Internal inductance and conductor loss associated with the ground plane of a microstrip line

In previous work, a closed-form expression for the current density on the ground plane of a microstrip line was presented. In this paper, we show how this formula for the current density is used to derive an expression for the internal inductance associated with the ground plane. Results are presented for different geometries that illustrate when the internal inductance of the ground becomes comparable to the external inductance of the microstrip line. We also illustrate that the integrals needed for the internal inductance calculation can be used to develop an expression for the conductor loss associated with the ground plane.