INTERCONNECT DELAY AND SLEW METRICS BASED ON THE LOGNORMAL DISTRIBUTION

A method of determining a circuit response (such as delay or slew) from a ramp input of an RC circuit calculates two circuit response parameters using a given circuit response metric based on a step input for the RC circuit, and extends the circuit response metric to a ramp input of the RC circuit by combining the first and second circuit response parameters to yield an estimated ramp response. The novel technique is based on the use of probability distribution functions and cumulative distribution functions to characterize the impulse response of the RC circuit, and the calculating steps derive the first and second circuit response parameters from such statistical distribution functions. In particular, the calculating steps may use a standard deviation or a mean of a probability distribution function corresponding to the circuit response parameter. In one application, the invention is used to estimate delay response for the ramp input of the RC circuit. In another application, the invention is used to estimate output slew for the ramp input of the RC circuit. New delay and slew metrics are also disclosed which are derived by matching one or more properties of the network impulse response to a lognormal distribution. For delay, the mean and variance of a probability distribution function (PDF) are correlated to the lognormal distribution. For slew, alternative metrics are provided; one slew metric correlates the mean and variance of the PDF to the lognormal distribution, while a second slew metric correlates the variance and skewness of the PDF to the lognormal distribution.