Transmission Line Reflection Coefficient Including High-Frequency Effects

This paper deals with the analytic determination of the current reflection coefficient for a wire above ground. The trajectory of the wire at the wire terminal is arbitrary and the wire is connected to the ground with an impedance. The reflection coefficient is approximated by an iterative approach for the solution of the so-called mixed potential integral equations. The iteration is initialized by the classical transmission line solution. The tangential electric field on the surface of the thin wire corresponding to the classical solution is then used as a distributed source to determine a correction term for the current. By this way, the scattering of the transverse electromagnetic modes at the discontinuity is included. Very good agreement between the analytic solution and a numerical one is observed. It is shown that broadband matching is not possible with a frequency-independent load. The importance of the incorporation of the high-frequency effects is highlighted by the evaluation of the natural frequencies for two specific wire configurations.