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feedback - EE 7329 Fall 2011 Handout on Feedback Analysis...

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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 signal-processing 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 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 [1]–[27]. The majority of these analyses can be categorized into two approaches—the two-port analysis based on loop gain [22], [24], [25] and the return-ratio 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 loop-gain-based two-port analysis, the return-ratio 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 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 1 A configuration when the forward gain block, the feedback block, or both are bilateral.
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EE 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 return-ratio-based 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 closed-loop 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 feedback-loop stability (as well as to give rise to a closed-loop transfer function), some observations from a stability standpoint will also be given in this note.
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