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計算索末菲爾德型積分的新方法--球面波級數(shù)展開法

江濱浩,  劉永坦

江濱浩, 劉永坦. 計算索末菲爾德型積分的新方法--球面波級數(shù)展開法[J]. 電子與信息學(xué)報, 2003, 25(2): 235-241.
引用本文: 江濱浩, 劉永坦. 計算索末菲爾德型積分的新方法--球面波級數(shù)展開法[J]. 電子與信息學(xué)報, 2003, 25(2): 235-241.
Jiang Binhao, Liu Yongtan. A new technique for computating sommerfeld type integrals-expantion of spherical wave functions[J]. Journal of Electronics & Information Technology, 2003, 25(2): 235-241.
Citation: Jiang Binhao, Liu Yongtan. A new technique for computating sommerfeld type integrals-expantion of spherical wave functions[J]. Journal of Electronics & Information Technology, 2003, 25(2): 235-241.

計算索末菲爾德型積分的新方法--球面波級數(shù)展開法

A new technique for computating sommerfeld type integrals-expantion of spherical wave functions

  • 摘要: 利用廣義阻抗邊界條件模擬和簡化地球表面對電磁場的影響。應(yīng)用圓柱波函數(shù)的球面波展開表達(dá)式,地平面上方水平電偶極子電磁場中的索末菲爾德型積分可表達(dá)成快速、絕對收斂的球面波展開式,利用積分路徑的變換和超幾何函數(shù)理論,展開式中的展開系數(shù)可表達(dá)成以大地表面復(fù)阻抗為宗量的第二類勒讓德函數(shù)。該展開式數(shù)學(xué)物理意義明顯,并且十分便于數(shù)值計算,該文給出的方法是求解下索末菲爾德半空間問題的精確、有效解析方法。
    Abstract: Generalized impedance boundary conditions are employed to simulate the effect of the earths surface on electromagnetic fields. The Sommerfeld type integrals contained in the electromagnetic fields of a horizontal electric dipole over the ground plane are expressed as a rapidly and absolutely convergent expansion of spherical wave functions; and the coefficients of the series are cast into the Legendre functions with argument for the complex surface impedance of the ground with the help of the techniques of the transformation of integration path and the hypergeometric functions. The obtained results have explicit mathematical and physical interpretation and can conveniently be used to calculate the fields. The technique described here is an accurate and efficient computation for the Sommerfeld type integrals.
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  • P. Giuseppe, L. V. John, The centennial of Sommerfelds diffraction problem, and short biography of Arnola Sommerfeld(1868-1951), Electromagnetics, 1998, 18(2), 103-116.[2]江濱浩,劉永坦,有限導(dǎo)電平面上電偶極子電磁場的解析公式,電波科學(xué)學(xué)報,1999,14(1),13-18.[3]江濱浩,劉永坦,Sommerfeld型積分的解析表達(dá)式,微波學(xué)報,2000,16(1),38-43.[4]胡俊,聶在平,索末菲爾德積分新方法-快速漢克爾變換,電子學(xué)報,1992,6(3),126-131.[5]S.O. Park, C. A. Balanis, Analytical technique to evaluate asymptotic part of the impedance matrix of Sommerfeld type integrals, IEEE Trans. on Antennas Propagat., 1997, 45(3), 798-805.[6]K.A. Michalski, Extrapolation methods for Sommerfeld integral tails[J].IEEE Trans. on Antennas Propagat.1998, 46(10):1405-1418[7]J.R. Wait.[J].Electromagnetic Wave Theory, New York, Harper Row.1985,:-[8]T.B.A. Senior, J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, Stevenage,UK, IEE press, 1995, Ch3.[9]T.B.A. Senior, J. L. Volakis, Higher order impedance and absorbing boundary conditions, IEEE Trans. on Antennas Propagat., 1997, 45(1), 107-114.[10]M.A. Ricoy, J. L. Volavis, Derivation of generalized transition/boundary conditions for planar multiple-layer structures, Radio Science, 1990, 25(4), 391-405.[11]J.A. Stratton, Electromagnetic Theory, New York, McGraw-Hill, 1941, 412-413.[12]數(shù)學(xué)手冊,北京,人民教育出版社,1979.[13]W. Magnus, F. Oberhettinger, R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Third Edition, New York, Chelsea Publishing, 1966.[14]I. S. Gradshteyn, I. M. Ryzhik, Table of Integral, Series, and Products, New York, Academic Press, 1980, 860.
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出版歷程
  • 收稿日期:  2001-07-29
  • 修回日期:  2002-06-17
  • 刊出日期:  2003-02-19

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