Nearly Direct Measurement of Relative Permittivity

A recently conceived technique for determining the relative permittivity of a material sample at a given frequency is more nearly direct than are prior techniques that involve measurement of such related non-electrical quantities as the size, shape, and/or weight of the specimen. The present technique involves only measurement of two voltages at the frequency in question, followed by calculation of the ratio between the voltages. The technique requires two circuits a test circuit and a reference circuit that are identical except as described below. Each circuit includes a capacitor C1 connected in series with a much larger capacitor C2 to form a voltage divider (see figure). C1 is a parallel-plate capacitor. The top electrode of C1 is connected to an AC signal source of voltage Va at the frequency of interest. The top electrode of C1 is surrounded by a guard electrode that, in turn, is surrounded by a grounded electrode. The bottom electrode of C1 is connected to the top electrode of C2. The bottom electrode of C2 is grounded. The volume enclosed by the top, bottom, and guard electrodes of C1 constitutes a sample cell. A material sample, having relative permittivity k at the frequency of interest, is placed in the sample cell. The exact shape and size of the sample volume is not critical and can be chosen to fit the material sample. What is critical is that (a) C2 in both circuits be identical and (b) the sample cell in the test circuit have the same size and shape as that in the reference circuit, so that the capacitances of the two sample cells are proportional to the permittivities of their contents.