Edge correction in the determination of dielectric constant

Abstract

An edge correction is often required in determining the dielectric constant of an insulating material by the capacitance method. Theoretical formulas by which the edge correction may be computed have been considered for a number of electrode arrangements. Some of these apply to circular electrodes and some to rectangular electrodes. The error in the dielectric constant which may arise from the use of these formulas is discussed for each of the different arrangements. The accuracies of the methods were experimentally determined by making measurements on the same specimens with the various arrangements of electrodes. The guard-ring arrangement was assumed to give the correct value of the dielectric constant, and the values obtained with the other arrangements were compared with it to determine their errors. Only two methods gave values which were in error by less than 1 percent. Both methods were for arrangements of electrodes in which one electrode was smaller than the other, one being for circular electrodes, the other for rectangular electrodes. Empirical equations were set up which gave values of the dielectric constant which were in error by less than 1 percent for all electrode arrangements, both for circular and rectangular electrodes. These equations are much simpler than the theoretical equations. CONTENTS Part 1. Theoretical Determination of Edge Correction Page r. Introduction _________________ __________ __ ___________________ ____ 748 II. Theory of edge correction with a single sheet of dielectric _____________ 749 1. Edge correction for circular electrodes ____________ _______ ___ 750 (a) Theoretical formula when a circular sheet of dielectric has electrodes of the same diameter as the sheeL ___ 751 (b) Theoretical formula when a sheet of dielectric has one large electrode and one small circular electrode _____ 752 (c) Theoretical formula when a sheet of dielectric extends beyond the circumferences of the electrodes ________ 753 (d) Elimination of the edge correction for circular electrodes by using a guard electrode _________________ 754 2. Edge correction for rectangular electrodes _____________ ______ 754 (a) Theoretical formula when a rectangular sheet of dielectric has electrodes covering both faces ________ 755 (b) Theoretical formula when a sheet of dielectric has one large electrode and one small rectangular electrode_ _ 755 (c) Theoretical formula when a sheet of dielectric extends beyond the edges of rectangular electrodes ________ 756 (d) Elimination of the edge correction for rectangular electrodes by using a guard electrode _ _ _ _ _ _ _ _ _ _ _ _ _ 756 747 748 Journal oj Research oj the National Bureau oj Standards Vol. He Page III. Theory of edge correction with two sheets of dielectric_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 756 1. Edge correction for circular electrodes ___ ____ ___ ___ ______ _____ 757 (a) Theoretical formula when the two sheets of dielectric and the elect.rodes have the same diameter ____ __ _____ 757 (b) Theoretical formula when the outer electrodes and the two sheets of dIelectric extend beyond the circumference of the cent er electrode_ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 758 (c) Theoretical formula when the two sheets of dielectric extend beyond the circumferences of the electrodes ___ 759 2. Edge correction for rectangular electrodes ______ _____ ___ ___ ___ _ 759 (a) Theoretical formula when the outer electrodes and the two sheets of dielectric extend beyond the perimet er of the center electrode ___ ___ ____ ____________ __ _____ _ 760 Part 2. Experimental Determination of the Edge Correction I. Introduction ________ ___ ____ ____ __ _____ _____ __ _____ _____ ________ _ 760 II. Arrangement of electrodes _______ _____ ___________________ _________ 761 III. Electrical measurements _______ __ __________________ _______________ 762 IV. Results ___ ___________________ _____ _______ ___ ____ _____ ____ __ _____ 763 1. Test of Kirchhoff's equation __ _____ ___ ___ __ ___________ ______ 763 2. Dielectric constants when theoretical equations were used _____ __ 764 (a) Circular electrodes ______________ ________ ______ ______ 764 (b) Rectangular electrodes ___ __ ___ ____ _______ ___________ 766 3. Determination of empirical equations ______ __ _____ _____ ______ 766 4. Dielectric constants when empirical equations were used ____ __ ___ 773 V. Summary _____________________ __ _________ __ ______ ______ ________ _ 775