Closed-Form Quasi-Static Solution for Capacitance and Conductance of Coplanar Waveguides

We present a closed-form quasi-static model for calculating the distributed capacitance and conductance of a coplanar waveguide (CPW) with finite-width ground electrodes on a two-layer substrate. The presented approach uses the conformal mapping technique and enables calculating these parameters for substrates, where the dielectric permittivity of the layers is increasing with their distance to the electrodes. This is often the case for silicon substrates used in electric and photonic integrated circuits. Our method is in good agreement with field simulations, while using this method can significantly reduce the computational complexity and hence calculation times.