Analysis of a class of coupled microstrip lines in a nonhomogeneous dielectric media

Abstract

In this paper, analysis of a class of coupled microstrip transmission lines is developed based on finite and infinite element methods. The microstrip line consists of two dielectric layers with two infinitesimally thin perfectly conducting strips clad on the dielectric layers. It is worthwhile to note that in this development the assumption that the finite transverse dimensions of the microstrip line structure are smaller than the operating wavelength resulting in the wave velocity is no longer independent of frequency and the quasi-static TEM mode approximation analysis can be provided. Coupled microstrip transmission lines have become an attractive means of microwave integrated circuits, namely filters, directional couplers, matching networks, delay lines, and equalizers. The system of coupled transmission lines has also found the use to connect electronic subsystems on modern avionics systems such as aircraft and missiles consisting of large closely coupled cable bundles. In the design of microwave integrated circuits MICs requires a knowledge to predict the electrical transmission properties of microstrip lines. These are namely characteristic impedances, eigenvectors, normal mode propagation constants, and network functions of the lines. A system of coupled microstrip transmission lines is analyzed with both the ordinary finite and infinite elements to solve for the potential and field distributions in the cross section of the microstrip line. A variational principle is applied to compute the Maxwellian capacitance or inductance matrix per unit length of the line. This analysis has the advantage of straightforwardly identifying propagation modes. The parameters of the microstrip line can be determined in terms of the capacitance or inductance matrix. The system of coupled transmission lines is assumed to be uniform along its longitudinal z-direction. The equivalent circuit for the coupled microstrip lines is developed and its application to the solution of wave propagation modes is demonstrated.