RU2062476C1 - Method of measurement of dielectric permittivity of sheet dielectric - Google Patents

Abstract

FIELD: study of materials. SUBSTANCE: method can be used for study of flat and non-flat sheet dielectrics. It consists in excitation of surface electric wave of any type in sheet dielectric 3 placed on metal backing 4 with smooth surface in parallel to surfaces of sheet dielectric 3 with the aid of SHF generator 1 and its modulation by pulse sequence of videopulse generator 2 and surface electric wave exciter 5 connected to output of SHF generator 1 and located in sheet dielectric 3, in registration of distribution curve Φ(h) of intensity of field of surface electric wave in free space above surface of sheet dielectric 3 in direction of normal to its surface with height h≥λ_es, where λ_es is length of excited surface electric wave with the help of high-resistance probe 6 and detector 8 connected in series and put on translation device and indicator- register 9 which is synchronized by pulses from video-pulse generator 2, in measurement of values U₁,U₂...U_N, of intensities of field on curve J(h) in points h₁,h₂...h_N from base of normal, in computation of lateral wave number pp_i of surface electric wave in free space over sections Δh_i= h_i+1-h_i of normal and in determination of dielectric permittivity ε_ri in each section Δh_i and of averaged value ε_ri of sheet dielectric from relations. EFFECT: increased accuracy of measurements, expanded class of examined dielectrics thanks to use of surface electric waves of higher types. 3 dwg, 2 tbl

Description

 The present invention relates to the field of radio engineering, and more specifically to the field of research of materials by radio engineering methods. It can be used in the study of flat and non-planar sheet dielectrics (LD), as well as in the study of the propagation of electromagnetic waves (EMW) in such dielectrics.

 A known method for determining the dielectric constant (DP) of an LD [1] comprising irradiating an LD of a linearly polarized electromagnetic wave through an inserted dielectric prism with an angle at a base parallel to the surface of the LD that is greater than the critical angle, dividing the electromagnetic wave reflected from the surface of the LD into orthogonal components, determining the ellipticity of the reflected electromagnetic wave, a change in the distance d between the base of the prism and the surface of the LD, recording the value of the distance d at which the ellipticity of the reflected electromagnetic wave takes a minimum the determination and determination of the LD of the LD by the well-known dependence connecting the DP with the value of d.

 The known device for determining the DP LD contains [1] a microwave generator, a polarizer, the input of which is connected to the output of the microwave generator, a first radio line consisting of a sequentially located output of a polarizer, a first angular rotation (UP) and a dielectric prism, a second radio line consisting of sequentially located a dielectric prism, a second UE and a reflected wave polarization divider (DPO), the first and second signal converters (PS), the inputs of which are connected to the outputs of the DPO, the meter of the ratio of two voltage Ii (ION), two inputs of which are connected to the outputs of the first and second substations, serially connected extremator and a clock generator (GTI), connected to the ION output, serially connected counter and recorder connected to the GTI output, a stepper motor, the input of which is connected to the same GTI output, and a measuring table associated with a stepper motor.

The analogue works as follows. The test LD is placed on the measuring table and the LD is brought under the base of the dielectric prism by moving the table. The amplitude-modulated electromagnetic wave from the output of the microwave generator is fed to the polarizer, in which the electromagnetic wave is converted into a linearly polarized wave with the orientation of the vector E at an angle of 45 ^o to the plane of incidence. This EMV using the first UP is sent through the first side face of the dielectric prism to its base and the surface of the LD. The reflected EMV through the second side face is sent to the second unitary enterprise, and from it to the entrance of the DPOV. The separated orthogonal components of the reflected EMW from the output of the DPOV are fed to the inputs of the first and second substations, the converted signals from the outputs of the substations are fed to the ION inputs. From the output of the latter, the signal of the ratio of the two voltages is fed to the extremator, from its output to the input of the GTI. GTI clock pulses are fed to the inputs of a counter with a recorder and a stepper motor. A stepped motor controlled by clock pulses moves the measuring table with the LD perpendicular to the base of the dielectric prism. At the moment of reaching the minimum ellipticity of the reflected EME, the extremator turns off the GTI, and thereby the operation of the stepper motor and the movement of the LD relative to the base of the dielectric prism. The number of clock pulses is read from the counter, the distance d between the base of the dielectric prism and the surface of the LD is calculated from this number. Determined by the known dependence of DP LD.

The disadvantage of the analogue is the frequency limitation associated with the presence of radio lines in the measuring path. The presence of radio lines limits the use of analog in the millimeter and less wavelength ranges, i.e. in the ranges for which the laws of geometrical optics are valid in a limited space, and near radio lines there are no foreign objects reflecting the electromagnetic field propagating along the radio lines and distorting the measurements. For example, in [2] it was shown that such measurements using radio lines are quite correct in the wavelength range λ _o ≅ 3 mm (frequency range f _o ≥100 GHz).

где d толщина исследуемого диэлектрика;
λ_p длина резонансной волны;
s шаг гребенчатой структуры;
t и h ширина и высота зубцов гребенчатой структуры.The closest in technical essence and the achieved positive effect is the selected as a prototype method for measuring the DP of plane-parallel dielectrics [3] which consists in placing the investigated dielectric on a metal comb structure, excitation in the studied plane-parallel dielectric of the lowest type of electric surface wave (PV E), frequency modulation of exciting microwave oscillations, measuring the output of the system "comb plane-insulator structure" resonance frequency f _p and EFINITIONS DP ε _r of the characteristic equation from the formula:

where d is the thickness of the investigated dielectric;
λ _p resonance wavelength;
s step of the comb structure;
t and h are the width and height of the teeth of the comb structure.

 A device for measuring DP according to the prototype comprises [3] a microwave generator with a frequency modulator, a transmitting antenna, the input of which is connected to the output of the microwave generator, a metal comb structure, a receiving antenna and an indicator, to the input of which a receiving antenna output is connected.

The measurement of DP plane-parallel dielectric device of the prototype is as follows. Place the test sheet of plane-parallel dielectric on the comb structure. Frequency-modulated oscillations of the microwave generator through the transmitting antenna excite in the system "comb structure plane-parallel dielectric" PV type E _oo . A frequency-modulated signal that has passed through this system is received by a receiving antenna and fed to an indicator. According to the indications of the indicator, the frequency dependence of the transmission coefficient of the system is built and the resonance frequency f _p is determined from this dependence, and then the wavelength λ _p corresponding to this frequency. Determine the DP of the investigated plane-parallel dielectric by the formula (1).

The prototype eliminates the lack of an analogue and allows one to determine the DP ε _{r of} plane-parallel LDs in the longer wavelength range, for example, decimetric, which is associated with the use of PV. However, the use of a comb type PV of E _oo leads to the fact that the DP can only be measured at resonance frequencies f _p , which are determined by the size of the comb structure and at which the self-matching conditions of the surface impedances of the structure and the LD are satisfied. At other operating frequencies other than resonant f _p , errors sharply increase, and measurements at higher types of waves E _{op are} impossible. In addition, the prototype does not allow the study of non-planar sheet dielectrics, for example, convex or concave.

 The aim of the present invention is to improve the accuracy of measurements and the expansion of the class of studied dielectrics through the use of higher-order PVEs and the measurement of the DP of non-flat LD.

где λ_оп длина возбужденной ПВЕ в свободном пространстве, м;
i порядок следования точек отсчета от основания нормали; a толщина ЛД, м; N число точек отсчета по нормали, N≥3.This goal is achieved by the fact that in the method for measuring the LD of an LD, which consists in the excitation in an LD placed on a metal substrate of a surface electric wave (PVE), measuring the parameters of this wave and determining the DP by calculation, it is new that metal is used as the substrate sheet with a smooth surface, parallel surfaces LD register Φ (h) distribution curve of the field intensity excited PVE in the headspace above the surface of the LD in the direction normal to its surface height h ≥ λ _op, zmeryayut on the transverse wave number p _i PVE at points h _1, h _2, h _N from the base of the normal values of the field intensities U _1, U _2, U _N, calculate Φ (h) of the distribution curve in the free space on the segments normal Δh _i h _{i +1} - h _i and determine the DP ε _ri on each of these segments Δh _i and the average value of ε _r LD from the relations:

where λ _{op the} length of the excited PVE in free space, m;
i the sequence of reference points from the base of the normal; a LD thickness, m; N is the number of reference points along the normal, N≥3.

 The presence of new significant features in the proposed technical solution indicates compliance with its criteria of the invention of "novelty."

 A technical solution is known in which an LD is placed on a metal sheet with a smooth surface parallel to the surfaces of the LD [4, p. 84]. In the known solution, the use of a metal substrate with a smooth surface allows one-sided PVE of any type to be excited in the LD. In the proposed technical solution, the use of a metal sheet with a smooth surface allows, in addition, to determine the dielectric constant of the dielectric, including non-planar, on any type of PVE, which leads to new properties of the proposed object.

A technical solution is known in which the values of the PVE field strengths in free space above the LD surface are measured at different points h _i and these measurements are used to find the localization height of the PVE field near the dielectric surface [4, p. 98] In the proposed technical solution, the values of the PVE field strengths at different points h _{i of the} normal to the surface of the LD are used to determine the DP of the LD in which the PVE is excited, which leads to new properties of the proposed object.

 A technical solution is known in which the number of reference points of the measured quantity N≥3 is selected and the measured value is accelerated by the ensemble of measurements [5] In the proposed technical solution, as well as in the known one, the choice of N≥3 and ensemble averaging increase the measurement accuracy.

Not found in the known technical solutions registration of the distribution curve Φ (h) of the field strength of the excited PVE in free space above the surface of the LD in the direction of the normal to its surface with a height h≥λ _op ; discretization of the determination of the transverse wave number p _{i of} PVE in free space and DP ε _ri along the normal segments Δh _i h _{i + 1} h _i ; the use of the transverse wave number p _i PVE in free space to determine the DP ε _ri ; averaging the electrophysical parameter of the dielectric material over the spatial coordinate.

 These unknown essential features in combination with the known ones allow us to achieve the goal in the proposed technical solution - to increase the accuracy of measurements and expand the functionality.

Improving the accuracy of measurements in the proposed technical solution is achieved through the use of a metal sheet with a smooth surface as an LD substrate; due to registration of the distribution curve Φ (h) of the field strength of the excited PVE in the free space above the LD surface in the direction of the normal to its surface with a height h≥λ _op ; due to the discretization of measurements of the strength U _{i of} the PVE field at points h ₁ , h ₂ , h _N from the base of the normal with a height h≥λ _op with the number of reference points N≥3; due to averaging the DP ε _r over the ensemble of measurements on the spatial coordinate.

The use of a smooth surface of the metal substrate and the distribution curve Φ (h) of the PVE field strength in the free space above the LD surface as factors that increase the measurement accuracy is manifested primarily in the fact that both factors do not assume, as in the prototype, the presence of resonances in the measurement system and with the same accuracy, unlike the prototype, operate at any frequency at which the conditions for the excitation and propagation of the PVE in the metal sheet-dielectric system are satisfied, while the protot n assumes measuring DP LD only at the resonance frequency ω _p, and while avoiding the resonance frequency up or down in frequency PD measurement accuracy decreases in proportion to the frequency offset from the resonance (see Eq. (1) description).

The choice of the normal height h≥λ _op makes it possible to exclude the influence of higher types of PVE waves in comparison with the excited type λ _op , which can also be excited in the LD metal substrate system. It is known [4, p. 98] that in the free space above the LD surface, almost all the transferred PVE energy is localized at a height h _o p ^-1 , where p is the transverse wave number of the PVE in free space. Since for surface waves of the “LD metal substrate” system always p <k _o , where k _o is the wave number of the PVE in free space, then h _o ≅λ _op , that is, the PVE is almost completely localized above the LD surface in space of height h _o ≅λ _op , where λ _{op is the} length of the excited type of PVE in free space. Since the wavelength of the subsequent higher type of PVE, for example, λ _{op + 2} , is much less than the wavelength of the previous type λ _op , the influence of the wave field strength λ _{op + 2} on the measured value of the wave field strength λ _op can only affect the surface of the LD, t e. at the normal point h ₁ closest to the LD surface, at the other points h ₂ , h ₃ , h _N , the field strength is E _{op + 2} <E _op and practically only E _op waves λ _{op are} measured.

And finally, discretization over the height of the normal and averaging over the ensemble of measured values at the spatial coordinate exclude the manifestation of random errors and gross misses. The expansion of the class of studied dielectrics is achieved through the use of a metal sheet with a smooth surface parallel to the surface of the LD as the substrate of the LD; due to the use of the transverse wave number p PVE in free space, calculated by measuring the PVE field strengths on the distribution curve of this field Φ (h), to determine the DP ε _r . Both of these factors make it possible to excite at any frequency at different LD thicknesses any type of PVE wave that can exist in the LD metal substrate system, register the PVE field distribution curve in free space, and measure the field strengths U ₁ , U ₂ , U _N the normal points h ₁ , h ₂ , h _N and in a non-planar LD with parallel surfaces, and the non-planarity of the LD is determined not by measurements, but only by the conditions of excitation and propagation of the PVE in the “LD metal substrate” system. Thus, the proposed technical solution allows to expand the range of working frequencies, the range of working thicknesses of the LD and the shape of this LD, i.e. carry out measurements of RP in non-planar LD with parallel surfaces (for example, heat-protective coating (TZP) of an aircraft at the location of TZP).

 The analysis proves the conformity of the proposed technical solution to the criteria of the invention "significant differences".

 In FIG. 1 shows a structural diagram of the measurements of DP LD; figure 2 distribution curve Φ (h) of the field strength of the PVE in free space above the surface of the LD in the direction normal to its surface; figure 3 is a graphical method for determining the DP by the calculated value of p (a graphical method for solving the characteristic equation).

The measurement of DP LD according to the proposed method is as follows. Place the LD on a smooth metal sheet. Excite in the PVE LD of the desired type by any known method, for example, using an asymmetric vertical vibrator [6] Register the distribution curve Φ (h) of the field strength of the excited PVE in the free space above the LD surface in the direction normal to its surface with a height h> λ _op , for example , h _o ≈1.5 λ _op using any known method, for example, by measuring the PVE field strength with a high-resistance probe [7] along the normal height and plotting with coordinates: the abscissa shows the magnitude of the measured field, the ordinate shows the normal height and from the base (LD surface). Divide the height of the normal into a number of segments at points h ₁ , h ₂ , h _N from the base of the normal, N≥3. At each point h _i measure the magnitude of the field strength PVE U ₁ , U ₂ , U _N. On each of the segments Δh _i h _{i + 1} - h _i calculate the transverse wave number p _i PVE in free space, for example, by the formula [4, p. 98]
p _i = (-lnU _{i + 1} / U _i ) / Δh _i (4).

Determine the DP εr _i on each such segment Δh _i according to the formula (2). Averaging DP ε _r on the spatial coordinate h _o according to the formula (3).

 A device for measuring DP LD according to the proposed method contains a microwave generator (HFM) 1, a video pulse generator (HMI) 2, the output of which is connected to an external modulation input of a MHF 1, LD 3, placed on a metal sheet 4 with a smooth surface parallel to the surfaces of the LD 3, pathogen PVE (VPVE) 5, located in the LD 3, a high-resistance probe 6, placed above the surface of the LD 3, a device 7 for fixing the high-resistance probe 6 and moving it along the normal to the surface of the LD 3, detector 8, to the input of which a high-resistance probe 6 is connected and indicator istrator 9, which is connected to the input of the output detector 8 and output to an input synchronization synchronization AIT 2.

The measurement of DP LD device is as follows. Modify the UHF 1 by the pulse sequence of the GVI 2. Simultaneously with the start of the modulation, the GVI 2 starts the indicator-recorder 9. The radio pulses from the output of the GVV 1 are fed to the input of the UHF 5 to excite the PVE in the LD 3. Register using a high-resistance probe 6, detector 8 and the indicator of registrar 9, the distribution curve Φ (h) of the PVE field strength in free space above the surface of the LD 3, moving the high-resistance probe 6 along the normal to the height h _o using device 7. Divide h _o into N 1 segments at points h ₁ , h ₂ , h _N. Measured at points h _i the field strength of the PVE in free space U ₁ , U ₂ , U _N. Calculate p _i on the segments Δh _i h _{i + 1} h _i , for example, by the formula (4). Εr _i and ε _{r are} determined by formulas (2) and (3).

 As an HFM 1, industrial microwave generators can be used, for example, ГЧ-37А, ГЧ-78, etc. as GVI 2 industrial generators of video pulses, for example G5-15, G5-54, etc. indicator-recorder 9 may be an oscilloscope, for example, C8-17, C1-74, etc. high-resistance probe can be made according to [7] Connection feeders can be made of industrial cables PK50-2-22 or PK5-15-16, etc.

 The R1104.500 laboratory setup for measuring the LD LD according to the proposed method comprises microwave generators of the type ГЧ-37А, ГЧ-78 and ГЧ-79, a video pulse generator G5-54, a 5 mm thick aluminum sheet with a size of 800x1200 mm, a high-resistance probe 1112-L932, a device probe movement 1112.LO15, S8-17 oscilloscope, antenna 1106. L305 in the form of a vertical asymmetric vibrator with a director and a reflector. Below are examples of the determination of DP LD in a laboratory setup P1104.500. Sheets of textolite and fiberglass with a thickness of 0.012 m and a size of 800x1200 mm and fluoroplast-4 with a thickness of 0.012 mm and a size of 400x500 mm were used.

 The measurement results are given in tables 1 and 2.

The measurement error with the C8-17 oscilloscope is δu ≅ ± 10%. 2 shows that the value ε _r determined by formulas (2) and (3) lies within the reference data.

We show that the proposed method is technically implemented and is a technical solution. The characteristic PVE equation propagating in a dielectric sheet placed on a metal substrate with a smooth surface parallel to the LD surfaces has the form [4, p. 80; 6, p. 804]
ε _r pa = qatg (qa) (5)
where ε _{r the} dielectric constant of the LD; p the transverse wave number of the PVE in free space above the surface of the LD, m ^-1 ; a LD thickness, m; q the transverse wave number of the PVE in the dielectric sheet, m ^-1 .

; λ_o длина возбужденной ПВЕ в свободном пространстве, м; ε_r диэлектрическая проницаемость материала ЛД.The wavenumbers p and q are related to the longitudinal wavenumber γ PVE (propagation constant of PVE) and wavenumbers in the free space K _o and in the dielectric K _{d by} known relations [4, p. 80]
p ² = γ ² -K $\genfrac{}{}{0ex}{}{\text{2}}{\text{o}}$ ; q ² = K $\genfrac{}{}{0ex}{}{\text{2}}{\text{d}}$ -γ ² (6)
where K _o = 2π / λ _o ;

; λ _{o the} length of the excited PVE in free space, m; ε _{r is the} dielectric constant of the LD material.

Из выражения (7) найдем решение для q, имеем:

или

Поставим выражение (8a) в характеристическое уравнение (5) ПВЕ, получим

Формула (9) суть формула (2) на стр.4 описания заявки.Add p ² and q ² to get:

From expression (7) we find a solution for q, we have:

or

We put expression (8a) in the characteristic equation (5) PVE, we obtain

Formula (9) is the essence of formula (2) on page 4 of the application description.

From the formula (9) it follows:
a) if the DP ε _r and the thickness a LD and the length λ _{o of the} excited PVE in free space are known, then one can determine the transverse wave number p PVE in free space as the root of the characteristic dispersion equation (9);
b) if the transverse wave number p of the PVE in the free space, the thickness a of the LD and the length λ _{o of the} excited PVE in the free space are known, then the DP ε _r can be determined as the root of the dispersion equation (9). In the proposed method, it is this possibility that is used, because the thickness a LD and the length λ _{o of the} excited PVE in free space are a priori known, which corresponds to the operating frequency f _o : λ _o cT _o , where c 3 • 10 ⁸ m / s; T _o 1 / f _o is the period of the operating frequency, and the transverse wave number p of the PVE in free space is determined by determining the values of the PVE field strengths at several points above the surface of the LD.

Figure 3 shows the solution of equation (9) (finding the root of the equation) for a sheet of fiberglass with a thickness of 0.012 at a frequency f _o 750 MHz.

 Figure 2 shows the distribution curve Φ (h) of the PVE field in free space above the surface of the LD as a function of the height of the normal to the surface of the LD.

 It is known [4, 6, 9] that the PVE does not propagate in free space in the direction normal to the surface of the LD (that is, there is no energy transfer in this direction) if the LD is flat and its curvature is k 0, and it takes place along with the transfer energy along the surface of the LD, energy transfer in the direction normal to the surface of the LD, i.e. radiation in this direction, if the LD is non-planar, i.e. its curvature k ≠ 0. We consider both cases.

 The case of a plane LD with curvature k 0.

In the case of a flat LD, the PVE does not propagate in the direction normal to the surface of the LD, the constant propagated PVE in free space in the direction normal to the LD surface (or the same thing, the transverse wave number p PV in free space) is purely imaginary, and the amplitude PVE fields in free space above the LD surface in the direction of the normal are distributed exponentially:
UU ₀ e ^-ph ,
where U is the amplitude of the PVE field at a height h from the surface;
U _{o the} amplitude of the field on the surface of the LD;
p the transverse wave number of the PVE in free space (the propagation constant of the PVE in free space in the direction normal to the surface of the LD);
h height from the surface of the LD.

Таким образом, определено поперечное волновое число в случае плоского ЛД с кривизной поверхности k 0 (радиус кривизны b k^-1 ∞).Formula (10) implies the possibility of determining the transverse wave number p by measuring the amplitude of the field U _i PVE in free space in the direction of the normal to the surface of the LD at at least two points. In fact, at the point h ₁ from the surface of the LD, the field amplitude is U ₁ U ₀ e ^-ph1 , at h ₂ > h ₁ this amplitude is U ₂ U ₀ e ^-ph2 . Divide U ₂ by U ₁ , we get U ₂ / U ₁ = exp [-p (h ₂ -h ₁ )] = exp (-pΔh). We logarithm the last expression and solve it with respect to p, we get:

Thus, the transverse wave number is determined in the case of a plane LD with a surface curvature k 0 (radius of curvature bk ^-1 ∞).

 The case of non-planar LD with curvature k ≠ 0 (radius of curvature b ≠ 8).

For a non-planar LD with a curvature k ≠ 0, the PVE field in free space above the LD surface is described by the expression [9, 10]
E _z = CH $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{ν}}$ (K _o h) e ^-jνΦ (12)
where E _{z is the} longitudinal component of the PV field in free space; C constant factor; H $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{ν}}$ Hankel function of the second kind, order n; K _o = 2π / λ _o ; λ _{o the} length of the excited wave in free space, m; h is the height normal to the surface of the LD; Φ azimuthal coordinate.

In PV, distributed along such surfaces, along with energy transfer along the surface (surface effect), energy transfer also occurs along the normal to the LD surface, i.e. radiation of PV energy into free space. Quantitatively radiated energy is determined by the ratio between the radius of curvature in the surface of the LD, the slowdown of the PV and losses in the dielectric, and the field structure along the normal height h has a different character depending on the height. The critical height is the height equal to
h _cr = b (ξ-1) (13)
At heights from the surface h≅h _cr, the field structure completely coincides with the structure of the PV field over a flat LD and is determined by formula (10). At heights from the surface h> h _cr, the PV field is completely radiated. At heights h≥h _{cr, there} is an exponential distribution by formula (10) and radiation. From (10) it follows that for practically realized decelerations by radiation of the PVE field above the surface of a nonplanar LD, one can neglect if the conditions k _o b≥40 are satisfied, where b is the radius of curvature of the surfaces of the LD. This implies the criterion for using the exponential law (10) for non-planar LDs:
b ≥ 6λ _o (14)
where λ _{o the} length of the excited wave in free space, m

где β потери на единицу длины, Нп/м; K_o= 2π/λ_o; b радиус кривизны, м; λ_o длина возбужденной ПВ в свободном пространстве, м; ξ замедление ПВЕ; x ≅ 1,05.If b <6λ _o , it is necessary when determining the transverse wave number p PVE to take into account radiation losses. The linear radiation loss is determined by:

where β loss per unit length, Np / m; K _o = 2π / λ _o ; b radius of curvature, m; λ _{o the} length of the excited PV in free space, m; ξ retardation of PVE; x ≅ 1.05.

Отсюда имеем

Из выражения (17) имеем

где все величины или измерены, или известны.Measurements of the amplitude of the field U PVE at two points h ₁ and h ₂ in the direction of the normal and in this case make it possible to determine the transverse wave number p PVE in free space. The measured values of the field amplitude at points h ₁ and h ₂ in this case are equal to:

Hence we have

From the expression (17) we have

where all quantities are either measured or known.

Thus, if we register the distribution curve of the PVE field strength in free space above the LD surface in the direction of the normal to its surface, measure the field values U ₁ , U ₂ , U _N PVE at the points h ₁ , h ₂ , h _{N of} this normal, then using formulas (11) or (18), one can calculate the transverse wave number p _{i of the} PVE on each normal segment Δh _i h _{i + 1} h _i , using formulas (2) or (9) determine the DP ε _ri on each such segment, and using the formula (3) to find the average value of the LD LD across the normal.

 Therefore, the proposed method is technically implemented and constitutes a technical solution. We show that the proposed technical solution gives a positive effect increases the accuracy of measurements and expands the functionality. As for the measurements of the DP of non-planar LD, it is shown on sheets 13-15 of the application that the proposed method can be used to measure the DP and non-planar LD as well as flat, while the curvature of the surface of the LD is determined not by the measurement method, but by the conditions of excitation and propagation of the PVE in a particular system "LD metal substrate".

The use of higher types of PVE waves is based on the property of surface waves that the exponential distribution law of the PV field in free space above the surface according to formulas (10) or (16) remains the same for any type of wave; in formulas (10) or (16), the quantity corresponding to the excited type of wave is determined as the transverse wave number p. The dispersion equation (2) or (9) also remains true for any type of waves, again using the p value corresponding to the excited type of wave in the "LD metal substrate with smooth surface" system. The “LD metal substrate with a smooth surface” system makes it possible to excite any type of PVE in it, although the practical use of one type or another is usually associated with the presence of a microwave generator and the sensitivity of receiving and recording equipment, i.e. fundamentally, the DP LD can be determined equally successfully on any type of PVE. These factors make it possible, firstly, to significantly expand the range of operating frequencies and make measurements not only on the lower type E _oo , but also on any other type of E _op without restrictions, and, secondly, to expand the range of thicknesses of sheet dielectrics, since at small thicknesses of the dielectric, it is always possible to switch to measurements for higher types of waves, for which the wavelengths are shorter, the deceleration and surface effect are more pronounced and are recorded much more easily.

где Δp p абсолютная погрешность измерения p_i на отрезке нормали Δh_i. Минимальная величина Δp определяется из выражения

Отсюда имеем p•Δh-1 = 0 и
Δh ≃ p^-1 (20)
Величина p по определению равна

, где γ постоянная распространения ПВ, K_o= 2π/λ_o, λ_o длина возбужденной волны в свободном пространстве. Обычно γ ≈1,05K_o, поэтому p≈0,3K_o. Подставим значение p≈0,3K_o в выражение (20), получим

Из выражения (21) следует, что минимальная погрешность измерения p_i получается тогда, если h≥λ_оп, а число точек разбиения N > 2, т.е. N≥3.As noted on sheets 5 to 7 of the description, an increase in accuracy is achieved through the use of the system “LD metal substrate with a smooth surface”, discretization of the determination of the transverse wave number p _i PVE from normal segments of height h≥λ _op , where λ _op is the working wave length in free space , averaging over the ensemble of measurements at the spatial coordinate (normal), and choosing the number of reference points at a height h of at least three. Discretization of the normal by a height h≥λ _op for measuring the field value U _i , calculating p _i PVE in the discretization sections and determining the DP ε _ri in each such section Δh _i eliminates, firstly, the errors associated with the field following, compared to the one used, wave type λ _{op + 2} , because the wave field λ _{op + 2 is} pressed to the dielectric surface and in the areas Δh _{i the} field strength measurements of the used wave λ _{op are} practically absent, and secondly, random errors of a single measurement. The choice of at least three measurement points U _i at the normal height h is associated with the optimal value of the segment giving the minimum error in determining p _i on this segment. Consider the exponential distribution law of field (10) on the interval Δh. We differentiate (10) with respect to p and pass to finite Δp increments, we obtain:

where Δp p is the absolute measurement error p _i on the normal interval Δh _i . The minimum value Δp is determined from the expression

Hence, we have p • Δh-1 = 0 and
Δh ≃ p ^-1 (20)
The value of p is by definition equal to

where γ is the propagation constant of the PV, K _o = 2π / λ _o , λ _{o the} length of the excited wave in free space. Usually γ ≈ 1.05K _o , therefore p≈0.3K _o . We substitute the value p≈0.3K _o in the expression (20), we obtain

From the expression (21) it follows that the minimum measurement error p _{i is} obtained if h≥λ _op , and the number of partition points is N> 2, i.e. N≥3.

Using the system "LD metal substrate with a smooth surface" makes it possible to abandon the resonance system of the prototype "LD comb structure" and to measure the DP with the same accuracy at any frequency at which the conditions for excitation and propagation of PVE in the system "LD metal substrate with a smooth surface " Measurement errors in such a system consist of measurement errors of heights h ₁ , h ₂ , h _N and voltages U ₁ , U ₂ , U _N , are determined by the errors of measuring devices, do not depend on the operating frequency and do not exceed ± 15% Compare the proposed method with the prototype when working at frequencies other than resonant or corresponding to higher types of waves, it is not possible, since measurements at these frequencies in the prototype are not defined. On the lower type of PVE, the wave E _oo , the corresponding resonant wave of the "LD comb structure" system, both the prototype and the proposed method give almost the same accuracy in measuring the LD LD; at other frequencies with a lower type of wave E _oo , different from the resonance frequency of the "LD comb structure" system, the proposed method gives more accurate results as many times as the operating frequency differs from the resonant frequency, which leads to an increase in accuracy by two or more times depending on the type and thickness of the dielectric and does not exceed ± 15%
A simplified measurement associated with the rejection of the comb structure as an LD substrate should be considered a positive effect of the proposed method, although the proposed method does not exclude the possibility of using such a substrate.

Information sources
1. V.A. Konev, S.A. Tihanovich. A method for determining the dielectric constant of sheet dielectrics and a device for its implementation. Auth. St. N 1176266 from 09.30.83, cl. G 01 R 27/26. Publ. 08/30/85. Bull. N 32.

 2. G.V. Kozlov. Measurement of the refractive indices of dielectrics in the millimeter wavelength range. PTE, 1971, N 4, p. 152 154.

 3. B.P. Ivanov, V.N. Kakhanin. A method of measuring the parameters of plane-parallel dielectrics. Auth. St. N 1161899 from 10.06.83, cl. G 01 R 27/26. Publ. 06/15/85. Bull. N 22.

 4. J.N. Feld, L.S. Benenson. Antenna feeder devices. Part 2, VVIA them. N.E. Zhukovsky. M. 1959, p. 70 98.

 5. A.I. Astaykin, A.P. Pomazkov. Method for probe plasma diagnostics and device for its implementation. Auth. St. N 1584726 from 12.28.88, cl. H 05 H 1 / 0O.

 6. M.A. Miller, V.I. Talanov. Using the concept of surface impedance in the theory of surface electromagnetic waves. Izv. Universities, Radiophysics, vol. 4, 1961, N 5, p. 795 830.

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 8. M. A. Miller, V. I. Talanov. A surface electromagnetic wave guided by a boundary with a small curvature. ZhTF, v.26, 1956, N 2, p.2755.

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Claims (1)

A method for measuring the dielectric constant of a sheet dielectric, which consists in exciting a surface electric wave in a sheet dielectric placed on a metal substrate, measuring the parameters of this wave and determining the dielectric constant by calculation, characterized in that, in order to improve the measurement accuracy and expand the class of studied dielectrics, due to the use of surface electric waves of the highest types and measurement of the dielectric constant of non-planar sheet dielectric trica, using as a substrate a metal sheet with a smooth surface parallel to the surfaces of the sheet dielectric, register the distribution Φ (h) of the field strength of the excited surface electric wave in the free space above the surface of the sheet dielectric in the direction normal to its surface with a height h≥ λ _op , measured the distribution curve at points h ₁ , h ₂ , h _N from the base of the normal value of the field strengths U ₁ , U ₂ , U _N , calculate the transverse wave number P _{i of the} surface electric wave in s free space on the normal segments Δh _i = h _{i + 1} -h _i and determine the dielectric constant ε _ri for each of the segments Δh _i and the average value ε _{r of the} sheet dielectric from the relations:

where λ _{op the} length of the excited surface electric wave in free space, m;
i the sequence of reference points from the base of the normal;
and the thickness of the dielectric sheet; m;
N is the number of reference points on the normals, N ≥3.

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