Date of Award

Spring 2008

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Electrical & Computer Engineering

Program/Concentration

Electrical Engineering

Committee Director

Ravindra P. Joshi

Committee Member

Juergen Kolb

Committee Member

Linda L. Vahala

Call Number for Print

Special Collections LD4331.E55 R64 2008

Abstract

This thesis investigates wave propagation along a nonlinear transmission line having a voltage-dependent capacitance. The telegrapher's equations that model wave propagation along such a transmission line are derived and shown to represent a nonlinear hyperbolic system of balance laws. The Lax-Friedrichs, Lax-Wendroff, and hybrid numerical schemes for obtaining approximate solutions to nonlinear hyperbolic systems of balance laws are presented, analyzed, and applied to the nonlinear telegrapher's equations. The Lax-Wendroff and hybrid schemes are invoked to numerically simulate wave propagation along a nonlinear transmission line. Simulations obtained via the hybrid scheme are used to briefly study the potential application of a nonlinear transmission line as a pulse generator.

Since they may generate ultra short (nanosecond) rise time voltage waveforms, nonlinear transmission lines could have applicability to pulsed power systems and high power microwaves. Moreover, short duration, high intensity voltage pulses have been demonstrated to penetrate biological cells and affect the internal organelles. Thus, such voltage shaping could provide the technological tools for intracellular manipulation and several potential biomedical engineering applications.

Though only one particular voltage-dependent capacitance was selected for the nonlinear transmission line analysis, the method described is general. Other voltage dependencies could be realized through suitable mate1ial tailoring, by using composites, and by sectioning the transmission line layout. These alterations would afford relative assessments of voltage wave propagation in nonlinear transmission lines, and also provide for analyses of "shock wave" generation.

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DOI

10.25777/wwgz-8z78

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