An efficient graph sparsification approach to scalable harmonic balance (HB) analysis of strongly nonlinear RF circuits

In the past decades, harmonic balance (HB) has been widely used for computing steady-state solutions of nonlinear radio-frequency (RF) and microwave circuits. However, using HB for simulating strongly nonlinear RF circuits still remains a very challenging task. Although direct solution methods can be adopted to handle moderate to strong nonlinearities in HB analysis, such methods do not scale efficiently with large-scale problems due to excessively long simulation time and huge memory consumption. In this work, we present a novel graph sparsification approach for generating preconditioners that can be efficiently applied for simulating strongly nonlinear RF circuits. Our approach first sparsifies RF circuit matrices that can be subsequently leveraged for sparsifying the entire HB Jacobian matrix. We show that the resultant sparsified Jacobian matrix can be used as a robust yet efficient preconditioner in HB analysis. Our experimental results show that when compared with existing state-of-the-art direct solvers, the proposed HB solver can more efficiently handle moderate to strong nonlinearities during the HB analysis of RF circuits, achieving more than 10X speedups and 8X memory reductions.