Exact closed-form expression of a sommerfeld integral for the impedance plane problem

Il Suek Koh, Jong Gwan Yook

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

A Sommerfeld integral for an impedance half-plane is one of the classical problems in electromagnetic theory. In this paper, the integral is evaluated into two series representations, which are expressed in terms of the exponential integral and the Lommel function, respectively. It is shown that the series expansions absolutely converge for any parameters, such as distance or surface impedance. Then based on the Lommel function expansion, an exact closed-form expression of the integral is formulated. This expression is written in terms of incomplete Weber integrals, which are directly related to incomplete cylindrical functions such as incomplete Lipschitz-Hankel integrals. Additionally, a complete asymptotic series of the integral is obtained based on the exponential integral expansion. With conventional methods such as steepest descent method, it is cumbersome to derive the divergent series. The validity of all the formulations derived in this paper is demonstrated through a comparison with a numerical integration of the integral for various situations.

Original languageEnglish
Pages (from-to)2568-2576
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Volume54
Issue number9
DOIs
Publication statusPublished - 2006 Dec 1

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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