Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Distortionless wave propagation in inhomogeneous media and transmission lines

Authors: V. Burke, R. J. Duffin and D. Hazony
Journal: Quart. Appl. Math. 34 (1976), 183-194
MSC: Primary 78.35; Secondary 94A05
DOI: https://doi.org/10.1090/qam/446098
MathSciNet review: 446098
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Abstract: Of concern are mechanical or electrical waves in a media which may be nonuniform and dissipative. The problem posed is to find conditions for the undistorted propagation of signals. The electrical transmission line is chosen as the general model. Along the length of the transmission line there are four functions which may be prescribed essentially arbitrarily. These are series resistance, series inductance, shunt conductance, and shunt capacitance. A differential equation is derived relating these functions which gives a necessary and sufficient requisite for distortionless transmission of a voltage wave. Various corollaries of this theorem are developed. For instance, it is shown that simultaneous voltage and current waves can be transmitted without distortion if and only if the characteristic impedance of the transmission line is positive at each point.

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DOI: https://doi.org/10.1090/qam/446098
Article copyright: © Copyright 1976 American Mathematical Society

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