The Effect of an Air Gap on the Coupling Between Two Planar Microstrip Lines

The finite difference (FD) technique is used to investigate the air yap effect on the coupling between two planar microstrip lines. The strip lines are embedded between a dielectric substrate and a dielectric overlay. The air gap between the substrate and the overlay is present due to the thickness of the strips and~or the roughness o f the planar surfaces. A quasi-static FD technique based on the solution of Laplace's equation is used to solve the potential distribution in the region around the strips. The FD mesh is truncated by an artificial boundary to allow for a numerical solution with the available computer resources. At this artificial boundary an approximate boundary condition is used to truncate the FD mesh. From the potential distribution, the charge and the capacitance and inductance matrices of the stripline system are evaluated. The coupling or crosstalk between the lines is then defined and computed. The effects of the conducting strips thickness and the properties o f the materials between the strips on the coupling are illustrated through numerical examples. Copyright © 1996 Published by Elsevier Science Ltd L Introduction Over the past few decades, microstrip transmission lines have been analyzed extensively. Reducing the coupling has become very important, since as the clock rates in computers increase so does the effect of coupling or cross talk between the lines. The main purpose of this work is to analyze the effect of the air gap on the coupling between two planar microstrip lines. Two different geometries are analyzed using the finite difference (FD) technique. Figures 1 and 2 show the geometries where the striplines are perfectly embedded between the substrate and the overlay in contrast with Figs 3 and 4 where an air gap is present due to the thickness of the strips and/or the roughness of the planar surfaces. Following the approach presented in (1, 2), an FD technique based on the solution of Laplace's equation is used to find the potential distribution around the strips. From the potential distribution the charges on the strips are computed using Gauss' law and then the capacitance and inductance matrices are evaluated. The capacitive coupling between the lines is then computed. Numerical data are obtained for these strip line geometries with and without air gap in order to show the effects of the air gap on the coupling between the lines. The developed program is capable of solving different geometries of multi conductor transmission lines arbitrarily positioned in an inhomogeneous dielectric space. An FD mesh generator program is also developed