Multi-interval Chebyshev collocation method for efficient high-accuracy RF circuit simulation

Abstract

Most RF circuit analysis tools use either shooting-Newton or harmonic balance methods. Neither can efficiently achieve high accuracy on strongly nonlinear circuits possessing waveforms with rapid transitions. We present a multi-interval-Chebyshev (MIC) method that discretizes the circuit equations by dividing the simulation domain into a set of intervals whose size is adaptively chosen and using Chebyshev polynomials to represent the solution in each interval. The MIC method has excellent stability properties, is as effective at solving nonlinear problems as shooting techniques, can achieve high resolution on a wide variety of circuits, and in conjunction with an appropriate preconditioner can be combined with matrix-implicit Krylov-subspace solvers to analyze large circuits with moderate computational cost.