Autonomous Volterra Algorithm for Steady-State Analysis of Nonlinear Circuits

Abstract

We present a novel algorithm, named autonomous Volterra (AV), that achieves efficient steady-state analysis of nonlinear circuits. With elegant analytic forms and availability of efficient solvers, AV constitutes a competitive steady-state algorithm besides the two mainstreams, namely, shooting Newton (SN) and harmonic balance (HB). Nonlinear systems are first captured in nonlinear differential algebraic equations, followed by expansion into linear Volterra subsystems. A key step of steady-state analysis lies in modeling each Volterra subsystem with autonomous nonlinear inputs. The steady-state solution of these subsystems then proceeds with a series of Sylvester equation solves, completely avoiding the guesses of initial condition and time stepping as in SN, as well as the uncertain length of Fourier series as in HB. Error control in AV is also straightforward by monitoring the norms of the Sylvester equation solutions. We further demonstrate that AV is readily parallelizable with superior scalability toward large-scale problems.