A wide-band 2π equivalent-circuit model for spiral inductors on silicon

For monolithic RF spiral inductor on high-loss silicon substrate, a novel physical model is proposed, in which functions of skin effect, proximity effect and eddy current losses in the substrate to frequency-dependent series parameters L, and P, are accounted in the light of modified partial equivalent element circuit methodology and if full-coupled transformer loop and, in the meanwhile, distributed characteristics of parasitic capacitance are captured by 2 pi equivalent-circuit. Up to 15GHz, the model reveals quite good accuracy within 8% with data from full-wave electromagnetic filed simulator, including equivalent inductor L-eff, resistor R-eff and quality factor Q and, hopefully, it can be applied to further theory research and optimum design of RFIC spiral inductor on Si.