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Identifying A(s) and β(s) in Single-Loop Feedback Circuits Using the Intermediate Transfer Function Approach.

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  • 1Integrated Microsystems Laboratory, Department of Electrical and Computer Engineering, McGill University, Montreal, QC H3A 0G4, Canada.

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Summary

This paper introduces an exact method to uniquely identify feedback parameters A and β in circuits, overcoming limitations of indirect measurement techniques. It also clarifies conditions where the product A × β accurately predicts closed-loop poles.

Keywords:
closed-loop operationintermediate transfer functionsloop transmission functionnegative feedback circuitsreturn ratiosingle-loop feedback topologies

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Area of Science:

  • Electrical Engineering
  • Control Systems Theory

Background:

  • Single-loop feedback circuits are commonly modeled using parameters A and β, fundamental to understanding negative feedback.
  • Existing theories on system behavior (stability, impedance control) rely on A and β, guiding circuit optimization.
  • Current methods for identifying A and β are indirect, computing the return ratio (L) and inferring A and β, which can be inaccurate.

Purpose of the Study:

  • To present an exact method for uniquely identifying individual feedback parameters A and β from circuit components.
  • To determine the specific circuit conditions under which the product A × β correctly predicts closed-loop poles.

Main Methods:

  • Development of a novel, exact analytical method for parameter identification.
  • Analysis of circuit conditions to establish the validity of the A × β product for closed-loop pole prediction.

Main Results:

  • An exact method is presented to uniquely determine parameters A and β individually.
  • Conditions are identified where the product A × β accurately reflects closed-loop pole behavior.
  • The limitations of indirect methods and the assumption of equivalence between zeros of (1 + L) and (1 + A × β) are highlighted.

Conclusions:

  • The proposed exact method provides a direct and accurate means to identify feedback parameters A and β.
  • Understanding the conditions for the validity of A × β is crucial for accurate closed-loop pole analysis.
  • This work advances the fundamental understanding and practical analysis of feedback circuits.