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 physics-based 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.
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