Analysis of RC interconnections under ramp input

Abstract

We give new methods for calculating the time-domain response for a finite-length distributed RC line that is stimulated by a ramp input. The following are our contributions. First, we obtain the solution of the diffusion equation for a seminfinite distributed RC line with ramp input. We then 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. Next, we 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. The delay estimates using this method are very close to SPICE-computing 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.