1. Introduction

Measurement of electromagnetic properties of existing and novel materials in new frequency ranges is an important issue of the day. Recently emerged new class of artificial materials composite materials (composites) are characterized by the negative refraction coefficient. Investigations showed that devices based on such materials can possess entirely unique

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

properties and characteristics [1]. Caused by technology progress, advance of composite materials into millimeter and especially sub-millimeter ranges requires knowing of information about their electromagnetic characteristics. On the other hand, the real part of dielectric permittivity ε<sup>0</sup> and dielectric loss-angle tangent tan δ of water, which is the main component of the whole series of food stuff and biological liquids, decrease with the wavelength shortening. Therefore, for effective control of their quality, we also should move to the specified ranges of the wavelengths. For measurement of electromagnetic characteristics of such substances, the application of the resonant techniques is needed due to their higher accuracy. The main point of such methods consists of observation of resonant curves of the oscillatory circuit, in which the sample of the studied substance is placed.

On the basis of the all above-stated, we can summarize that the goal of investigations, performed in this chapter, is theoretical and experimental research of the considered ОR, which will allow to measure, in millimeter and in sub-millimeter ranges, the electromagnetic characteristics of composite materials and biological liquids, as well as to control the quality of

Resonant Systems for Measurement of Electromagnetic Properties of Substances at V-Band Frequencies

http://dx.doi.org/10.5772/intechopen.73643

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In the ОR, axial-symmetric modes are confined by caustics and hence they are with low diffraction losses. Placing of perfectly conducting boundary (Figure 1, dotted lines) in the area of exponentially vanishing intensity, almost does not affect the field pattern in OR. Our method

Therefore, the task transforms to the study of the cavity resonator and approximate solution for the OR is achieved by selecting only modes with near axis distributed intensity (exponentially vanishing near conical boundary) from the cavity spectrum. We noticed that such

Let us consider the cavity as a body of revolution with perfectly conducting boundary and dielectric bead located in the bottom of the cylindrical part (Figure 1). We assume that the resonator is filled with a homogeneous isotropic medium having specific dielectric and magnetic conductivities ε1, μ<sup>1</sup> in the area (1) and ε2, μ<sup>2</sup> in the area (2). We consider only axialsymmetric TE modes with Eφ, Hr and Ez are components of the electromagnetic field in the

cylindrical coordinate system with the axis z, coinciding with the axis of symmetry.

approach for the electrodynamic model of the ОR was proposed in [4].

food stuff.

2.1. Resonator model

is based on such physical principles.

2. Open resonator with a dielectric bead

Figure 1. Geometric model of the OR with the dielectric bead.

Comparing the resonance curves corresponding to the cases of resonator with and without sample allows determining both ε<sup>0</sup> and tg δ using the Q-factor and frequency shift. Open resonators (ОR) are used as circuits in millimeter and sub-millimeter ranges for such measurements. The peculiarity of such resonant systems consists of the fact that, apart from high Qfactor, their geometrical dimensions account a few tens of wavelengths, and coupling with free space provides an additional mode selection and free access to the resonant volume. However, such resonant systems are applicable to use just for investigations of substances with low losses. In the case of high losses, sample thickness should not exceed the size of the skin layer since it can result in oscillation suppression in such resonant systems. This circumstance imposes limitations to the application of the ОR in the research of electromagnetic characteristics of composite materials and biological liquids, quality control of food stuffs since they are characterized by high losses. Therefore, the most promising resonant system to use for investigations of such substances is the ОR proposed in [2, 3]. It represents symbiosis of the ОR and the segment of the oversized waveguide, which could be both circular and rectangular. A distinctive feature of such resonant systems is that they are characterized by the single frequency response in the wide range of frequencies [3]. It is an advantage at investigations of electromagnetic characteristics of substances. At placement of the sample in the waveguide part of the ОR, the measurement accuracy increases due to keeping high Q-factor, and therefore, the range of the analyzed values ε<sup>0</sup> and tanδ extends.

The studied sample having the shape of a bead is located in the bottom of the circular waveguide segment, in which there is a plane wave front of the propagating ТЕ<sup>01</sup> mode. It allows measuring samples, the thickness of which exceeds the wavelength of the excited oscillation. At the research of substances with the application of the ОR having a cylindrical shape, difficulties related to their positioning in resonant volume may arise. At each measurement, the samples should be placed in the area with the same electric field intensity. The proposed resonator allows solving of this problem. The sample should be located along the ОR axis, where the electric field intensity of the excited oscillation is minimal. It provides analyzing of substances with high losses. In the case of the ОR having the segment of the oversized rectangular waveguide with the ТЕ<sup>10</sup> mode, it is expedient to use the samples of a cylindrical shape. They should be located in the waveguide part parallel to the vector of the electric field intensity of the mode.

On the basis of the all above-stated, we can summarize that the goal of investigations, performed in this chapter, is theoretical and experimental research of the considered ОR, which will allow to measure, in millimeter and in sub-millimeter ranges, the electromagnetic characteristics of composite materials and biological liquids, as well as to control the quality of food stuff.
