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EE 7329, Fall 2011
Handout on Feedback Analysis
 1 
Return Ratio Analysis of Feedback Circuits
Yun Chiu
I.
I
NTRODUCTION
The precision circuit technique of implementing linear analog signalprocessing
functions with nonlinear devices has thus far been based upon the stabilized feedback
amplifier invented by Harold Black in 1927 [1]. The most significant benefit derived
from negative feedback is the desensitization of the closedloop 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 [1]–[27]. The majority of these analyses can be categorized
into two approaches—the twoport analysis based on loop gain [22], [24], [25] and the
returnratio analysis [6], [7], [9], [17], [21], [23], although the names loop gain and return
ratio have been used interchangeably in the literature.
It was noted in [11] that it appears that return ratio was first introduced by Bode [17].
In contrast to the complex procedures involved in the loopgainbased twoport analysis,
the returnratio method embodies a somewhat simpler approach in feedback circuit
analysis [10]–[12]. Especially, in a bilateral feedback configuration,
1
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 singleloop feedback, care must be taken in applying the developed formulas
and procedures to bilateral and/or multiloop feedback circuits. Specifically, the return
ratio calculated in a bilateral configuration depends on the exact loop breakpoint, as will
1
A configuration when the forward gain block, the feedback block, or both are bilateral.
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View Full DocumentEE 7329, Fall 2011
Handout on Feedback Analysis
 2 
be shown later in this note. A closer examination of the discrepancies reveals that
multiple feedback loops exist in a bilateral feedback circuit, violating the assumptions of
the returnratiobased analysis. In addition, this observation offers more insight on the
much debated difference between loop gain and return ratio—although the end results of
the closedloop gain are the same, the two approaches may reach at vastly different
intermediate results for the loop transmission [10]–[12]. As perhaps the predominant
motivation for the derivation of return ratio or loop gain is to study the feedbackloop
stability (as well as to give rise to a closedloop transfer function), some observations
from a stability standpoint will also be given in this note.
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 Fall '11
 YUNCHIU

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