CN1155816C - Method for measuring complex dielectric constant of solid dielectric medium - Google Patents

Abstract

The present invention relates to a method for measuring the complex dielectric constant of solid dielectric. The method mainly solves the defects that the existing resonant cavity method and open cavity method require large-volume test samples, and the perturbation method requires the volume of test samples to be far smaller than that of resonant cavities. In the method, a hardware test system is equivalent to the cascade connection of a plurality of network elements, and the complex dielectric constant of a test sample is inversely solved by using a microwave network. The method makes a measurement cavity equivalent to a section of transmission line by using the matrix analysis of network cascade connection, coupling holes at both ends of the cavity are equivalent to two two-port networks, the test sample is equivalent to a two-port network, the measured value of a complex dielectric constant is obtained by the transformation of the resonance frequency and the quality factor of two equivalent networks of a front resonant cavity and a back resonant cavity, and the test sample is put in the front resonant cavity and the back resonant cavity. Since a complicated problem about an electromagnetic field is converted into the simple cascade connection of a plurality of network elements, the present invention achieves a simple form and can be easily extended to other hardware test systems in different forms. Simultaneously, the volume of the test sample can be small or large, the range of a measurable dielectric constant can be enlarged, and the obtained complex dielectric constant is a closed type result, which is favourable for realizing the automatic test of the system in real time.

Description

Method for measuring complex dielectric constant of solid dielectric medium

The present invention relates to a kind of measuring method, is the method for measuring complex dielectric constant of solid dielectric medium specifically.

The develop rapidly of modern communication and microelectronic is had higher requirement to new material.Therefore, accurately measuring complex dielectric is important problems in the material parameter of microwave region.Complex permittivity is defined as $\widetilde{\mathrm{\ϵ}}={\mathrm{\ϵ}}_0\·{\mathrm{\ϵ}}_r={\mathrm{\ϵ}}_0\·{\mathrm{\ϵ}}^{\′}(1-j\tan \mathrm{\δ}),$ DIELECTRIC CONSTANT in the vacuum ₀=8.854 * 10 ^-12Method/rice, ε _rFor complex phase to specific inductive capacity, ε ' is the complex permittivity real part, tan δ is a loss tangent.The measurement of complex permittivity mainly is meant ε ' and tan δ measurement under the characteristic frequency.The measurement of complex dielectric constant of solid dielectric medium has diverse ways in different frequency ranges, but mostly is to utilize measuring system to determine this dielectric complex permittivity in the variation of inserting some parameter under the two kinds of different conditions in dielectric front and back.Relatively Chang Yong measuring system is a resonator system, because when system is in resonant condition, can accurately measure resonance frequency and quality factor, and quality factor are high more, and measuring accuracy is high more.When frequency was low, resonator system utilized tunable capacitor and inductance to form, and main surveying instrument is a HF Q meter, and the frequency range that can survey is from 50kHz to 50MHz, and the Q value is between 20 to 300.Because the distribution parameter effect of this frequency range is not obvious, so new Study of test method and development are slower.Standard GB 9622.9-88 has provided concrete implementation method and computing formula.At the microwave low side, transmission line is widely used as measuring system.The system that standard GB 9533-88 provides forms and operation instruction, mainly put into transmission line and cause standing wave node skew and the standing wave complex permittivity of definite this medium recently according to media samples, be characterized in that sample is cylindric, and only be useful in the measurement of 0.4～2.0GHz scope.Measuring system commonly used in 2～20GHz scope is a cavity resonator, and national standard has provided three kinds of different measuring methods.Wherein, the Resonant-cavity Method that standard GB 5597-85 provides is to utilize column type high quality factor test chamber to measure complex permittivity, and the method for beginning to speak that standard GB 7265.2-87 provides is to utilize the resonance characteristic measuring media complex permittivity of medium block.The common drawback of these two kinds of measuring methods is that the volume of requirement sample is bigger.The perturbation method formula that standard GB 7265.1-87 provides is that complementary field obtains under the condition in perturbation ante-chamber internal field when perturbation, must be under 1 situation in relative frequency deviation, higher accuracy is just arranged, otherwise will introduce bigger theoretical error, therefore, the deficiency of perturbation method is the volume that the volume of sample will be far smaller than resonator cavity.For this reason, develop again on the basis of perturbation method and various new measuring principles and method, these methods mainly are to use the hardware system of perturbation method, and adopt different complex permittivity inversion algorithms.For example, sabet, K.F.etc.Inverse algorithm for integral equation formulation ofdielectric loaded cavities.Proceedings of the 1996 International Geoscience and RemoteSensing Symposium, IGARSS ' 96.Part 2 (of 4) p 1346-1348. document has proposed to utilize full wave analysis method emulation loading chambers structure, makes that sample can be big arbitrarily under the situation that does not influence the resonator coupling.Liang, C.H.; Xie, Y.J.The accurate variational analysis for themeasurement of the complexdielectric constant of asample rod inserted in a cavity.Microwave and OpticalTechnology Letters vol.5, no.5, May 1992, and p.209-11. document has proposed to adopt has the consumption variational method to come the inverting complex permittivity.The common drawback of these two kinds of methods is calculation of complex, is unfavorable for realizing Auto-Test System.

The objective of the invention is to overcome the deficiency of above-mentioned existing measuring technology, provide a kind of calculating simple, realize the method for measuring complex dielectric constant of solid dielectric medium of Auto-Test System easily.

The technical scheme that realizes the object of the invention is that the hardware testing system equivalence is the cascade of a plurality of network elements, calculates the complex permittivity of sample with microwave network parameters.Concrete grammar is:

1. utilize network cascade matrix analysis, be respectively a with wide, high, long, the measurement cavity equivalence of b and l is one section transmission line, is two two-port networks with the coupling aperture equivalence at cavity two ends, as shown in Figure 2.If θ ₀Be the cavity electrical length, B ₀Be both sides coupling aperture diaphragm equivalent susceptance, E is a driving source voltage, Z _SAnd Z _LBe respectively source impedance and loaded impedance, adopt normalized parameter, i.e. guide properties impedance Z ₀=1, the condition of resonance of cavity is

${\mathrm{\θ}}_0={\tan }^{-1}\left(\frac{2}{{\stackrel{\‾}{B}}_0}\right)--\left(1\right)$

For general circular hole diaphragm, B ₀＜0, then further be written as

${\mathrm{\θ}}_0=\mathrm{n\π}-{\tan }^{-1}\left(\frac{2}{\left|{\stackrel{\‾}{B}}_0\right|}\right),(n=\mathrm{1,2},...)--\left(2\right)$

Quality factor

$Q_0=\frac{\mathrm{\πl}/{\mathrm{\λ}}_{g0}}{(1+{\stackrel{\‾}{B}}_0^2)/2+\mathrm{\αl}}{\left(\frac{{\mathrm{\λ}}_{g0}}{{\mathrm{\λ}}_0}\right)}^2--\left(3\right)$

α is the attenuation constant of transmission line in the formula, λ _G0And λ ₀Be respectively waveguide wavelength and free space operation wavelength, and satisfy ${\left(\frac{1}{{\mathrm{\λ}}_{g0}}\right)}^2={\left(\frac{1}{{\mathrm{\λ}}_0}\right)}^2+{\left(\frac{1}{2a}\right)}^2--\left(4\right)$

2. with the sample equivalence two-port network, as shown in Figure 3.B establishes B and equals B for putting into two mother rib lateral rotundum diaphragm equivalent susceptances behind the sample ₀, θ ₁And θ ₂Be the equivalent electric length that sample is put into some the cavity both ends of the surface, itself and equal θ, note θ=θ ₀+ Δ θ.Work as θ ₁=θ ₂The time, can reach desirable resonant condition.[a] is the normalization equivalent network of sample, and condition of resonance is:

$[2{\stackrel{\‾}{a}}_{11}-\frac{{\stackrel{\‾}{B}}_0}{2}({\stackrel{\‾}{a}}_{12}+{\stackrel{\‾}{a}}_{21})]\cos \mathrm{\θ}-[{\stackrel{\‾}{B}}_0{\stackrel{\‾}{a}}_{11}+({\stackrel{\‾}{a}}_{12}+{\stackrel{\‾}{a}}_{21})\sin \mathrm{\θ}=({\stackrel{\‾}{a}}_{12}-{\stackrel{\‾}{a}}_{21})(\frac{1}{{\stackrel{\‾}{B}}_0}+\frac{1}{2}{\stackrel{\‾}{B}}_0)--\left(5\right)$

In the formula, a ₁₁, a ₁₂, a ₂₁It is respectively sample normalization equivalent two port matrix parameter.

The expression formula of quality factor is

$\frac{1}{Q}=\frac{1}{Q_0}+\frac{\mathrm{Re}\left({\stackrel{\‾}{Z}}_{\mathrm{in}}\right)}{\mathrm{\πl}}{\mathrm{\λ}}_g{\left(\frac{\mathrm{\λ}}{{\mathrm{\λ}}_g}\right)}^2--\left(6\right)$

λ and λ in the following formula _gBe respectively free space operation wavelength and the waveguide wavelength behind the loading sample, Re (Z _In) expression puts into the input impedance real part in chamber to the dielectric sample post of band loss.

3. the conversion of the resonance frequency of resonator cavity equivalent network and quality factor draws the measured value of complex permittivity before and after being put into by sample.Fig. 4 supposes that sample is cylindrical, and radius is r, and thinks that the own loss of resonant cavity is far smaller than the loss that media samples causes.

Can obtain the relative dielectric constant real part through deriving is

${\mathrm{\ϵ}}^{\′}=1+\frac{1}{4}\left(\frac{\mathrm{al}}{{\mathrm{\πr}}^2}\right)\frac{4}{(\sqrt{\left|\cos {\mathrm{\θ}}_0\right|}+\frac{1}{\sqrt{\left|\cos {\mathrm{\θ}}_0\right|}})-2(1-\cos \mathrm{\Δ\θ})}\left[{\left(\frac{\mathrm{\λ}}{{\mathrm{\λ}}_g}\right)}^2(-\frac{2\sin \mathrm{\Δ\θ}}{{\mathrm{\θ}}_0})\right]--\left(7\right)$

Loss tangent is

$\tan \mathrm{\&delta;}=\frac{\mathrm{\&xi;}}{{4\mathrm{\&epsiv;}}^{\&prime;}}\left(\frac{\mathrm{al}}{{\mathrm{\&pi;r}}^2}\right)(\frac{1}{Q}-\frac{1}{Q_0}),$ ? $\mathrm{\&xi;}=\frac{{\sin }^2({\mathrm{\&theta;}}_0/2)}{{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="C0011380300081.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2{\mathrm{\&theta;}}_0}\&CenterDot;\frac{1}{1+b\left|{\tan \mathrm{\&theta;}}_0\right|/2}--\left(8\right)$

Work as θ ₀→ (2k+1) π, Δ θ → 0 o'clock can draw the relative dielectric constant real part by (7) formula and is

${\mathrm{\&epsiv;}}^{\&prime;}=1+\frac{1}{4}\left(\frac{\mathrm{al}}{{\mathrm{\&pi;r}}^2}\right)(-\frac{2\mathrm{\&Delta;f}}{f_0})--\left(9\right)$

When ξ → 1, can draw loss tangent by (8) formula and be

$\tan \mathrm{\&delta;}=\frac{1}{{4\mathrm{\&epsiv;}}^{\&prime;}}\left(\frac{\mathrm{al}}{{\mathrm{\&pi;r}}^2}\right)(\frac{1}{Q}-\frac{1}{Q_0})--\left(10\right)$

(9) formula and (10) formula perturbation method formula commonly used just.

The present invention is owing to be converted to the cascade of simple a plurality of network elements with the electromagnetic problems of complexity, thereby is easy to expand to other multi-form hardware testing system; Calculate dielectric complex permittivity owing to utilize resonator system to put into different resonance frequency and the quality factor in sample front and back simultaneously, thus the sample of tolerable large volume, and the feasible expanded range that can survey specific inductive capacity; In addition because the complex permittivity that obtains is a succinct enclosed result, so, help realizing real-time Auto-Test System.

Below provide cavity resonator structure of the present invention and equivalent network figure

Fig. 1 is the cavity resonator structure figure that measures dielectric complex permittivity.

Fig. 2 is the equivalent network of no sample cavity

Fig. 3 is the network equivalent network that the sample cavity is arranged

Fig. 4 is the input impedance calculating chart that the sample cavity is arranged

Resonator cavity measuring system shown in Figure 1 mainly is made up of 3 parts.The 1st, resonator cavity and extraneous electromagnetic energy coupling aperture have two coupling apertures respectively, and are in shapes such as the central authorities of end face, the desirable circle of coupling aperture, ellipse on two end faces of resonator cavity.The 2nd, resonator cavity is rectangular cavity generally speaking.The 3rd, sample, sample can be arbitrary shape, is cylinder and rectangular column generally speaking.The uncontinuity of sample only otherwise influence cavity is coupled, volume can be big arbitrarily.A, b, l are respectively that rectangular cavity xsect broadside size, narrow limit size, chamber are long, and r is the radius of cylindrical sample.

Among Fig. 2, θ ₀Be the cavity electrical length, B ₀Be both sides coupling aperture diaphragm equivalent susceptance, E is a driving source voltage.Adopt normalized parameter, the guide properties impedance Z ₀=1.Z _SAnd Z _LBe respectively source impedance and loaded impedance.The condition of resonance that draws cavity is (1) formula.For general circular hole diaphragm, B ₀＜0, the condition of resonance that then draws cavity is (2) formula, and the quality factor that draw are (3) formula, and satisfies (4) formula.

Fig. 3 is that sample is put into the equivalent network that removes driving source and load behind the resonator cavity.B is for putting into garden, both sides pore membrane sheet equivalent susceptance behind the sample, and according to setting of the present invention, it equals B ₀θ ₁And θ ₂Be the equivalent electric length that sample is put into some the cavity both ends of the surface, itself and equal θ, note θ=θ ₀+ Δ θ.Work as θ ₁=θ ₂The time, can reach desirable resonant condition.[a] is the normalization equivalent network matrix of sample, draws condition of resonance and is (5) formula, and the quality factor that draw are (6) formula.

Fig. 4 is the input impedance calculating chart that the sample cavity is arranged.Here suppose that sample is circular, and think that the own loss of resonant cavity is far smaller than the loss that media samples causes.Draw complex phase specific inductive capacity is (7) formula, draw loss tangent and be (8) formula.Work as θ ₀→ (2k+1) π, Δ θ → 0 o'clock, (7) formula becomes (9) formula, and when ξ → 1, (8) formula becomes (10) formula.

Claims (1)

1. method of measuring complex dielectric constant of solid dielectric medium is characterized in that the hardware testing system equivalence is the cascade of a plurality of network elements, utilizes the resonant parameter of microwave system to calculate the complex permittivity of sample, and step is as follows:

[1] utilize network cascade matrix analysis, be respectively a with wide, high, long, the measurement cavity equivalence of b and l is one section transmission line, is two two-port networks with the coupling aperture equivalence at cavity two ends, establishes θ ₀Be the cavity electrical length, B ₀Be both sides coupling aperture diaphragm equivalent susceptance, E is a driving source voltage, Z _SAnd Z _LBe respectively source impedance and loaded impedance, adopt normalized parameter, i.e. guide properties impedance Z ₀=1, the condition of resonance of cavity is

${\mathrm{\&theta;}}_0={\tan }^{-1}\left(\frac{2}{{\stackrel{\&OverBar;}{B}}_0}\right)--\left(1\right)$

For general circular hole diaphragm, B ₀＜0, then condition of resonance is

${\mathrm{\&theta;}}_0=\mathrm{n\&pi;}-{\tan }^{-1}\left(\frac{2}{\left|{\stackrel{\&OverBar;}{B}}_0\right|}\right),(n=\mathrm{1,2},...)--\left(2\right)$

Quality factor are

$Q_0=\frac{\mathrm{\&pi;l}/{\mathrm{\&lambda;}}_{g0}}{(1+{\stackrel{\&OverBar;}{B}}_0^2)/2+\mathrm{\&alpha;l}}{\left(\frac{{\mathrm{\&lambda;}}_{g0}}{{\mathrm{\&lambda;}}_0}\right)}^2--\left(3\right)$

α is the attenuation constant of transmission line in the formula, λ _G0And λ ₀Be respectively waveguide wavelength and free space operation wavelength, and satisfy ${\left(\frac{1}{{\mathrm{\&lambda;}}_{g0}}\right)}^2={\left(\frac{1}{{\mathrm{\&lambda;}}_0}\right)}^2+{\left(\frac{1}{2a}\right)}^2--\left(4\right)$

[2] with the sample equivalence be a two-port network, B establishes B and equals B for putting into two mother rib lateral rotundum diaphragm equivalent susceptances behind the sample ₀, θ ₁And θ ₂Be the equivalent electric length that sample is put into some the cavity both ends of the surface, itself and equal θ, note θ=θ ₀+ Δ θ works as θ ₁=θ ₂The time, can reach desirable resonant condition, [a] is the normalization equivalent network of sample, condition of resonance is:

$[2{\stackrel{\&OverBar;}{a}}_{11}-\frac{{\stackrel{\&OverBar;}{B}}_0}{2}({\stackrel{\&OverBar;}{a}}_{12}+{\stackrel{\&OverBar;}{a}}_{21})]\cos \mathrm{\&theta;}-[{\stackrel{\&OverBar;}{B}}_0{\stackrel{\&OverBar;}{a}}_{11}+({\stackrel{\&OverBar;}{a}}_{12}+{\stackrel{\&OverBar;}{a}}_{21})\sin \mathrm{\&theta;}=({\stackrel{\&OverBar;}{a}}_{12}-{\stackrel{\&OverBar;}{a}}_{21})(\frac{1}{{\stackrel{\&OverBar;}{B}}_0}+\frac{1}{2}{\stackrel{\&OverBar;}{B}}_0)--\left(5\right)$

In the formula, a ₁₁, a ₁₂, a ₂₁Be respectively sample normalization equivalent two port matrix parameter,

The expression formula of quality factor is

$\frac{1}{Q}=\frac{1}{Q_0}+\frac{\mathrm{Re}\left({\stackrel{\&OverBar;}{Z}}_{\mathrm{in}}\right)}{\mathrm{\&pi;l}}{\mathrm{\&lambda;}}_g{\left(\frac{\mathrm{\&lambda;}}{{\mathrm{\&lambda;}}_g}\right)}^2--\left(6\right)$

λ and λ in the following formula _gBe respectively free space operation wavelength and the waveguide wavelength behind the loading sample, Re (Z _In) expression puts into the input impedance real part in chamber to the dielectric sample post of band loss;

[3] put into by sample before and after the conversion of the resonance frequency of resonator cavity equivalent network and quality factor draw the measured value of complex permittivity, if sample is cylindrical, and think that the own loss of resonant cavity is far smaller than the loss that media samples causes, can obtain the relative dielectric constant real part to be

${\mathrm{\&epsiv;}}^{\&prime;}=1+\frac{1}{4}\left(\frac{\mathrm{al}}{{\mathrm{\&pi;r}}^2}\right)\frac{4}{(\sqrt{\left|\cos {\mathrm{\&theta;}}_0\right|}+\frac{1}{\sqrt{\left|\cos {\mathrm{\&theta;}}_0\right|}})-2(1-\cos \mathrm{\&Delta;\&theta;})}\left[{\left(\frac{\mathrm{\&lambda;}}{{\mathrm{\&lambda;}}_g}\right)}^2(-\frac{2\sin \mathrm{\&Delta;\&theta;}}{{\mathrm{\&theta;}}_0})\right]--\left(7\right)$

Loss tangent is

$\tan \mathrm{\&delta;}=\frac{\mathrm{\&xi;}}{{4\mathrm{\&epsiv;}}^{\&prime;}}\left(\frac{\mathrm{al}}{{\mathrm{\&pi;r}}^2}\right)(\frac{1}{Q}-\frac{1}{Q_0}),$ $\mathrm{\&xi;}=\frac{{\sin }^2({\mathrm{\&theta;}}_0/2)}{{\cos }^2{\mathrm{\&theta;}}_0}\&CenterDot;\frac{1}{1+b\left|{\tan \mathrm{\&theta;}}_0\right|/2}--\left(8\right)$

In the formula, r is the radius of cylinder shape medium sample.

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