Time-domain performance bound analysis for analog and interconnect circuits considering process variations

Time-Domain worst case or performance bound estimation for analog integrated circuits and interconnect circuits are crucial for both analog and digital circuit design and optimization in the presence of process variations. In this paper, we present a novel non-Monte-Carlo (MC) performance bound analysis technique in time domain. The new method consists of several steps. First the symbolic transient modified nodal analysis (MNA) formulation of the circuit matrices of (linearized) analog and interconnect circuits at a time step is formed. Then the closed-form expressions of the interested performance in terms of variational parameters of the circuit matrices of (linearized) analog and interconnect circuits are derived via a graph-based symbolic analysis method. Then time-domain performance response bound of current time step are obtained by a nonlinear constrained optimization process subject to the parameter variations and variational circuit state bounds computed from the previous time step. We study the bounds computed by the proposed against the different sigma bounds by the standard MC method, which shows that the proposed method is more efficient for computing high sigma bounds than the MC method. Experimental results show that the new method can deliver order of magnitudes speedup over the standard Monte Carlo simulation on some typical analog circuits and interconnect circuits with high accuracy.