Floating electrodes in electric-field calculations

This note gives suggestions on modeling floating electrodes in EStat, RFE2, HiPhi or RFE3. A floating electrode is a piece of metal whose potential you don’t know in advance. For example, metal grading rings in an pulsed-voltage insulator have potentials determined by capacitive division in the structure.

To begin, consider a dielectric-type electrostatic calculation in EStat or HiPhi. The term dielectric solution implies that all regions have zero conductivity. Normally, we represent metal parts as fixed-potential regions with assigned voltages. In the case of a floating electrode, we don’t know the voltage to assign. We do know that the electric fields inside the region are approximately zero. This condition holds inside a dielectric region if the relative dielectric constant is large, ?r » 1. We can therefore represent a floating electrode as a dielectric region. The numerical calculation tells us the voltage by effectively determining the capacitive division. You must be careful in the choice of ?r. A value of 10,000 will ensure that electric fields are quite small inside the region. The choice of 1,000,000 will not greatly improve the accuracy and may impede the solution convergence. If you observe a solution that looks non-physical, it is probably because it has not converged.

In resistive solutions with EStat or HiPhi, assign a conductivity ? to a floating electrode that is much higher than that of surrounding regions. The programs RFE2 and RFE3 solve for harmonic electric fields in materials that may carry both displacement and real currents. In this case, assign relatively high values of both relative dielectric constant and conductivity. The codes give both the amplitude and phase of self-consistent potentials on floating electrodes determined by the properties of surrounding materials.