4. Open resonator with a segment of rectangular waveguide

A new electrodynamic system appears when inserting the segment of the short-circuited rectangular waveguide in the center of one of the ОR mirrors [24]. Cross-section sizes of the waveguide a � b are chosen by the condition of the peak efficiency of the ТЕ<sup>10</sup> mode excitation by the fundamental mode ТЕМ00q. One can consider such ОR as a resonant cell for measurement of composite materials and biological liquids electromagnetic specifications as well as to control the quality of food stuff in millimeter and in sub-millimeter ranges.

We consider the hemispherical ОR with a rectangular waveguide located in the center of the flat mirror. Reflection from the waveguide horn is neglected. We consider the resonator mirrors apertures as an infinite one. Omitting intermediate computations, we write down in the final form the expression, determining efficiency of the TE10 mode excitation in the waveguide of the OR, using the TEM00<sup>q</sup> mode [25].

$$\eta = \frac{16\pi}{\tilde{a}\tilde{b}} \mathcal{O}^2 \left(\frac{\tilde{b}}{2}\right) \left\{ e^{-\left(\pi/2\tilde{a}\right)^2} + \frac{e^{-\left(\tilde{a}/2\right)^2}}{2} \left[ \mathcal{W}^\* \left(\frac{\pi}{2\tilde{a}} + i\frac{\tilde{a}}{2}\right) - \mathcal{W}\left(\frac{\pi}{2\tilde{a}} + i\frac{\tilde{a}}{2}\right) \right] \right\} \tag{20}$$

Block diagram of the experimental setup, which was used for carrying out research of the hemispherical ОR with the segment of the oversized rectangular waveguide, is shown in

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

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47

The ОR is formed by the flat mirror 5, having aperture 60 mm, and by the spherical focusing mirror 4, having a curvature radius R = 113 mm and aperture 60 mm. In the center of the flat mirror, the segment of the oversized short-circuited rectangular waveguide 6 is located, crosssection sizes of which have been chosen in such a way to meet the peak efficiency condition of the ТЕ<sup>10</sup> mode excitation by the fundamental mode of the ОR. As it turned out, for presented dimensions of the resonator at λ ¼ 4.203 mm and L=R ¼ 0.7 (in [26] it was shown that approximately at such normalized distance between mirrors of the hemispherical ОR, the Q-factor of the fundamental mode is maximal) such condition corresponds to a ¼ 23.7 mm and b ¼ 16.5 mm. The plunge 7 provides changing the waveguide length. Taking into account the dimensions of the waveguide, such ОR will be the most promising in the short-wave part

The resonator is excited by the slot coupling element, having sizes 3.6 � 0.16 mm, located in the center of the spherical mirror. The adjusting attenuator 2 is included into the setup for decoupling of the frequency generator and the resonator. Alignment to resonance is implemented by moving the spherical mirror 4 with the elements of the waveguide along the resonator axis. The input waveguide is oriented in such a manner that the vector E of the

Receiving transmission line consists of the auxiliary line of the directional coupler 3, measuring polarizing attenuator 8, detector 10, resonant amplifier 11 and oscillograph 12. The resonant wavemeter 9 is included into the setup for monitoring frequency of the high-frequency generator 1. A double-stub matcher 13 is installed in the branch of the matched load 14 of the directional couplers 3. The photo of the OR and the experimental unit is represented in

The above-described procedure is used for computing of the resonant reflection factor of the resonator. Results of measurement of the resonant reflection factor on the distance between mirrors L=R of the hemispherical ОR, are shown in Figure 13 (curve 1). In the resonator, ТЕМ00<sup>q</sup> mode is excited. Identification of the oscillations modes was performed using the

fundamental mode ТЕ<sup>10</sup> is orthogonal to the plane of the drawing (Figure 11).

Figure 11.

Figure 12.

of millimeter and sub-millimeter ranges.

Figure 11. Block diagram of the experimental unit.

Here, w<sup>0</sup> is the radius of the beam waist of the fundamental mode on the flat mirror, ~a ¼ a=w0; <sup>~</sup><sup>b</sup> <sup>¼</sup> <sup>b</sup>=w0; <sup>Ф</sup> <sup>~</sup>b=2<sup>Þ</sup> � is the probability integral and W½ðπ=2~aÞ þ ið � ~a=2Þ is the integral of the complex argument probability.

Dependence <sup>η</sup> <sup>~</sup>a; <sup>~</sup>b<sup>Þ</sup> � , computed using (Eq. (20)), is presented in Figure 10. As evident from the figure, at <sup>~</sup><sup>a</sup> <sup>¼</sup> 2.844 and <sup>~</sup><sup>b</sup> <sup>¼</sup> 1.98, the efficiency of the ТЕ<sup>10</sup> mode excitation in the rectangular waveguide, located in the center of the ОR flat mirror, using ТЕМ00<sup>q</sup> fundamental mode of the resonator is maximal and equal to 0.881.

As a result of the theoretical analysis, it was demonstrated that the efficiency of the ТЕ<sup>10</sup> mode excitation in the segment of the rectangular waveguide, using the ОR fundamental oscillation, can amount the value about 90%. Therefore, such resonant system should have good selective properties, that is, an advantage for the analysis of dielectric samples with high losses. Besides, since the cross-section sizes a � b of the rectangular waveguide segment several times exceed radius of the beam waist w<sup>0</sup> of the fundamental ОR mode, then it should be considered as the oversized.

In such ОR, losses should increase, since ohmic losses in the walls of the rectangular waveguide segment are added. It would result in a decrease of the loaded Q-factor QL and, as a consequence, in decrease of the resonant system sensitivity. Therefore, in order to understand how the rectangular waveguide segment will influence the spectral and energy specifications of the considered resonant system, experimental researches have been carried out [25].

Figure 10. Efficiency of TE10 mode excitation in the rectangular waveguide versus its cross-section sizes.

Block diagram of the experimental setup, which was used for carrying out research of the hemispherical ОR with the segment of the oversized rectangular waveguide, is shown in Figure 11.

The ОR is formed by the flat mirror 5, having aperture 60 mm, and by the spherical focusing mirror 4, having a curvature radius R = 113 mm and aperture 60 mm. In the center of the flat mirror, the segment of the oversized short-circuited rectangular waveguide 6 is located, crosssection sizes of which have been chosen in such a way to meet the peak efficiency condition of the ТЕ<sup>10</sup> mode excitation by the fundamental mode of the ОR. As it turned out, for presented dimensions of the resonator at λ ¼ 4.203 mm and L=R ¼ 0.7 (in [26] it was shown that approximately at such normalized distance between mirrors of the hemispherical ОR, the Q-factor of the fundamental mode is maximal) such condition corresponds to a ¼ 23.7 mm and b ¼ 16.5 mm. The plunge 7 provides changing the waveguide length. Taking into account the dimensions of the waveguide, such ОR will be the most promising in the short-wave part of millimeter and sub-millimeter ranges.

The resonator is excited by the slot coupling element, having sizes 3.6 � 0.16 mm, located in the center of the spherical mirror. The adjusting attenuator 2 is included into the setup for decoupling of the frequency generator and the resonator. Alignment to resonance is implemented by moving the spherical mirror 4 with the elements of the waveguide along the resonator axis. The input waveguide is oriented in such a manner that the vector E of the fundamental mode ТЕ<sup>10</sup> is orthogonal to the plane of the drawing (Figure 11).

Receiving transmission line consists of the auxiliary line of the directional coupler 3, measuring polarizing attenuator 8, detector 10, resonant amplifier 11 and oscillograph 12. The resonant wavemeter 9 is included into the setup for monitoring frequency of the high-frequency generator 1. A double-stub matcher 13 is installed in the branch of the matched load 14 of the directional couplers 3. The photo of the OR and the experimental unit is represented in Figure 12.

The above-described procedure is used for computing of the resonant reflection factor of the resonator. Results of measurement of the resonant reflection factor on the distance between mirrors L=R of the hemispherical ОR, are shown in Figure 13 (curve 1). In the resonator, ТЕМ00<sup>q</sup> mode is excited. Identification of the oscillations modes was performed using the

Figure 11. Block diagram of the experimental unit.

mirrors apertures as an infinite one. Omitting intermediate computations, we write down in the final form the expression, determining efficiency of the TE10 mode excitation in the wave-

Here, w<sup>0</sup> is the radius of the beam waist of the fundamental mode on the flat mirror, ~a ¼ a=w0;

figure, at <sup>~</sup><sup>a</sup> <sup>¼</sup> 2.844 and <sup>~</sup><sup>b</sup> <sup>¼</sup> 1.98, the efficiency of the ТЕ<sup>10</sup> mode excitation in the rectangular waveguide, located in the center of the ОR flat mirror, using ТЕМ00<sup>q</sup> fundamental mode of the

As a result of the theoretical analysis, it was demonstrated that the efficiency of the ТЕ<sup>10</sup> mode excitation in the segment of the rectangular waveguide, using the ОR fundamental oscillation, can amount the value about 90%. Therefore, such resonant system should have good selective properties, that is, an advantage for the analysis of dielectric samples with high losses. Besides, since the cross-section sizes a � b of the rectangular waveguide segment several times exceed radius of the beam waist w<sup>0</sup> of the fundamental ОR mode, then it should be considered as the

In such ОR, losses should increase, since ohmic losses in the walls of the rectangular waveguide segment are added. It would result in a decrease of the loaded Q-factor QL and, as a consequence, in decrease of the resonant system sensitivity. Therefore, in order to understand how the rectangular waveguide segment will influence the spectral and energy specifications

of the considered resonant system, experimental researches have been carried out [25].

Figure 10. Efficiency of TE10 mode excitation in the rectangular waveguide versus its cross-section sizes.

<sup>2</sup> <sup>W</sup><sup>∗</sup> <sup>π</sup>

2~a þ i ~a 2 � �

is the probability integral and W½ðπ=2~aÞ þ ið � ~a=2Þ is the integral of the

, computed using (Eq. (20)), is presented in Figure 10. As evident from the

� � � � <sup>8</sup>

� <sup>W</sup> <sup>π</sup> 2~a þ i ~a 2 9 = ;

(20)

guide of the OR, using the TEM00<sup>q</sup> mode [25].

<sup>Ф</sup><sup>2</sup> <sup>~</sup><sup>b</sup> 2 !

e �ð Þ <sup>π</sup>=<sup>2</sup>~<sup>a</sup> <sup>2</sup>

46 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

< : þ e �ð Þ <sup>~</sup>a=<sup>2</sup> <sup>2</sup>

<sup>η</sup> <sup>¼</sup> <sup>16</sup><sup>π</sup> ~a~b

complex argument probability.

�

resonator is maximal and equal to 0.881.

<sup>~</sup><sup>b</sup> <sup>¼</sup> <sup>b</sup>=w0; <sup>Ф</sup> <sup>~</sup>b=2<sup>Þ</sup> �

Dependence <sup>η</sup> <sup>~</sup>a; <sup>~</sup>b<sup>Þ</sup>

oversized.

Dependence Г<sup>r</sup> ¼ ψð Þ L=R for the same mode when segment of the oversized rectangular waveguide is located in the center of the flat resonator mirror (curve 2) is shown in that diagram. The segment length is S ¼ 19.082 mm, which accounts nine-and-half waveguide wavelengths. At the

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

difference does not exceed 0.5%. The length of the waveguide is chosen in such a way to remove reflection of the Gaussian beam from the plunge, like from the second resonator mirror. Presence of the rectangular waveguide segment results in an increase of the ОR ohmic losses in the whole tuning range. It is seen from a comparison of the reflection factors of the considered resonator (curve 2) and the empty hemispherical ОR (curve 1). In whole range of the resonator tuning, only the fundamental mode is excited, which confirms the above-stated conclusion about selective properties of the ОR with the segment of the oversized rectangular waveguide. That conclusion follows from the absence of the Г<sup>r</sup> abrupt changes, which, as stated earlier, are caused by interaction of the considered mode with other modes of the resonant system. From the presented diagram one can see, that at the distance between resonator mirrors L=R ¼ 0.276, the reflection factor has the minimum value equal to 0.329. When defining cross-section sizes of the rectangular waveguide, we supposed L=R ¼ 0.7. The radius of the fundamental mode beam waist on the

From this relation, it follows that w<sup>0</sup> will be the same at L=R ¼ 0.7 and L=R ¼ 0.3. Since in such resonator only the fundamental mode exists, then such behavior of Г<sup>r</sup> is related to efficiency of the waveguide mode ТЕ<sup>10</sup> excitation by means of the ОR mode ТЕМ0015. The difference between experimentally obtained value L=R ¼ 0.276 and the computed one (in this case L=R ¼ 0.3), at which η should have its peak value, and accounts for 8%. Such difference shows good agreement

The dependence of reflection from resonator on the length of the oversized rectangular waveguide segment for certain mode is of the practical interest as well. We assume that in the hemispherical ОR (Figure 13, curve 1), a no degenerate mode should exist. Moreover, the distance between resonator mirrors should correspond to low diffraction losses. Therefore, in terms of the diagram presented in Figure 13, we choose the mode ТЕМ<sup>0016</sup> (L=R = 0.295, Г<sup>r</sup> ¼

Figure 14. Dependence of reflectivity factor Г<sup>r</sup> on the waveguide half waves number m, keeping along rectangular

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � ð Þ λ=2a

q

2

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). Apparently, the

49

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>q</sup> � � <sup>r</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L <sup>R</sup> <sup>1</sup> � <sup>L</sup> R

[28].

λ πR

same time, calculated value S ¼ 9λw=2 ¼ 18.988 mm (λ<sup>w</sup> ¼ λ=

flat mirror of the hemispherical ОR is defined by the expression w<sup>0</sup> ¼

between computational and experimental results.

waveguide for ТЕМ<sup>0016</sup> mode of the ОR oscillations.

0.257). Results of the measurements are presented in Figure 14.

Figure 12. The photo of the OR with the segment of rectangular waveguide and the experimental unit.

Figure 13. Dependencies of the reflection factor Г<sup>r</sup> on the distance between mirrors L=R for TEM00q mode in the hemispherical ОR (1) and resonator with the segment of the oversized waveguide (2).

perturbation technique [13]. The technique described in [27] was applied for the definition of the Г<sup>r</sup> character.

As can be seen from Figure 13, with decrease of the distance between mirrors, the reflection factor from the resonator diminishes. It is related to the reduction of the diffraction and ohmic losses in the resonant system. Exceptions include the cases of the interaction of the considered oscillation with other oscillations excited in the ОR (L=R ¼ 0.351, L=R ¼ 0.259, L=R ¼ 0.183, L=R ¼ 0.089), that it is displayed in the stepwise change of the Гr. The distance between mirrors L=R ¼ 0.501 corresponds to the semi-confocal geometry of the resonator. The increase of the number of modes interacting with ТЕМ00<sup>q</sup> mode at L=R < 0.3 is related with reduction of the losses in the resonant system for specified distances between reflectors.

Dependence Г<sup>r</sup> ¼ ψð Þ L=R for the same mode when segment of the oversized rectangular waveguide is located in the center of the flat resonator mirror (curve 2) is shown in that diagram. The segment length is S ¼ 19.082 mm, which accounts nine-and-half waveguide wavelengths. At the same time, calculated value S ¼ 9λw=2 ¼ 18.988 mm (λ<sup>w</sup> ¼ λ= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � ð Þ λ=2a 2 q ). Apparently, the difference does not exceed 0.5%. The length of the waveguide is chosen in such a way to remove reflection of the Gaussian beam from the plunge, like from the second resonator mirror. Presence of the rectangular waveguide segment results in an increase of the ОR ohmic losses in the whole tuning range. It is seen from a comparison of the reflection factors of the considered resonator (curve 2) and the empty hemispherical ОR (curve 1). In whole range of the resonator tuning, only the fundamental mode is excited, which confirms the above-stated conclusion about selective properties of the ОR with the segment of the oversized rectangular waveguide. That conclusion follows from the absence of the Г<sup>r</sup> abrupt changes, which, as stated earlier, are caused by interaction of the considered mode with other modes of the resonant system. From the presented diagram one can see, that at the distance between resonator mirrors L=R ¼ 0.276, the reflection factor has the minimum value equal to 0.329. When defining cross-section sizes of the rectangular waveguide, we supposed L=R ¼ 0.7. The radius of the fundamental mode beam waist on the

flat mirror of the hemispherical ОR is defined by the expression w<sup>0</sup> ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi λ πR ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L <sup>R</sup> <sup>1</sup> � <sup>L</sup> R <sup>q</sup> � � <sup>r</sup> [28]. From this relation, it follows that w<sup>0</sup> will be the same at L=R ¼ 0.7 and L=R ¼ 0.3. Since in such resonator only the fundamental mode exists, then such behavior of Г<sup>r</sup> is related to efficiency of the waveguide mode ТЕ<sup>10</sup> excitation by means of the ОR mode ТЕМ0015. The difference between experimentally obtained value L=R ¼ 0.276 and the computed one (in this case L=R ¼ 0.3), at which η should have its peak value, and accounts for 8%. Such difference shows good agreement between computational and experimental results.

The dependence of reflection from resonator on the length of the oversized rectangular waveguide segment for certain mode is of the practical interest as well. We assume that in the hemispherical ОR (Figure 13, curve 1), a no degenerate mode should exist. Moreover, the distance between resonator mirrors should correspond to low diffraction losses. Therefore, in terms of the diagram presented in Figure 13, we choose the mode ТЕМ<sup>0016</sup> (L=R = 0.295, Г<sup>r</sup> ¼ 0.257). Results of the measurements are presented in Figure 14.

perturbation technique [13]. The technique described in [27] was applied for the definition of

Figure 13. Dependencies of the reflection factor Г<sup>r</sup> on the distance between mirrors L=R for TEM00q mode in the

Figure 12. The photo of the OR with the segment of rectangular waveguide and the experimental unit.

48 Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing

As can be seen from Figure 13, with decrease of the distance between mirrors, the reflection factor from the resonator diminishes. It is related to the reduction of the diffraction and ohmic losses in the resonant system. Exceptions include the cases of the interaction of the considered oscillation with other oscillations excited in the ОR (L=R ¼ 0.351, L=R ¼ 0.259, L=R ¼ 0.183, L=R ¼ 0.089), that it is displayed in the stepwise change of the Гr. The distance between mirrors L=R ¼ 0.501 corresponds to the semi-confocal geometry of the resonator. The increase of the number of modes interacting with ТЕМ00<sup>q</sup> mode at L=R < 0.3 is related with reduction of

the losses in the resonant system for specified distances between reflectors.

hemispherical ОR (1) and resonator with the segment of the oversized waveguide (2).

the Г<sup>r</sup> character.

Figure 14. Dependence of reflectivity factor Г<sup>r</sup> on the waveguide half waves number m, keeping along rectangular waveguide for ТЕМ<sup>0016</sup> mode of the ОR oscillations.

From the figure, one can see that moving the plunge from the surface of the flat mirror (m ¼ 0) along the waveguide up to four waveguide half waves (m ¼ 4), increase of the losses is observed (Г<sup>r</sup> growth from 0.257 till 0.322). This apparently could be explained by transformation of the Gaussian beam into the waveguide wave. At further increasing of the waveguide segment length up to m ¼ 8, there is insignificant growth of loss is caused by ohmic losses in the waveguide segment. If m is increased further, then, Г<sup>r</sup> is almost without any change.

of liquid dielectrics. For performing measurements, the pipe with the sample is placed into the oversized rectangular waveguide parallel to the vector of electric intensity of the ТЕ<sup>10</sup> mode. For reduction of the losses inserted into the resonant system, it can be displaced to one of the

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51

The A.Ya. Usikov's Institute for Radio Physics and Electronics of the NAS of Ukraine, Kharkiv,

[1] Vendik IB, Vendik OG. Metamaterials and their application in the technology of

[2] Kuzmichev IK, Glybytskiy GM, Melezhik PN. Open cavity for measuring the dielectric permittivity of materials. Patent 67978 A Ukraine, МПК<sup>7</sup> G 01 R 27/26; 2004 (in Russian)

[3] Kuzmichev IK, Melezhik PN, Poedinchuk AY. An open resonator for physical studies. International Journal of Infrared and Millimeter Waves. 2006;27:857-869. DOI: 10.1007/

[4] Il'inckiy AS, Slepyan GY. Oscillations and Waves in the Electrodynamic Systems with the

[5] Kuzmichev IK, Popkov AY. An open resonator for measuring electrical physical parameters of substances. Part I. Resonator model. Fizicheskie Osnovy Priborostroeniy. 2013;2:94-

[6] Kuzmichev IK, Popkov AY. Quasi-Optical Resonance Systems in the Millimeter Range Technology. Germany: LAP LAMBERT Academic Publishing; 2014. p. 173 (in Russian)

[7] Yegorov VN. Resonance methods in dielectric research in microwave range. Pribory and

[8] Wainshtein LА. Electromagnetic Waves. Moskow: Radio i Svyaz; 1988. p. 440 (in Russian)

[9] Popkov AY, Poyedinchuk AY, Kuzmichev IK. Resonant cavities in the form of bodies of revolution of complex geometry: A numerical algorithm for calculating the spectrum. Telecommunications and Radio Engineering. 2010;69:341-354. DOI: 10.1615/Telecom

superhigh frequencies (survey). ZhTF. 2013;83:3-28 (in Russian)

Losses. Moskow: Izd-vo MGU; 1983. p. 232 (in Russian)

Tekhnika Eksperimenta. 2007;2:5-38 (in Russian)

side walls of the waveguide.

Kuzmichev Igor K.\* and Popkov Aleksey Yu.

\*Address all correspondence to: kuzmichev.igr@i.ua

Author details

Ukraine

References

s10762-006-9122-7

103 (in Russian)

RadEng.v69.i4.40

Considered here resonant system will be the most promising at the analysis of biological liquids and food stuffs, the basic element of which is water (wines, juices, drinks). For carrying out measurements, a pipe made of the material of lower permittivity than that of a sample is placed into the oversized rectangular waveguide parallel to the vector of electric field intensity of the ТЕ<sup>10</sup> mode. For reduction of losses inserted to the resonant system, it can be displaced to one of the side walls of the waveguide.

## 5. Conclusions

The cavity with the dielectric layer, being an electrodynamic model of the hemispherical ОR with the segment of the oversized circular waveguide and dielectric bead, is considered in this chapter. As a result of the carried out theoretical analysis, it is shown that dependence of the frequency upon the thickness of the dielectric bead, located on the bottom of the cavity cylindrical part, has a quasi-periodic behavior. Such behavior is related to the amplitude distribution of Е<sup>φ</sup> - component of the axial-symmetric mode at the top of the sample. The weak dependence of frequency on the bead thickness takes place when near to the sample top the node of the electric field component of the standing wave in the resonator is located. If in the area of the sample top, there is an antinode of the electric field component of the standing wave in the resonator, and the frequency dependence on the sample thickness is strong. Measurement of the permittivity and the tangent losses of beads, made of Teflon and Plexiglas at the various thickness, using the ОR with the segment of the oversized circular waveguide, have been carried out. Obtained values ε<sup>0</sup> <sup>2</sup> and tanδ are in agreement with the data of the other authors. In such a way, the proposed resonant system can be applied for measurement of electromagnetic parameters of substances in the short wave part of the millimeter and submillimeter ranges, both with high and with low losses.

The hemispherical ОR, with the segment of the rectangular oversized waveguide located in the center of the flat mirror, has been considered in this chapter as well. As a result of the carried out theoretical analysis, it was demonstrated that efficiency of the ТЕ<sup>10</sup> mode excitation in such waveguide by means of the resonator fundamental mode ТЕМ00q can reach the value ~90% at cross-section sizes <sup>~</sup><sup>a</sup> <sup>¼</sup> 2.844 and <sup>~</sup><sup>b</sup> <sup>¼</sup> 1.98. The experimental researches carried out by the authors made it possible to establish that the resonator with the segment of the rectangular oversized waveguide possesses selective properties in the wide band of frequencies. Presence of the rectangular waveguide segment does not result in an abrupt increase of the ohmic losses. These circumstances are advantageous for application of such resonator for research of dielectric substances. Considered resonant system will be the most promising for the analysis of liquid dielectrics. For performing measurements, the pipe with the sample is placed into the oversized rectangular waveguide parallel to the vector of electric intensity of the ТЕ<sup>10</sup> mode. For reduction of the losses inserted into the resonant system, it can be displaced to one of the side walls of the waveguide.
