Equation-Based Solutions to Coupled, Asymmetrical, Lossy, and Nonuniform Microstrip Lines for Tab-Routing Applications

Abstract

In this paper, analytical equation-based solutions are derived to allow quick and accurate calculations directly from the physical parameters of coupled, asymmetrical, lossy, and nonuniform microstrip lines with interdigital trapezoidal tabs incorporated, resulting in their corresponding scattering parameters. Capacitance and inductance matrices under a quasi-static condition are derived from the cross-sectional dimensions of asymmetrical coupled microstrip lines with unequal widths. They are converted into a frequency-dependent resistance–inductance–conductance–capacitance model, allowing complete equation-based solutions to their four-port Z-matrix, S-matrix, and ABCD-matrix. As an application example of tackling the complexity of transmission lines, the derived analytical method is applied to a transitional structure with linearly varying trace width in tabbed microstrip lines by the method of segmentation. In addition, a new concept of tab-coupling fringing capacitance is specifically introduced to compensate for underestimated mutual capacitance at tab positions, which will improve the accuracy of the proposed approach. Numerical modeling results from commercial simulation tools are compared for validation purposes. As a conclusion, the proposed method and its versatility are demonstrated with applications to practical high-speed and high-density printed circuit board designs, which renders itself effective and efficient in an optimization process.