Analysis of N-Conductor Transmission Line Systems with Non-Linear Loads with Application to CAD Design of Digital Circuits

A computer model has been developed f or sim ulating N-conductor transm ission lines term inated w ith non­ linear complex loads. A modal analysis is used to describe incident and reflected waves on the transm ission lines. The loads are modeled as parallel R-C netw orks w ith a vol­ tage dependent resistance and source. For each load a m atrix differential equation is w ritten for the unknown load voltage due to some incident voltage. The m atrix equation is solved num erically using a first order finite difference approximation. The problem o f calculating crosstalk and pulse distortion in digital printed circuits has largely been ignored in the past due to the relatively low effective frequencies at w hich these circuits operate. However, in the past five years, the bandwidth o f digital devices has increased dram atically w ith the result that pulse risetim es and falltim es have decreased. At the same tim e, the density of digital devices on printed circuit cards has risen. The net result has been increasing problems due to crosstalk and pulse distortion in these circuits. The crosstalk and pulse dis­ tortion can cause false triggering o f level sen­ sitive devices w ith the result being a mal­ functioning circuit. Therefore, the need for a Computer Aided Design (CAD) package for analyzing coupling and pulse distortion in digital circuits has become evident. In th is paper, th e m icrostrip (Fig. l ) or buried m icrostrip lines are analyzed using a quasi-static model. The follow ing superposi­ tion integral is solved for the unknown charge distribution p (x ) in a given m ulti­ conductor printed circuit configuration using iterative techniques [ l l V ( x ) = f G (xr,x' ) p(x' )dx' CH2294-7/86/000-0174 $01,00(c )l986 IEEE 174 w here G (x ,x' ) = Green's function for the structure. The resulting charge distribution is used to solve for the per unit length capacitance and inductance m atrices o f the transmission lin e system .