CN104569618A - Dielectric property testing method for dielectric materials - Google Patents

Abstract

A dielectric property testing method for dielectric materials includes connecting an upper coaxial transmission line and a lower coaxial transmission line with a vector network analyzer, enabling an upper cylindrical resonance cavity and a lower cylindrical resonance cavity to be aligned to each other and contact, stimulating a TE0np resonance mode in the cylindrical resonance cavity so that insertion loss of resonance peak in the upper cylindrical resonance cavity and the lower cylindrical resonance cavity is at the minimum, and measuring cavity resonance frequency and quality factor; arranging a dielectric substrate to be tested between an upper strip-shaped conductor flange and a lower strip-shaped conductor flange; stimulating the TE0np resonance mode in the cylindrical resonance cavities and adjusting a coupling ring to enable the insertion loss of the resonance peak in the upper and lower cylindrical resonance cavities to be the minimum, and measuring the prediction value of relative dielectric constant of the dielectric substrate to be tested; calculating dielectric property parameter value of the dielectric materials of the dielectric substrate to be tested.

Description

Dielectric performance of dielectric material method of testing

Technical field

The present invention relates to high frequency pcb substrate dielectric properties field tests, more particularly, the present invention relates to a kind of dielectric performance of dielectric material method of testing adopting division right cylinder resonator cavity, described method such as can be used for measuring high frequency and prints the dielectric properties of base material.

Background technology

Dielectric properties are that high frequency prints one of important performance parameter of base material, and it is all vital for accurately testing the production of dielectric properties to high-frequency circuit design, high-frequency electronic product of high frequency printing base material, sizing and debugging; For some application, the measuring accuracy of the specific inductive capacity of printed board requires within 2%.

The measuring accuracy of dielectric properties is relevant to factors such as frequency, homogeneity, anisotropy, temperature, surfacenesses, and for anisotropic material, checkout area direction is vital.High frequency prints the anisotropic material that base material is made up of the polycomponent such as organic resin and reinforcing material.Along with electronics are constantly to high frequency, low-loss future development, high frequency is printed base material test frequency and is brought up to present 10GHz from initial 1MHz, even arrives 20GHz.

Although the research of dielectric properties method of testing just has bibliographical information from mid-term in last century, along with improving constantly of test frequency, the development of material, many method of testings are also not suitable for high frequency printing base material.Therefore, select suitable testing scheme to study it to have important practical significance to the development of high frequency printing base material.

Summary of the invention

Technical matters to be solved by this invention is for there is above-mentioned defect in prior art, provides a kind of and tests easy for installation and can meet the dielectric performance of dielectric material method of testing that high frequency prints the high requirement of base material loss accuracy test.

In order to realize above-mentioned technical purpose, according to the present invention, provide the dielectric performance of dielectric material method of testing adopting division right cylinder resonator cavity.

Described division right cylinder resonator cavity comprises: upper Cylindrical resonant cavity separated from one another and lower Cylindrical resonant cavity; Wherein, upper Cylindrical resonant cavity comprises one end and closes the Upper cylindrical shape cavity of one end open, a pair top strip conductive ledge be arranged on the openend of Upper cylindrical shape cavity, the top coupling ring being arranged in Upper cylindrical shape inside cavity and the top coaxial transmission line be connected with top coupling ring; And wherein, top coaxial transmission line through the roof of Upper cylindrical shape cavity or sidewall top coupling ring is connected to outside; Wherein, lower Cylindrical resonant cavity comprises one end and closes the lower cylindrical shape cavity of one end open, a pair bottom strip conductive ledge be arranged on the openend of lower cylindrical shape cavity, the bottom coupling ring being arranged in lower cylindrical shape inside cavity and the bottom coaxial transmission line be connected with bottom coupling ring; And wherein, bottom coaxial transmission line through the roof of lower cylindrical shape cavity or sidewall bottom coupling ring is connected to outside.

Described dielectric performance of dielectric material method of testing comprises:

First step: top coaxial transmission line is connected to vector network analyzer, is connected to vector network analyzer by bottom coaxial transmission line;

Second step: Cylindrical resonant cavity is contacted with lower Cylindrical resonant cavity alignment relative, to make the opening of Upper cylindrical shape cavity rectify openend to lower cylindrical shape cavity, and top strip conductive ledge contacts with bottom strip conductive ledge;

Third step: pass through vector network analyzer, top coupling ring is made to excite TE0np mode of resonance in upper Cylindrical resonant cavity, and bottom coupling ring excites TE0np mode of resonance in lower Cylindrical resonant cavity, and regulate top coupling ring and bottom coupling ring to make the insertion loss of harmonic peak in Cylindrical resonant cavity and lower Cylindrical resonant cavity minimum, measure cavity resonance frequency and quality factor thus;

4th step: arrange testing medium substrate between top strip conductive ledge and bottom strip conductive ledge, the distance wherein between top strip conductive ledge and bottom strip conductive ledge equals the thickness of testing medium substrate;

5th step: pass through vector network analyzer, top coupling ring is made to excite TE0np mode of resonance in upper Cylindrical resonant cavity, and bottom coupling ring excites TE0np mode of resonance in lower Cylindrical resonant cavity, and regulate top coupling ring and bottom coupling ring to make the insertion loss of harmonic peak in Cylindrical resonant cavity and lower Cylindrical resonant cavity minimum, measure the discreet value of the relative dielectric constant of testing medium substrate thus;

6th step: the discreet value of relative dielectric constant that the cavity resonance frequency obtained according to third step and quality factor, the 5th step obtain and the size of dielectric substrate, calculate the dielectric properties parameter value of the dielectric material of testing medium substrate.

Preferably, in a first step, by top microwave cable, top coaxial transmission line is connected to vector network analyzer, by bottom microwave cable, bottom coaxial transmission line is connected to vector network analyzer.

Preferably, top coupling ring and bottom coupling ring are positioned opposite on the direction of the cylindrical cross-section radius of upper Cylindrical resonant cavity and lower Cylindrical resonant cavity.

Preferably, top coupling ring is placed in most strength, magnetic field in Cylindrical resonant cavity, and plane of a loop is vertical with the magnetic line of force of resettlement place; Bottom coupling ring is placed in most strength, magnetic field in lower Cylindrical resonant cavity, and plane of a loop is vertical with the magnetic line of force of resettlement place.

Preferably, the cylindrical cross-section radius of upper Cylindrical resonant cavity and lower Cylindrical resonant cavity is equal.

Preferably, the chamber appearance etc. of upper Cylindrical resonant cavity and lower Cylindrical resonant cavity.

Preferably, the diameter of testing medium substrate is not less than 4/3 times of the cylindrical cross-section radius of Cylindrical resonant cavity and lower Cylindrical resonant cavity.

Accompanying drawing explanation

By reference to the accompanying drawings, and by reference to detailed description below, will more easily there is more complete understanding to the present invention and more easily understand its adjoint advantage and feature, wherein:

Fig. 1 schematically shows the cross section structure figure of division right cylinder resonator cavity under the state of not arranging testing medium substrate that dielectric performance of dielectric material method of testing according to the preferred embodiment of the invention adopts.

Fig. 2 schematically shows the cross section structure figure of division right cylinder resonator cavity under the state arranging testing medium substrate that dielectric performance of dielectric material method of testing according to the preferred embodiment of the invention adopts.

Fig. 3 schematically shows the process flow diagram of dielectric performance of dielectric material method of testing according to the preferred embodiment of the invention.

Fig. 4 and Fig. 5 schematically show the test johning knot composition of the division right cylinder resonator cavity that dielectric performance of dielectric material method of testing according to the preferred embodiment of the invention adopts.

It should be noted that, accompanying drawing is for illustration of the present invention, and unrestricted the present invention.Note, represent that the accompanying drawing of structure may not be draw in proportion.Further, in accompanying drawing, identical or similar element indicates identical or similar label.

Embodiment

In order to make content of the present invention clearly with understandable, below in conjunction with specific embodiments and the drawings, content of the present invention is described in detail.

Fig. 1 and Fig. 2 schematically shows the division right cylinder resonator cavity that dielectric performance of dielectric material method of testing according to the preferred embodiment of the invention adopts.

As depicted in figs. 1 and 2, divide right cylinder resonator cavity according to the preferred embodiment of the invention to comprise: upper Cylindrical resonant cavity 100 separated from one another and lower Cylindrical resonant cavity 200.

Wherein, upper Cylindrical resonant cavity 100 comprises one end and closes the Upper cylindrical shape cavity 101 of one end open, a pair top strip conductive ledge 102 be arranged on the openend of Upper cylindrical shape cavity 101, the top coupling ring 103 being arranged in Upper cylindrical shape cavity 101 inside and the top coaxial transmission line 104 be connected with top coupling ring 103.

And wherein, top coaxial transmission line 104 through the roof of Upper cylindrical shape cavity 101 or sidewall top coupling ring 103 to be connected to outside (being such as connected to external testing instrument).

Similarly, wherein, lower Cylindrical resonant cavity 200 comprises one end and closes the lower cylindrical shape cavity 201 of one end open, a pair bottom strip conductive ledge 202 be arranged on the openend of lower cylindrical shape cavity 201, the bottom coupling ring 203 being arranged in lower cylindrical shape cavity 201 inside and the bottom coaxial transmission line 204 be connected with bottom coupling ring 203.

And wherein, bottom coaxial transmission line 204 through the roof of lower cylindrical shape cavity 201 or sidewall bottom coupling ring 203 to be connected to outside (being such as connected to external testing instrument).

Wherein, when specifically measuring, Cylindrical resonant cavity 100 and lower Cylindrical resonant cavity 200 alignment relative should be made to arrange, to make the opening of Upper cylindrical shape cavity 101 rectify openend to lower cylindrical shape cavity 201, and top strip conductive ledge 102 is parallel just to bottom strip conductive ledge 202.

When concrete measurement testing medium substrate 300, arrange testing medium substrate 300 between top strip conductive ledge 102 and bottom strip conductive ledge 202, and the thickness that the distance between top strip conductive ledge 102 and bottom strip conductive ledge 202 equals testing medium substrate 300 (is assumed to be d).

Wherein, when specifically measuring, top coupling ring 103 excites TE in upper Cylindrical resonant cavity 100 _0npmode of resonance, and bottom coupling ring 203 excites TE in lower Cylindrical resonant cavity 200 _0npmode of resonance.

Preferably, top coupling ring 103 and bottom coupling ring 203 are positioned opposite on the direction of the cylindrical cross-section radius of upper Cylindrical resonant cavity 100 and lower Cylindrical resonant cavity 200.

And preferably, top coupling ring 103 is placed in most strength, magnetic field in Cylindrical resonant cavity 100, and plane of a loop is vertical with the magnetic line of force of resettlement place; Bottom coupling ring 203 is placed in most strength, magnetic field in lower Cylindrical resonant cavity 200, and plane of a loop is vertical with the magnetic line of force of resettlement place.Thus, the field intensity of jamming pattern can be made to be minimum and jamming pattern can not be energized or be coupled.

Preferably, the cylindrical cross-section radius of upper Cylindrical resonant cavity 100 and lower Cylindrical resonant cavity 200 is equal (is assumed to be a); Further preferably, the chamber appearance etc. (being assumed to be L) of upper Cylindrical resonant cavity 100 and lower Cylindrical resonant cavity 200.

By distribution and the test philosophy of division right cylinder resonator cavity electromagnetic field, electric field can extend to outside resonator cavity along sample, therefore, for reducing the error of calculation of theoretical model, should ensure to obtain enough decay in electric field intensity before arrival sample edge (r=b).For the testing sample of thinner (testing medium substrate 300 thickness h≤1mm), usual sample diameter only need several millimeter larger than resonator cavity diameter, but for thicker testing sample, the diameter of sample just needs enough large.Through considering, preferably, the diameter of testing medium substrate 300 .That is, preferably, the diameter of testing medium substrate 300 is not less than 4/3 times of the cylindrical cross-section radius of Cylindrical resonant cavity 100 and lower Cylindrical resonant cavity 200.

Like this, because division right cylinder resonator cavity is symmetrical, the TE that upper part cylindrical cavity region (that is, upper Cylindrical resonant cavity 100) excites is supposed _0npmould, electric field only has diameter of phi direction:

$E_{{\mathrm{\φ}}_u}=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{A}_u{U}_n{R}_{n_u}\left(\mathrm{\ρ}\right)Z_{n_u}\left(z\right)---(2-61)$

In formula, A _nunknown mode coefficient, the radial fundamental function that need determine, longitudinal function, U _nbeing constant, defining for improving conditioned matrix.Suppose A _nand U _nall non-vanishing for all n values, (2-61) is substituted into vector wave equation

${\▿}^2\stackrel{\→}{E}+{\mathrm{\ω}}^2{\mathrm{\μ}}_0{\mathrm{\ϵ}}_0{\mathrm{\ϵ}}_a^{\′}\stackrel{\→}{E}=0---(2-62)$

Obtain

$\frac{1}{R_{n_u}}\frac{1}{\mathrm{\ρ}}\frac{\∂}{\∂\mathrm{\ρ}}\left(\mathrm{\ρ}\frac{{\∂R}_{n_u}}{\∂\mathrm{\ρ}}\right)-\frac{1}{{\mathrm{\ρ}}^2}+k_u^2=-\frac{1}{Z_{n_u}}\frac{{\∂}^2{Z}_{n_u}}{{\∂z}^2}=k_n^2---(2-63)$

In formula ω=2 π f, be separation constant, f is frequency, ε ' _ait is the air relative dielectric constant in upper part cylindrical cavity region.Suppose free dependence e in region ^{j ω t}.

Solve with variable separation with , the method is applied to formula (2-63)

$E_{{\mathrm{\φ}}_u}(\mathrm{\ρ},z)=\underset{n-1}{\overset{\∞}{\mathrm{\Σ}}}{A}_n{U}_n[C_n^{\′}{J}_1\left(h_{n_u}\mathrm{\ρ}\right)+D_n^{\′}{Y}_1\left(h_{n_u}\mathrm{\ρ}\right)]\·\left[A_n^{\′}\sin \right[p_{n_u}(L+\frac{d}{2}-z)]+B_n^{\′}\cos [p_{n_u}(L+\frac{d}{2}-z)\left]\right]---(2-64)$

A ' in formula _n, B ' _n, C ' _nwith D ' _nconstant, J ₁first kind Bessel's equation first, Y ₁equations of The Second Kind Bessel's equation, $p_{n_u}^2=k_u^2-h_{n_u}^2.$

Suppose that the bottom of metal waveguide wall and cylindrical cavity is all good conductor.Therefore, the boundary condition of transverse electric field is:

$E_{{\mathrm{\φ}}_y}(\mathrm{\ρ},z=L+\frac{d}{2})=0,0\≤\mathrm{\ρ}\≤a---(2-65)$

infinite,

$E_{{\mathrm{\φ}}_u}(\mathrm{\ρ}=a,z)=0,\frac{d}{2}\≤z\≤L+\frac{d}{2}---(2-67)$

B′ _n＝0 (2-68)

D′ _n＝0 (2-69)

$h_{n_u}=\frac{j_{1,n}}{a}---(2-70)$

Wherein j _{1, n}j ₁n zero, will substitute into upper boundary conditions in (2-64), then can be reduced to

$E_{{\mathrm{\φ}}_u}(\mathrm{\ρ},z)=\underset{n-1}{\overset{\∞}{\mathrm{\Σ}}}{A}_n{U}_n{J}_1\left(h_{n_u}\mathrm{\ρ}\right)\sin \left[p_{n_u}(L+\frac{d}{2}-z)\right]---(2-71)$

From the differential form of Faraday's law magnetic-field component can be drawn with formula (2-71)

$H_{{\mathrm{\ρ}}_u}(\mathrm{\ρ},z)=-\frac{1}{\mathrm{j\ω}{\mathrm{\μ}}_0}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{p}_{n_u}{A}_n{U}_n{J}_1\left(h_{n_u}\mathrm{\ρ}\right)\cos \left[p_{n_u}(L+\frac{d}{2}-z)\right]---(2-72)$

$H_{z_u}(\mathrm{\ρ},z)=-\frac{1}{\mathrm{j\ω}{\mathrm{\μ}}_0}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{h}_{n_u}{A}_n{U}_n{J}_0\left(h_{n_u}\mathrm{\ρ}\right)\sin \left[p_{n_u}(L+\frac{d}{2}-z)\right]---(2-73)$

Although division right cylinder resonator cavity is not closed cavity, there is good conductor boundary at assumes samples radius ρ=b place.B value enough large with guarantee Electric and magnetic fields arrive conductor border time decay.B value can affect the measuring accuracy of dielectric properties.

The electric field in assumes samples region is:

$E_{{\mathrm{\φ}}_s}=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{B}_n{V}_n{R}_{n_s}\left(\mathrm{\ρ}\right)Z_{n_s}\left(z\right)---(2-74)$

B in formula _nunknown pattern coefficient, radial fundamental function to be determined, it is longitudinal function.Increase factor Ⅴ _nimprove array condition.Suppose B _nand V _nall non-vanishing for all n values, (2-75) is substituted into vector wave equation

${\▿}^2\stackrel{\→}{E}+{\mathrm{\ω}}^2{\mathrm{\μ}}_0{\mathrm{\ϵ}}_0{\mathrm{\ϵ}}_s^{\′}\stackrel{\→}{E}=0---(2-75)$

Obtain

$\frac{1}{R_{n_s}}\frac{1}{\mathrm{\ρ}}\frac{\∂}{\∂\mathrm{\ρ}}\left(\mathrm{\ρ}\frac{{\∂R}_{n_s}}{\∂\mathrm{\ρ}}\right)-\frac{1}{{\mathrm{\ρ}}^2}+k_s^2=-\frac{1}{Z_{n_s}}\frac{{\∂}^2{Z}_{n_s}}{{\∂z}^2}=k_n^2---(2-76)$

In formula be separation constant, f is frequency, ε ' _sit is the relative dielectric constant of sample.

Solve with variable separation with the method is applied to formula (2-76)

$E_{{\mathrm{\φ}}_s}(\mathrm{\ρ},z)=\underset{n-1}{\overset{\∞}{\mathrm{\Σ}}}{B}_n{V}_n[C_n^{\′}{J}_1\left(h_{n_s}\mathrm{\ρ}\right)+D_n^{\′}{Y}_1\left(h_{n_s}\mathrm{\ρ}\right)]\·[A_n^{\′}\sin \left(p_{n_s}z\right)+B_n^{\′}\cos \left(p_{n_s}z\right)]---(2-77)$

A ' in formula _n, B ' _n, C ' _nwith D ' _nconstant, J ₁first kind Bessel's equation first, Y ₁equations of The Second Kind Bessel's equation, $p_{n_s}^2=k_s^2-h_{n_s}^2.$

For increasing the susceptibility of division right cylinder resonator cavity, should be maximum at the electric field of sample area.Therefore, only TE is considered _0npmode of resonance, the half wave number p along z-axis is an odd-integral number, and this mode electric field is symmetrical about z=0, maximum at the z=0 place, center of sample.Suppose that the bottom of metal waveguide wall and cylindrical cavity is all good conductor, the boundary condition of transverse electric field is:

$E_{{\mathrm{\φ}}_s}(\mathrm{\ρ},z=-\frac{d}{2})=E_{{\mathrm{\φ}}_s}(\mathrm{\ρ},z=\frac{d}{2}),0\≤\mathrm{\ρ}\≤b---(2-78)$

(ρ=0 is z) infinite, $0\≤z\≤\frac{d}{2}---(2-79)$

(ρ＝b,z)＝0, $0\≤z\≤\frac{d}{2}---(2-80)$

A′ _n＝0 (2-81)

D′ _n＝0 (2-82)

$h_{n_s}=\frac{j_{1,n}}{b}---(2-83)$

Wherein j _{1, n}j ₁n zero, will substitute into upper boundary conditions in (2-77), then can be reduced to

$E_{{\mathrm{\φ}}_s}(\mathrm{\ρ},z)=\underset{n-1}{\overset{\∞}{\mathrm{\Σ}}}{B}_n{V}_n{J}_1\left(h_{n_s}\mathrm{\ρ}\right)\cos \left(p_{n_s}z\right)---(2-84)$

From the differential form of Faraday's law magnetic-field component can be drawn with formula (2-84)

$H_{{\mathrm{\ρ}}_s}(\mathrm{\ρ},z)=-\frac{1}{\mathrm{j\ω}{\mathrm{\μ}}_0}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{p}_{n_s}{B}_n{V}_n{J}_1\left(h_{n_s}\mathrm{\ρ}\right)\sin \left({\mathrm{\ρ}}_{n_s}z\right)---(2-85)$

$H_{z_s}(\mathrm{\ρ},z)=-\frac{1}{\mathrm{j\ω}{\mathrm{\μ}}_0}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{h}_{n_s}{B}_n{V}_n{J}_0\left(h_{n_s}\mathrm{\ρ}\right)\cos \left(p_{n_s}z\right)--(2-86)$

For making division right cylinder resonator cavity realize resonance, first adopt tangential electric field at z=d/2 continuous print boundary condition:

$E_{{\mathrm{\φ}}_u}(z=\frac{d}{2})=E_{{\mathrm{\φ}}_s}(z=\frac{d}{2}),0\≤\mathrm{\ρ}\≤b---(2-87)$

(2-71) and (2-84) is substituted into (2-87)

$\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{B}_n{V}_n{J}_1\left(h_{n_s}\mathrm{\ρ}\right)\cos \left(p_{n_s}\frac{d}{2}\right)=\left\{\begin{array}{cc}\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{A}_n{U}_n{J}_1\left(h_{n_u}\mathrm{\ρ}\right)\sin \left(p_{n_u}L\right),& 0\≤\mathrm{\ρ}\≤a\\ 0,& a\≤\mathrm{\ρ}\≤b\end{array}\right.---(2-88)$

Adopt orthogonal modes that the infinite sum of formula (2-88) left-hand component is become a single item.Suppose that conductor boundary is good conductor, all material in division right cylinder resonator cavity is loss-free, and the orthogonality relation in upper part cylindrical cavity region is

${\∫}_{\mathrm{\φ}=0}^{2\mathrm{\π}}{\∫}_{\mathrm{\ρ}=0}^a[E_{{\mathrm{\φ}}_u}^{\left(n\right)}\×H_{{\mathrm{\ρ}}_u}^{\left(m\right)}]\·{\stackrel{\→}{a}}_z\mathrm{\ρd\ρd\φ}=F{\mathrm{\δ}}_{\mathrm{mn}}---(2-89)$

The relation of sample area is

${\∫}_{\mathrm{\φ}=0}^{2\mathrm{\π}}{\∫}_{\mathrm{\ρ}=0}^b[E_{{\mathrm{\φ}}_s}^{\left(n\right)}\×H_{{\mathrm{\ρ}}_s}^{\left(m\right)}]\·{\stackrel{\→}{a}}_z\mathrm{\ρd\ρd\φ}={\mathrm{G\δ}}_{\mathrm{mn}}---(2-90)$

In formula, F and G is normaliztion constant, δ _mnit is the kronecker δ function.

For simplified style (2-88), be multiplied by formula both sides adopt orthogonality relation equation (2-89), or be multiplied by adopt orthogonality relation equation (2-90).Electric field must not only z=d/2 (0≤ρ≤a) is continuous, and must be zero extending to ρ=b good conductor flange place.Sample area only has and allows to adopt electric field boundary condition at (0≤ρ≤b) under orthogonality relation pattern.Therefore be multiplied by formula (2-88) both sides integrate at sample area xsect

$\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{A}_n{U}_n\frac{{\mathrm{ah}}_{\mathrm{nu}}}{h_{\mathrm{ms}}^2-h_{\mathrm{nu}}^2}{J}_0\left(h_{\mathrm{nu}}a\right)J_1\left(h_{\mathrm{ms}}a\right)\sin \left(p_{\mathrm{nu}}L\right)=B_m{V}_m\frac{b^2}{2}{J}_0^2\left(h_{\mathrm{ms}}b\right)\cos \left(p_{\mathrm{ms}}\frac{d}{2}\right)---(2-91)$

Second boundary condition adopts continuous print tangent magnetic field

$H_{{\mathrm{\ρ}}_s}(z=\frac{d}{2})=H_{{\mathrm{\ρ}}_u}(z=\frac{d}{2}),0\≤\mathrm{\ρ}\≤a---(2-92)$

(2-72) and (2-85) is substituted into (2-92) obtain

$\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{p}_{n_s}{B}_n{V}_n{J}_1\left(h_{n_s}\mathrm{\ρ}\right)\sin \left({\mathrm{\ρ}}_{n_s}\frac{d}{2}\right)=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{p}_{n_a}{A}_n{U}_u{J}_1\left(h_{n_s}\mathrm{\ρ}\right)\cos \left(p_{n_a}L\right),0\≤\mathrm{\ρ}\≤a---(2-93)$

Again adopt orthogonality relation that the infinite sum on (2-93) right side is reduced to single item mutually.For magnetic field, there is orthogonality relation in (2-89) or (2-90) in principle.But, select residual orthogonality relation, because convergence can reduce error relatively.Therefore, formula (2-89) is adopted.

Be multiplied by (2-93) both sides integrate at upper chamber zone cross-sectional

$A_n{U}_n{p}_{n_u}\frac{a^2}{2}{J}_0^2\left(h_{n_u}a\right)\cos \left(p_{n_u}L\right)=\underset{n=1}{\overset{\∞}{\mathrm{\Σ}}}{B}_m{V}_m\frac{{\mathrm{ap}}_{m_s}{h}_{n_u}}{h_{m_s}^2-h_{n_u}^2}{J}_1\left(h_{m_s}a\right)J_0\left(h_{n_u}a\right)\sin \left(p_{m_s}\frac{d}{2}\right)---(2-94)$

For mating boundary condition accurately, the infinite number pattern of Upper cylindrical cavity area and sample area must be comprised.Result has unknown constant A _nand B _ninfinite system of equations.In order to simplify the limited system becoming linear algebraic equation, the pattern count in each region must be shortened.If select the pattern count in cylindrical cavity region to be N _ube N with the pattern count of sample area _s, form two equation system by (2-92) and (2-94)

QA＝RB (2-95)

SA＝PB (2-96)

Wherein

$Q_{\mathrm{mn}}=U_n\frac{a{h}_{n_u}}{h_{m_s}^2-h_{n_u}^2}{J}_1\left(h_{m_s}a\right)J_0\left(h_{n_u}a\right)\sin \left(p_{n_u}L\right)---(2-97)$

$R_{\mathrm{mm}}=V_m\frac{b^2}{2}{J}_0^2\left(h_{m_s}b\right)\cos \left(p_{m_s}\frac{d}{2}\right)---(2-98)$

$S_{\mathrm{nn}}=U_n{p}_{n_u}\frac{a^2}{2}{J}_0^2\left(h_{n_u}a\right)\cos \left(p_{n_u}L\right)---(2-99)$

$P_{\mathrm{nm}}=V_m\frac{a{p}_{m_s}{h}_{n_a}}{h_{m_s}^2-h_{n_u}^2}{J}_1\left(h_{m_s}a\right)J_0\left(h_{n_u}a\right)\sin \left(p_{m_s}\frac{d}{2}\right)---(2-100)$

Note: R and S is diagonal matrix.

(2-95) system equation represented with (2-96) can be rewritten as

[Z][X]＝0 (2-101)

Wherein

$\left[\begin{array}{c}Z\end{array}\right]=\left[\begin{array}{cc}Q& -R\\ S& -P\end{array}\right]---(2-102)$

$\left[\begin{array}{c}X\end{array}\right]=\left[\begin{array}{c}A\\ B\end{array}\right]---(2-103)$

The linear system equation that condition of resonance is formed has nontrivial solution, ought but only have

det[Z]＝0 (2-104)

Can the resonance frequency f of through type (2-104) iterative computation known sample specific inductive capacity division right cylinder resonator cavity, calculate the sample permittivity of known resonant frequency.

First the test of sample loss tangent must know the quality factor Q dividing right cylinder resonance when sample exists:

$Q=\frac{\mathrm{\ω}(W_a+W_s)}{P_e+P_f+P_w+P_s}---(2-105)$

W in formula _aand W _sin cylinder body cavity and the average energy of sample area storage, P _e, P _w, P _fand P _sbe respectively bottom cylinder body cavity, energy loss that chamber wall, edge and sample are per second.When determining that resonance has the energy loss can ignoring coupling ring time very weak coupling (<-50db).

When obtaining the relative dielectric constant ε of sample _r' after, only there are two unknown quantitys in formula (2-105) right-hand member, the surface resistivity R of right cylinder resonator cavity _swith the losstangenttanδ of sample, we can obtain R by measurement sample being loaded to front cavity (h=0) _s, then loading the quality factor of rear resonator cavity by measuring sample, just can obtain the loss tangent of testing sample:

$\tan \mathrm{\&delta;}=\frac{\frac{\mathrm{\&omega;}(W_s+W_a)}{Q}-P_c-P_{\mathrm{\&omega;}}-P_f}{{\mathrm{\&epsiv;}}_0{{\mathrm{\&epsiv;}}_r}^{\&prime;}\frac{{\mathrm{\&pi;b}}^2}{4}\underset{n=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{\left|B_n\right|}^2{\left|V_n\right|}^2{J_0}^2\left(h_{\mathrm{ns}}b\right)[d+\frac{\sin \left(p_{\mathrm{ns}}d\right)}{p_{\mathrm{ns}}}]}---(2-106)$

Based on said structure and above-mentioned principle analysis, each step of method of the present invention will be specifically described below.Particularly, Fig. 3 schematically shows the process flow diagram of dielectric performance of dielectric material method of testing according to the preferred embodiment of the invention.

As shown in Figure 3, dielectric performance of dielectric material method of testing comprises according to the preferred embodiment of the invention:

First step S1: top coaxial transmission line 104 is connected to vector network analyzer 400 by top microwave cable 105, is connected to vector network analyzer 400 by bottom coaxial transmission line 204 by bottom microwave cable 205;

Second step S2: Cylindrical resonant cavity 100 is contacted with lower Cylindrical resonant cavity 200 alignment relative, to make the opening of Upper cylindrical shape cavity rectify openend to lower cylindrical shape cavity 201, and top strip conductive ledge 102 contacts (as shown in Figure 4) with bottom strip conductive ledge 202;

Third step S3: by vector network analyzer 400, top coupling ring 103 is made to excite TE0np mode of resonance in upper Cylindrical resonant cavity, and bottom coupling ring 203 excites TE0np mode of resonance in lower Cylindrical resonant cavity, and regulate top coupling ring 103 and bottom coupling ring 203 to make the insertion loss of harmonic peak in Cylindrical resonant cavity and lower Cylindrical resonant cavity minimum, measure cavity resonance frequency and quality factor thus;

4th step S4: arrange testing medium substrate 300 between top strip conductive ledge and bottom strip conductive ledge, the distance wherein between top strip conductive ledge and bottom strip conductive ledge equals the thickness (as shown in Figure 5) of testing medium substrate;

5th step S5: by vector network analyzer 400, top coupling ring 103 is made to excite TE0np mode of resonance in upper Cylindrical resonant cavity, and bottom coupling ring 203 excites TE0np mode of resonance in lower Cylindrical resonant cavity, and regulate top coupling ring 103 and bottom coupling ring 203 to make the insertion loss of harmonic peak in Cylindrical resonant cavity and lower Cylindrical resonant cavity minimum, measure the discreet value of the relative dielectric constant of testing medium substrate 300 thus;

6th step S6: utilize control treatment device 500 (such as computing machine), the discreet value of relative dielectric constant that the cavity resonance frequency obtained according to third step S3 and quality factor, the 5th step S5 obtain and the size of dielectric substrate 300, calculate the dielectric properties parameter value of the dielectric material of testing medium substrate 300.

In concrete operations, such as, before measurement test, first vector network analyzer can be opened, more than preheating half an hour.Then connect microwave test cable (completing final connection with torque spanner) on request, and the TRL calibrating device utilizing network analyzer to carry is calibrated to network analyzer, to reduce the systematic error introduced from network analyzer.Open control microcomputer, regulate coupling ring to make the insertion loss of harmonic peak minimum, then run cavity test procedure, measure cavity resonance frequency and quality factor, and be saved in cavity test result.

After cavity test terminates, the testing sample after stringent clean and dry process is inserted in division right cylinder resonator cavity, and inputs the dimensional parameters of sample, then run sample test subroutine.Owing to have employed the method for iteration in dielectric properties counting subroutine, therefore the discreet value of detected materials relative dielectric constant is needed, then in conjunction with the dimensional parameters of sample, and the cavity resonance frequency recorded and quality factor, calculate the dielectric properties value of dielectric material.After having tested, preserve test data, shut down computer and network analyzer.

Generally, the advantage dividing right cylinder resonator cavity method of testing according to the preferred embodiment of the invention at least also comprises the following aspects:

(1) sample of high frequency material division right cylinder resonator cavity is harmless, easy to prepare, as long as ensure flatness of substrate.

(2) test fixture processing is relatively easy, and cost is low.

(3) test easy for installation, can test as long as print is placed on during installation between two cylindrical cavities.

(4) printing base material topmost advantage for high frequency is that the measuring accuracy of other method of testing loss tangent is relatively high, if comprise conductor losses, typical uncertainty is Δ ε ' _r/ ε ' _r=± 0.2%, Δ tan δ=± 5 × 10 ^-5, high frequency can be met and print the high requirement of base material loss accuracy test.

Be understandable that, although the present invention with preferred embodiment disclose as above, but above-described embodiment and be not used to limit the present invention.For any those of ordinary skill in the art, do not departing under technical solution of the present invention ambit, the technology contents of above-mentioned announcement all can be utilized to make many possible variations and modification to technical solution of the present invention, or be revised as the Equivalent embodiments of equivalent variations.Therefore, every content not departing from technical solution of the present invention, according to technical spirit of the present invention to any simple modification made for any of the above embodiments, equivalent variations and modification, all still belongs in the scope of technical solution of the present invention protection.

Claims (8)

1. adopt a dielectric performance of dielectric material method of testing for division right cylinder resonator cavity, described division right cylinder resonator cavity comprises: upper Cylindrical resonant cavity separated from one another and lower Cylindrical resonant cavity; Wherein, upper Cylindrical resonant cavity comprises one end and closes the Upper cylindrical shape cavity of one end open, a pair top strip conductive ledge be arranged on the openend of Upper cylindrical shape cavity, the top coupling ring being arranged in Upper cylindrical shape inside cavity and the top coaxial transmission line be connected with top coupling ring; And wherein, top coaxial transmission line through the roof of Upper cylindrical shape cavity or sidewall top coupling ring is connected to outside; Wherein, lower Cylindrical resonant cavity comprises one end and closes the lower cylindrical shape cavity of one end open, a pair bottom strip conductive ledge be arranged on the openend of lower cylindrical shape cavity, the bottom coupling ring being arranged in lower cylindrical shape inside cavity and the bottom coaxial transmission line be connected with bottom coupling ring; And wherein, bottom coaxial transmission line through the roof of lower cylindrical shape cavity or sidewall bottom coupling ring is connected to outside.

2. dielectric performance of dielectric material method of testing according to claim 1, is characterized in that, described dielectric performance of dielectric material method of testing comprises:

First step: top coaxial transmission line is connected to vector network analyzer, is connected to vector network analyzer by bottom coaxial transmission line;

Second step: Cylindrical resonant cavity is contacted with lower Cylindrical resonant cavity alignment relative, to make the opening of Upper cylindrical shape cavity rectify openend to lower cylindrical shape cavity, and top strip conductive ledge contacts with bottom strip conductive ledge;

Third step: pass through vector network analyzer, top coupling ring is made to excite TE0np mode of resonance in upper Cylindrical resonant cavity, and bottom coupling ring excites TE0np mode of resonance in lower Cylindrical resonant cavity, and regulate top coupling ring and bottom coupling ring to make the insertion loss of harmonic peak in Cylindrical resonant cavity and lower Cylindrical resonant cavity minimum, measure cavity resonance frequency and quality factor thus;

4th step: arrange testing medium substrate between top strip conductive ledge and bottom strip conductive ledge, the distance wherein between top strip conductive ledge and bottom strip conductive ledge equals the thickness of testing medium substrate;

5th step: pass through vector network analyzer, top coupling ring is made to excite TE0np mode of resonance in upper Cylindrical resonant cavity, and bottom coupling ring excites TE0np mode of resonance in lower Cylindrical resonant cavity, and regulate top coupling ring and bottom coupling ring to make the insertion loss of harmonic peak in Cylindrical resonant cavity and lower Cylindrical resonant cavity minimum, measure the discreet value of the relative dielectric constant of testing medium substrate thus;

6th step: the discreet value of relative dielectric constant that the cavity resonance frequency obtained according to third step and quality factor, the 5th step obtain and the size of dielectric substrate, calculate the dielectric properties parameter value of the dielectric material of testing medium substrate.

3. dielectric performance of dielectric material method of testing according to claim 1, it is characterized in that, in a first step, by top microwave cable, top coaxial transmission line is connected to vector network analyzer, by bottom microwave cable, bottom coaxial transmission line is connected to vector network analyzer.

4. dielectric performance of dielectric material method of testing according to claim 1 and 2, is characterized in that, top coupling ring and bottom coupling ring are positioned opposite on the direction of the cylindrical cross-section radius of upper Cylindrical resonant cavity and lower Cylindrical resonant cavity.

5. dielectric performance of dielectric material method of testing according to claim 1 and 2, is characterized in that, top coupling ring is placed in most strength, magnetic field in Cylindrical resonant cavity, and plane of a loop is vertical with the magnetic line of force of resettlement place; Bottom coupling ring is placed in most strength, magnetic field in lower Cylindrical resonant cavity, and plane of a loop is vertical with the magnetic line of force of resettlement place.

6. dielectric performance of dielectric material method of testing according to claim 1 and 2, is characterized in that, the cylindrical cross-section radius of upper Cylindrical resonant cavity and lower Cylindrical resonant cavity is equal.

7. dielectric performance of dielectric material method of testing according to claim 1 and 2, is characterized in that, the chamber appearance etc. of upper Cylindrical resonant cavity and lower Cylindrical resonant cavity.

8. dielectric performance of dielectric material method of testing according to claim 1 and 2, is characterized in that, the diameter of testing medium substrate is not less than 4/3 times of the cylindrical cross-section radius of Cylindrical resonant cavity and lower Cylindrical resonant cavity.