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.

**[1]**R. Courant,*Hyperbolic partial differential equations and applications*, in E. F. Backenbach (ed.),*Modern mathematics for the engineer*, McGraw-Hill, 1956, pp. 92-109**[2]**O. Heaviside,*Electrical papers*, Electrician**2**, 125 (1887)**[3]**S. K. Ghosh,*Responses in a non-uniform electrical transmission line*, J. Inst. Eng. (India), Elec. Eng. Div.,**51**, 329-330 (1971)**[4]**C. R. Burrows,*The exponential transmission line*, Bell System Technical Journal**17**, 555-573 (1938)**[5]**F. Bolinder,*Fourier transforms in the theory of inhomogeneous transmission lines*, Proc. IRE,**38**, 1354 (1950) MR**0046911****[6]**R. E. Collin,*The optimum tapered transmission line matching section*, Proc. IRE**44**, 539-548 (1956)**[7]**Staff, Bell Telephone Labs.,*Transmission systems for communications*, Bell Telephone Labs., 1964**[8]**O. K. Mawardi,*Generalized solutions of Webster's horn theory*, J. Acous. Soc. Amer.**21**, 323-330 (1949) MR**0032346****[9]**R. J. Duffin,*Distributed and lumped networks*, J. Math. Mech.**8**, 793-826 (1959) MR**0106032****[10]**R. J. Duffin,*The extremal length of a network*, J. Math. Anal. Appl.**5**, 200-215 (1962) MR**0143468****[11]**R. J. Duffin,*Equipartition of energy in wave motion*, J. Math. Anal. Appl.**32**, 386-391 (1970) MR**0269190**

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DOI:
https://doi.org/10.1090/qam/446098

Article copyright:
© Copyright 1976
American Mathematical Society