RU2694110C1 - Method of determining dielectric permeability and thickness of multilayer dielectric coatings on metal in the microwave range - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: use: to determine dielectric permeability and thickness of multilayer solid samples on metal surface. Essence of the invention consists in the fact that the method consists in creation of UHF electromagnetic field of traveling surface wave of type E above surface of dielectric-metal in single-mode mode, measurement on the normal to dielectric-metal surface of the attenuation coefficient and determining the relative dielectric permeability of the coating e and its thickness b, additionally excite surface electromagnetic waves of the E-type in series at 2N-wavelengths, N is number of layers of coating, attenuation factor of each surface electromagnetic wave is measured, based on measurement results is system of 2N-dispersion equations, and relative dielectric permeability ε_n, ε_n+1, …, ε_N and thickness b_n, b_n+1, …, b_N layers of multilayer coating are determined by solving this system.

EFFECT: possibility of increasing accuracy and reliability of measurement of dielectric permeability and thickness of multilayer dielectric coatings at their selective control with obtaining information on each layer separately.

1 cl, 3 dwg, 1 tbl

Description

The present invention relates to a measurement technique, in particular, to devices for determining the dielectric constant and thickness of multi-layer solid samples on a metal surface, and can be used to control the quality of solid multi-layer dielectric coatings on metal during the development and operation of radio absorbing materials and coatings, as well as chemical, paint and varnish and other industries.

The closest in technical essence to the proposed invention (prototype) is a microwave method for determining the dielectric constant and thickness of dielectric coatings on metal [Patent RU №2193184, IPC ⁷ G01N 22/00, G01R 27/26, Appl. 01/23/01. Publ. 11/20/02. Bulletin 32], which consists in creating a microwave electromagnetic field of a traveling surface wave of type E above the dielectric-metal surface in a single-mode mode, measuring the attenuation coefficient normal to the dielectric-metal surface and determining the relative dielectric constant ε of the coating and its thickness b.

The disadvantages of this method are the low accuracy and accuracy of the measurement of the dielectric constant and thickness of multilayer dielectric coatings.

The technical result of the proposed invention is to improve the accuracy and reliability of measuring the dielectric constant and thickness of multilayer dielectric coatings with their selective control with obtaining information about each layer separately.

This technical result is achieved by the fact that in a known microwave method for determining the dielectric constant and thickness of dielectric coatings on a metal in the microwave range, which consists in creating a microwave electromagnetic field of a traveling surface type E wave above the dielectric-metal surface in a single-mode mode, measured along the normal to the surface dielectric-metal attenuation coefficient and determination of the relative dielectric constant of the coating ε and its thickness b, additionally excite surface electro E-type magnetic waves are successively at 2N - wavelengths, N is the number of coating layers, the attenuation coefficient of each surface electromagnetic wave is measured, the measurement results form a system of 2N -dispersion equations, and the relative permittivities ε _n , ε _{n + 1} , ..., ε _N and thickness b _n , b _{n + 1} , ..., b _N layers of the multilayer coating is determined by solving this system.

The invention consists in the following. In the prototype, the attenuation coefficient α _{y is} measured for two wavelengths of the E-type surface wave in a single-mode mode, which makes it possible to compose a system of two equations with unknown relative dielectric constant ε and thickness b and obtain their unique values by solving this system for single-layer coating. When controlling multilayer coatings with the number of layers N, the prototype does not allow one to uniquely determine the dielectric constant ε _n , ε _{n + 1} , ..., ε _N and the thicknesses b _n , b _{n + 1} , ..., b _{N of the} individual layers of the coating, since the measurement does not take into account the change in the phase coefficient of the surface wave in individual layers of the coating. In addition, for an acceptable measurement accuracy, it is necessary to preserve the single-mode excitation mode of the surface wave field. Thus, the use of a prototype to control a multilayer dielectric coating with the number of layers N allows only one integral integral of the dielectric constant ε _av and thickness b _cp to be determined taking into account the simultaneous influence of all the layers of the coating, which leads to ambiguity in the interpretation of the results and does not allow to obtain measurement information on the relative dielectric constants ε _n, ε _{n + 1,} ..., ε _N and thicknesses b _n, b _{n + 1,} ..., b _N of individual layers of the coating, which reduces the reliability and tochnos and measurements.

и производят измерение их коэффициентов затухания

при этом ограничения на одномодовость возбуждаемой поверхностной волны нет, что позволяет использовать любые другие высшие типы мод волны Е- типа. Это позволяет определить относительные диэлектрические проницаемости ε_n, ε_n+1, …, ε_N и толщины b_n, b_n+1, …, b_N отдельных слоев многослойного покрытия путем составления и решения системы из 2N дисперсионных уравнений с 2N неизвестными, входными параметрами для которых являются измеренные коэффициенты затухания

при этом каждое уравнение позволяет учесть изменение коэффициента фазы в отдельных слоях покрытия и тип моды поверхностной волны.The proposed method in contrast to the prototype allows to increase the reliability and accuracy of measuring the dielectric constant and thickness of multilayer dielectric coatings. The investigated multilayer dielectric coating with the number of layers N has 2N unknown measured parameters: N unknown dielectric constants ε _n , ε _{n + 1} , ..., ε _N and N unknown thicknesses b _n , b _{n + 1} , ..., b _N. In the proposed method, the E-type surface electromagnetic waves are additionally excited at 2N-wavelengths

and measure their attenuation

at the same time, there is no limit on the single-mode nature of the excited surface wave, which allows using any other higher types of E-type wave modes. This allows us to determine the relative dielectric permeabilities ε _n , ε _{n + 1} , ..., ε _N and thickness b _n , b _{n + 1} , ..., b _{N of the} individual layers of the multilayer coating by compiling and solving a system of 2N dispersion equations with 2N unknown, input parameters for which are measured attenuation factors

Moreover, each equation allows to take into account the change in the phase coefficient in the individual layers of the coating and the type of surface wave mode.

FIG. 1 shows one of the possible options for implementing the proposed method for determining the dielectric constant and thickness of multilayer dielectric coatings on a metal in the microwave range, where the numbers denote 1 - the unit measuring the attenuation coefficients of the E-type surface wave, 2 - the receiving antenna, 3 - the microwave generator, 4 - E-type surface wave excitation antenna, 5 - metal surface; 6 - multilayer dielectric coating with the number of layers N and unknown values of the relative dielectric constant ε _n , ε _{n + 1} , ..., ε _N and thickness b _n , b _{n + 1} , ..., b _N layers, 7 - unit for determining the relative dielectric constant and the thickness of the multilayer coating. The purpose of the elements of the scheme.

The purpose of the unit for measuring the attenuation coefficients of an E-type 1 surface wave follows from the name of the unit itself. Measurement of attenuation coefficients can be carried out according to the results of indirect measurements of the field strength of an E-type surface wave normal to the surface of the coating [P. Fedyunin, A. Kazmin. Methods of radio wave monitoring of the parameters of protective coatings for aircraft. M .: Fizmatlit. 2013. p. 122].

Автономный цифровой вольтметр на многоканальном АЦП. Электронный журнал Радиолоцман, 2012, ноябрь. С. 67-70. URL: http://www.rlocman.ru /book/book.html?di=144227 (Дата обращения: 11.07.2018)].The unit for measuring the attenuation coefficients of an E-type 1 surface wave can be implemented, for example, on the basis of microwave detector diodes, an analog-to-digital converter, a microcontroller, and a personal electronic computer (PC) [Branislav Korenko and Marek

Stand-alone digital voltmeter on a multi-channel ADC. Electronic Journal Radiolotsman, 2012, November. Pp. 67-70. URL: http://www.rlocman.ru/book/book.html?di=144227 (Revised: 07.07.2018)].

Receiving antenna 2 is inherent in the analog. The receiving antenna can be implemented on the basis of a half-wave vibrator [Fedyunin PA, Kazmin A.I. Methods of radio wave monitoring of the parameters of protective coatings for aircraft. M: Fizmatlit. 2013. p. 117].

The microwave generator 3 is inherent in the analog and realizes the formation of the microwave signal at a given wavelength for the E-type 4 surface wave excitation antenna. The microwave generator can be built on the basis of microcircuits of the type HMC586LC4B and ADF4158 6.1 GHz Fractional-N Frequency Synthesizer. [Electronic resource] URL: http://www.analog.com/media/en/technical-documentation/data- sheets /ADF4158.pdf (Revised: 07.07.2018)].

An antenna for the excitation of E-type 4 surface waves is inherent in the analogue and implements the sequential excitation of E-type surface waves in a multilayer dielectric coating with the number of layers N and unknown values of relative dielectric constant ε _n , ε _{n + 1} , ..., ε _N and thicknesses b _n , b _{n + 1} , ..., b _N layers 6 on a metal base 5. An antenna for the excitation of E-type surface waves can be implemented on the basis of a pyramidal horn [P. Fedyunin, A. A. Kazmin. Methods of radio wave monitoring of the parameters of protective coatings for aircraft. M .: Fizmatlit. 2013. p. 117, p. 146-147].

The purpose of the block for determining the relative dielectric constant and thickness of the multilayer coating 7 follows from the name of the block itself. The unit for determining the relative dielectric constant and thickness of the multilayer coating 7 can be implemented by solving 2N - dispersion equations obtained by generalizing the transverse resonance method [David M. Pozar Microwave engineering. USA: John Wiley & Sons, 2012. PP 153-154] for a coating case with the number of layers N.

Each of the 2N dispersion equations is composed as follows.

, где N - количество слоев покрытия. Область над многослойным покрытием для удобства составления дальнейших расчетных выражений формально берется в виде отдельного слоя покрытия с номером N+1 и диэлектрической проницаемостью ε_N+1=ε₀, где ε₀ - электрическая постоянная.As the initial data for the compilation of the dispersion equation, it is assumed that the multilayer dielectric coating is characterized by relative dielectric permeabilities ε _n and thicknesses b _n ,

where N is the number of layers of the coating. The area above the multilayer coating for the convenience of compiling further design expressions is formally taken as a separate coating layer with the number N + 1 and the dielectric constant ε _{N + 1} = ε ₀ , where ε ₀ is the electric constant.

FIG. 2 shows the design scheme for finding the dispersion equation of a multilayer dielectric coating on a metal base with the number of layers N + 1 using the transverse resonance method.

Based on the transverse resonance method [David M. Pozar Microwave engineering. USA: John Wiley & Sons, 2012. PP 153-154] each layer of a multilayer dielectric coating is mapped to a quadrupole, which is a segment of the transmission line with a length equal to the thickness of the layer b _n and the corresponding characteristic resistance Z _n . Thus, the multilayer dielectric coating is replaced by an equivalent circuit of related transmission lines. The equivalent circuit of the multilayer dielectric coating is shown in FIG. 3

The dispersion equation of a multilayer dielectric coating on the basis of the obtained equivalent circuit is compiled under the condition of its operation in “resonance” - the moment when the surface wave in the multilayer dielectric coating has a critical frequency. Moreover, as a dispersion equation for eigen waves in a multilayer dielectric coating, the transverse resonance equation can be used, written for an arbitrarily selected reference cross section at ₀ [formula (3.206) P. 154 [David M. Pozar Microwave engineering. USA: John Wiley & Sons, 2012]:

и

- эквивалентные характеристические сопротивления «вверх» и «вниз» относительно произвольно выбранного опорного сечения у₀.Where

and

- equivalent characteristic resistance "up" and "down" with respect to an arbitrarily selected reference section y ₀ .

For convenience of further transformations, the boundary between the metal base and the first coating layer is chosen as the reference cross section y ₀ .

The attenuation coefficient of the surface wave field α _у is related to the propagation constant γ and the phase coefficient q _{n of the} surface wave of individual layers of a multilayer dielectric coating by the following dependencies [S. Baskakov. Electrodynamics and propagation of radio waves. M .: High School. 1992. p. 311, p. 314]:

- the area above the multilayer coating with the number of layers N:

λ - длина волны генератора;where γ is the propagation constant of the surface wave; k ₀ is the wavenumber of free space,

λ is the generator wavelength;

- in each layer of a multilayer dielectric coating with the number of layers N:

ε_n - относительная диэлектрическая проницаемость n-слоя покрытия; N - число слоев покрытия.where k _n is the wave number of the n-layer of the coating,

ε _n is the relative dielectric constant of the n-layer of the coating; N is the number of coating layers.

Taking into account expressions (2, 3), the characteristic resistances of the coating layers for E-type surface waves Z _n , Z _{n + 1} , ..., Z _{N + l} [Formula 5, R.89 [Andreas Patrovsky, Ke Wu Dielectric Slab Mode Antenna for Integrated Millimeter-wave Transceiver Front-ends // Universal Journal of Electrical and Electronic Engineering, 2013. No. 1 (3)] are expressed in terms of the attenuation coefficient of the surface wave field α _y :

-characteristic resistance of the area above the multilayer coating with the number of layers N:

с - скорость света в свободном пространстве; λ - длина волны генератора, ε₀ - электрическая постоянная;

- мнимая единица; Z₀ - характеристическое свободного пространства;where ω = 2πƒ is the circular frequency,

c is the speed of light in free space; λ is the generator wavelength, ε ₀ is the electric constant;

- imaginary unit; Z ₀ - characteristic of free space;

- the characteristic resistance of each layer of a multilayer dielectric coating with the number of layers N:

с - скорость света в свободном пространстве, λ - длина волны генератора; ε_n - относительная диэлектрическая проницаемость n-слоя покрытия; N - число слоев покрытия.where q _n is the phase coefficient of the surface wave, determined by expression (3); ε ₀ is the electric constant; ω = 2πƒ - circular frequency,

c is the speed of light in free space, λ is the generator wavelength; ε _n is the relative dielectric constant of the n-layer of the coating; N is the number of coating layers.

относительно опорного сечения у₀ представляет собой эквивалентное характеристическое сопротивление слоев с

. Его можно получить путем последовательного применения формулы трансформации волновых сопротивлений методом теории цепей [формула 4, Р.89 [Andreas Patrovsky, Ke Wu Dielectric Slab Mode Antenna for Integrated Millimeter-wave Transceiver Front-ends // Universal Journal of Electrical and Electronic Engineering, 2013. №1(3)]:Characteristic resistance "up"

relative to the reference section y ₀ is the equivalent characteristic resistance of the layers with

. It can be obtained by successively applying the formula of wave resistance transformation by the method of the theory of circuits [Formula 4, R.89 [Andreas Patrovsky, Ke Wu Dielectric Slab Mode Antenna for Integrated Millimeter-wave Transceiver Front-ends // Universal Journal of Electrical and Electronic Engineering, 2013 # 1 (3)]:

- характеристическое сопротивление n-слоя покрытия, нагруженного на характеристическое сопротивление n+1-слоя покрытия; Z_n - характеристическое сопротивление n-слоя покрытия; Z_n+1 - характеристическое сопротивление n+1 -слоя покрытия.Where

- the characteristic resistance of the n-layer of the coating, loaded on the characteristic resistance of the n + 1-layer of the coating; Z _n - the characteristic resistance of the n-layer coating; Z _{n + 1} is the characteristic resistance of the n + 1 coating layer.

путем трансформации сопротивлений слоев многослойного покрытия приведена на фиг 3.The design scheme for finding the characteristic resistance "up"

by transforming the resistance of the layers of the multilayer coating is shown in Fig 3.

Based on FIG. 3 and expressions (8) the successive stages of transformation are represented by the following recursive formula, valid for the number of coating layers N from 2 and more:

относительно опорного сечения у₀ равно характеристическому сопротивлению

полученному в результате последовательной трансформации сопротивлений слоев с номерами

Thus, the equivalent characteristic resistance "up"

with respect to the reference section y ₀ is equal to the characteristic resistance

resulting from the sequential transformation of the resistance of the layers with the numbers

так как ниже его слоев покрытия нет.Characteristic resistance "down" relative to the reference section at _{0 is} assumed to be zero

since there are no layers below it.

Thus, the final dispersion equation for a multilayer dielectric coating based on (1) is represented as follows:

- эквивалентное характеристическое сопротивление слоев покрытия

определяемое по рекурсивной формуле (9).Where

- equivalent characteristic resistance of coating layers

determined by the recursive formula (9).

The device works as follows.

Before starting the measurements, the number of layers N of the multilayer dielectric coating under investigation is introduced into the unit for determining the relative dielectric constants and thicknesses 7.

.Using the microwave generator 3 and the E-type 4 surface wave excitation antenna in the multilayer dielectric coating under study, with the number of layers N, the E-type surface electromagnetic waves are successively excited at 2N - wavelengths

.

, соответственно.Using the receiving antenna 2 and the attenuation coefficient measurement unit 1 for each of the 2N E-type surface waves, the attenuation coefficient values are measured

, respectively.

поступают в блок определения относительных диэлектрических проницаемостей и толщин 7.Measured attenuation factors

enter the unit for determining the relative dielectric constant and thickness 7.

и коэффициентами затухания

соответственно, составляют дисперсионное уравнение вида (11). Получают 2N - дисперсионных уравнений.For each of the 2N E-type surface waves with wavelengths

and attenuation coefficients

accordingly, constitute the dispersion equation of the form (11). Get 2N - dispersion equations.

The solution of a system of 2N - dispersion equations with 2N unknowns ε _n , ε _{n + 1} , ..., ε _N and b _n , b _{n + 1} , ..., b _N :

- дисперсионные уравнения многослойного покрытия с числом слоев N для каждой длины волны поверхностной волны Е-типа

соответственно,Where

- dispersion equations of a multilayer coating with the number of layers N for each wavelength of an E-type surface wave

respectively,

allows you to make a selective determination of the relative dielectric constant ε _n , ε _{n + 1} , ..., ε _N and thickness b _n , b _{n + 1} , ..., b _N multi-layer coating with the number of layers N.

To test the performance of the method, experimental studies have been carried out to measure the relative dielectric constant and thickness of multilayer microwave dielectric materials. Microwave dielectric materials of the company Rogers widely used for the manufacture of multilayer printed circuit boards were investigated. Two, three and four layer coatings were made and investigated on the basis of these materials [Bogdanov Yu., Kochemasov V., Khasyanov E. Foil dielectrics - how to choose the best option for printed circuit boards of the RF / microwave ranges. Part 1 // Printed circuit. 2013. №2. Pp. 156-168].

The relative dielectric constant and thickness of the coating samples were measured under laboratory conditions at room temperature. The working wavelengths of the generator are as follows:

The values of relative dielectric constants and thicknesses correspond to the data given in [Bogdanov Yu., Kochemasov V., Khasyanov E. Foil dielectrics - how to choose the best option for high frequency / high frequency printed circuit boards. Part 1 // Printed circuit. 2013. №2. Pp. 156-168].

The average measurement errors of the relative dielectric constant and thickness averaged over 50 measurements for each sample are shown in the table.

The presented experimental data of multilayer microwave dielectric coatings showed the fundamental possibility of measuring the relative dielectric constant with a relative error of no more than 5% and the thickness of the coating with a relative error of no more than 3% based on the developed method.

Thus, the proposed method allows to increase the reliability and accuracy of measuring the relative dielectric constant and thickness of multilayer dielectric coatings with their selective control with obtaining information about each layer separately.

The method of determining the dielectric constant and thickness of multilayer dielectric coatings on a metal in the microwave range

Claims (1)

Method for determining dielectric constant and thickness of dielectric coatings on a metal in the microwave range, consisting in creating a microwave electromagnetic field of a traveling surface type E wave over the dielectric-metal surface in a single-mode mode, measuring the attenuation coefficient normal to the surface of the dielectric-metal and determining the relative dielectric constant Coatings ε and its thickness b, characterized in that they additionally excite E-type surface electromagnetic waves successively in 2N lengths x waves, N - the number of layers of the coating, measured the attenuation coefficient of each surface electromagnetic wave, in the measuring results comprise a system of 2N-dispersion equations and the relative dielectric constants ε _n, ε _{n + 1,} ..., ε _N and thickness b _n, b _{n +1} , ..., b _N layers of the multilayer coating is determined by solving this system.

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