case.

The question is, how to interpret the total and the partial solutions to analyse and design a circuit. Unfortunately there are not many practical examples.

Read Bode's original text and have a look at http://www.fox.ece.ufl.edu/Multiple-Loop_Feedback.html

JosefC
  • 256
  • 1
  • 5
1

For my opinion, the main question is: For which purpose do you intend to apply Bode`s method for anylyses for multiple feedback circuits? I am not sure, if the following will answer your question - nevertheless:

In most cases, one is interested in stability properties of the whole system (consisting of multiple feedback loops). To me more specific: Which of the several loops is the most critical one (smallest stability margin)?

To find an answer to this question, you must open only one of the loops - one after the other. So, a system of n loops will have n different loop gains with n different stability margins. And - of course - for each of these n loops the classical method for finding this margin can be applied.

LvW
  • 24,857
  • 2
  • 23
  • 52