The accurate measurement of permittivity by means of an open resonator

TLDR: In this paper, a method for the measurement of permittivity at microwave frequencies using an open resonator is proposed, and an experimental procedure is developed, and a thorough experimental study of the method has shown that experimental errors can be made very small indeed.

Abstract: A method for the measurement of permittivity at microwave frequencies using an open resonator is proposed. The theory of the method is developed, and an experimental procedure is evolved and justified. It is shown that the present method has advantages over other open resonator methods which have been proposed, and a thorough experimental study of the method has shown that experimental errors can be made very small indeed. Since the very beginnings of modern microwave techniques in the 1940s, many alternative methods of measuring the complex permittivity of gases, liquids and solids have been devised. Most of these have employed a cavity resonator or a length of waveguide as a means of defining the configuration of the electromagnetic field with the precision needed for accurate quantitative analysis of the experimental results. Although very satisfactory results have been obtained using such methods, they become increasingly difficult to apply as the wavelength decreases. For the solid dielectric materials with which the present paper is exclusively concerned, a major problem is the accurate machining of a specimen of the material to fit closely into the resonator or waveguide. Even very small air gaps between the dielectric material and the metal wall can cause large errors, and this problem is obviously more serious at shorter wavelengths since the fractional error corresponding to a given absolute error in the dimensions of the specimen is inversely proportional to the wavelength. Another difficulty is encountered at very high frequencies in the resonant cavity method of measurement of the loss tangent of a dielectric material when this has a small value. The accuracy of measurement begins to decrease when the loss tangent falls below the reciprocal of the Q factor of the empty resonant cavity. Since this Q factor varies as fo , where f0 is the resonant frequency it is clear that the method is unsatisfactory for low-loss materials at high frequencies. The pioneer work of Culshaw & Anderson (I962) on the measurement of permittivity and dielectric loss with a millimetre wave Fabry-Perot interferometer was the first successful attempt to use an open resonator for this purpose. However, the use of parallel-plane mirrors rather than spherical mirrors gives rise to a field distribution within the resonator which is not readily amenable to mathematical analysis. Moreover, the diffraction losses are much larger than is the case when spherical mirrors are used in a suitable configuration.