TEM wave propagation in a microstrip line on a substrate of circular segment cross section

摘要

TEM mode wave propagation in a microstrip transmission line on a dielectric substrate of circular segment cross section is of concern. A suggested design of a microstrip is convenient for manufacturing and allows to miniaturize microstrips since there is no lateral fringing effect of the substrate in the transmitted fundamental TEM mode. By using the bipolar orthogonal coordinates, the plane potential problem is reformulated in the form of trigonometric dual integral equations. The discontinuous integrals containing Legendre functions of complex degree and the Abel integral equation are employed to reduce the dual equations to a Fredholm equation of the second kind. The structure of the Fredholm integral equation allows to obtain a simple approximate solution. Basing on this solution, rigorous approximate formulas for the characteristic impedance are derived. The characteristic impedance of a microstrip transmission line on a silicon substrate is computed and plotted as an example.