A Hierarchical Electromagnetic-Circuit Technique for Statistical Analysis of RF Circuits in the Spectral Domain
With continuing trends towards miniaturization of circuits and inclusion of multiple, complex functionalities on a single chip, the effect of process variations on circuit performance is assuming critical importance. In view of increasing frequency of operation, accurate variability analysis of RF/Microwave circuits would require modeling of the variability in the passive elements through a field solver. In this paper, a method for enabling accurate statistical analysis of a low noise amplifier and its differential version is proposed. The on-chip spiral inductors are modeled through an EM (Electromagnetic) solver, while the circuit part is modeled through SPICE. The proposed approach relies on application of the RS (Response Surface) methodology to the y-parameters of both the circuit and the inductors independently and expressing the eventual performance measures through a suitable combination of these y-parameters. The eventual performance measures are expressed through a hierarchical approach in terms of the underlying Gaussian random variables representing both the circuit and EM process parameters. An RSMC (Rapid Response Surface Monte Carlo) analysis on these derived response surfaces furnishes the PDFs and can also be used to predict the yield based on different qualifying criteria and objective functions. Several advantages of this method are outlined.