Our invention is a method that accurately characterizes the distribution of any electrical response parameters of interest (such as delay and power consumption) of electronic circuits in the presence of manufacturing process variations in the fabrication process. Monte Carlo simulations based Regression method (Okada et al., ICCAD 2003, Li et al., DAC 2004) Taylor series based method (Zhang et al., DAC 2005) are the existing methods that are typically used in characterizing the impact of process variations on the circuit delay and power. Monte Carlo based Regression methods require a large number of simulations for practical electronic circuits and thus have a high computational cost. Taylor series based methods can typically provide only a first or a second order series expansion due to the difficulty in obtaining the higher order derivatives of electrical response parameters. The first or the second order expansions result in significant error in approximating the mean and variance of these electrical parameters.On the contrary, our method can provide a very accurate expansion of any order based on the accuracy requirements of the user and the available computational resources. Our approach, for the first time. accounts for the underlying probability distribution of the random variables that represent uncertainties. Given any probability distribution of the random variables (whether symmetric or asymmetric), our approach always finds the optimal set of orthonormal polynomials for representing the circuit's response. The optimality is with respect to the speed of convergence of the series expansion for the circuit's response (order of the expansion). Our approach provides significant speed-up as compared to the golden standard Monte Carlo simulations method, usually over 100X for comparable accuracy in obtaining the moments of the probability density function of a circuit's electrical response characteristics (such as delay and power consumption). Apart from obtaining expansions for circuit response characteristics as functions of random variables representing uncertainties in the circuit's component parameters, our method also provides a means to obtain these expansions as functions of mean values of the circuit's component parameters. This alleviates the need to re-run simulations of the circuit every time a change in the mean value of a circuit's parameter is made. This feature in our method results in enhanced speed-ups over the existing methods.
|Published - Jun 9 2005