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

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.