Delay macromodels for point-to-point MCM interconnections

We develop delay macromodels for lossless as well as lossy point-to-point MCM transmission lines using a systematic model construction procedure that includes dimensional analysis. The result for lossless lines confirms earlier work and extends it to the case of nonlinear drivers and capacitive termination. For lossy lines, we show that dimensional analysis allows us to reduce the complexity of the delay expression without any loss in accuracy. A second-order polynomial fit to a four-argument delay function is shown to yield predictions that are within 5% of detailed circuit simulation at a fraction of the computational cost. We illustrate the applications of these macromodels in studying the effects of packaging technology on signal delay and in sensitivity analysis