Active-passive co-synthesis of multi-GigaHertz radio frequency circuits with broadband parametric macromodels of on-chip passives

Synthesis of multi-GigaHertz radio frequency circuits brings together difficult challenges related to simulation, extraction and multidimensional space search. The standard approach of mapping all electromagnetic parasitics into parametric RLC models prior to synthesis is extremely restrictive especially when broadband and full-wave models with high accuracy are needed. In the presented approach, a two-stage macromodel that creates broadband, accurate parametric representations of passives, in particular spiral inductors, is developed. The broadband nature is captured through the Vector Fitting algorithm. The macromodels are implemented via efficient nonlinear, multidimensional regression using Relevance Vector Machine, and are coupled into circuit simulators through admittance parameters. Subsequently, optimization on both active and passive parameters are carried out simultaneously, thereby bypassing the ad hoc nature of two stage (actives and passives) approximate optimization. Two standard low-noise amplifier topologies are synthesized with tight performance constraints at center frequencies 5, 10 and 12 GigaHertz in order to demonstrate the frequency scalability of the methodology.