A new time-domain macromodel for transient simulation of uniform/nonuniform multiconductor transmission-line interconnections

A rational-function hybrid-parameter model for gen- eral multiconductor transmission lines is derived from a spectral- method solution of the telegrapher equations, using Chebyshev polynomials to represent spatial variation. Time-domain macro- model is then generated by a recursive convolution algorithm which can be simulated efficiently with arbitrary terminations. Results from a transient simulator implementing the approach are presented to demonstrate the accuracy, efficiency and stability of the derived macromodel. I. INTRODUCTION Today's high-speed logic families, with subnanosecond switching speeds, demand that the physical interconnections such as in multichip modules and printed circuit boards conform with the results of distributed-element theory. The design of state-of-the-art VLSI circuits, therefore, requires accurate and effi- cient simulation tools for transmission lines (modeling inter- connections) terminated in linear/nonlinear networks. Among numerous simulation techniques available, one ap- proach (1)-(5) solves the telegrapher equations (associated with general transmission lines) in the frequency domain. Inverse fast Fourier transform or numerical (analytical in some cases (5)) in- verse Laplace transform is then used to transform the frequency- domain data into an equivalent time-domain description (known as the impulse-response or Green's function). The dynamic inter- action of the transmission line with the terminal networks is evaluated by convolving the impulse-response with the port variables. The long duration of the impulse response often re- quires computation that increases quadratically with the simula- tion time. The numerical inverse transform techniques require numerous samples of the frequency-domain function. In addition, some of the frequency-dependent matrix parameters have wide fre- quency spectrums and often do not become zero as the frequency approaches infinity. The high-frequency limiting values of these parameters cannot, in general, be determined analytically. Consequently, the band-limiting action of the inverse transform techniques will introduce ringing and aliasing error in the im- pulse response data. To avoid the time-consuming direct convolution, a recursive convolution technique has been developed (6) that requires the impulse-response to be expressed as sum of exponentials in time domain (i.e. rational-function approximations in s-domain, s being the Laplace transform variable). Pade approximation (and a moment matching technique) used for this purpose (7)-(9) has