There are many kinds of transmission lines such as uniform, nonuniform and nonlinear ones terminated by linear and/or nonlinear subnetworks. The nonuniform transmission lines are crucial in integrated circuits and printed circuit boards, because these circuits have complex geometries and layout between the multi layers, and most of the transmission lines possess nonuniform characteristics. On the other hand, the nonlinear transmission line have been focused in the fields of communication and instrumentation. Here, we present a new numerical method for analyzing nonuniform and nonlinear transmission lines with linear and/or nonlinear terminations. The waveforms at any points along the lines are described by the Fourier expansions. The partial differential equations representing the circuit are transformed into a set of ordinary differential equations at each frequency component, where for nonlinear transmission line, the perturbation technique is applied. The method is efficiently applied to weakly nonlinear transmission line. The nonuniform transmission lines terminated by a nonlinear subnetwork are analyzed by hybrid frequency-domain method. The stability for stiff circuit is improved by introducing compensation element. The efficiency of our method is illustrated by some examples.

This paper discusses pulse responses of multi-conductor transmission lines terminated by linear and nonlinear subnetworks. At first step, the circuit is partitioned into a linear transmission lines and nonlinear subnetworks by the substitution voltage sources. Then, the linear subnetworks are solved by a well-known phasor technique, and the nonlinear subnetworks by a numerical integration technique. The variational value at each iteration is calculated by a frequency domain relaxation method to the associated linearized time-invariant sensitivity circuit. Although the algorithm can be efficiently applied to weakly nonlinear circuits, the convergence ratio for stiff nonlinear circuits becomes very small. Hence, we recommend to introduce a compensation element which plays very important role to weaken the nonlinearity. Thus, our algorithm is very simple and can be efficiently applied to wide classes of nonlinear circuits.