CN115963327A - Microwave material electromagnetic parameter measuring method - Google Patents

Microwave material electromagnetic parameter measuring method Download PDF

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Publication number
CN115963327A
CN115963327A CN202310124445.XA CN202310124445A CN115963327A CN 115963327 A CN115963327 A CN 115963327A CN 202310124445 A CN202310124445 A CN 202310124445A CN 115963327 A CN115963327 A CN 115963327A
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sample
parameter
electromagnetic
measured
reflection
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梁家军
张俊
黄冠龙
杨健
林活怡
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Foshan Lanpuda Technology Co ltd
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Foshan Lanpuda Technology Co ltd
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Abstract

The invention discloses a method for measuring electromagnetic parameters of a microwave material, and relates to the technical field of electromagnetic fields and microwave engineering. The electromagnetic parameter measuring apparatus of the present invention comprises: the device comprises a vector network analyzer, a measuring clamp, a waveguide coaxial converter with a waveguide tube, a coaxial cable with stable amplitude and stable phase and a processor connected with the vector network analyzer. The method comprises the following steps: the measuring device is connected into the straight-through, reflection and transmission calibration piece to test S parameters in 3 states, a sample to be tested is placed into the sample clamp and connected into the measuring device to be tested to obtain the S parameters, test data are led into the calculation software, a TRL (true return language) calibration algorithm is adopted to carry out data processing, and an improved NRW (non-return) transmission/reflection algorithm is adopted to process the data processed by the TRL calibration algorithm to obtain the electromagnetic parameters of the material. The invention solves the calibration problem, the multi-value problem and the half-wave resonance problem commonly encountered in the material electromagnetic parameter testing process, and improves the microwave material electromagnetic parameter testing precision.

Description

Microwave material electromagnetic parameter measuring method
Technical Field
The invention relates to the technical field of electromagnetic fields and microwave engineering, in particular to a method for measuring electromagnetic parameters of a microwave material.
Background
With the rapid development of information technology, microwave materials are widely applied in the fields of aerospace, microwave communication, remote sensing, biomedicine and the like. From Maxwell's electromagnetic field theory, it can be known that the interaction of a material and an electromagnetic field can be characterized by two basic electromagnetic parameters, namely, a relative complex permittivity and a relative complex permeability, and the electromagnetic property of the material in the electromagnetic field can be described. In the production process of microwave materials, accurate testing of electromagnetic parameters (dielectric constant and magnetic permeability) of the materials is an important link of microwave material production, and is directly related to the performance of related electronic equipment and systems, so that how to improve the testing precision of the electromagnetic parameters of the microwave materials is very important.
The measurement method of electromagnetic parameters is related to the form, dispersion characteristics and applied frequency band of the measured material, and mainly includes a resonance method and a transmission reflection method.
The existing electromagnetic parameter calculation software based on the transmission reflection method is used for calculating the electromagnetic parameter of a sample material, namely the relative complex dielectric constant, according to the S parameter inversion of the vector network test
Figure SMS_1
And a relative complex permeability->
Figure SMS_2
. The current test method has the problems of difficult calibration, multiple value and half-wave resonance.
Disclosure of Invention
The invention provides a microwave material electromagnetic parameter measuring method, which solves the problems of calibration, multi-value and half-wave resonance commonly encountered in the material electromagnetic parameter testing process and improves the microwave material electromagnetic parameter testing precision.
The invention also provides a microwave material electromagnetic parameter measuring system.
A microwave material electromagnetic parameter measuring method adopts an electromagnetic parameter measuring device to measure, and the measuring process comprises the following steps:
s1: respectively accessing a Through, a reflection and a transmission Line calibration piece to an electromagnetic parameter measuring device for testing to obtain S parameter matrixes in 3 states:
Figure SMS_3
、/>
Figure SMS_4
and &>
Figure SMS_5
；
S2: putting a sample to be tested into a measuring clamp and connecting the sample to be tested into an electromagnetic parameter measuring device for testing to obtain an S parameter matrix
Figure SMS_6
Will >>
Figure SMS_7
、/>
Figure SMS_8
、/>
Figure SMS_9
And &>
Figure SMS_10
Automatically importing matched electromagnetic parameter calculation software;
s3: performing data processing on the 4S parameter matrixes by adopting a TRL calibration algorithm in electromagnetic parameter calculation software to obtain S parameter matrixes of two end surfaces of the sample to be measured
Figure SMS_11
；
S4: using NRW transmission/reflection algorithm to pair S parameter matrix
Figure SMS_12
And performing inversion to solve and obtain the electromagnetic parameters of the dielectric material, wherein the NRW transmission/reflection algorithm is specifically a Nicolson-Ross-Weir transmission/reflection algorithm.
Preferably, the electromagnetic parameter measuring device comprises a vector network analyzer, a measuring clamp, a waveguide coaxial converter with a waveguide tube, a coaxial cable with stable amplitude and stable phase and a processor, wherein the vector network analyzer is connected with the processor, and electromagnetic parameter calculation software is arranged in the processor; the vector network analyzer is connected with the processor to realize communication, and the processor is internally provided with the electromagnetic parameter calculation software; two ports of the vector network analyzer are respectively connected with the amplitude-stabilized phase-stabilized coaxial cable and the waveguide coaxial converter containing the waveguide tube; the waveguide coaxial converter containing the waveguide tube comprises two waveguide coaxial converters containing the waveguide tube, the measuring clamp is connected between the two waveguide coaxial converters containing the waveguide tube, and when the measuring clamp is placed into the sample to be measured, the measuring clamp and the two waveguide coaxial converters containing the waveguide tube are fixed through screws to realize mechanical connection; the waveguide coaxial converter with the waveguide tube is of an integrated structure and comprises the waveguide coaxial converter and a rectangular waveguide tube. The Through calibration piece is air with the length of 0, the reflection calibration piece is a metal reflection plate with a specific length, and the transmission Line calibration piece is a precise waveguide section with the length of 1/8 or 1/4 or 3/8 times of the wavelength of the waveguide.
Preferably, the process of obtaining the S parameter matrices of the two end surfaces of the sample to be measured in step S3 is as follows: two ports of the vector network analyzer are defined as a port 1 and a port 2 respectively, the whole from the port 1 to one end of a sample to be measured is defined as an error box A, and the whole from the port 2 to the other end of the sample to be measured is defined as an error box B.
Error box A is represented as
Figure SMS_13
And error box B is expressed as->
Figure SMS_14
Then the vector network analyzer is connected from port 1 to port 2, specifically the error box A, to be testedThe sample and error box B is regarded as a cascade network consisting of three two-port networks, and S parameter matrixes of ports 1 and 2 of the vector network analyzer are obtained through measurement
Figure SMS_15
Specifically, it is represented as:
Figure SMS_16
(1)
wherein the parameters with subscripts a and B represent the S-parameters of the error boxes a and B respectively,
Figure SMS_20
input reflection parameter, representing said error box A, based on a predetermined criterion>
Figure SMS_23
An output reflection parameter, representing the error box A, is greater than or equal to>
Figure SMS_27
A back transmission parameter, representing the error box A, is greater than>
Figure SMS_18
Representing the forward transmission parameters of the error box a, device for selecting or keeping>
Figure SMS_21
Input reflection parameter, representing said error box B>
Figure SMS_25
Represents an output reflection parameter of the error box B, is greater than>
Figure SMS_29
A back transmission parameter, representing the error box B>
Figure SMS_17
Representing the forward transmission parameters of the error box B. The parameter with the subscript M represents the S parameter, which is directly obtained from the measurement by the vector network analyzer, is present in the interior of the vessel>
Figure SMS_22
Represents an input reflection parameter, < '> or <' > of the cascade network>
Figure SMS_26
Represents an output reflection parameter, < '> or <' > of the cascade network>
Figure SMS_30
Represents a reverse transmission parameter, < '> or <' > of the cascaded network>
Figure SMS_19
Representing a forward transmission parameter of the cascaded network. />
Figure SMS_24
、
Figure SMS_28
Respectively representing a forward signal error and a reverse signal error between two ports of the vector network analyzer when a sample to be detected is accessed;
Figure SMS_31
(2)
s parameter matrix of two end faces of sample to be measured
Figure SMS_32
，/>
Figure SMS_33
Represents an input reflection parameter of the sample to be examined, < '> or <' >>
Figure SMS_34
Represents an output reflection parameter of the sample to be examined, < '> or <' >>
Figure SMS_35
A reverse transmission parameter which represents the sample to be examined>
Figure SMS_36
Expressing the forward transmission parameter of the sample to be detected, and obtaining the forward transmission parameter by inverse solution according to the formula (1): />
Figure SMS_37
(3)
Wherein
Figure SMS_38
(4)
Based on the S parameter matrix in 3 states obtained in step S1:
Figure SMS_41
、/>
Figure SMS_43
and &>
Figure SMS_45
(ii) a S parameter matrixes obtained when the vector network analyzer measures a straight-Through, a reflection and a transmission Line calibration piece are respectively set as
Figure SMS_40
=/>
Figure SMS_44
、/>
Figure SMS_46
=/>
Figure SMS_47
、/>
Figure SMS_39
=/>
Figure SMS_42
(ii) a Specifically, the following formula:
Figure SMS_48
(5)
Figure SMS_49
(6)
Figure SMS_50
(7)
wherein the amount with subscript M is a known amount,
Figure SMS_51
and &>
Figure SMS_52
The coefficient is an unknown equation coefficient and can be obtained by the solution of the joint type (5), (6) and (7); the combined vertical type (5), (6) and (7) can solve 10 unknown parameters, particularly
Figure SMS_53
And &>
Figure SMS_54
Substituting the 10 solved parameters into the formula (3) to solve the S parameter matrix of the two end surfaces of the sample to be tested>
Figure SMS_55
。
Preferably, step S4 adopts NRW transmission/reflection algorithm to match S parameter matrix
Figure SMS_56
The inversion process is as follows:
the sample medium to be measured reflects and transmits electromagnetic waves, and the single reflection coefficient at the interface A of air and the medium is set as
Figure SMS_58
Then the reflection coefficient at the medium-air interface B is ≥>
Figure SMS_62
The thickness of the sample to be tested is->
Figure SMS_65
The transmission coefficient between the dividing plane A and B is ^ or ^>
Figure SMS_60
S parameter matrix for two end faces of a sample to be tested>
Figure SMS_66
Comprises:>
Figure SMS_68
and &>
Figure SMS_57
；/>
Figure SMS_61
And
Figure SMS_64
and reflection coefficient>
Figure SMS_67
And a transmission coefficient->
Figure SMS_59
The relationship of (c) is expressed as:
Figure SMS_69
(8)
Figure SMS_70
(9)
Figure SMS_71
(10)
Figure SMS_72
(11)
relative complex dielectric constant and relative complex permeability of sample to be measured and propagation constant of sample section to be measured
Figure SMS_73
The relationship of (1) is:
Figure SMS_74
(12)
wherein the content of the first and second substances,
Figure SMS_75
for the transmission wavelength of electromagnetic waves in the air>
Figure SMS_76
Is the cutoff wavelength of the rectangular waveguide>
Figure SMS_77
Is a relative complex dielectric constant, is->
Figure SMS_78
Is a relative complex permeability;
transmission coefficient of sample to be measured
Figure SMS_79
Propagation constant->
Figure SMS_80
And the thickness of the sample to be determined>
Figure SMS_81
The relationship of (1) is:
Figure SMS_82
(13)
therefore, the transmission coefficient of the sample to be measured
Figure SMS_83
Can be related to the relative complex dielectric constant and relative complex permeability of the sample to be measured; at the same time, the reflection coefficient->
Figure SMS_84
It is also possible to relate the relative complex permittivity and relative complex permeability of the sample to be measured by means of the wave impedance, namely:
Figure SMS_85
(14)
Figure SMS_86
(15)
Figure SMS_87
(16)
wherein the content of the first and second substances,
Figure SMS_88
and &>
Figure SMS_89
Expressed as characteristic impedances of the air region and the sample section to be examined in the transmission line, respectively>
Figure SMS_90
Indicates the permeability of the vacuum->
Figure SMS_91
Represents the speed of light; the reflection factor is determined by the formulae (10), (11) and (12)>
Figure SMS_92
Comprises the following steps: />
Figure SMS_93
(17)
By combining the above formulas, the relative complex permeability of the sample to be measured can be obtained respectively
Figure SMS_94
And a relative complex dielectric constant>
Figure SMS_95
Comprises the following steps:
Figure SMS_96
(18)
Figure SMS_97
(19)
wherein Λ is the attenuation of the sample to be measured and is expressed as:
Figure SMS_98
(20)
according to the analysis process, the rectangular waveguideThe electromagnetic parameter of the sample to be tested is tested, the S parameter is tested in the rectangular waveguide, and the reflection coefficient of the sample to be tested is calculated by utilizing the S parameter
Figure SMS_99
And a transmission coefficient->
Figure SMS_100
And then the electromagnetic parameter->
Figure SMS_101
And &>
Figure SMS_102
。
Preferably, the present invention further comprises solving the multivalue problem of the obtained electromagnetic parameters, wherein the process comprises:
in the process of obtaining the electromagnetic parameters of the sample to be measured through calculation, the formula (20) relates to the reciprocal of the transmission coefficient
Figure SMS_103
Calculating a natural logarithm operation; as shown in formula (21), is selected>
Figure SMS_104
Is a complex number, the imaginary part of the result of the known mathematical software solving the natural logarithm of the complex number only occurs in &>
Figure SMS_105
In between, exceed>
Figure SMS_106
In the range, jump of an imaginary part can occur in continuous measuring frequency, thereby causing wrong electromagnetic parameter calculation results; aiming at the problem, a derivation method is adopted to solve the problem;
Figure SMS_107
，(n=0,1,2…) (21)
n is a natural number; α and β represent a specific constant;
derivation methodUtilizes the characteristic that the electromagnetic parameters of a dielectric material are not changed in a certain frequency range, and is shown in the formula (18)
Figure SMS_108
With respect to the frequency f derivative, i.e.:
Figure SMS_109
(22)
wherein the content of the first and second substances,
Figure SMS_112
is the current electromagnetic wave frequency->
Figure SMS_114
Is the waveguide cut-off frequency->
Figure SMS_116
Is the speed of light; />
Figure SMS_111
Represents a reflection factor->
Figure SMS_115
In respect of frequency->
Figure SMS_117
Is greater than or equal to>
Figure SMS_118
Represents a transmission coefficient pick>
Figure SMS_110
In respect of frequency->
Figure SMS_113
A derivative of (d);
based on the formula (22) will involve
Figure SMS_119
Association>
Figure SMS_120
The first derivative of (2) is solved by a difference quotient method as follows:
Figure SMS_121
(23)/>
Figure SMS_122
(24)
Figure SMS_124
represents->
Figure SMS_126
At the current electromagnetic wave frequency->
Figure SMS_128
Increase/or>
Figure SMS_125
Later change amount>
Figure SMS_127
Represents->
Figure SMS_129
At the current electromagnetic wave frequency->
Figure SMS_130
Increase/or>
Figure SMS_123
The latter amount of variation;
derivative of equation (22)
Figure SMS_131
Is reversely solved to be out of the position>
Figure SMS_132
To determine ∑ of equation (21)>
Figure SMS_133
The value is obtained.
Preferably, the invention also includes that when the thickness of the sample to be tested is larger than
Figure SMS_134
A half-wave resonance problem solving method is carried out on the obtained electromagnetic parameters, and then the obtained electromagnetic parameters are subjected to the half-wave resonance>
Figure SMS_135
The transmission wavelength of the electromagnetic wave in the sample to be measured is as follows:
transmission coefficient of electromagnetic wave when it is propagated in medium without loss or with extremely small loss angle
Figure SMS_138
Is close to 1; at certain frequency points, a sample thickness of ^ or ^ meeting the requirements to be measured appears>
Figure SMS_140
So that->
Figure SMS_142
In the case of (1), wherein
Figure SMS_136
Is a positive integer; />
Figure SMS_139
The transmission wavelength of the electromagnetic wave in the sample to be measured is such that->
Figure SMS_141
，/>
Figure SMS_143
As denominator, results in a reflection factor ^ of the formula (10)>
Figure SMS_137
The calculation results of the electromagnetic parameter calculation method generate large deviation at the frequency points and the vicinity thereof, thereby causing the deviation of the calculation results of the electromagnetic parameters of the material; the phenomenon that the calculation result is deviated when the thickness of the sample to be detected is exactly integral multiple of the half-wave length of the sample to be detected is a half-wave resonance phenomenon;
for high loss or magnetic materials, due to the transmission coefficient
Figure SMS_144
The amplitude-frequency characteristic of the signal is decreased, so that half-wave resonance does not occur, and the obtained->
Figure SMS_145
Value and->
Figure SMS_146
The value is the real electromagnetic parameter measured value of the sample to be measured;
for non-magnetic low loss materials, due to the relative complex permeability
Figure SMS_147
And therefore is->
Figure SMS_148
Value to substitute->
Figure SMS_149
A value; from the formula (19):
Figure SMS_150
=/>
Figure SMS_151
(25)
by using
Figure SMS_152
Value instead of>
Figure SMS_153
Value, half-wave resonance phenomenon can be weakened;
the measurement result is stable in the whole measurement frequency band; on the basis of the above-mentioned information, to further eliminate
Figure SMS_154
The reflection coefficient Γ can be calculated by equation (26) instead of equations (14) to (16):
Figure SMS_155
(26)
wherein the content of the first and second substances,
Figure SMS_156
is the characteristic impedance of the air region in the transmission line>
Figure SMS_160
The normalized characteristic impedance of the sample to be detected; />
Figure SMS_163
The selection principle of the sign after square opening is based on>
Figure SMS_158
Re represents a function of the real part of the complex number, the sum of the sign and the sign of Z>
Figure SMS_159
Are positively correlated; calculation of the reflection factor->
Figure SMS_162
At this time, is greater or less>
Figure SMS_164
Has not occurred solely in the denominator of the formula and is therefore ≥ er>
Figure SMS_157
Then the reflection factor is calculated using equation (26)>
Figure SMS_161
The large fluctuation does not occur, so that the calculation results of the equations (18) and (19) do not exhibit the large fluctuation.
Compared with the prior art, the invention has the beneficial effects that: the technical scheme of the invention is that the waveguide coaxial converter and the rectangular waveguide tube are integrally processed, mechanical errors caused by direct connection of the waveguide coaxial converter and the rectangular waveguide tube through a flange plate are eliminated, and the operation is simple and convenient. Secondly, a TRL calibration algorithm is written into electromagnetic parameter calculation software, and accurate calibration can be provided for a vector network which does not support TRL calibration. Thirdly, solving the multi-valued problem in the solving process by adopting a relatively practical derivation method. Fourthly, for the half-wave resonance problem which appears in the calculation result of the nonmagnetic low-loss material, an improved calculation method is adopted to eliminate the half-wave resonance phenomenon.
Drawings
Fig. 1 is a block diagram of an electromagnetic parameter measuring device corresponding to the electromagnetic parameter measuring method of the present invention.
Fig. 2 is a schematic diagram of transmission and reflection of electromagnetic waves by a sample medium to be measured.
Fig. 3 is a schematic diagram of a cascaded network.
Fig. 4 is a schematic diagram of S parameters of a cascade network composed of an error box a, a sample to be measured, and an error box B.
FIG. 5 is a schematic view of a test calibration piece.
FIG. 6 is a drawing showing
Figure SMS_165
Relative to frequency>
Figure SMS_166
Graph of the variation of (c).
Detailed Description
The invention is applied to measuring the relative complex dielectric constant and the relative complex permeability of a medium material, and the adopted rectangular waveguide method belongs to one of transmission reflection methods. In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the following formulas and accompanying drawings.
Device constitution
The invention optimizes the material electromagnetic parameter measuring device based on the traditional rectangular waveguide method (as shown in figure 1), and the waveguide coaxial converter and the rectangular waveguide tube are integrally processed, so that the mechanical error caused by the direct connection of the waveguide coaxial converter and the rectangular waveguide tube through a flange plate is eliminated, the complexity of the measuring device is reduced, and the operation is simple and convenient.
In this embodiment, a method for measuring electromagnetic parameters of a microwave material is disclosed, in which an electromagnetic parameter measuring device is used for measurement, and the measurement process includes the following steps:
s1: the electromagnetic parameter measuring device is respectively connected with a straight-Through, a reflection and a transmission Line calibration piece for testing to obtain an S parameter matrix under 3 states:
Figure SMS_167
、/>
Figure SMS_168
and &>
Figure SMS_169
；
S2: putting a sample to be tested into a measuring clamp and connecting the sample to be tested into an electromagnetic parameter measuring device for testing to obtain an S parameter matrix
Figure SMS_170
Will>
Figure SMS_171
、/>
Figure SMS_172
、/>
Figure SMS_173
And &>
Figure SMS_174
Automatically importing matched electromagnetic parameter calculation software;
s3: performing data processing on the 4S parameter matrixes by adopting a TRL calibration algorithm in electromagnetic parameter calculation software to obtain S parameter matrixes of two end surfaces of the sample to be measured
Figure SMS_175
；
S4: using NRW transmission/reflection algorithm to pair S parameter matrix
Figure SMS_176
And (4) carrying out inversion, and solving to obtain the electromagnetic parameters of the dielectric material, wherein the NRW transmission/reflection algorithm is specifically a Nicolson-Ross-Weir transmission/reflection algorithm.
Specifically, the electromagnetic parameter measuring device comprises a vector network analyzer, a measuring clamp, a waveguide coaxial converter containing a waveguide tube, a stable-amplitude and stable-phase coaxial cable and a processor, wherein the vector network analyzer is connected with the processor to realize communication, and electromagnetic parameter calculation software is arranged in the processor; two ports of the vector network analyzer are respectively connected with the amplitude-stabilized phase-stabilized coaxial cable and the waveguide coaxial converter containing the waveguide tube; the waveguide coaxial converter containing the waveguide tube comprises two waveguide coaxial converters containing the waveguide tube, the measuring clamp is connected between the two waveguide coaxial converters containing the waveguide tube, and when the measuring clamp is placed into the sample to be measured, the measuring clamp and the two waveguide coaxial converters containing the waveguide tube are fixed through screws to realize mechanical connection; the waveguide coaxial converter with the waveguide tube is of an integrated structure and comprises the waveguide coaxial converter and a rectangular waveguide tube. The Through calibration piece is air with the length of 0, the reflection calibration piece is a metal reflection plate with a specific length, and the transmission Line calibration piece is a precise waveguide section with the length of 1/8 or 1/4 or 3/8 times of the wavelength of the waveguide.
FIG. 2 shows the reflection and transmission of electromagnetic waves by the sample medium to be measured, and the single reflection coefficient at the interface A of air and the medium is set as
Figure SMS_179
Then the reflection coefficient at the medium-air interface B is +>
Figure SMS_181
Based on the measured medium thickness>
Figure SMS_183
The transmission coefficient between the dividing plane A and B is ^ or ^>
Figure SMS_178
，/>
Figure SMS_180
And &>
Figure SMS_182
And the reflection coefficient->
Figure SMS_184
And a transmission coefficient->
Figure SMS_177
The relationship of (c) is expressed as:
Figure SMS_185
(101)
Figure SMS_186
(102)
Figure SMS_187
(103)
Figure SMS_188
(104)
relative complex dielectric constant and relative complex permeability of material and propagation constant of sample segment to be measured
Figure SMS_189
The relationship of (1) is:
Figure SMS_190
(105)
wherein the content of the first and second substances,
Figure SMS_191
for the transmission wavelength of electromagnetic waves in the air>
Figure SMS_192
Is the cutoff wavelength of the rectangular waveguide>
Figure SMS_193
Is a relative complex dielectric constant, is->
Figure SMS_194
Is a relative complex permeability.
Transmission coefficient of sample to be measured
Figure SMS_195
Propagation constant->
Figure SMS_196
And the thickness of the sample to be determined>
Figure SMS_197
The relationship of (1) is:
Figure SMS_198
(106)
therefore, the transmission coefficient of the sample to be measured
Figure SMS_199
Can be correlated to the relative complex permittivity and relative complex permeability of the sample to be measured. At the same time, reflection coefficient>
Figure SMS_200
The relative complex permittivity and the relative complex permeability of the sample to be measured can also be related by the wave impedance, i.e.:
Figure SMS_201
(107)
Figure SMS_202
(108)
Figure SMS_203
(109)
wherein, the first and the second end of the pipe are connected with each other,
Figure SMS_204
and &>
Figure SMS_205
Expressed respectively as the characteristic impedance of the air region in the transmission line and of the sample section to be examined, in>
Figure SMS_206
Indicates the permeability of the vacuum->
Figure SMS_207
Indicating the speed of light. The reflection factor is determined by the equations (103), (104) and (105)>
Figure SMS_208
Comprises the following steps: />
Figure SMS_209
(110)
By combining the above formulas, the relative complex permeability and the relative complex permittivity of the measured medium can be respectively obtained as follows:
Figure SMS_210
(111)
Figure SMS_211
(112)
wherein Λ is the attenuation of the sample to be measured, and can be expressed as:
Figure SMS_212
(113)
according to the theoretical analysis, the test of the electromagnetic parameters of the medium by the rectangular waveguide transmission line is summarized as the test of S parameters in the rectangular waveguide, and the reflection coefficient of the sample to be tested is calculated by utilizing the S parameters
Figure SMS_213
And a transmission coefficient->
Figure SMS_214
And then the electromagnetic parameters of the sample to be detected are solved.
TRL calibration
When the rectangular waveguide and the test fixture for the sample to be tested are connected, due to the existence of the waveguide coaxial converter, the measurement reference surface is not calibrated to the two end surfaces of the sample to be tested after one calibration, S parameters of the two end surfaces of the sample to be tested are required to be measured in the electromagnetic parameter test, the S parameters of the two end surfaces of the non-sample are processed by adopting an NRW algorithm, and the calculation result has a large error. The invention adopts a TRL calibration algorithm to calibrate the reference end surfaces of the vector network measurement S parameters to the two end surfaces of the sample to be measured, and provides correct S parameter data for NRW algorithm processing.
The TRL calibration method is based on calibration of an S parameter network, two ports of a vector network analyzer are defined as a port 1 and a port 2 respectively, an error box A is integrally defined from the port 1 to one end of a sample to be tested, and an error box B is integrally defined from the port 2 to the other end of the sample to be tested. Error box A is represented as follows from two-port network correlation theory
Figure SMS_215
And error box B is expressed as->
Figure SMS_216
Then, the part of the vector network from port 1 to port 2, specifically, the error box a, the sample to be measured, and the error box B, can be regarded as a cascade network composed of three two-port networks, and fig. 4 is a schematic diagram of S parameters of the cascade network.
Wherein the parameters with subscripts A and B denote the S-parameters of the error boxes A and B, respectively,
Figure SMS_219
input reflection parameter, representing said error box A, based on a predetermined criterion>
Figure SMS_224
An output reflection parameter, representing the error box A, is greater than or equal to>
Figure SMS_228
An inverse transmission parameter representing said error box A, based on a predetermined criterion>
Figure SMS_217
A forward transmission parameter representing the error box A, is greater than or equal to>
Figure SMS_222
Representing the input reflection parameters of the error box B,
Figure SMS_226
represents an output reflection parameter of the error box B, is greater than>
Figure SMS_230
A back transmission parameter, representing the error box B>
Figure SMS_220
Representing the forward transmission parameters of the error box B. The parameter with the subscript M represents the S parameter, directly obtained by the vector net measurement, which is based on the value of the subscript M>
Figure SMS_223
Represents an input reflection parameter, < '> or <' > of the cascade network>
Figure SMS_227
Represents an output reflection parameter, < '> or <' > of the cascade network>
Figure SMS_231
Represents a reverse transmission parameter, < '> or <' > of the cascaded network>
Figure SMS_218
Representing a forward transmission parameter of the cascaded network. In the dashed frame of FIG. 4 are the S parameters of both end faces of the sample to be examined,. Sup.>
Figure SMS_221
、/>
Figure SMS_225
Respectively representing the forward signal error and the reverse signal error between two ports of the vector network when the tested device is accessed. According to the Meisen formula, the S parameter is measured for the saggites ports 1 and 2>
Figure SMS_229
Specifically, it can be expressed as:
Figure SMS_232
(114)
wherein
Figure SMS_233
(115)
As shown in FIG. 4, S parameters of two end faces of the sample to be measuredNumber matrix [ S ]]=
Figure SMS_234
，/>
Figure SMS_235
Represents an input reflection parameter of the sample to be examined, < '> or <' >>
Figure SMS_236
An output reflection parameter representing the sample to be tested, and>
Figure SMS_237
a reverse transmission parameter which represents the sample to be examined>
Figure SMS_238
The forward transmission parameter representing the sample to be measured can be obtained by inverse solution according to equation (114):
Figure SMS_239
(116)
wherein
Figure SMS_240
(117)
To solve for equation (116), the S-parameters measured directly by the vector net are needed, and the S-parameters and forward and reverse signal errors of error boxes a and B need to be known. To obtain these 10 errors, data processing using the TRL calibration algorithm is required. The advantage of TRL calibration is that the accuracy is only partially related to the quality, repeatability of the TRL calibration piece, and not completely determined by the calibration piece. Three calibration pieces, namely, through calibration, reflect calibration and Line calibration, are respectively accessed to a measurement system for testing, as shown in fig. 5; order to
Figure SMS_241
，/>
Figure SMS_242
S parameter matrixes obtained when Through, reflex and Line are respectively measured for the vector network, so that the S parameter matrixes can be obtainedTo 12 equations, as shown in equations (118) to (120):
Figure SMS_243
(118)/>
Figure SMS_244
(119)
Figure SMS_245
(120)
wherein the amount with subscript M is a known amount,
Figure SMS_246
and &>
Figure SMS_247
The coefficient of an unknown equation can be solved through the joint equations (118), (119) and (120). The joint type (118), (119) and (120) can solve 10 unknown parameters, specifically, the specific finger
Figure SMS_248
And &>
Figure SMS_249
Substituting the solved 10 parameters into an equation (116), so that S parameters (or corresponding parameters) of two end surfaces of the sample to be tested can be solved>
Figure SMS_250
。
4. Multiple value problem solution
Formula (113) relates to the reciprocal of the transmission coefficient in the solving process
Figure SMS_251
And (5) calculating a natural logarithm operation. As shown in formula (121), is selected>
Figure SMS_252
Is a complex number, the imaginary part of the solution of the mathematical software to the natural logarithm of the complex number only occurs in &>
Figure SMS_253
In between, exceed>
Figure SMS_254
In this range, jumps in the imaginary part occur in the continuous measuring frequency, which leads to erroneous electromagnetic parameter calculations. Aiming at the problem, the invention adopts two practical solutions: derivation methods and imaginary part compensation methods.
Figure SMS_255
(n=0,1,2…) (121)
n is a natural number; α and β represent a specific constant;
1. method of derivation
By using the characteristic that the electromagnetic parameters of the dielectric material are not changed in a certain frequency range, the dielectric material is aligned with the formula (111)
Figure SMS_256
With respect to frequency f, i.e. derivation
Figure SMS_257
(122)
Wherein the content of the first and second substances,
Figure SMS_260
is the current electromagnetic wave frequency->
Figure SMS_263
Is the waveguide cut-off frequency->
Figure SMS_265
Is the light speed->
Figure SMS_259
Represents a reflection coefficient>
Figure SMS_262
In relation to frequency>
Figure SMS_264
Is greater than or equal to>
Figure SMS_266
Represents a transmission coefficient pick>
Figure SMS_258
In respect of frequency->
Figure SMS_261
The derivative of (c).
Finally, the problem is summarized based on the formula (22) relating to
Figure SMS_267
Make a relationship>
Figure SMS_268
The invention adopts a difference quotient method, and the solving method is as follows:
Figure SMS_269
(123)/>
Figure SMS_270
(124)
Figure SMS_273
represents->
Figure SMS_275
At the current electromagnetic wave frequency->
Figure SMS_277
Increase/or>
Figure SMS_272
The latter amount of change->
Figure SMS_274
Represents->
Figure SMS_276
At the current electromagnetic wave frequency->
Figure SMS_278
Increase/or>
Figure SMS_271
The latter amount of variation;
derivative of equation (122)
Figure SMS_279
Can be reversely solved out>
Figure SMS_280
To determine ∑ of equation (121) based on the unique value of (c), thereby determining ∑ of>
Figure SMS_281
The value is obtained.
2. Method of imaginary part compensation
Mathematical software solution
Figure SMS_282
The third term on the right side of the formula (121) is not considered, thus obtained->
Figure SMS_283
Is shown in dashed lines in fig. 6, but this is not a->
Figure SMS_284
The real imaginary part of (c). Based on the equations (equations 105 and 106) of the propagation constant, it can be seen that>
Figure SMS_285
The change of the real imaginary part of (1) with the frequency is not periodic, but is linearly increased as shown by a solid line in fig. 6, which is the theoretical basis of the imaginary part compensation method.
When the measurement frequency increases (
Figure SMS_289
) If there is a->
Figure SMS_291
，/>
Figure SMS_294
Is a positive integer, <' > based on>
Figure SMS_288
A function representing the imaginary part of a complex number can be determined->
Figure SMS_292
Has made a periodic jump in the imaginary part, in which case->
Figure SMS_295
And ^ or greater than or equal to (121) corresponding to all subsequent bins>
Figure SMS_297
Value is assigned a value of->
Figure SMS_286
。/>
Figure SMS_290
And/or>
Figure SMS_293
With smaller intervals, ensuring +>
Figure SMS_296
Does not vary more than->
Figure SMS_287
。
The most critical of the imaginary part compensation method is the initial value of the formula (121)
Figure SMS_298
Determination of (4), in general when a thinner sample sheet is taken for testing, a determination is made that>
Figure SMS_299
There are exceptions, however. To ensure that the exact initial value is obtained no matter what thickness of the sample is selected>
Figure SMS_300
The invention uses the already mentioned derivation method for determining the initial value->
Figure SMS_301
。
5. Half-wave resonance problem solution
When the thickness of the measured medium is larger than
Figure SMS_303
When the NRW transmission/reflection method is used, half-wave resonance is a problem. When the electromagnetic wave propagates in the medium without loss or with extremely small loss angle, the transmission coefficient->
Figure SMS_306
Is close to 1. At certain frequency points, a sample thickness which satisfies the criterion of being measured appears>
Figure SMS_308
Is a positive integer, is selected>
Figure SMS_304
Is the transmission wavelength of the electromagnetic wave in the sample to be measured>
Figure SMS_307
So that->
Figure SMS_309
So that in formula (103) < is >>
Figure SMS_310
，/>
Figure SMS_302
As denominator, results in a reflection factor ^ of equation (103)>
Figure SMS_305
The calculation results of the electromagnetic parameter calculation method generate large deviation at the frequency points and the vicinity thereof, thereby causing the deviation of the calculation results of the electromagnetic parameters of the material. The half-wave resonance phenomenon is called because the calculation result is deviated when the thickness of the sample to be measured is exactly integral multiple of the half-wavelength of the sample to be measured.
For high loss or magnetic materials, due to the transmission coefficient
Figure SMS_311
The amplitude-frequency characteristic shows a decreasing rule, so that a half-wave resonance phenomenon does not occur, and the obtained->
Figure SMS_312
Value and->
Figure SMS_313
The value is the real electromagnetic parameter measured value of the measured medium. Whereas for non-magnetic low-loss materials the relative complex permeability is such that>
Figure SMS_314
Can therefore be used +>
Figure SMS_315
Value to substitute->
Figure SMS_316
The value is obtained. From equation (112): />
Figure SMS_317
=/>
Figure SMS_318
(125)
By using
Figure SMS_319
Value to substitute->
Figure SMS_320
Value, half-wave resonance phenomenon can be weakened;
the measurement result is stable in the whole measurement frequency band. On the basis of the above-mentioned information, to further eliminate
Figure SMS_321
The reflection factor ^ is calculated using the formula (126) instead of the formulae (107) to (109)>
Figure SMS_322
：
Figure SMS_323
(126)
Wherein the content of the first and second substances,
Figure SMS_325
is the characteristic impedance of the air region in the transmission line>
Figure SMS_329
Is the normalized characteristic impedance of the sample to be measured. />
Figure SMS_331
The selection principle of the sign after square opening is based on>
Figure SMS_326
Re denotes a function of the real part of the complex number, the positive and negative sum of Z->
Figure SMS_328
Are positively correlated. Calculation of a reflection coefficient in accordance with formula (126)>
Figure SMS_330
At this time>
Figure SMS_332
Has not occurred solely in the denominator of the formula and is therefore ≥ er>
Figure SMS_324
Then, the reflection coefficient is calculated using equation (126)>
Figure SMS_327
And large fluctuation does not occur, so that the calculation results of the formula (111) and the formula (112) do not show large fluctuation.
The invention discloses a material electromagnetic parameter measuring method, which takes a rectangular waveguide method as an example in the embodiment to explain the content of the invention in detail and has the following advantages: firstly, the coaxial converter of waveguide and rectangular waveguide adopt integrated processing, eliminate the two and directly link the mechanical error that causes when the ring flange, simple and convenient operation. Secondly, a TRL calibration algorithm is written into electromagnetic parameter calculation software, and accurate calibration can be provided for vector nets which do not support TRL calibration. Thirdly, solving the multi-valued problem in the solving process by adopting a practical derivation method and an imaginary part compensation method. Fourthly, for the half-wave resonance problem which appears in the calculation result of the nonmagnetic low-loss material, an improved calculation method is adopted to eliminate the half-wave resonance phenomenon.
The above-described embodiments of the present invention do not limit the scope of the present invention. Any modification, equivalent replacement, and improvement made within the spirit and scope of the present invention shall be included in the protection scope of the claims of the present invention.

Claims (6)

1. A microwave material electromagnetic parameter measuring method is characterized in that an electromagnetic parameter measuring device is adopted for measurement, and the measuring process comprises the following steps:
s1: respectively accessing a Through, a reflection and a transmission Line calibration piece to an electromagnetic parameter measuring device for testing to obtain S parameter matrixes in 3 states:
Figure QLYQS_1
、/>
Figure QLYQS_2
and &>
Figure QLYQS_3
；
S2: putting a sample to be tested into a measuring clamp and connecting the sample to be tested into an electromagnetic parameter measuring device for testing to obtain an S parameter matrix
Figure QLYQS_4
Will>
Figure QLYQS_5
、/>
Figure QLYQS_6
、/>
Figure QLYQS_7
And &>
Figure QLYQS_8
Automatically importing electromagnetic parameter calculation software;
s3: performing data processing on the 4S parameter matrixes by adopting a TRL calibration algorithm in electromagnetic parameter calculation software to obtain S parameter matrixes of two end surfaces of the sample to be measured
Figure QLYQS_9
；
S4: using NRW transmission/reflection algorithm to pair S parameter matrix
Figure QLYQS_10
And carrying out inversion, and solving to obtain the electromagnetic parameters of the sample to be detected.
2. The measuring method according to claim 1, wherein the electromagnetic parameter measuring device comprises a vector network analyzer, the measuring clamp, a waveguide coaxial converter with a waveguide tube, a coaxial cable with a stable amplitude and a stable phase and a processor, wherein the vector network analyzer is connected with the processor to realize communication, and the processor is internally provided with the electromagnetic parameter calculating software; two ports of the vector network analyzer are respectively connected with the amplitude-stabilized phase-stabilized coaxial cable and the waveguide coaxial converter containing the waveguide tube; the waveguide coaxial converter containing the waveguide tube comprises two waveguide coaxial converters containing the waveguide tube, the measuring clamp is connected between the two waveguide coaxial converters containing the waveguide tube, and when the measuring clamp is placed into the sample to be measured, the measuring clamp and the two waveguide coaxial converters containing the waveguide tube are fixed through screws to realize mechanical connection; the waveguide coaxial converter with the waveguide tube is of an integrated structure and comprises the waveguide coaxial converter and a rectangular waveguide tube.
3. The measurement method according to claim 2, wherein the step S3 of obtaining the S parameter matrices of the two end faces of the sample to be measured comprises:
two ports of the vector network analyzer are defined as a port 1 and a port 2 respectively, an error box A is integrally defined from the port 1 to one end of a sample to be detected, and an error box B is integrally defined from the port 2 to the other end of the sample to be detected; error box A is represented as
Figure QLYQS_11
And error box B is expressed as->
Figure QLYQS_12
Considering the part of the vector network analyzer from port 1 to port 2, specifically the error box A, the sample to be measured and the error box B, as a cascade network consisting of three two-port networks, and measuring to obtain S parameter matrixes of ports 1 and 2 of the vector network analyzer
Figure QLYQS_13
Specifically, it is represented as:
Figure QLYQS_14
(1)
wherein the parameters with subscripts a and B represent the S-parameters of the error boxes a and B respectively,
Figure QLYQS_17
an input reflection parameter, representing the error box A, is greater than or equal to>
Figure QLYQS_22
An output reflection parameter, representing the error box A, is greater than or equal to>
Figure QLYQS_26
A back transmission parameter, representing the error box A, is greater than>
Figure QLYQS_18
A forward transmission parameter representing the error box A, is greater than or equal to>
Figure QLYQS_21
An input reflection parameter, representing the error box B>
Figure QLYQS_25
Represents an output reflection parameter of the error box B, is greater than>
Figure QLYQS_28
A back transmission parameter, representing the error box B>
Figure QLYQS_16
A forward transmission parameter representing the error box B; the parameters with subscript M represent the S-parameters directly obtained by the vector network analyzer measurements,
Figure QLYQS_20
represents an input reflection parameter, < '> or <' > of the cascade network>
Figure QLYQS_24
Represents an output reflection parameter, < '> or <' > of the cascade network>
Figure QLYQS_27
Represents a reverse transmission parameter, < '> or <' > of the cascaded network>
Figure QLYQS_15
A forward transmission parameter representative of the cascaded network; />
Figure QLYQS_19
、/>
Figure QLYQS_23
Respectively representing a forward signal error and a reverse signal error between two ports of the vector network analyzer when a sample to be detected is accessed;
Figure QLYQS_29
(2)
s parameter matrix of two end faces of sample to be measured
Figure QLYQS_30
，/>
Figure QLYQS_31
Represents an input reflection parameter of the sample to be examined, < '> or <' >>
Figure QLYQS_32
An output reflection parameter representing the sample to be tested, and>
Figure QLYQS_33
a reverse transmission parameter representing the sample to be tested, a>
Figure QLYQS_34
Expressing the forward transmission parameter of the sample to be detected, and obtaining the forward transmission parameter by inverse solution according to the formula (1):
Figure QLYQS_35
(3)
wherein
Figure QLYQS_36
(4)
Based on the S parameter matrix in 3 states obtained in step S1:
Figure QLYQS_38
、/>
Figure QLYQS_41
and &>
Figure QLYQS_43
(ii) a S parameter matrixes obtained when the vector network analyzer measures the straight-Through, the reflection and the transmission Line calibration piece are respectively set as
Figure QLYQS_39
=/>
Figure QLYQS_42
、/>
Figure QLYQS_44
=/>
Figure QLYQS_45
、/>
Figure QLYQS_37
=/>
Figure QLYQS_40
(ii) a Specifically, the following formula:
Figure QLYQS_46
(5)
Figure QLYQS_47
(6)/>
Figure QLYQS_48
(7)
wherein the amount with subscript M is a known amount,
Figure QLYQS_49
and &>
Figure QLYQS_50
The coefficient is an unknown equation coefficient and can be obtained by the solution of the joint type (5), (6) and (7); the combined vertical type (5), (6) and (7) can solve 10 unknown parameters, particularly
Figure QLYQS_51
And &>
Figure QLYQS_52
Substituting the solved 10 parameters into the formula (3), so that the S parameter matrix on two end surfaces of the sample to be detected can be solved>
Figure QLYQS_53
。
4. The measurement method according to claim 3, wherein the step S4 adopts NRW transmission/reflection algorithm to S parameter matrix
Figure QLYQS_54
The inversion process is as follows:
the sample medium to be measured reflects and transmits electromagnetic waves, and the single reflection coefficient at the interface A of air and the medium is set as
Figure QLYQS_57
Then the reflection coefficient at the medium-air interface B is ≥>
Figure QLYQS_60
The thickness of the sample to be detected is->
Figure QLYQS_63
The transmission coefficient between the dividing plane A and B is ^ or ^>
Figure QLYQS_58
S parameter matrix for two end faces of a sample to be tested>
Figure QLYQS_62
Comprises:>
Figure QLYQS_65
and &>
Figure QLYQS_55
；/>
Figure QLYQS_61
And &>
Figure QLYQS_64
And the reflection coefficient->
Figure QLYQS_66
And a transmission coefficient->
Figure QLYQS_56
The relationship of (c) is expressed as:
Figure QLYQS_67
(8)
Figure QLYQS_68
(9)
Figure QLYQS_69
(10)
Figure QLYQS_70
(11)
relative complex dielectric constant and relative complex permeability of sample to be measured and propagation constant of sample section to be measured
Figure QLYQS_71
The relationship of (1) is:
Figure QLYQS_72
(12)
wherein the content of the first and second substances,
Figure QLYQS_73
for the transmission wavelength of the electromagnetic wave in the air->
Figure QLYQS_74
Is the cut-off wavelength of a rectangular waveguide>
Figure QLYQS_75
Is a measure of the relative complex dielectric constant, device for combining or screening>
Figure QLYQS_76
Is a relative complex permeability;
transmission coefficient of sample to be measured
Figure QLYQS_77
Propagation constant->
Figure QLYQS_78
And the thickness of the sample to be determined>
Figure QLYQS_79
The relationship of (1) is:
Figure QLYQS_80
(13)
therefore, the transmission coefficient of the sample to be measured
Figure QLYQS_81
Can be associated with the relative complex dielectric constant and the relative complex permeability of the sample to be measured; at the same time, the reflection coefficient->
Figure QLYQS_82
It is also possible to relate the relative complex permittivity and relative complex permeability of the sample to be measured by means of the wave impedance, namely: />
Figure QLYQS_83
(14)
Figure QLYQS_84
(15)
Figure QLYQS_85
(16)
Wherein, the first and the second end of the pipe are connected with each other,
Figure QLYQS_86
and &>
Figure QLYQS_87
Expressed as characteristic impedances of the air region and the sample section to be examined in the transmission line, respectively>
Figure QLYQS_88
Indicates the permeability of the vacuum->
Figure QLYQS_89
Represents the speed of light; the reflection factor is determined by the formulae (10), (11) and (12)>
Figure QLYQS_90
Comprises the following steps:
Figure QLYQS_91
(17)
by combining the above formulas, the relative complex permeability and the relative complex permittivity of the sample to be measured can be respectively obtained as follows:
Figure QLYQS_92
(18)
Figure QLYQS_93
(19)
wherein Λ is the attenuation of the sample to be measured and is expressed as:
Figure QLYQS_94
(20)
calculating the reflection coefficient of the sample to be measured by using the S parameter
Figure QLYQS_95
And transmission ofCoefficient>
Figure QLYQS_96
And then the electromagnetic parameter->
Figure QLYQS_97
。
5. The measurement method according to claim 4, further comprising solving the multivalued problem of the obtained electromagnetic parameters by:
in the process of obtaining the electromagnetic parameters of the sample to be measured by calculation, the formula (20) relates to the reciprocal of the transmission coefficient
Figure QLYQS_98
Calculating a natural logarithm operation; as shown in equation (21):
Figure QLYQS_99
，n=0,1,2… (21)
n is a natural number; α and β represent a specific constant;
in pair formula (18)
Figure QLYQS_100
With respect to the frequency f derivative, i.e.:
Figure QLYQS_101
(22)
wherein the content of the first and second substances,
Figure QLYQS_103
is the current electromagnetic wave frequency->
Figure QLYQS_106
Is the waveguide cut-off frequency->
Figure QLYQS_108
Is the light speed->
Figure QLYQS_104
Represents a reflection factor->
Figure QLYQS_107
In respect of frequency->
Figure QLYQS_109
Is greater than or equal to>
Figure QLYQS_110
Represents a transmission coefficient pick>
Figure QLYQS_102
In respect of frequency->
Figure QLYQS_105
A derivative of (d); />
Based on the formula (22) will involve pairs
Figure QLYQS_111
Association>
Figure QLYQS_112
The first derivative of (2) is solved by a difference quotient method as follows:
Figure QLYQS_113
(23)
Figure QLYQS_114
(24)
Figure QLYQS_116
represents->
Figure QLYQS_118
In the present frequency of electromagnetic waves>
Figure QLYQS_120
Increase/or>
Figure QLYQS_117
The latter amount of change->
Figure QLYQS_119
Represents->
Figure QLYQS_121
At the current electromagnetic wave frequency->
Figure QLYQS_122
Increase/or>
Figure QLYQS_115
The latter amount of variation;
derivative of equation (22)
Figure QLYQS_123
On the contrary, solve>
Figure QLYQS_124
To determine ∑ of equation (21)>
Figure QLYQS_125
The value is obtained.
6. The method of claim 4 or 5, further comprising measuring when the thickness of the sample to be measured is greater than
Figure QLYQS_126
A half-wave resonance problem solving method is carried out on the obtained electromagnetic parameters, and then the obtained electromagnetic parameters are subjected to the half-wave resonance>
Figure QLYQS_127
The transmission wavelength of the electromagnetic wave in the sample to be detected;
for high-loss or magnetic materials, obtained
Figure QLYQS_128
Value and->
Figure QLYQS_129
The value is the real electromagnetic parameter measured value of the sample to be measured;
for nonmagnetic low-loss materials, use
Figure QLYQS_130
Value to substitute->
Figure QLYQS_131
A value; as can be seen from formula (19):
Figure QLYQS_132
=/>
Figure QLYQS_133
(25)
by using
Figure QLYQS_134
Value instead of>
Figure QLYQS_135
Value, half-wave resonance phenomenon can be weakened;
in order to further weaken the influence caused by the half-wave resonance problem, the reflection coefficient is calculated by adopting an expression (26) instead of expressions (14) to (16)
Figure QLYQS_136
：
Figure QLYQS_137
(26)
Wherein the content of the first and second substances,
Figure QLYQS_138
is the characteristic impedance of the air region in the transmission line>
Figure QLYQS_139
The normalized characteristic impedance of the sample to be detected; />
Figure QLYQS_140
The selection principle of the sign after square opening is based on>
Figure QLYQS_141
Re denotes a function of the real part of the complex number, the positive and negative sum of Z->
Figure QLYQS_142
Are positively correlated. />
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Application publication date: 20230414