Modeling and Analysis of a Long Thin Conducting Stripline

Abstract

A long thin good conducting stripline embedded in a dielectric and centered between two large conducting plates, i.e. the stripline environment, is considered. The stripline is modeled as infinitely long, infinitely thin, and perfectly conducting by first considering a stripline of finite length, thickness, and conductivity in a dielectric layer. Starting from Maxwell's equations and assuming that the current on the stripline is a propagating wave in length direction, asymptotic expressions for the fields inside and in the neighbourhood of the stripline are deduced. These expressions are used to model the stripline in the stripline environment, which leads to a boundary value problem for the electric potential. This problem is solved by two dierent approaches, leading to integral equations for the current and for an auxiliary function describing the electric potential. A relation between the current and the auxiliary function is deduced, which is used to obtain asymptotic expressions for current and impedance. Results are compared with a numerical solution of the integral equation for the current and with results in literature. A stripline is a special type of electromagnetic transmission line, which is used for the excitation of antennas. For high frequency applications, a stripline is modeled usually as infinitely long, infinitely thin, and perfectly conducting, because the skin depth, as defined by Landau and Lifshitz (1), is much smaller than the thickness of the stripline, and the thickness is much smaller than all other characteristic length scales. By this model, the electromagnetic fields of a number of planar striplines can be computed by means of conformal mapping theory, if a transverse electromagnetic wave (TEM) is assumed, see Collin (2, Chapter 3, Part 2, and Appendix III) and Wheeler (3). In this paper, we present the modeling of a stripline as infinitely long, infinitely thin, and, perfectly conducting in more detail. We deduce asymptotic expressions for the fields inside and in the neighbourhood of a long thin good conducting stripline in a dielectric layer. After that, we apply the model to calculate the electromagnetic field of a stripline in a so-called stripline environment, not by conformal mapping theory, but from both an integral equation for the current and an integral equation for an auxiliary function describing the electric potential. Figure 1 shows an intersection of a stripline in a stripline environment and the geometry of the stripline itself. The stripline is a long thin good conducting strip of width 2a and thickness 2b with b ? a. In the stripline environment, the stripline is centered between two good conducting plates, called ground plates, which are c ∞ 2003 Kluwer Academic Publishers. Printed in the Netherlands.