Hierarchical Harmonic-Balance Methods for Frequency-Domain Analog-Circuit Analysis

As a widely adopted frequency-domain method, harmonic balance (HB) provides efficient steady-state circuit analysis for analog and RF circuits. The conventional matrix-implicit Krylov subspace technique with the block-diagonal (BD) preconditioner has made it possible to compute the steady-state responses of large-scale circuits. However, not all HB problems, particularly strongly nonlinear circuit problems, can be solved reliably or efficiently using the standard BD-preconditioning technique. In this paper, hierarchical HB methods are proposed wherein robust preconditioning is provided via solution of a set of approximate linearized HB problems of progressively smaller size across multiple levels of the problem hierarchy. These subproblems are constructed using the same matrix-implicit formulation to retain the memory efficiency of Krylov subspace methods. Moreover, the number of allocated Krylov subspace matrix solvers, hence the memory usage, is significantly reduced via a recently introduced solver-sharing technique. The efficiency of our hierarchical preconditioning technique is further improved by adopting a one-step correction to the standard BD preconditioner and a multigrid-motivated iterative scheme. It has been shown that the proposed approaches can achieve up to 10 runtime speedup over the popular BD preconditioner and robust convergence even for strongly nonlinear circuits for which the BD preconditioner fails to converge.