A new equivalent circuit model for on-chip spiral transformers in CMOS RFICs

A new compact model has been introduced to model on-chip spiral transformers.Unlike conventional models,which are often a compound of two spiral inductor models（i.e.,the combination of two coupledΠor 2-Πsub-circuits）,our new model only uses 12 elements to model the whole structure in the form of T topology.The new model is based on the physical meaning,and the process of model derivation is also presented.In addition,a simple parameter extraction procedure is proposed to get the elements＇ values without any fitting and optimization. In this procedure,a new method has been developed for the parameter extraction of the ladder circuit,which is commonly used to represent the skin effect.In order to verify the model＇s validity and accuracy,we have compared the simulated and measured self-inductance,quality factor,coupling coefficient and insertion loss,and an excellent agreement has been found over a broad frequency range up to the resonant frequency.

Analysis and modeling of on-chip transformers under two ground conditions

Two fabricated on-chip transformers under different ground conditions（i.e.,CG and IG types） have been measured to compare their different characteristics.With the aid of the electromagnetic（EM） solver,we have analyzed the differences from the electric and magnetic aspects,and different effects in these aspects can be described with the lumped capacitor and inductor from the perspective of the equivalent circuit model.A physicsbased equivalent circuit model is proposed to model transformers under different ground conditions.In addition, the simple parameter extraction procedure for the corresponding model is also provided.All the model parameters are extracted and agree with the analysis.In order to verify the model＇s validity and accuracy,we have compared the modeled and measured S-parameters,and an excellent agreement has been found over a broad frequency range.