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10 - Return-ratio analysis

from Section I - Foundations

Published online by Cambridge University Press:  02 December 2010

Rahul Sarpeshkar
Affiliation:
Massachusetts Institute of Technology
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Summary

You don't understand anything until you learn it more than one way.

Marvin Minsky

In this chapter, we shall discuss a feedback technique for analyzing linear circuits, invented by Hendrik W. Bode in his landmark book, Network Analysis and Feedback Amplifier Design published in 1945. The technique, known as return-ratio analysis, allows one to compute the return ratio of an active dependent generator or passive impedance in a linear circuit as a function of its dependent gain or of its passive impedance, respectively. The return ratio is a quantity analogous to the loop transmission in a feedback loop: just as we can use the loop transmission in a feedback loop to analyze how the dynamics of the loop changes as we vary its dc gain, we can use the return ratio of an element to analyze how transfer functions in the circuit change as we vary the dependent gain or passive impedance of the element. The return ratio also gives us a measure of the robustness of the circuit to changes in the gain or impedance of the element in the same manner that the loop transmission gives us a measure of the robustness of a feedback loop to changes in its feedforward gain. The return ratio explicitly realizes that circuits are composed of bidirectional elements and loading such that the creation of unidirectional block diagrams with feedforward gain a(s) and feedback gain f(s) to analyze them is not unique and sometimes cumbersome.

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Ultra Low Power Bioelectronics
Fundamentals, Biomedical Applications, and Bio-Inspired Systems
, pp. 240 - 272
Publisher: Cambridge University Press
Print publication year: 2010

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References

Bode, Hendrik W.. Network analysis and feedback amplifier design (New York: Van Nostrand, 1945).Google Scholar
Blackman, R. B.. Effect of feedback on impedance. Bell Systems Technical Journal, 22 (1943).CrossRefGoogle Scholar
Middlebrook, R. D.. Null double injection and the extra element theorem. IEEE Transactions on Education, 32 (1989), 167–180.CrossRefGoogle Scholar
Vorpérian, Vatché. Fast Analytical Techniques for Electrical and Electronic Circuits (Cambridge; New York: Cambridge University Press, 2002).CrossRefGoogle Scholar

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  • Return-ratio analysis
  • Rahul Sarpeshkar, Massachusetts Institute of Technology
  • Book: Ultra Low Power Bioelectronics
  • Online publication: 02 December 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511841446.010
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  • Return-ratio analysis
  • Rahul Sarpeshkar, Massachusetts Institute of Technology
  • Book: Ultra Low Power Bioelectronics
  • Online publication: 02 December 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511841446.010
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Return-ratio analysis
  • Rahul Sarpeshkar, Massachusetts Institute of Technology
  • Book: Ultra Low Power Bioelectronics
  • Online publication: 02 December 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511841446.010
Available formats
×