Calculations of the fringing capacitance of cylindrical electrodes
Andrew P. Gregory, T.E. Hodgetts, R.N. Clarke, G J Hill · 2023
The accuracy of measurements of dielectric permittivity made with admittance cells and similar instruments is often limited by the effects of fringing-capacitance. These effects can be reduced by a physical approach that requires an additional electrode that is known as a guard ring, or by numerical corrections derived from calculations of the fringing capacitance. This report studies electrostatic calculations of fringing capacitance for a two-electrode capacitor consisting of a rod or disc that is enclosed by a longer surrounding cylinder or reentrant cylinder. The space between the ends of the electrodes is filled by air and an optional sheet of a uniform dielectric. Comparisons are made between calculations with several types software, including finite-element modelling, boundary-element modelling and mode matching. Corrections for the effects of fringing capacitance on measurements of permittivity by the Lynch method are derived for two radio-frequency instruments. For a Hartshorn and Ward apparatus resonant at 6 MHz, the corrections are found to improve measurement accuracy, but for a reentrant cavity resonant at 300 MHz they are not consistent with observations.