Chapter 7 - Nonuniform Transmission Lines

Abstract

This chapter deals with the explanation of nonuniform transmission lines. Modern high-density integrated circuits are characterized by interconnections with varying cross sections and bends due to the severe geometrical constraints and the placement of vias for signal redistribution. In some cases, the nonuniformity of the line is intentional, as with transmission lines designed for impedance matching, pulse shaping, and analog signal processing. The chapter shows that the terminal behavior of a lossless nonuniform two-conductor transmission line may be represented by an equivalent circuit. An ideal two-conductor line is characterized directly in the time domain by using d’Alembert's solution for the wave equation. The equations of nonuniform transmission lines cannot be solved analytically in the time domain. However, they can be solved through a numerical–analytical method in the Laplace domain. Therefore, the approach to be followed for nonuniform lines is first to determine the characteristic relations of the two-port in the Laplace domain and then to transform them in the time domain.