Abstract
The representation of the normalized point impedance of a uniform transmission line by means of a bipolar coordinate system is extended to propagation in nonuniform transmission lines and stratified media (even with a turning point, provided certain asymptotic approximations are also made). The normalized impedance is the solution of a generalized Riccati equation. It is solved approximately by applying the circle diagram to a set of homogeneous lines such that the stepwise varying wavenumber approximates the continuously varying one. The technique is applied to obtain the reflection from and transmission through layers, the eigenvalues and eigenfunctions, and Green's functions. Some further applications will be discussed. [This research is supported by the ONR Acoustics Program.]
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