Analysis of RC interconnections under ramp input

We present a general and, in the limit, exact approach to compute the time-domain response for finite-length RC lines under ramp input, by summing distinct diffusions starting at either end of the line. We also obtain analytical expressions for the finite time-domain voltage response for an open-ended finite RC line and for a finite RC line with capacitive load. Delay estimates using our new method are very close to SPICE-computed delays. Finally, we present a general recursive equation for computing the higher-order diffusion components due to reflections at the source and load ends. Future work extends our method to response computations in general interconnection trees by modeling both reflection and transmission coefficients at discontinuities.