A broadband and scalable model for on-chip inductors incorporating substrate and conductor loss effects

A new T-model is developed to accurately simulate the broadband characteristics of on-Si-chip spiral inductors, up to 20 GHz. The spiral coil and substrate RLC networks built in the model play a key role responsible for conductor loss and substrate loss in the wideband regime, which cannot be accurately described by the conventional π-model. Good match with the measured S-parameters, L(ω), Re(Z_in(ω)), and Q(ω) proves the proposed T-model. Besides the broadband feature, scalability is justified by the good match with a linear function of coil numbers for all model parameters employed in the RLC networks. The satisfactory scalability manifest themselves physical parameters rather than curve fitting. A parameter extraction flow is established through equivalent circuit analysis to enable automatic parameter extraction and optimization. This scalable inductor model will facilitate optimization design of on-chip inductor and the accuracy proven up to 20 GHz can improve RF circuit simulation accuracy demanded by broadband design.