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Volume 25 Issue 2
Feb.  2003
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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.

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

  • Received Date: 2001-07-29
  • Rev Recd Date: 2002-06-17
  • Publish Date: 2003-02-19
  • 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]江滨浩,刘永坦,有限导电平面上电偶极子电磁场的解析公式,电波科学学报,1999,14(1),13-18.[3]江滨浩,刘永坦,Sommerfeld型积分的解析表达式,微波学报,2000,16(1),38-43.[4]胡俊,聂在平,索末菲尔德积分新方法-快速汉克尔变换,电子学报,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]数学手册,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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