02-Scattering - EE 541, Fall 2009: Course Notes #2...

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EE 541, Fall 2009: Course Notes #2 Scattering Parameters: Concept, Theory, and Applications Dr. John Choma Professor of Electrical Engineering University of Southern California Ming Hsieh Department of Electrical Engineering University Park: Mail Code: 0271 Los Angeles, California 90089–0271 213–740–4692 [USC Office] 213–740–8677 [USC Fax] johnc@usc.edu ABSTRACT: This report introduces the scattering parameter concept from two perspectives. First, the scattering parameters are shown to be an effective vehicle for charac- terizing the high frequency I/O characteristics of two port networks. Such meas- urement effectiveness derives from the fact that scattering parameter measure- ments obviate problems invariably incurred at very high frequencies by the actions of either short-circuiting or open circuiting network ports. The second perspective is the utility of scattering analyses in the design of lossless two port filters, which are fundamental to modern communication systems. Original: November 2002
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Course Notes #2 University of Southern California J. Choma August 2006 68 Scattering Parameters 1.0. INTRODUCTION The short circuit admittance, open circuit impedance, hybrid h–, and hybrid g– parameters are commonly used to formulate two port circuit models that macroscopically inter- relate the driving point input and output impedance and forward and reverse transfer characteristics of relatively complex linear networks. These models are simple architectures in that they embody only four electrical parameters whose measurement or calculation exploit the electrical implications of short or open circuits imposed at the input and output ports of the net- work undergoing study. Although the parameterization of these conventional two port models can generally be executed straightforwardly and accurately at relatively low signal frequencies, high signal processing frequencies present at least two challenges in broadband electronics. The first of these challenges is that the unavoidable parasitic inductance implicit to circuit intercon- nects renders perfect short circuits an impossibility at very high signal frequencies. Moreover, very low impedance paths at either the input or the output port of electronic circuits may force embedded active devices to function nonlinearly or even to fail because of excessive current conduction. Second, the inherent potential instability of most high frequency or broadband elec- tronic networks is exacerbated when these networks are constrained to operate with open cir- cuited input or output ports. For example, attempts to measure the open circuit impedance parameters of a broadband electronic circuit are invariably thwarted by parasitic network oscilla- tions incurred by the action of opening either an input or an output network port.
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02-Scattering - EE 541, Fall 2009: Course Notes #2...

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