A Hierarchical Electromagnetic-Circuit Technique for Statistical Analysis of RF Circuits in the Spectral Domain

Spectral domain statistical analysis of RF circuits, combining a circuit simulator, which models the circuit part and a full-wave field solver, which models the passive elements, is presented in this paper. This paper first illustrates the importance of the knowledge of correlation information in accurately modeling the probability density functions (PDFs) of eventual objective functions using a simple transmission line paradigm. Next, this paper looks at the statistical study of on-chip RF passives using the spiral inductor as an example. It is shown that larger process variations necessitate modeling by means of a quadratic response surface to preserve accuracy. This results in nonindependent non-Gaussian nonclosed-form PDFs for the equivalent-circuit parameters of the passives. This paper then proposes a hierarchical technique to perform statistical analysis of RF circuits based on y-parameter representation for the circuit and the passive element parts. The proposed technique obviates the need for optimization steps to derive the equivalent-circuit parameters for the electromagnetic objects and the need to compute the correlation matrix between the circuit equivalent elements, while maintaining accuracy. The proposed approach is illustrated for the statistical analysis of an RF amplifier and its differential version operating at 15.78 GHz. PDFs of various quantities of interest are derived and yield measures are computed.