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We propose a new method to measure the complex permittivity (CP) of a high loss liquid at millimetre wavelength. The method is based on the use of an exact-calculated quasi-optical layered ball dielectric resonator. A monitored liquid is placed outside of the ball and does not disturb the spherical symmetry of the resonator. A dielectric layer between the ball and a liquid is used to dose the losses in the resonator induced by the measured high loss liquid. We obtained and numerically analysed the characteristic equations for resonant eigenfrequencies and also built the electromagnetic field distribution in the resonator. The resonant frequencies and Q-factor of the resonator are studied for various resonator and monitored liquid parameters. We found theoretically, and then confirmed experimentally, the optimal resonator parameters and an operating frequency mode to provide maximum sensitivity during CP measurement of a liquid. The CP measurement of a water–alcohol solution was carried out using the proposed method. Quite good agreement between our results and the results from other sources was obtained. The package of original computer software applications was designed to automate the experiment and calculate the CP values of high loss liquids using experimental data for the resonant frequency and Q-factor.

We propose a new microwave method of dielectric permittivity measurement in a small volume (less than 5 × 10−2 cm3) of a high loss liquid sample. The method is based on the use of the hemispherical dielectric filled resonator, which contains a small hemispherical central cavity filled with the measured liquid. The characteristic equation for eigenfrequencies of electromagnetic oscillations in this resonator has been obtained and analysed. On this basis, the operating mode of oscillations and optimal sizes of the measuring cavity and resonator have been found. We discovered the effect of electromagnetic field extrusion of the small central cavity filled with the liquid at large values of the real and imaginary parts of the dielectric permittivity. The method has been implemented experimentally in the X band. The found theoretical effect of the field extrusion has been confirmed experimentally. The equation for the calculation of the complex dielectric permittivity of a liquid via the measured values of the resonator quality factor and resonant frequency has been found.

The propagation of an electromagnetic wave in a dielectric rod placed in a high loss liquid was studied theoretically and experimentally. It is shown that the wave has a bulk character in the rod and a surface character in the liquid. The attenuation and phase velocity of this wave have strong dependence upon the dielectric properties of the liquid and the rod, while the phase velocity of this wave exceeds the light velocity in the rod material. It enables one to consider the studied wave to be similar to the Zenneck wave. A characteristic equation for the structure under study was derived and analyzed. The attenuation and phase velocity of this wave in the presence of distilled water and a water–ethanol solution were measured. Owing to these data, the real and imaginary parts of the complex permittivity of high loss liquids under test were determined. We have good agreement between the theoretical and experimental results. A differential dielectrometer based on the usage of the Zenneck wave was designed. Thus, the complex permittivity of high loss liquids with sufficiently high accuracy can be obtained. It is also possible to record a rather small difference between two similar liquids according to their dielectric properties.

A measuring resonator in the form of a dielectric sphere is proposed for the measurement of low dielectric losses in the millimetre-wave range in liquids. The dielectric sphere resonator (DSR) was made from sapphire crystal with extremely low dielectric losses in the millimetre-wave range. Owing to this super-high-quality oscillations of 'whispering gallery' type are excited in a DSR. The spatial distributions of the electric and magnetic field strengths of E -and H -type oscillations both inside the sphere and in the surrounding liquid are considered. The expression connecting the measured quality of the DSR and the dielectric loss angle of the liquid is found. The condition for the choice of optimal parameters of the resonator for the measurement of the dielectric losses in various liquids is obtained also. The DSR method for the measurement of low dielectric losses in the millimetre-wave range in liquids is described.