CHAPTER 4 High-frequency electromagnetic coupling to transmission lines: electrodynamics correction to the TL approximation S.V. Tkachenko 1 , F. Rachidi 2 & J.B. Nitsch 1 1 Otto-von-Guericke-University Magdeburg, Magdeburg, Germany. 2 Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland. Abstract A system of integral-differential equations for evaluating currents and potentials induced by external electromagnetic field on a wire of different geometric form above a perfectly conducting ground is derived under the thin-wire approxima- tion. Based on the perturbation theory, an iterative procedure is proposed to solve the derived coupling equations, where the zero-iteration term is determined by using the transmission line approximation. The method can be applied both in the frequency domain and in the time domain. The proposed iterative procedure con- verges rapidly to exact analytical solutions for the case of infinite and semi-infinite straight wires, and to the Numerical Electromagnetics Code (NEC) solution for straight and bent wires of infinite length. Moreover, with only one iteration, an excellent approximation to the exact solution can be obtained. 1 Introduction The use of transmission line (TL) approximation for the calculation of the response of long lines to an external exciting electromagnetic field has permitted to solve a large range of problems related mainly to lightning and electromagnetic pulse (EMP) effects. The accuracy of the TL approximation has been investigated in different papers (e.g. [1–3]). The TL approximation is mainly limited by the con- dition that the transverse dimensions of the line and its return path (essentially the line height) should be much smaller than the minimum significant wavelength of the exciting electromagnetic field l min . Therefore, for cases when this condition is www.witpress.com, ISSN 1755-8336 (on-line) WIT Transactions on State of the Art in Science and Engineering, Vol 29, © 2008 WIT Press doi:10.2495/978-1-84564-063-7/04