Files in this item
Files  Description  Format 

application/pdf Serwy_Roger.pdf (792kB)  (no description provided) 
Description
Title:  The limits of Brune's impedance 
Author(s):  Serwy, Roger 
Advisor(s):  Allen, Jont B. 
Department / Program:  Electrical & Computer Eng 
Discipline:  Electrical & Computer Engr 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  M.S. 
Genre:  Thesis 
Subject(s):  Impedance
Positive Real Brune Impedance Reflectance Timedomain impedance Discretetime impedance cinfinite cfinite 
Abstract:  The impedance concept as popularized by Oliver Heaviside in the 1880s may be used to model physical systems that may or may not include wave propagation. Otto Brune in 1931 coined the term and then provided a proof that ``positive real" is a necessary and sufficient condition for network synthesis using lumped elements. Brune's impedance, described using a ratio of polynomials, represents a fundamentally limited subset of impedance functions. Quite notably, all lumpedelement networks do not support wave propagation. Two classes of impedances emerge in this analysis, the cfinite and cinfinite. These two classes separate the physical assumption of wave propagation used in modeling an impedance structure. The cinfinite class deals with impedances where the speed of wave propagation is infinite and, as a consequence, describes simultaneous systems. The cfinite class describes systems with a finite wave speed, and thus describes nonsimultaneous systems. These two classes have unique mathematical properties in both the time and frequency domains. Unfortunately, the traditional approach to impedance as an exclusive frequencydomain concept hides the distinction between the cfinite and cinfinite impedance classes. This thesis will explore these two classes, as well as how both classes can approximate each other. The cfinite impedance class offers an alternative way of formulating Ohm's law in the time domain by means of a reflectance, a special Möbius transformation of the impedance formula. Reflectance offers an alternative means of expressing Ohm's law by means of wave propagation. This Möbius transformation also allows for a reformulation of positive real (PR), which is used to develop a test for the PR property of a rational function. 
Issue Date:  20120918 
URI:  http://hdl.handle.net/2142/34330 
Rights Information:  Copyright 2012 Roger David Serwy 
Date Available in IDEALS:  20120918 
Date Deposited:  201208 
This item appears in the following Collection(s)

Dissertations and Theses  Electrical and Computer Engineering
Dissertations and Theses in Electrical and Computer Engineering 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois