Sensitivity computation in piecewise approximate circuit simulation

Both direct and adjoint methods are applied to the computation of time-domain transient sensitivities in the already efficient SPECS piecewise approximate circuit simulation environment. By exploiting the event-driven nature of SPECS, the computation, storage, and interpolation of the Jacobians that specify the appropriate linearized circuit during the forward simulation is not required to obtain sensitivities. Both direct and adjoint methods require only a marginal computational overhead and provide equivalent results. The choice of the method to use depends on the ratio of the number of outputs to the number of parameters. More parameters favor the adjoint method and more outputs favor the direct. The overall efficiency of both SPECS and its time-domain sensitivity extension allows it to be applied to realistic circuits that, due to their large size, had previously made such analysis impractical. Simulation results on industrial circuits of up to 1500 MOS transistors show that transient sensitivities can be efficiently computed for large circuits