The synthesis of infinite lines

Author:
C. B. Sharpe

Journal:
Quart. Appl. Math. **21** (1963), 105-120

DOI:
https://doi.org/10.1090/qam/153299

MathSciNet review:
153299

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Abstract | References | Additional Information

Abstract: The class of nonuniform lines having solutions which exhibit an out-going wave behavior at infinity and which have a rational input admittance is considered. Necessary and sufficient conditions are given for a rational function to be realizable as the input admittance of an infinite line. A closed-form expression is derived by means of which the characteristic impedance of a line in this class can be constructed from its input admittance. It is shown that this solution to the synthesis problem is unique once the limiting value of at infinity or at the input is specified. An example in the application of the technique is presented.

**[1]**C. B. Sharpe,*An alternative derivation of Orlov's synthesis formula for non-uniform lines*, Inst. Elect. Eng. Monograph No. 483E, 1-4 (1961)**[2]**S. A. Schelkunoff,*Remarks concerning wave propagation in stratified media*, Comm. Pure Appl. Math.**4**, 117-128 (1951) MR**0045035****[3]**I. Kay and H. E. Moses,*Reflectionless transmission through dielectrics and scattering potentials*, New York Univ. Inst. Math. Sci. Res. Rep. No. EM-91 (1956) MR**0090367****[4]**L. D. Faddeyev,*Obratnaya zadacha kvantovoi teorii rasseyaniya*, Uspekhi Matem. Nauk.**14**, 57-119 (1959) [*The inverse problem in the quantum theory of scattering*, Transl. by B. Seckler, New York Univ. Inst. Math. Sci. Res. Rep. No. EM-165 (1960)]**[5]**I. Kay,*The inverse scattering problem*, New York Univ. Inst. Math. Sci. Res. Rep. No. EM-74 (1955) MR**0070004****[6]**I. Kay,*The inverse scattering problem when the reflection coefficient is a rational function*, Comm. Pure Appl. Math.**13**, 371-393 (1960) MR**0114540****[7]**Y. A. Marchenko,*Vosstanovlenie potentsial'noi energii po phazam rasseyannikh voln*, (*Reconstruction of potential energy from the phase of scattered waves*) Doklady Akad. Nauk. SSSR**104**, 695-698 (1955)**[8]**O. N. Litvinenko, Synthesis of inhomogeneous lines on the basis of an input impedance specified in the form of a rational function of frequency (in Russian) Radiotekhnika i Elektronika**16**, 1825-1831 (1961)

Additional Information

DOI:
https://doi.org/10.1090/qam/153299

Article copyright:
© Copyright 1963
American Mathematical Society