A Wideband Predictive “Double-$\pi$” Equivalent-Circuit Model for On-Chip Spiral Inductors

A new wideband predictive ldquodouble-pirdquo equivalent-circuit model for on-chip spiral inductors is presented, in which the model parameters are analytically calculated with layout and process parameters. In the model, five major parasitic effects, including skin effect, proximity effect, distributed effect, substrate capacitive loss, and inductive loss, are implemented together. Considering skin effect and proximity effect simultaneously, a new equation of high-frequency resistance is proposed, and accordingly, two coupled transformer loops are developed, respectively, to calculate the network parameters of skin effect, proximity effect, and substrate inductive coupling effect independently. In order to analytically calculate substrate capacitive loss in multiturn inductors, a quasi-linear relationship between capacitive coupling effect and proximity effect is established. A series of inductors with different geometries are fabricated in two standard RFCMOS processes to verify the model. Excellent agreements have been obtained between the measured data and the proposed model within a wide frequency range. Since a clear relationship between circuit components and fabrication parameters is defined, it can precisely predict the performance of the inductors and become more flexible in RFIC design.