A projection-based reduction approach to computing sensitivity of steady-state response of nonlinear circuits

This paper presents a new algorithm for computing the sensitivity of steady-state responses of nonlinear circuits with respect to an arbitrary network parameter. The proposed algorithm is based on circuit-reduction techniques obtained through nonlinear-projection approaches. The main idea in the proposed sensitivity-computation algorithm is based on projecting the adjoint system of equations onto a subspace of smaller dimension. Continuation methods are then applied on the reduced system to trace the solution trajectory of the adjoint system in the reduced space. We show that once the steady-state solution has been obtained using nonlinear order reduction, the computational cost required to compute sensitivity is only a limited number of forward/backward substitutions. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed algorithm.