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The limits of Brune’s impedance

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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 Urbana-Champaign
Degree: M.S.
Genre: Thesis
Subject(s): Impedance Positive Real Brune Impedance Reflectance Time-domain impedance Discrete-time impedance c-infinite c-finite
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 lumped-element networks do not support wave propagation. Two classes of impedances emerge in this analysis, the c-finite and c-infinite. These two classes separate the physical assumption of wave propagation used in modeling an impedance structure. The c-infinite class deals with impedances where the speed of wave propagation is infinite and, as a consequence, describes simultaneous systems. The c-finite class describes systems with a finite wave speed, and thus describes non-simultaneous systems. These two classes have unique mathematical properties in both the time and frequency domains. Unfortunately, the traditional approach to impedance as an exclusive frequency-domain concept hides the distinction between the c-finite and c-infinite impedance classes. This thesis will explore these two classes, as well as how both classes can approximate each other. The c-finite 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: 2012-09-18
URI: http://hdl.handle.net/2142/34330
Rights Information: Copyright 2012 Roger David Serwy
Date Available in IDEALS: 2012-09-18
Date Deposited: 2012-08
 

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