Fast statistical analysis of nonlinear analog circuits using model order reduction

The reduction of the computational cost of statistical circuit analysis, such as Monte Carlo (MC) simulation, is a challenging problem. In this paper, we propose to build macromodels capable of reproducing the statistical behavior of all repeated MC simulations in a single simulation run. The parameter space is sampled similarly to the MC method and the resulting nonlinear models are reduced simultaneously to a small macromodel using nonlinear model order reduction method based on projection, perturbation theory and linearization techniques. We demonstrate the effectiveness of the proposed method for three applications: a current mirror, an operational transconductance amplifier, and a three inverter chain under the effect of current factor and threshold voltage variations. Our experimental results show that our method provides a speedup in the range 100-500 over 1000 samples of MC simulation.