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An accurate hierarchical electromagnetic-circuit technique for statistical analysis of RF circuits

Modeling process variations in circuits is becoming necessary as the technology continues to shrink in size. When this is coupled with increasing frequencies of operation of circuits in communication systems (>10 GHz), the use of full-wave field solvers is necessary to model the on-chip passive components such as spiral inductors and transformers. Thus it becomes necessary to couple full-wave field solvers and SPICE-like simulators for accurate statistical analysis of RF circuits. The present paper reviews the issues associated with using circuit models for electromagnetically modeled passive elements in conjunction with SPICE for statistical analysis. It then proposes a method which circumvents the outlined limitations.