Closed-form expressions for the optimization of high speed electro-optical modulators

Compact closed-form mathematical expressions for the propagation parameters (characteristic impedance, effective permittivity and attenuation) of coplanar waveguides (CPW) are presented. The formulas take into account asymmetric structures, thick electrodes and two-layered substrates, and thus are perfectly tailored for the optimization of electro-optical modulators. Excellent agreements, within a range of frequencies up to 100 GHz, are found with full-wave finite elements results from commercial software (HFSS) and with measures reported in the literature, for material and geometrical CPW parameters of practical relevance for the design of electro-optical modulators