Efficient harmonic balance simulation using multi-level frequency decomposition

Efficient harmonic balance (HB) simulation provides a useful tool for the design of RF and microwave integrated circuits. For practical circuits that can contain strong nonlinearities, however, HB problems cannot be solved reliably or efficiently using conventional techniques. Various preconditioning techniques have been proposed to facilitate a robust and efficient analysis based on Krylov subspace linear solvers. In This work we introduce a multi-level frequency domain preconditioner based on a hierarchical frequency decomposition approach. At each Newton iteration, we recursively solve a set of smaller problems to provide an effective preconditioner for the large linearized HB problem. Compared to the standard single-level block diagonal preconditioner, our experiments indicate that our approach provides a more robust, memory efficient solution while offering a 2-9× speedup for several strongly nonlinear HB problems in our experiments.