Thermal Noise Compliant Synthesis of Linear Lumped Macromodels

This paper addresses the synthesis of equivalent circuits from black box state-space macromodels, as produced by model order reduction or rational curve fitting schemes. The emphasis is here on thermal noise compliance, intended as the guarantee that the produced netlists can be safely used in standard circuit solvers to perform thermal noise analysis, in addition to usual DC, AC, and transient simulations. Due to the fact that SNR is a key figure of merit in nearly all signal processing analog circuits, noise analysis is mandatory in design and verification of most analog and RF/millimeter-wave electronic applications. However, common macromodel synthesis approaches rely on components that do not (and cannot) have an associated thermal noise model, such as controlled sources or negative circuit elements. Therefore, macromodel-based noise analyses are generally not possible with currently available approaches. We propose a circuit realization derived from the classical resistance extraction synthesis, with suitable modifications for enhancing macromodel sparsity and efficiency. The resulting equivalent netlist, which is compatible with any standard circuit solver, is shown to produce exact noise characteristics, even if its elements are derived through a mathematical procedure, totally unrelated to the actual topology of the physical system under modeling. The procedure is validated by several examples.