On the computation of Infeld’s function used in evaluating the admittance of prolate spheroidal dipole antennas
Authors:
T. Do-Nhat and R. H. MacPhie
Journal:
Quart. Appl. Math. 54 (1996), 721-725
MSC:
Primary 78A50; Secondary 33C90
DOI:
https://doi.org/10.1090/qam/1417235
MathSciNet review:
MR1417235
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Abstract: The Infeld function expressed in terms of the outgoing prolate spheroidal radial wave function and its derivative, and employed in the expression of the input self-admittance of prolate spheroidal antennas, has accurately been calculated by using a newly developed asymptotic expression for large degree $n$. This asymptotic power series has been derived by using a perturbation method with a perturbation parameter $\epsilon = 1/\left ( {\lambda _{1n}} - {h^2} \right )$, where ${\lambda _{1n}}$ is the spheroid’s eigenvalue for the given parameter $h$ of the spheroidal wave function.
L. Infeld, The influence of the width of the gap upon the theory of antennas, Quart. Appl. Math. 5, 113–132 (1947)
J. D. Kotulski, Transient radiation from antennas: Early time response of the spherical antenna and the late time response of the prolate spheroidal impedance antenna, Univ. of Illinois at Chicago, Illinois, Ph. D. Dissertation, 1983
T. Do-Nhat and R. H. MacPhie, The input admittance of thin prolate spheroidal dipole antennas with finite gap widths, IEEE Trans. AP-43, 1995, pp. 1243–1252
C. Flammer, Spheroidal Wave Functions, Stanford University Press, Stanford, Calif., 1957
B. P. Sinha and R. H. MacPhie, On the computation of the prolate spheroidal radial functions of the second kind, J. Math. Phys. 16, 2378–2381 (1975)
T. Do-Nhat and R. H. MacPhie, On the accurate computation of the prolate spheroidal radial functions of the second kind, Quart. Appl. Math. 54, 677–685 (1996)
J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1980
L. Infeld, The influence of the width of the gap upon the theory of antennas, Quart. Appl. Math. 5, 113–132 (1947)
J. D. Kotulski, Transient radiation from antennas: Early time response of the spherical antenna and the late time response of the prolate spheroidal impedance antenna, Univ. of Illinois at Chicago, Illinois, Ph. D. Dissertation, 1983
T. Do-Nhat and R. H. MacPhie, The input admittance of thin prolate spheroidal dipole antennas with finite gap widths, IEEE Trans. AP-43, 1995, pp. 1243–1252
C. Flammer, Spheroidal Wave Functions, Stanford University Press, Stanford, Calif., 1957
B. P. Sinha and R. H. MacPhie, On the computation of the prolate spheroidal radial functions of the second kind, J. Math. Phys. 16, 2378–2381 (1975)
T. Do-Nhat and R. H. MacPhie, On the accurate computation of the prolate spheroidal radial functions of the second kind, Quart. Appl. Math. 54, 677–685 (1996)
J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics, Springer-Verlag, New York, 1980
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Article copyright:
© Copyright 1996
American Mathematical Society