An adaptive graph sparsification approach to scalable harmonic balance analysis of strongly nonlinear post-layout 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 post-layout 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 prohibitively large memory consumption. In this paper, we present a novel graph sparsification approach for automatically generating preconditioners that can be efficiently applied for simulating strongly nonlinear post-layout RF circuits. Our approach allows to sparsify time-domain circuit modified nodal analysis 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 the prior state-of-the-art direct solution method, the proposed solver can more efficiently handle moderate to strong nonlinearities during the HB analysis of RF circuits, achieving up to 20× speedups and 6× memory reductions.