A Unified Equivalent-Circuit Model for Coplanar Waveguides With Silicon-Substrate Skin-Effect Modeling

In this paper, a novel unified equivalent-circuit model with silicon (Si)-substrate skin-effect modeling is demonstrated to describe the performance of coplanar waveguide (CPW) lines with a wide range of dimensions and substrate resistivities, up to 110 GHz. HFSS is used to simulate the CPWs on 8000-, 15-, and 0.015-Ω·cm resistivity Si substrates. The electric field distributions of the CPWs are analyzed and compared, to demonstrate that the operation mode of the line on the 0.015-Ω·cm resistivity Si substrate is the skin-effect mode and is different compared to the commonly used quasi-TEM mode in high-resistivity substrates. A novel unified equivalent circuit is developed to model all the three operation modes for CPWs (the slow-wave mode, the skin-effect mode, and the dielectric quasiTEM mode). Agilent Momentum is used to compare with the model up to 110 GHz. CPWs with different substrate resistivities and geometries are then fabricated for verification. The results show that this model can be applied to CPWs with various geometries on different resistivity substrates. Since the model is physics based and analytical, it can be easily included with other device models for RF applications.