Frequency-Independent Asymmetric Double-$pi $Equivalent Circuit for On-Chip Spiral Inductors: Physics-Based Modeling and Parameter Extraction

We present a frequency-independent compact model for silicon on-chip spiral inductors with an asymmetric double-$pi $equivalent circuit incorporating high-order parasitics such as skin effect and proximity effect. A set of partition factors for parameter ratios between the input and output segments has been introduced and derived from physical analysis to characterize the non-symmetrical feature of the inductor. A novel approach to extracting the model parameters is also developed based on measured$S$-parameters. As demonstrated for a series of inductors with different geometries fabricated by 0.18-$muhbox m$CMOS process, the partition factors derived from the physical model are consistent with the extracted parameters, and the model can simulate precisely the inductor characteristics including the asymmetric admittances over a wide frequency rang beyond the self-resonant frequency without fitting parameters.