Capacitance corrections for the guard, edge and corner situations

摘要

The present standards for the accurate measurement of the dielectric constant give corrections to account for the edge and guard gap capacitances. It is maintained that these published corrections are unsatisfactory. The author calculates the guard gap corrections for an arbitrary dielectric constant, comments on the value of using thick electrodes, and calculates the corrections for unguarded disk capacitors and for square capacitors. These edge corrections increase logarithmically as the spacing is decreased and are of lesser importance for high-dielectric-constant samples. It is shown that the disk and the square plate capacitors give rise to quite similar excess capacitances. These results are also useful for the evaluation of microstrip capacitances. It is shown that there are no additive corner effects, even though the charge density has a corner singularity. A theoretical prediction of a power law dependence (exponent approximately=-0.7) at the square corner is confirmed numerically.