Fast analytical approximations of the transient response of coupled lossy interconnects in VLSI circuits with frequency-dependent parameters for higher hierarchical simulation levels

This paper presents a quasi-analytical approach to analyse cross-talk, propagation delay, distortion on interconnects in high-speed integrated circuits, packages and boards. The approach is based upon a novel multipoint Pade approximation technique and approximates the transfer functions of single as well as coupled lossy transmission lines in the complex s-domain as rational functions. Transmission lines with both frequency-dependent (due to substrate losses) as well as frequency-independent parameters can be taken into account. This makes the method useful for the simulation of interconnects at higher hierarchical simulation levels where mostly only an RC-modelling of the transmission lines are carried out. Simulation results of four examples are presented to illustrate the application of the analysis. A comparison with results obtained from more stringent numerical simulations show very good agreement.