CN103149449A - Single-port coaxial line complex permittivity measuring device and method based on mode matching - Google Patents

Abstract

The invention provides a single-port coaxial line complex permittivity measuring device and a method based on mode matching. The single-port coaxial line complex permittivity measuring device comprises a coaxial line cable connector, a coaxial waveguide section and a terminal short circuit metal plate, wherein the coaxial line cable connector, the coaxial waveguide section and the terminal short circuit metal plate are connected in sequence, the lateral dimension of the coaxial waveguide section is not dependent on the size of the coaxial line cable connector, and the coaxial waveguide section works in a multimode state. The measuring method relates to the measuring device and a vector network analyzer. A reflection coefficient of a sensing device which is filled in substance to be measured is measured through the vector network analyzer and then through data processing, a complex permittivity of the substance is achieved through inversion. Due to the fact that a multimode matching model is used in the inversion process, the coaxial waveguide section can works in the multimode state, so that the design and processing demands of measuring and sensing devices are lowered and an upper limit of working frequency is improved.

Description

Single port coaxial line type complex dielectric constant measuring apparatus and method based on the mould coupling

Technical field

The present invention relates to a kind of single port coaxial line type complex dielectric constant measuring apparatus and method based on the mould coupling.

Background technology

The complex permittivity of measurement of species is significant in scientific research and commercial production, especially in the frequency microwave frequency range.Along with developing rapidly of electronic technology, the survey frequency scope of vector network analyzer is increasing, precision is more and more higher, complex permittivity frequency domain measuring method based on vector network analyzer is widely studied, wherein a kind of wide-band width measurement method commonly used is coaxial axis method, the method has been filled the reflection-transmission coefficient of the coaxial waveguide of sample by measurement, according to the mathematical relation between the complex permittivity of reflection-transmission coefficient and sample, be finally inversed by the complex permittivity under different frequency.Traditional coaxial axis method requires to fill in the coaxial waveguide of sample and only has the TEM ripple, and mathematical model is fairly simple like this, but when practical application, need to carry out particular design to the coaxial cable junction of different size, does not have higher mode to be energized out with assurance.

Summary of the invention

The invention provides a kind of coaxial waveguide of terminal short circuit of utilizing and the material complex permittivity is carried out the method for wide-band width measurement.

A kind of single port coaxial line type complex dielectric constant measuring apparatus based on the mould coupling comprises the coaxial fitting, coaxial waveguide section and the terminal short circuit sheet metal that are connected successively; The lateral dimension of coaxial waveguide section does not rely on the size of coaxial fitting; The coaxial waveguide section works in the multimode state.

Described coaxial fitting is SMA or N-type head.

A kind of single port coaxial line type method for measuring complex dielectric constant based on the mould coupling of described device, step is as follows:

1) calibration vector network analyzer is elected alignment surface as the z=-L face, calibrates;

2) measure the reflection coefficient of empty measurement mechanism, obtain equivalent electric length from the z=-L face to the z=0 face and the length d of coaxial waveguide section;

3) measure the reflection coefficient of the measurement mechanism of having filled sample;

4) according to step 2), 3) measurement data carry out Inversion Calculation, obtain the complex permittivity of sample under different frequency:

Three kinds of patterns of TEM, TM and TE are arranged in coaxial waveguide, and the higher mode of excitation only has TM _0mMould, the TM in coaxial waveguide _0mThe modular function of mould is Z (ζ _amρ)=J ₁(ζ _amρ)+G _amN ₁(ζ _amρ), wherein ρ is radial coordinate, J ₁And N ₁Respectively the first kind and the Equations of The Second Kind Bessel function of single order, G _amScale-up factor, ζ _amTM _0mThe horizontal transmission function of mould, the left and right sides, surface of discontinuity place represent with subscript a and b respectively, and direct problem model mode expansion is:

$E_{\mathrm{a\ρ}}=A_{a0}(1+{\mathrm{\Γ}}_{a0})(1/\mathrm{\ρ})+\underset{m=1}{\overset{\∞}{\mathrm{\Σ}}}{A}_{\mathrm{am}}{Z}_1\left({\mathrm{\ζ}}_{\mathrm{am}}\mathrm{\ρ}\right)$

$E_{\mathrm{b\ρ}}=A_{b0}(1+{\mathrm{\Γ}}_{b0})(1/\mathrm{\ρ})+\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{A}_{\mathrm{bn}}(1+{\mathrm{\Γ}}_{\mathrm{bn}})Z_1\left({\mathrm{\ζ}}_{\mathrm{bn}}\mathrm{\ρ}\right)$

Wherein A represents the incident wave amplitude of each pattern, is unknown quantity, and Y represents the mode admittance of each pattern:

$Y_{\mathrm{<figure-callout\; id="0"\; label="a"\; filenames="130129172613.png"\; state="\{\{state\}\}">a</figure-callout>}0}=\sqrt{\frac{{\mathrm{\&epsiv;}}_a}{{\mathrm{\&mu;}}_0}}$ $Y_{\mathrm{am}}=\frac{\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_a{\mathrm{\&mu;}}_0}}{k_{\mathrm{zam}}}$

${\mathrm{<figure-callout\; id="0"\; label="Y\; b"\; filenames="130129172613.png"\; state="\{\{state\}\}">Y</figure-callout>}}_b=\sqrt{\frac{{\mathrm{\&epsiv;}}_b}{{\mathrm{\&mu;}}_0}}$ $Y_{\mathrm{bn}}=\frac{\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_0}}{k_{\mathrm{zbn}}}$

Represent that each pattern is at the ratio of surface of discontinuity place's reflection wave and incident wave:

${\mathrm{\&Gamma;}}_{\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="130129172613.png"\; state="\{\{state\}\}">b</figure-callout>}0}=-\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="130129172613.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_{0}d}\right)$

${\mathrm{\&Gamma;}}_{\mathrm{bn}}=-\exp \left(j2k_{\mathrm{zbn}}d\right)$

Wherein ω is the angular frequency of measuring, ε _a, ε _bRespectively the specific inductive capacity of the filling material of coaxial fitting and coaxial waveguide section, k _zamAnd k _zbnIt is the longitudinal propagation constant of each pattern:

$k_{\mathrm{zam}}=-j\sqrt{{\mathrm{\&zeta;}}_{\mathrm{am}}^2-{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}_a{\mathrm{\&mu;}}_0}$

$k_{\mathrm{zbn}}=-j\sqrt{{\mathrm{\&zeta;}}_{\mathrm{bn}}^2-{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_0}$

Have according to surface of discontinuity place boundary condition:

R ₄≤ρ≤R ₂

E _aρ＝0,R ₁≤ρ≤R ₄

E _bρ＝0,R ₂≤ρ≤R ₃

Wherein, R ₁, R ₂Respectively the radius of the internal and external conductor of standard coaxial joint, R ₄, R ₃It is respectively the radius of the internal and external conductor of coaxial waveguide section;

Utilize the orthogonality of Bessel function, can solve Г with numerical method _a0/ A _a0, i.e. the reflection coefficient of whole measurement mechanism; On the basis of direct problem model, with the inverse problem algorithm, the reflection coefficient of measuring is finally inversed by the complex permittivity of testing sample.

Beneficial effect of the present invention: this method is based on the mould Matching Model in coaxial cable, do not require and only have the TEM ripple in sample, the sampling receptacle of any size can directly connect with concentric cable, and the upper limit of survey frequency also significantly improves because being not limited to the TEM ripple.Owing to having used the mould Matching Model in the data inversion process, so have the survey frequency wide ranges, sensing device is simple in structure and the measuring accuracy advantages of higher.

Description of drawings

Accompanying drawing 1 is based on the single port coaxial line type complex dielectric constant measuring apparatus structural representation of mould coupling.

Accompanying drawing 2 is based on the single port coaxial line type method for measuring complex dielectric constant schematic diagram of mould coupling.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described further.Based on single port coaxial line type complex dielectric constant measuring apparatus structure such as the accompanying drawing 1 of mould coupling, wherein 1 is the standard coaxial cable joint, the 2nd, and as the coaxial waveguide section of sampling receptacle, the 3rd, short circuit sheet metal.The standard coaxial cable joint here can be that SMA or N-type are first-class, the lateral dimension of coaxial waveguide section 2 does not rely on coaxial fitting 1, this application scenario for the large capacity sampling receptacle of needs is very favourable, and the internal and external conductor diameter of coaxial waveguide section 2 can design arbitrarily according to functional need.

The measuring method schematic diagram as shown in Figure 2, wherein 4 is vector network analyzers, the 5th, measure concentric cable, the 6th, measure sensing device.

Measuring process is as follows:

1. calibration vector network analyzer: elect alignment surface as the z=-L face, calibrate vowing net.

2. measure the reflection coefficient of empty sensing device (being that filling material is air), to obtain equivalent electric length from the z=-L face to the z=0 face and the length d of coaxial waveguide section 2.

3. measure the reflection coefficient of the sensing device of having filled sample.

4. above measurement data is carried out Inversion Calculation, obtain the complex permittivity of sample under different frequency.

The below provides data inversion method.Because this problem is the inverse problem of a standard, so at first need to set up the direct problem model, used is the mould Matching Model here.So-called mould coupling refers to, if the somewhere physical dimension is undergone mutation in waveguide, each pattern size of the field of surface of discontinuity both sides can be determined at the boundary condition of surface of discontinuity according to electromagnetic field so.

Three kinds of patterns of TEM, TM and TE are arranged in coaxial waveguide, and in coaxial configuration as shown in Figure 1, because the incident wave of coming from concentric cable only has the TEM ripple, and surface of discontinuity has axial symmetry, so the higher mode of excitation only has TM _0mMould, the TM in coaxial waveguide _0mThe modular function of mould is Z (ζ _amρ)=J ₁(ζ _amρ)+G _amN ₁(ζ _amρ), wherein ρ is radial coordinate, J ₁And N ₁Respectively the first kind and the Equations of The Second Kind Bessel function of single order, G _amScale-up factor, ζ _amTM _0mThe horizontal transmission function of mould.Like this electromagnetic field of the left and right sides, surface of discontinuity place (representing take subscript a and b respectively) can with mode expansion as:

$E_{\mathrm{a\&rho;}}=A_{a0}(1+{\mathrm{\&Gamma;}}_{a0})(1/\mathrm{\&rho;})+\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{A}_{\mathrm{am}}{Z}_1\left({\mathrm{\&zeta;}}_{\mathrm{am}}\mathrm{\&rho;}\right)$

$E_{\mathrm{b\&rho;}}=A_{b0}(1+{\mathrm{\&Gamma;}}_{b0})(1/\mathrm{\&rho;})+\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{A}_{\mathrm{bn}}(1+{\mathrm{\&Gamma;}}_{\mathrm{bn}})Z_1\left({\mathrm{\&zeta;}}_{\mathrm{bn}}\mathrm{\&rho;}\right)$

Wherein A represents the incident wave amplitude of each pattern, is unknown quantity, and Y represents the mode admittance of each pattern:

$Y_{\mathrm{<figure-callout\; id="0"\; label="a"\; filenames="130129172613.png"\; state="\{\{state\}\}">a</figure-callout>}0}=\sqrt{\frac{{\mathrm{\&epsiv;}}_a}{{\mathrm{\&mu;}}_0}}$ $Y_{\mathrm{am}}=\frac{\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_a{\mathrm{\&mu;}}_0}}{k_{\mathrm{zam}}}$

${\mathrm{<figure-callout\; id="0"\; label="Y\; b"\; filenames="130129172613.png"\; state="\{\{state\}\}">Y</figure-callout>}}_b=\sqrt{\frac{{\mathrm{\&epsiv;}}_b}{{\mathrm{\&mu;}}_0}}$ $Y_{\mathrm{bn}}=\frac{\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_0}}{k_{\mathrm{zbn}}}$

Represent that each pattern is at the ratio of surface of discontinuity place's reflection wave and incident wave:

${\mathrm{\&Gamma;}}_{\mathrm{<figure-callout\; id="0"\; label="b"\; filenames="130129172613.png"\; state="\{\{state\}\}">b</figure-callout>}0}=-\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="130129172613.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_{0}d}\right)$

${\mathrm{\&Gamma;}}_{\mathrm{bn}}=-\exp \left(j2k_{\mathrm{zbn}}d\right)$

Wherein ω is the angular frequency of measuring, ε _a, ε _bRespectively the specific inductive capacity of the filling material of coaxial fitting and coaxial waveguide section, k _zamAnd k _zbnIt is the longitudinal propagation constant of each pattern:

$k_{\mathrm{zam}}=-j\sqrt{{\mathrm{\&zeta;}}_{\mathrm{am}}^2-{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}_a{\mathrm{\&mu;}}_0}$

$k_{\mathrm{zbn}}=-j\sqrt{{\mathrm{\&zeta;}}_{\mathrm{bn}}^2-{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_0}$

Have according to surface of discontinuity place boundary condition:

R ₄≤ρ≤R ₂

E _aρ＝0,R ₁≤ρ≤R ₄

E _bρ＝0,R ₂≤ρ≤R ₃

Wherein, R ₁, R ₂Respectively the radius of the internal and external conductor of standard coaxial joint, R ₄, R ₃It is respectively the radius of the internal and external conductor of coaxial waveguide section.

Above-mentioned formula has been described the total electromagnetic field that is combined to form of infinite a plurality of patterns, and the amplitude of each pattern reduces along with the increase of pattern exponent number, when carrying out numerical evaluation, as long as limited enough pattern of intercepting.Utilize the orthogonality of Bessel function, can solve with numerical method

Be the reflection coefficient of whole sensing device, this is the solution procedure of direct problem.

On the basis of direct problem model, can the reflection coefficient of measuring be finally inversed by with simple inverse problem algorithm (as Newton iteration method) complex permittivity of sample.

Claims (3)

1. the single port coaxial line type complex dielectric constant measuring apparatus based on the mould coupling, is characterized in that, it comprises coaxial fitting (1), coaxial waveguide section (2) and the terminal short circuit sheet metal (3) that is connected successively; The lateral dimension of coaxial waveguide section (2) does not rely on the size of coaxial fitting (1); Coaxial waveguide section (2) works in the multimode state.

2. device according to claim 1, is characterized in that, described coaxial fitting (1) is SMA or N-type head.

3. the single port coaxial line type method for measuring complex dielectric constant based on the mould coupling that installs according to claim 1, is characterized in that, step is as follows:

1) calibration vector network analyzer (4), elect alignment surface as the z=-L face, calibrates;

2) measure the reflection coefficient of empty measurement mechanism, obtain equivalent electric length from the z=-L face to the z=0 face and the length d of coaxial waveguide section (2);

3) measure the reflection coefficient of the measurement mechanism of having filled sample;

4) according to step 2), 3) measurement data carry out Inversion Calculation, obtain the complex permittivity of sample under different frequency: three kinds of patterns of TEM, TM and TE are arranged in coaxial waveguide, and the higher mode of excitation only has TM _0mMould, the TM in coaxial waveguide _0mThe modular function of mould is Z (ζ _amρ)=J ₁(ζ _amρ)+G _amN ₁(ζ _amρ), wherein ρ is radial coordinate, J ₁And N ₁Respectively the first kind and the Equations of The Second Kind Bessel function of single order, G _amScale-up factor, ζ _amTM _0mThe horizontal transmission function of mould, the left and right sides, surface of discontinuity place represent with subscript a and b respectively, and direct problem model mode expansion is:

$E_{\mathrm{a\&rho;}}=A_{a0}(1+{\mathrm{\&Gamma;}}_{a0})(1/\mathrm{\&rho;})+\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{A}_{\mathrm{am}}{Z}_1\left({\mathrm{\&zeta;}}_{\mathrm{am}}\mathrm{\&rho;}\right)$

$E_{\mathrm{b\&rho;}}=A_{b0}(1+{\mathrm{\&Gamma;}}_{b0})(1/\mathrm{\&rho;})+\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{A}_{\mathrm{bn}}(1+{\mathrm{\&Gamma;}}_{\mathrm{bn}})Z_1\left({\mathrm{\&zeta;}}_{\mathrm{bn}}\mathrm{\&rho;}\right)$

Wherein A represents the incident wave amplitude of each pattern, is unknown quantity, and Y represents the mode admittance of each pattern:

$Y_{a0}=\sqrt{\frac{{\mathrm{\&epsiv;}}_a}{{\mathrm{\&mu;}}_0}}$ $Y_{\mathrm{am}}=\frac{\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_a{\mathrm{\&mu;}}_0}}{k_{\mathrm{zam}}}$

$Y_{b0}=\sqrt{\frac{{\mathrm{\&epsiv;}}_b}{{\mathrm{\&mu;}}_0}}$ $Y_{\mathrm{bn}}=\frac{\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_0}}{k_{\mathrm{zbn}}}$

Represent that each pattern is at the ratio of surface of discontinuity place's reflection wave and incident wave:

${\mathrm{\&Gamma;}}_{b0}=-\exp \left(j2\mathrm{\&omega;}\sqrt{{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_{0}d}\right)$

${\mathrm{\&Gamma;}}_{\mathrm{bn}}=-\exp \left(j2k_{\mathrm{zbn}}d\right)$

Wherein ω is the angular frequency of measuring, ε _a, ε _bRespectively the specific inductive capacity of the filling material of coaxial fitting (1) and coaxial waveguide section (2), k _zamAnd k _zbnIt is the longitudinal propagation constant of each pattern:

$k_{\mathrm{zam}}=-j\sqrt{{\mathrm{\&zeta;}}_{\mathrm{am}}^2-{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}_a{\mathrm{\&mu;}}_0}$

$k_{\mathrm{zbn}}=-j\sqrt{{\mathrm{\&zeta;}}_{\mathrm{bn}}^2-{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}_b{\mathrm{\&mu;}}_0}$

Have according to surface of discontinuity place boundary condition:

R ₄≤ρ≤R ₂

E _aρ＝0,R ₁≤ρ≤R ₄

E _bρ＝0,R ₂≤ρ≤R ₃

Wherein, R ₁, R ₂Respectively the radius of the internal and external conductor of standard coaxial joint (1), R ₄, R ₃It is respectively the radius of the internal and external conductor of coaxial waveguide section (2);

Utilize the orthogonality of Bessel function, can solve Г with numerical method _a0/ A _a0, i.e. the reflection coefficient of whole measurement mechanism; On the basis of direct problem model, with the inverse problem algorithm, the reflection coefficient of measuring is finally inversed by the complex permittivity of testing sample.

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