RESONATORS FOR ACCURATE DIELECTRIC MEASUREMENTS IN CONDUCTING LIQUIDS

The compact, rugged, re-entrant radio-frequency resonator [A. R. H. Go odwin, J. B. Mehl, and M. R. Moldover, Rev Sci. Instrum. 67, 4294 (199 6)] was modified for accurate measurements of the zero-frequency diele ctric constant (relative electric permittivity) epsilon(r) of moderate ly conducting liquids such as impure water. The modified resonator has two modes with frequencies near 216/root epsilon(r) MHz and 566/root epsilon(r) MHz. The results for epsilon(r) at both frequencies were co nsistent within 0.0002 epsilon(r), verifying that the low-frequency li mit had been attained with water samples with conductivities in the ra nge 100-2500 mu S/m. The results for water and for the insulating liqu id cyclohexane were within 0.0005 epsilon(r) of literature values. The present analysis is based on a simplified equivalent circuit that acc ounts for the loading of the resonator by the external instrumentation . This circuit can easily be generalized for a resonator with three or more modes. The present resonator has a thick gold plating on its int erior surfaces. With the plating, the quality factors Q of the resonan ces varied in a predictable way with frequency and temperature. Predic table es were essential for obtaining accurate values of epsilon(r).