Conductive substrate losses in coplanar and microstrip transmission lines

The effect of a conductive substrate, such as silicon, on the attenuation of microstrip (MS) lines has been investigated in the past. No such treatment exists for coplanar (CPW) lines, and experimental data on the additional attenuation due to a finite conductivity of the substrate is extremely scarce. Using basic transmission line theory, simple expressions have been derived for the losses caused by a conductive substrate for both the coplanar and the microstrip lines. For microstrip lines, good agreement is obtained with previously published theoretical and experimental data on conducting silicon substrates. In contrast to the case for microstrip lines, where the conductive substrate losses are independent of the line impedance, a dependence is found for coplanar lines.