The Induced EMF Method as an Alternative to the Iterative Method for the Approximation of the Reflection Coefficient on Thin Wires

One way to find an analytic approximation of the input impedance of thin wire antennas is to make an educated guess of the current distribution, which is then used for the induced electromotive force (EMF) method. This method is frequently described in the literature and yields accurate results. In this article, it is shown that this method can be used to approximate the transmission line reflection coefficient while including high-frequency effects. It is, hence, applicable to smaller wave lengths than the classical transmission line theory. Two general problems are considered: 1) the infinite wire with a lumped impedance above ground and 2) the semi-infinite wire with an arbitrary port configuration above ground. For both configurations, the reflection coefficient is approximated using the induced EMF method. An important intermediate step is to find exact equations that relate the input impedance and the reflection coefficient. The results are compared to an exact solution and an iterative one, which is used in recent publications. It is shown that the induced EMF method is a good alternative to the iterative method. The novelty of this article is the utilization of the induced EMF method for the analytic approximation of the transmission line reflection coefficient and linking the input impedance and the reflection coefficient.