EE 7329, Fall 2011
Handout on Feedback Analysis
- 1 -
Return Ratio Analysis of Feedback Circuits
The precision circuit technique of implementing linear analog signal-processing
functions with nonlinear devices has thus far been based upon the stabilized feedback
amplifier invented by Harold Black in 1927 . The most significant benefit derived
from negative feedback is the desensitization of the closed-loop gain against active
device parameter variations. This desensitization also leads to low distortion and noise
rejection, which are highly desirable features of precision amplifiers. In addition, the
employment of negative feedback allows a designer to modify the input and output
impedances and to widen the bandwidth of a circuit, which proves to be useful techniques
in making design tradeoffs in practice.
The downside of negative feedback, however, is the potential of instability, which
entails a long history of efforts of analyzing the loop transmission and studying the
stability of feedback circuits –. The majority of these analyses can be categorized
into two approaches—the two-port analysis based on loop gain , ,  and the
return-ratio analysis , , , , , , although the names loop gain and return
ratio have been used interchangeably in the literature.
It was noted in  that it appears that return ratio was first introduced by Bode .
In contrast to the complex procedures involved in the loop-gain-based two-port analysis,
the return-ratio method embodies a somewhat simpler approach in feedback circuit
analysis –. Especially, in a bilateral feedback configuration,
it requires little or
no manipulation of the original circuit topology in analyzing the loop transmission.
However, as the original treatments of both return ratio and loop gain were developed for
unilateral single-loop feedback, care must be taken in applying the developed formulas
and procedures to bilateral and/or multi-loop feedback circuits. Specifically, the return
ratio calculated in a bilateral configuration depends on the exact loop breakpoint, as will
A configuration when the forward gain block, the feedback block, or both are bilateral.