Scalable modeling of layout parameters in CMOS integrated stacked millimeter wave transformer

The scalable modeling of CMOS integrated stacked millimeter wave transformer is presented. The model parameters are only related to the layout and process data. So this model is scalable with the two factors. We provide simple and accurate expressions for the self-inductance, mutual coupling inductance, oxide capacitance and the mutual coupling capacitance. High frequency effect and thick metal effect are considered, so the model is accurate at high frequency and can be used at millimeter wave IC design. The model is generated by these equations directly, and no further fitting or optimization is required. The model is verified by 65nm and 40nm CMOS technology transformers. We compare S-parameters, self-inductance of each coil, and coupling coefficient. A very close agreement has been obtained.