Macromodeling for RF passives via circuit reduction of VPEC model

To accelerate the macromodel generation for RF passive components considering parasitics, we introduce the vector potential equivalent circuit (VPEC) to efficiently model the massively coupled passives, like transmission lines and inductors. It enables the passive sparsification of the inductance matrix by pruning the small off-diagonal elements with the desired accuracy. To further reduce the model order, we apply a hierarchical s-domain circuit reduction to generate a reduced driving-point impedance function, and then use Brune's one-port network synthesis to realize the impedance function by a low-order RLCM ladder circuit as the compact macromodel. We have applied this method to generate the macromodel for the spiral inductor during the design of a cross-coupled LC oscillator. The synthesized lower-order macromodel is accurate up to 10 GHz with 50X speedup in the time-domain simulation.