CN103901278A - Method for measuring material complex permittivity based on substrate integrated waveguide round resonant cavities - Google Patents

Abstract

The invention relates to the technical field of testing of material complex permittivity, in particular to a method for measuring material complex permittivity based on substrate integrated waveguide round resonant cavities. The method comprises the steps that firstly, the substrate integrated waveguide round resonant cavities with different resonant frequencies (work frequencies) are machined; secondly, for the substrate integrated waveguide round resonant cavities with the same resonant frequency, a sample with material identical to that of a dielectric layer 2, a standard sample with the known complex permittivity and a sample to be measured are respectively loaded, swept-frequency signals are fed respectively through a vector network analyzer, and the resonant frequencies and the quality factors of the three samples are tested; finally, simultaneous equations are established and solved, and then the complex permittivity of the sample to be measured at the work frequency of the corresponding substrate integrated waveguide round resonant cavity can be obtained. A multi-frequency-point clock test of the material complex permittivity can be completed in the mode that the substrate integrated waveguide round resonant cavities with other work frequencies are used and the same test process is repeated. The method for measuring material complex permittivity based on the substrate integrated waveguide round resonant cavities has the advantages that the sizes of the substrate integrated waveguide round resonant cavities are small, machining is convenient, and the precision of a measurement result is high.

Description

Based on the material method for measuring complex dielectric constant in substrate integration wave-guide circular resonant chamber

Technical field

The present invention relates to material complex permittivity technical field of measurement and test, particularly the material method for measuring complex dielectric constant based on microwave cavity.

Background technology

Microwave material has been widely used in the every field of microwave as electromagnetic transmission medium, such as microwave circuit, communication, radar invisible etc.The electromagnetic parameter of dielectric material generally refers to complex permittivity and complex permeability, conventionally with plural form ε (j ω)=ε ' (j ω)-j ε, " (j ω); μ (j ω)=μ ' (j ω)-j μ " (j ω) represents, it is to describe material and two the most basic characteristic parameters of electromagnetic field interaction.Accurately understand electromagnetic parameter value, be absolutely necessary in the types of applications of microwave frequency band for application and the material of microwave energy.

The electromagnetic parameter testing technology of material, through the development of nearly decades, has formed the more complete scientific system of a set of ratio.At present, in microwave and millimere-wave band, the electromagnetic parameter test method of material can be divided into Transmission line method, the large class of Resonant-cavity Method two by measuring principle.But these two kinds of methods all exist some problems separately, such as Transmission line method measuring accuracy is not high, make sample inconvenience, and calibration accuracy requires high; Resonant-cavity Method is the test of carrying out based on perturbation method, be only suitable for the test in single-frequency point, multifrequency point test need to be carried out in multiple resonator cavitys that work in different frequency, and this is that rectangle or circular resonator cavity all can increase testing cost greatly for Metal cavity.

Plane resonant circuit technology is because of easy to process cheap, compares Metal cavity with the obvious advantage and be widely used in the measurement of material dielectric constant.For example, researchist adopts circuited microstrip loop resonator, microstrip coupled dielectric resonator to carry out Measuring Dielectric Constant, but because the quality factor of the planar circuits such as microstrip line are lower, radiation loss is larger, thereby measures accurate not.

Summary of the invention

The invention provides a kind of material method for measuring complex dielectric constant based on substrate integration wave-guide circular resonant chamber, the method is carried out material complex-permittivity measurement based on substrate integration wave-guide circular resonant chamber, has high, the radiationless loss of quality factor, tests feature accurately; Meanwhile, adopt the substrate integration wave-guide circular resonant chamber of multiple different resonance frequencies, can realize multifrequency point and measure.

Technical solution of the present invention is:

Based on the material method for measuring complex dielectric constant in substrate integration wave-guide circular resonant chamber, comprise the following steps:

Step 1: processing has the substrate integration wave-guide circular resonant chamber of different resonance frequencies.The structure in described substrate integration wave-guide circular resonant chamber as shown in Figure 1, 2, the dielectric-slab that is all coated with metal conducting layer by tow sides processes, comprise metal conducting layer 1, dielectric layer 2, lower metal conducting layer 3, described dielectric layer 2 is between upper metal conducting layer 1 and lower metal conducting layer 3, and some rounded equally distributed plated-through holes 4 link together upper metal conducting layer 1 and lower metal conducting layer 3.The mode of operation in described substrate integration wave-guide circular resonant chamber adopts second higher mode TM ₂₁₀mould, design add man-hour corresponding to the substrate integration wave-guide circular resonant chamber size of this pattern by resonance frequency f ₂₁₀obtain by formula (1):

$f_{210}=\frac{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000483824060000012.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;}\sqrt{{\mathrm{\&mu;}}_r{\mathrm{\&epsiv;}}_r}}\sqrt{{\left(\frac{p_{21}}{a_{\mathrm{eff}}}\right)}^2}---\left(1\right)$

Wherein c is the light velocity, μ _rthe relative permeability of dielectric layer 2, ε _rthe relative dielectric constant of dielectric layer 2, p ₂₁the=5.136th, first zero point of second order Bessel's function, a _effbe the equivalent redius in described substrate integration wave-guide circular resonant chamber, the relation between the real radius a in it and described substrate integration wave-guide circular resonant chamber can be determined by (2) formula:

$a_{\mathrm{eff}}=a-\frac{{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000483824060000012.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{0.95b}---\left(2\right)$

Wherein D is the diameter of plated-through hole 4, b is the center of circle spacing of adjacent two plated-through holes 4 on same level cross section, and the real radius a in described substrate integration wave-guide circular resonant chamber is the distance between the center of circle of any one plated-through hole 4 on same level cross section and the geometric center in described substrate integration wave-guide circular resonant chamber.

Described substrate integration wave-guide circular resonant chamber also has a power feed hole 5 and a test sample loads hole 6, described power feed hole is carried out feed by coaxial feed joint 7, when feed, the outer conductor of coaxial feed joint 7 and upper metal conducting layer 1 are electrically connected, and the inner wire of coaxial feed joint 7 inserts power feed hole 5 and is electrically connected with lower metal conducting layer 3.It is a cylindrical hole that described test sample loads hole 6, is positioned at apart from power feed hole 5 geometric centers peak electric field place farthest.

Step 2: the different resonance frequency substrate integration wave-guide circular resonant chamber that has that adopts step 1 to process is tested the complex permittivity of dielectric sample to be measured.Detailed process is as follows:

First adopt same substrate integration wave-guide circular resonant chamber, the frequency of operation to dielectric sample to be measured in this substrate integration wave-guide circular resonant chamber, this substrate integration wave-guide adds resonance frequency f corresponding to man-hour in design ₂₁₀under complex permittivity test, comprise the following steps:

Step 2-1: the resonance frequency f while measuring the zero load of described substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁.Sample identical and identical with dielectric layer 2 materials with test sample loading hole 6 shapes of concrete employing loads on test sample and loads in hole 6, and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole 5, measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁; The now resonance frequency f in substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁resonance frequency f while being exactly the zero load of described substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁.

Step 2-2: the resonance frequency f while measuring described substrate integration wave-guide circular resonant chamber loading standard specimen ₂and quality factor q ₂.One of concrete employing loads on test sample with test sample loading hole 6 shapes standard model identical and that complex permittivity is known and loads in hole 6, and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole 5, measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₂and quality factor q ₂.

Step 2-3: the resonance frequency f while measuring described substrate integration wave-guide circular resonant chamber loading testing sample ₃and quality factor q ₃.Testing sample identical with test sample loading hole 6 shapes of concrete employing loads on test sample and loads in hole 6, and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole 5, measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₃and quality factor q ₃.

Step 2-4: the complex permittivity of calculating testing sample.

First simultaneous formula (3) and (4), calculates perturbation constant A and B:

${\mathrm{\&epsiv;}}_2^{,}=\frac{{\mathrm{A\&epsiv;}}_1^{,}{V}_c}{V_s}\left(\frac{f_1-f_2}{f_2}\right)+{\mathrm{\&epsiv;}}_1^{,}---\left(3\right)$

$\tan {\mathrm{\&delta;}}_2=\frac{{\mathrm{\&epsiv;}}_2^{,,}}{{\mathrm{\&epsiv;}}_2^{,}}=\frac{{\mathrm{BV}}_c}{V_s}\left(\frac{Q_1-Q_2}{Q_1{Q}_2}\right)\frac{1}{{\mathrm{\&epsiv;}}_2^{,}}+\tan {\mathrm{\&delta;}}_1---\left(4\right)$

Simultaneous formula (5) and (6) again, the complex permittivity of calculating testing sample:

${\mathrm{\&epsiv;}}_3^{,}=\frac{{\mathrm{A\&epsiv;}}_1^{,}{V}_c}{V_s}\left(\frac{f_1-f_3}{f_3}\right)+{\mathrm{\&epsiv;}}_1^{,}---\left(5\right)$

$\tan {\mathrm{\&delta;}}_3=\frac{{\mathrm{\&epsiv;}}_3^{,,}}{{\mathrm{\&epsiv;}}_3^{,}}=\frac{{\mathrm{BV}}_c}{V_s}\left(\frac{Q_1-Q_3}{Q_1{Q}_3}\right)\frac{1}{{\mathrm{\&epsiv;}}_3^{,}}+\tan {\mathrm{\&delta;}}_1---\left(6\right)$

In formula (3)～formula (6): V _cthe volume in described substrate integration wave-guide circular resonant chamber, V _sthe volume that test sample loads hole 6,

the real part of the complex permittivity of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the real part of the complex permittivity of standard model material under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of standard model material under described substrate integration wave-guide frequency of operation,

the real part of the complex permittivity of testing sample material under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of testing sample material under described substrate integration wave-guide frequency of operation,

the loss tangents of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the loss tangent of standard model material under described substrate integration wave-guide frequency of operation,

the loss tangent of testing sample material under described substrate integration wave-guide frequency of operation.

Then the same substrate integration wave-guide circular resonant chamber of using other frequency of operation instead, repeating step 2-1, to the operation of step 2-4, can record the complex permittivity of testing medium sample under corresponding frequency of operation.

It should be noted that:

One, resonance frequency f when step 2-1 measures the zero load of described substrate integration wave-guide circular resonant chamber in technique scheme ₁and quality factor q ₁time, be after described substrate integration wave-guide circular resonant chamber machines, adopt to load on test sample with the sample of dielectric layer 2 same materials and load and test in hole 6.In fact resonance frequency f when, substrate integration wave-guide circular resonant chamber is unloaded ₁and quality factor q ₁also can be in the process of substrate integration wave-guide circular resonant chamber, before loading hole 6 processing, tests by sample completing after power feed hole 5 processing.Resonance frequency f while carrying out the zero load of described substrate integration wave-guide circular resonant chamber after can avoiding like this sample loading sky to process ₁and quality factor q ₁the error of test, but be unfavorable for the processing in substrate integration wave-guide circular resonant chamber.

Two, substrate integration wave-guide circular resonant provided by the invention chamber, the mode of operation adopting has four maximum field positions in resonator cavity, and 90 °, interval Homogeneous Axisymmetrical distributes.Maximum field is determined by feed placement at the particular location of circumferencial direction, is determined by resonator cavity radius at the particular location of radial direction.Test sample loads hole 6 and is positioned at apart from power feed hole geometric center peak electric field place farthest, and this position is apart from the distance R at cavity center _sdetermined by following formula:

$R_s=\frac{p_{\max 1}}{p_{21}}\&times;a_{\mathrm{eff}}---\left(7\right)$

Wherein, p _max1second order Bessel's function corresponding argument value while getting first maximum value, 3.056, p ₂₁first zero point of second order Bessel's function, 5.136.

Three, in order to ensure that measurement result has higher accuracy and sensitivity, the volume V in substrate integration wave-guide circular resonant chamber _cvolume V with test sample loading hole 6 _sratio should be arranged between 200～400.

Four, the present invention can realize the high precision measurement of low-loss microwave solid-state material complex permittivity.Sample only need be processed to load the identical shape in hole 6 and size with sample, when measurement, adds a cover sheet metal at post two ends, hole.The present invention is equally also applicable to carry out the test of liquid and powdered sample.

The invention has the beneficial effects as follows:

One, substrate integration wave-guide circular resonant of the present invention chamber perturbation method is tested, and substrate integration wave-guide is easy to process, with low cost compared with Metal cavity, high compared with other plane resonantor quality factor such as microstrip lines, measuring accuracy is high.

Two, the present invention adopts substrate integration wave-guide circular resonant chamber, and in the time of same equifrequent work, circular cavity is less compared with rectangular cavity volume, further reduces costs.

Three, the substrate integration wave-guide circular resonant chamber that the present invention adopts is higher compared with rectangular cavity quality factor, and higher figure of merit is conducive to realize higher measuring accuracy.

Four, the present invention adopts substrate integration wave-guide circular resonant chamber, only need determine this parameter of radius while carrying out Resonator design; Adopt the TM with axial symmetry simultaneously ₂₁₀mould, is convenient to rapid Design; And rectangular cavity has two parameters of length and width to determine, design is comparatively complicated.Therefore, can design a series of different frequency resonator cavitys by easy formula, can multiple discrete frequencies be tested in broad frequency range, stable performance.

Five, to sample require lowly, be suitable for the test of solid, powder and fluid sample, solidify to wait and anticipate without sample being made to paraffin, test result is more credible.

Brief description of the drawings

Fig. 1 is the vertical view in substrate integration wave-guide circular resonant chamber in the present invention.

Fig. 2 is the cut-open view in substrate integration wave-guide circular resonant chamber in the present invention.

Embodiment

Based on the material method for measuring complex dielectric constant in substrate integration wave-guide circular resonant chamber, comprise the following steps:

Step 1: processing has the substrate integration wave-guide circular resonant chamber of different resonance frequencies.The structure in described substrate integration wave-guide circular resonant chamber as shown in Figure 1, 2, the dielectric-slab that is all coated with metal conducting layer by tow sides processes, comprise metal conducting layer 1, dielectric layer 2, lower metal conducting layer 3, described dielectric layer 2 is between upper metal conducting layer 1 and lower metal conducting layer 3, and some rounded equally distributed plated-through holes 4 link together upper metal conducting layer 1 and lower metal conducting layer 3.The mode of operation in described substrate integration wave-guide circular resonant chamber adopts second higher mode TM ₂₁₀mould, design add man-hour corresponding to the substrate integration wave-guide circular resonant chamber size of this pattern by resonance frequency f ₂₁₀obtain by formula (1):

$f_{210}=\frac{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000483824060000012.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;}\sqrt{{\mathrm{\&mu;}}_r{\mathrm{\&epsiv;}}_r}}\sqrt{{\left(\frac{p_{21}}{a_{\mathrm{eff}}}\right)}^2}---\left(1\right)$

Wherein c is the light velocity, μ _rthe relative permeability of dielectric layer 2, ε _rthe relative dielectric constant of dielectric layer 2, p ₂₁the=5.136th, first zero point of second order Bessel's function, a _effbe the equivalent redius in described substrate integration wave-guide circular resonant chamber, the relation between the real radius a in it and described substrate integration wave-guide circular resonant chamber can be determined by (2) formula:

$a_{\mathrm{eff}}=a-\frac{{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000483824060000012.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{0.95b}---\left(2\right)$

Wherein D is the diameter of plated-through hole 4, b is the center of circle spacing of adjacent two plated-through holes 4 on same level cross section, and the real radius a in described substrate integration wave-guide circular resonant chamber is the distance between the center of circle of any one plated-through hole 4 on same level cross section and the geometric center in described substrate integration wave-guide circular resonant chamber.

Described substrate integration wave-guide circular resonant chamber also has a power feed hole 5 and a test sample loads hole 6, described power feed hole is carried out feed by coaxial feed joint 7, when feed, the outer conductor of coaxial feed joint 7 and upper metal conducting layer 1 are electrically connected, and the inner wire of coaxial feed joint 7 inserts power feed hole 5 and is electrically connected with lower metal conducting layer 3.It is a cylindrical hole that described test sample loads hole 6, is positioned at apart from power feed hole 5 geometric centers peak electric field place farthest.

Step 2: the different resonance frequency substrate integration wave-guide circular resonant chamber that has that adopts step 1 to process is tested the complex permittivity of dielectric sample to be measured.Detailed process is as follows:

First adopt same substrate integration wave-guide circular resonant chamber, the frequency of operation to dielectric sample to be measured in this substrate integration wave-guide circular resonant chamber, this substrate integration wave-guide adds resonance frequency f corresponding to man-hour in design ₂₁₀under complex permittivity test, comprise the following steps:

Step 2-1: the resonance frequency f while measuring the zero load of described substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁.Sample identical and identical with dielectric layer 2 materials with test sample loading hole 6 shapes of concrete employing loads on test sample and loads in hole 6, and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole 5, measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁; The now resonance frequency f in substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁resonance frequency f while being exactly the zero load of described substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁.

Step 2-2: the resonance frequency f while measuring described substrate integration wave-guide circular resonant chamber loading standard specimen ₂and quality factor q ₂.One of concrete employing loads on test sample with test sample loading hole 6 shapes standard model identical and that complex permittivity is known and loads in hole 6, and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole 5, measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₂and quality factor q ₂.

Step 2-3: the resonance frequency f while measuring described substrate integration wave-guide circular resonant chamber loading testing sample ₃and quality factor q ₃.Testing sample identical with test sample loading hole 6 shapes of concrete employing loads on test sample and loads in hole 6, and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole 5, measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₃and quality factor q ₃.

Step 2-4: the complex permittivity of calculating testing sample.

First simultaneous formula (3) and (4), calculates perturbation constant A and B:

${\mathrm{\&epsiv;}}_2^{,}=\frac{{\mathrm{A\&epsiv;}}_1^{,}{V}_c}{V_s}\left(\frac{f_1-f_2}{f_2}\right)+{\mathrm{\&epsiv;}}_1^{,}---\left(3\right)$

$\tan {\mathrm{\&delta;}}_2=\frac{{\mathrm{\&epsiv;}}_2^{,,}}{{\mathrm{\&epsiv;}}_2^{,}}=\frac{{\mathrm{BV}}_c}{V_s}\left(\frac{Q_1-Q_2}{Q_1{Q}_2}\right)\frac{1}{{\mathrm{\&epsiv;}}_2^{,}}+\tan {\mathrm{\&delta;}}_1---\left(4\right)$

Simultaneous formula (5) and (6) again, the complex permittivity of calculating testing sample:

${\mathrm{\&epsiv;}}_3^{,}=\frac{{\mathrm{A\&epsiv;}}_1^{,}{V}_c}{V_s}\left(\frac{f_1-f_3}{f_3}\right)+{\mathrm{\&epsiv;}}_1^{,}---\left(5\right)$

$\tan {\mathrm{\&delta;}}_3=\frac{{\mathrm{\&epsiv;}}_3^{,,}}{{\mathrm{\&epsiv;}}_3^{,}}=\frac{{\mathrm{BV}}_c}{V_s}\left(\frac{Q_1-Q_3}{Q_1{Q}_3}\right)\frac{1}{{\mathrm{\&epsiv;}}_3^{,}}+\tan {\mathrm{\&delta;}}_1---\left(6\right)$

In formula (3)～formula (6): V _cthe volume in described substrate integration wave-guide circular resonant chamber, V _sthe volume that test sample loads hole 6,

the real part of the complex permittivity of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the real part of the complex permittivity of standard model material under described substrate integration wave-guide frequency of operation, the imaginary part of the complex permittivity of standard model material under described substrate integration wave-guide frequency of operation,

the real part of the complex permittivity of testing sample material under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of testing sample material under described substrate integration wave-guide frequency of operation,

the loss tangents of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the loss tangent of standard model material under described substrate integration wave-guide frequency of operation,

the loss tangent of testing sample material under described substrate integration wave-guide frequency of operation.

Then the same substrate integration wave-guide circular resonant chamber of using other frequency of operation instead, repeating step 2-1, to the operation of step 2-4, can record the complex permittivity of testing medium sample under corresponding frequency of operation.

This method of testing is tested based on single port, and quality factor used are all passed through S ₁₁three dB bandwidth and resonance frequency determine.As embodiment, five resonator cavitys that work in different frequency are designed, frequency of operation 0.915GHz, 1.2GHz, 1.48GHz, 1.91GHz and 2.45GHz respectively during without perturbation, that substrate adopts is cheap Taconic RF35, substrate parameter is (specific inductive capacity 3.5, loss tangent 0.0018).

In above five resonator cavitys, the sample of differing dielectric constant is tested, the known dielectric constant medium of employing is (ε ^"=5, loss tangent=0.05), result is as shown in the table:

The measurement result of table 1 based on emulated data

Result show except real part of permittivity be that 1, other real parts measurement relative errors are all less than 2.5%, other relative error basic controlling are in 5% except 0 for loss tangent, this has shown measurement validity of the present invention.

Claims (4)

1. the material method for measuring complex dielectric constant based on substrate integration wave-guide circular resonant chamber, comprises the following steps:

Step 1: processing has the substrate integration wave-guide circular resonant chamber of different resonance frequencies; The dielectric-slab that described substrate integration wave-guide circular resonant chamber is all coated with metal conducting layer by tow sides processes, comprise metal conducting layer (1), dielectric layer (2), lower metal conducting layer (3), described dielectric layer (2) is positioned between metal conducting layer (1) and lower metal conducting layer (3), and some rounded equally distributed plated-through holes (4) link together upper metal conducting layer (1) and lower metal conducting layer (3); The mode of operation in described substrate integration wave-guide circular resonant chamber adopts second higher mode TM ₂₁₀mould, design add man-hour corresponding to the substrate integration wave-guide circular resonant chamber size of this pattern by resonance frequency f ₂₁₀obtain by formula (1):

$f_{210}=\frac{c}{2\mathrm{\&pi;}\sqrt{{\mathrm{\&mu;}}_r{\mathrm{\&epsiv;}}_r}}\sqrt{{\left(\frac{p_{21}}{a_{\mathrm{eff}}}\right)}^2}---\left(1\right)$

Wherein c is the light velocity, μ _rthe relative permeability of dielectric layer (2), ε _rthe relative dielectric constant of dielectric layer (2), p ₂₁the=5.136th, first zero point of second order Bessel's function, a _effbe the equivalent redius in described substrate integration wave-guide circular resonant chamber, the relation between the real radius a in it and described substrate integration wave-guide circular resonant chamber can be determined by (2) formula:

$a_{\mathrm{eff}}=a-\frac{D^2}{0.95b}---\left(2\right)$

Wherein D is the diameter of plated-through hole (4), b is the center of circle spacing of adjacent two plated-through holes (4) on same level cross section, and the real radius a in described substrate integration wave-guide circular resonant chamber is the distance between the center of circle of any one plated-through hole (4) on same level cross section and the geometric center in described substrate integration wave-guide circular resonant chamber;

Described substrate integration wave-guide circular resonant chamber also has a power feed hole (5) and a test sample loads hole (6), described power feed hole is carried out feed by coaxial feed joint (7), when feed, the outer conductor of coaxial feed joint (7) and upper metal conducting layer (1) electrical connection, the inner wire of coaxial feed joint (7) inserts power feed hole (5) and is electrically connected with lower metal conducting layer (3); It is a cylindrical hole that described test sample loads hole (6), is positioned at apart from power feed hole (5) geometric center peak electric field place farthest;

Step 2: the different resonance frequency substrate integration wave-guide circular resonant chamber that has that adopts step 1 to process is tested the complex permittivity of dielectric sample to be measured; Detailed process is as follows:

First adopt same substrate integration wave-guide circular resonant chamber, the frequency of operation to dielectric sample to be measured in this substrate integration wave-guide circular resonant chamber, this substrate integration wave-guide adds resonance frequency f corresponding to man-hour in design ₂₁₀under complex permittivity test, comprise the following steps:

Step 2-1: the resonance frequency f while measuring the zero load of described substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁; Sample identical and identical with dielectric layer (2) material with test sample loading hole (6) shape of concrete employing loads on test sample and loads in hole (6), and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole (5), measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁; The now resonance frequency f in substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁resonance frequency f while being exactly the zero load of described substrate integration wave-guide circular resonant chamber ₁and quality factor q ₁;

Step 2-2: the resonance frequency f while measuring described substrate integration wave-guide circular resonant chamber loading standard specimen ₂and quality factor q ₂; One of concrete employing loads on test sample with test sample loading hole (6) shape standard model identical and that complex permittivity is known and loads in hole (6), and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole (5), measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₂and quality factor q ₂;

Step 2-3: the resonance frequency f while measuring described substrate integration wave-guide circular resonant chamber loading testing sample ₃and quality factor q ₃; Testing sample identical with test sample loading hole (6) shape of concrete employing loads on test sample and loads in hole (6), and cover tightly upper and lower two end faces with sheet metal, then the sweep check signal of vector network analyzer output is passed through to concentric cable feed-in power feed hole (5), measure the now resonance frequency f in substrate integration wave-guide circular resonant chamber ₃and quality factor q ₃;

Step 2-4: the complex permittivity of calculating testing sample;

First simultaneous formula (3) and (4), calculates perturbation constant A and B:

${\mathrm{\&epsiv;}}_2^{,}=\frac{{\mathrm{A\&epsiv;}}_1^{,}{V}_c}{V_s}\left(\frac{f_1-f_2}{f_2}\right)+{\mathrm{\&epsiv;}}_1^{,}---\left(3\right)$

$\tan {\mathrm{\&delta;}}_2=\frac{{\mathrm{\&epsiv;}}_2^{,,}}{{\mathrm{\&epsiv;}}_2^{,}}=\frac{{\mathrm{BV}}_c}{V_s}\left(\frac{Q_1-Q_2}{Q_1{Q}_2}\right)\frac{1}{{\mathrm{\&epsiv;}}_2^{,}}+\tan {\mathrm{\&delta;}}_1---\left(4\right)$

Simultaneous formula (5) and (6) again, the complex permittivity of calculating testing sample:

${\mathrm{\&epsiv;}}_3^{,}=\frac{{\mathrm{A\&epsiv;}}_1^{,}{V}_c}{V_s}\left(\frac{f_1-f_3}{f_3}\right)+{\mathrm{\&epsiv;}}_1^{,}---\left(5\right)$

$\tan {\mathrm{\&delta;}}_3=\frac{{\mathrm{\&epsiv;}}_3^{,,}}{{\mathrm{\&epsiv;}}_3^{,}}=\frac{{\mathrm{BV}}_c}{V_s}\left(\frac{Q_1-Q_3}{Q_1{Q}_3}\right)\frac{1}{{\mathrm{\&epsiv;}}_3^{,}}+\tan {\mathrm{\&delta;}}_1---\left(6\right)$

In formula (3)～formula (6): V _cthe volume in described substrate integration wave-guide circular resonant chamber, V _sthe volume that test sample loads hole 6,

the real part of the complex permittivity of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the real part of the complex permittivity of standard model material under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of standard model material under described substrate integration wave-guide frequency of operation,

the real part of the complex permittivity of testing sample material under described substrate integration wave-guide frequency of operation,

the imaginary part of the complex permittivity of testing sample material under described substrate integration wave-guide frequency of operation,

the loss tangents of dielectric layer 2 materials under described substrate integration wave-guide frequency of operation,

the loss tangent of standard model material under described substrate integration wave-guide frequency of operation,

the loss tangent of testing sample material under described substrate integration wave-guide frequency of operation;

Then the same substrate integration wave-guide circular resonant chamber of using other frequency of operation instead, repeating step 2-1, to the operation of step 2-4, can record the complex permittivity of testing medium sample under corresponding frequency of operation.

2. the material method for measuring complex dielectric constant based on substrate integration wave-guide circular resonant chamber according to claim 1, is characterized in that, resonance frequency f when described substrate integration wave-guide circular resonant chamber is unloaded ₁and quality factor q ₁test be in the process of substrate integration wave-guide circular resonant chamber, before sample loads hole (6) processing, test completing after power feed hole (5) processing, to save step 2-1.

3. the material method for measuring complex dielectric constant based on substrate integration wave-guide circular resonant chamber according to claim 1, it is characterized in that, test sample loads hole (6) and is positioned at apart from power feed hole geometric center peak electric field place farthest, and this position is apart from the distance R at cavity center _sdetermined by following formula:

$R_s=\frac{p_{\max 1}}{p_{21}}\&times;a_{\mathrm{eff}}---\left(7\right)$

Wherein, p _max1second order Bessel's function corresponding argument value while getting first maximum value, 3.056, p ₂₁first zero point of second order Bessel's function, 5.136.

4. the material method for measuring complex dielectric constant based on substrate integration wave-guide circular resonant chamber according to claim 1, is characterized in that, the volume V in substrate integration wave-guide circular resonant chamber _cvolume V with test sample loading hole 6 _sratio should be arranged between 200～400.

Images