CN102608431B

CN102608431B - 1GHz～8GHz Coaxial-Dielectric Circular Waveguide Resonant Cavity and Dielectric Parameter Test Method

Info

Publication number: CN102608431B
Application number: CN201210063977.9A
Authority: CN
Inventors: 倪尔瑚; 倪郁青; 朱永花
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2012-03-12
Filing date: 2012-03-12
Publication date: 2014-01-29
Anticipated expiration: 2032-03-12
Also published as: CN102608431A

Abstract

The invention discloses a coaxial-dielectric circular waveguide resonant cavity for measurement of a dielectric medium with frequency range of 1GHz-8GHz, and a dielectric testing method. An adjustable short-circuiter with a travel of 100mm is arranged at one end of an air coaxial measuring line formed by an outer conductor, an inner conductor and an axially moving probe, and an input coupling loop is arranged on the adjustable short-circuiter. A cylindrical dielectric sample is arranged at a gap between the inner conductor and a metal short circuit board at the other end of the coaxial measuring line, and the cylindrical dielectric sample and the coaxial line outer conductor form a dielectric circular waveguide. TEM (transverse electromagnetic) wave in the coaxial line and TM 01 wave in the sample are combined in resonance to obtain a complex dielectric constant of a material. The difficulty in preparation of the coaxial line and insertion and tight fit of ring samples is overcome, electromagnetic field distribution of the sample is unrelated to sample size and operating frequency, and error of matching of the sample radial size with a metal wall is no longer a main factor causing uncertainty of measurement. The dielectric material with the relative dielectric constant of 1-100 (or higher) can be measured.

Description

1GHz～8GHz Coaxial-Dielectric Circular Waveguide Resonant Cavity and Dielectric Parameter Test Method

技术领域 technical field

本发明涉及谐振腔电介质测试方法，尤其涉及一种用于1GHz～8GHz电介质测量的同轴线-介质圆波导谐振腔及介电参数测试方法。The invention relates to a method for testing the dielectric of a resonant cavity, in particular to a coaxial line-dielectric circular waveguide resonant cavity and a method for testing dielectric parameters used for dielectric measurement of 1GHz to 8GHz.

背景技术 Background technique

在微波频段，非磁性介质的基本电学参数，即相对介电常数ε_r、介质损耗角正切tanδ，是研究材料和研制相应介质元器件，如基片、介质谐振器、介质滤波器、介质天线、微带天线、低温共烧陶瓷(LTCC)、微波模块、微波集成的基础。众所周知，在频率1GHz～8GHz的电介质测量，当前常用的同轴线传输测试方法是圆环样品的反射-传输测量或圆柱样品的反射-传输测量。前者由于样品与同轴线内、外导体的配合间隙，导致非常可观的测量偏差，并随介电常数的增大而快速升高。后者由于同轴线-充满介质圆波导组合结构中存在一系列TM_0p模，使计算极其复杂。本方法采用同轴线-圆波导组合结构的谐振原理，使在同轴线和同轴线内导体内导体与金属短路板之间的间隔处充满介质而形成的组合腔体在最低波模谐振。这样，被同轴线-介质圆波导这个不连续界面所激励起的只有TM₀₁模。导致在同轴线中只有TEM导行波和TM₀₁消逝波，介质圆波导中只有TM₀₁消逝波或导行波。从而实现在TM₀₁模下测量材料的ε_r和tanδ。这不仅克服了在同轴线中制备和插入紧密配合的圆环状样品的困难，而且实现了样品中电磁场分布与样品尺寸及工作频率无关，以及样品径向尺寸与金属壁的配合误差不再是引起测量不确定性的主要因素。可以用于测量介电常数从接近于1到约为100的介质材料。特别适宜于单面敷金属板基片和泡沫材料的测量。In the microwave frequency band, the basic electrical parameters of non-magnetic media, namely the relative permittivity ε _r and the dielectric loss tangent tan δ, are important for researching materials and developing corresponding dielectric components, such as substrates, dielectric resonators, dielectric filters, and dielectric antennas. , microstrip antenna, low temperature co-fired ceramics (LTCC), microwave module, the basis of microwave integration. As we all know, for the dielectric measurement at a frequency of 1 GHz to 8 GHz, the current commonly used coaxial line transmission test method is the reflection-transmission measurement of the circular sample or the reflection-transmission measurement of the cylindrical sample. Due to the fit gap between the sample and the inner and outer conductors of the coaxial line, the former leads to a very considerable measurement deviation, which increases rapidly with the increase of the dielectric constant. The latter makes the calculation extremely complicated due to the existence of a series of TM _Op modes in the coaxial line-dielectric filled circular waveguide composite structure. This method adopts the resonance principle of the coaxial line-circular waveguide combined structure, so that the combined cavity formed by filling the space between the coaxial line and the inner conductor of the coaxial line and the metal short circuit board with medium resonates in the lowest wave mode. . In this way, only the TM ₀₁ mode is excited by the discontinuous interface of the coaxial line-dielectric circular waveguide. As a result, there are only TEM guided waves and TM ₀₁ evanescent waves in the coaxial line, and only TM ₀₁ evanescent waves or guided waves in the dielectric circular waveguide. In this way, the ε _r and tan δ of the material can be measured under the TM ₀₁ mode. This not only overcomes the difficulty of preparing and inserting a tightly fitted ring-shaped sample in the coaxial line, but also realizes that the electromagnetic field distribution in the sample has nothing to do with the sample size and operating frequency, and the matching error between the radial size of the sample and the metal wall is no longer is the main factor causing measurement uncertainty. It can be used to measure dielectric materials with a dielectric constant from close to 1 to about 100. It is especially suitable for the measurement of single-sided metal-clad substrates and foam materials.

发明内容 Contents of the invention

本发明的目的是克服现有技术的不足，提供一种1GHz～8GHz的同轴线-介质圆波导谐振腔的介电参数测试装置及其测试方法。The purpose of the present invention is to overcome the deficiencies of the prior art, and provide a 1GHz-8GHz coaxial line-dielectric circular waveguide resonator dielectric parameter testing device and testing method thereof.

1GHz～8GHz频段用于电介质测量的同轴线-介质圆波导谐振腔的测量装置包括同轴线外导体、同轴线内导体、可移动探针、可调节短路器、输入耦合环、圆柱介质样品、金属短路板、微波输入信号和输出驻波信号；同轴线外导体和同轴线内导体为同轴结构、同轴线外导体上设有轴向缝隙，在轴向缝隙上设有可移动探针构成空气同轴测量线；空气同轴测量线的一端设有行程为100mm的可调节短路器，可调节短路器上设有输入耦合环；空气同轴测量线另一端端部设有金属短路板，同轴线内导体与金属短路板之间设有间隔，在间隔内充满圆柱介质样品，圆柱介质样品、金属短路板与同轴线外导体构成介质圆波导；输入耦合环与微波输入信号相接，从可移动探针探测到谐振时的输出驻波信号振幅，得到电压驻波比，与输出驻波信号相位有关的长度由可调节短路器的刻度读出。The coaxial line-dielectric circular waveguide resonator measuring device used for dielectric measurement in the 1GHz~8GHz frequency band includes coaxial outer conductor, coaxial inner conductor, movable probe, adjustable short circuit, input coupling ring, cylindrical dielectric Sample, metal short circuit board, microwave input signal and output standing wave signal; the outer conductor of the coaxial line and the inner conductor of the coaxial line are of a coaxial structure, the outer conductor of the coaxial line is provided with an axial slot, and the axial slot is provided with The movable probe constitutes the air coaxial measurement line; one end of the air coaxial measurement line is provided with an adjustable short circuit with a stroke of 100mm, and the adjustable short circuit is provided with an input coupling ring; the other end of the air coaxial measurement line is provided with a There is a metal short circuit board, and there is a gap between the inner conductor of the coaxial line and the metal short circuit board, and the cylindrical dielectric sample is filled in the gap, and the cylindrical dielectric sample, the metal short circuit board and the outer conductor of the coaxial line form a dielectric circular waveguide; the input coupling ring and the The microwave input signal is connected, and the amplitude of the output standing wave signal at resonance is detected from the movable probe to obtain the voltage standing wave ratio, and the length related to the phase of the output standing wave signal is read from the scale of the adjustable short circuit.

所述的同轴线外导体内径与同轴线内导体外径之比为2.3～3.5。所述同轴线外导体上的轴向缝隙长度为200mm、宽度为1mm、离圆柱介质样品表面的距离为10mm。所述的圆柱介质样品的厚度为1～12mm。The ratio of the inner diameter of the outer conductor of the coaxial line to the outer diameter of the inner conductor of the coaxial line is 2.3-3.5. The axial slit on the outer conductor of the coaxial line has a length of 200 mm, a width of 1 mm, and a distance of 10 mm from the surface of the cylindrical medium sample. The thickness of the cylindrical medium sample is 1-12 mm.

1GHz～8GHz的同轴线-介质圆波导谐振腔的介电参数测试方法是：利用最低次波模谐振，使同轴线中仅有TEM导行波和TM₀₁消逝波，介质中只存在TM₀₁消逝波或导行波；用测量第一个波节到样品表面的距离和电压驻波比，求值材料在TM₀₁模下的ε_r和tanδ，方法的具体步骤如下：The test method of the dielectric parameters of the coaxial line-dielectric circular waveguide resonator from 1GHz to 8GHz is: using the lowest sub-mode resonance, so that there are only TEM guided wave and TM ₀₁ evanescent wave in the coaxial line, and only TM exists in the medium. ₀₁ evanescent wave or guided traveling wave; by measuring the distance from the first node to the sample surface and the voltage standing wave ratio, evaluate the ε _r and tanδ of the material under the TM ₀₁ mode. The specific steps of the method are as follows:

(1)测量谐振下的第一个波节到样品表面的距离l₀：(1) Measure the distance l ₀ from the first wave node under resonance to the sample surface:

在给定频率v_r下，放入介质样品，调节短路器达到腔体谐振，记下同轴线-介质圆波导状态时可调节短路器的读数L_i，用金属短路板取代样品，再次调节短路器，使在相同频率下重新谐振，记下同轴线-短路板状态时可调节短路器读数L₀，得出第一个波节到样品表面的距离为：At a given frequency v _r , put in a dielectric sample, adjust the short circuit to achieve cavity resonance, record the reading L _i of the short circuit in the state of the coaxial line-dielectric circular waveguide, replace the sample with a metal short circuit, and adjust again Short circuit, so that it resonates at the same frequency, record the reading L ₀ of the short circuit when recording the state of the coaxial line-short circuit board, and obtain the distance from the first wave node to the sample surface as:

l₀＝c/(2v_r)-(L₀-L_i) (1)l ₀ ＝c/(2v _r )-(L ₀ -L _i ) (1)

这里，c是空气中的光速，Here, c is the speed of light in air,

(2)测量谐振下的电压驻波比s：(2) Measure the voltage standing wave ratio s at resonance:

用接到输出探针的传感器-微波功率计，移动测量线上的可移动探针，测定同轴线-介质圆波导状态时在上述谐振频率v_r下驻波峰值和谷值的功率计读数P_imax和P_imin，有Use the sensor-microwave power meter connected to the output probe, move the movable probe on the measurement line, and measure the power meter readings of the standing wave peak value and valley value at the above-mentioned resonant frequency v _r when the coaxial line-dielectric circular waveguide is in the state P _imax and P _imin , with

s_i＝(P_imin/_Pimax)^1/2 (2)s _i =(P _imin / _Pimax ) ^1/2 (2)

用金属短路板取代圆柱介质样品，调节短路器，使在相同频率下重新谐振，再次移动测量线上的可移动探针，测定同轴线-短路板状态下的驻波峰值和谷值的功率计读数P_0max和P_0min，有Replace the cylindrical dielectric sample with a metal short circuit board, adjust the short circuit device to resonate at the same frequency, move the movable probe on the measurement line again, and measure the standing wave peak and valley power in the coaxial line-short circuit board state Gauge readings P _0max and P _0min , with

s₀＝(P_0min/P_0max)^1/2 (3)s ₀ =(P _0min /P _0max ) ^1/2 (3)

得由介质样品引起的电压驻波比为：The VSWR caused by the dielectric sample is obtained as:

s＝s_i-s₀·2v_rl₀/c (4)s＝s _i -s ₀ ·2v _r l ₀ /c (4)

(3)计算材料的复介电常数

用测得的谐振-驻波参数l₀和s，按式(3) Calculate the complex permittivity of the material

With the measured resonance-standing wave parameters l ₀ and s, according to the formula

$j j \frac{{22 k k}_{00} a a {\overset{^^}{ϵ ϵ}}_{r r}}{ln ln ((a a / / b b))} (({y the y}_{00} - - {y the y}_{q q} {x x}_{q q})) = = \frac{11 - - js js \cdot \cdot tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))}{s the s - - j j tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))} - - - - - - ((1818))$

编写的复数迭代程序，求解复介电常数

式(18)中：A complex iterative program written to solve the complex permittivity

In formula (18):

${y the y}_{00} = = \frac{coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {λ λ}_{i i}^{22} {a a}^{33}} \cdot \cdot \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} - - - - - - ((66))$

${y the y}_{q q} = = - - \frac{coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {a a}^{33} (({λ λ}_{i i}^{22} - - {ξ ξ}_{q q}^{22}))} \cdot \cdot \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} - - - - - - ((77))$

x_q＝y_q/A_qn (8)x _q = y _q /A _qn (8)

${A A}_{qn qn} = = \frac{{λ λ}_{i i}^{22} coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {a a}^{33} {(({λ λ}_{i i}^{22} - - {γ γ}_{q q}^{22}))}^{22}} \cdot &Center Dot; \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} + + \frac{11}{{\overset{^^}{ϵ ϵ}}_{r r}} \cdot &Center Dot; \frac{11}{44 a a {γ γ}_{q q}} [[\frac{{a a}^{22} {Z Z}_{11}^{22} (({ξ ξ}_{q q} a a))}{{b b}^{22} {Z Z}_{11}^{22} (({ξ ξ}_{q q} b b))} - - 11]] - - - - - - ((99))$

以及，贝塞尔函数的线性组合And, the linear combination of Bessel functions

Z₁(ξ_qa)＝J₁(ξ_qa)+J₀(ξ_qa)N₁(ξ_qa)/N₀(ξ_qa) (10)Z ₁ (ξ _q a)＝J ₁ (ξ _q a)+J ₀ (ξ _q a)N ₁ (ξ _q a)/N ₀ (ξ _q a) (10)

Z₁(ξ_qb)＝J₁(ξ_qb)-J₀(ξ_qb)N₀(ξ_qb)/N₀(ξ_qb) (11)Z ₁ (ξ _q b)=J ₁ (ξ _q b)-J ₀ (ξ _q b)N ₀ (ξ _q b)/N ₀ (ξ _q b) (11)

上述各式中：2a是同轴线外导体内径，2b是同轴线内导体外径，d是圆柱样品厚度，J₀、J₁和N₀、N₁分别是第一类和第二类另阶、一阶贝塞尔函数，ξ_q是按式Among the above formulas: 2a is the inner diameter of the outer conductor of the coaxial line, 2b is the outer diameter of the inner conductor of the coaxial line, d is the thickness of the cylindrical sample, J ₀ , J ₁ and N ₀ , N ₁ are the first type and the second type respectively Another order, first order Bessel function, ξ _q is according to the formula

J₀(ξ_qa)N₀(ξ_qb)-J₀(ξ_qb)N₀(ξ_qa)＝0 (12)J ₀ (ξ _q a)N ₀ (ξ _q b)-J ₀ (ξ _q b)N ₀ (ξ _q a)＝0 (12)

编写的迭代程序得到的第一个解，并有The first solution obtained by the iterative program written, and has

${γ γ}_{q q} = = \sqrt{{ξ ξ}_{q q}^{22} - - {k k}_{00}^{22}} - - - - - - ((1313))$

λ_i＝2.4048/a (14)λ _i =2.4048/a (14)

${γ γ}_{i i} = = \sqrt{{λ λ}_{i i}^{22} - - {k k}^{22}} - - - - - - ((1515))$

K₀＝ω/c，

ω＝2πv_r (16)K ₀ =ω/c,

ω＝2πv _r (16)

式中：γ_q是同轴线对TM₀₁波的传播常数，是实数，传播消逝波；γ_i是介质圆波导对TM₀₁波的复传播常数；ω是谐振圆频率；k₀是空气中的波数；k是介质中的波数；式(14)是第一类另阶贝塞尔函数J₀(λ_ia)＝0的第一个解。In the formula: γ _q is the propagation constant of the coaxial line to the TM ₀₁ wave, which is a real number, propagating the evanescent wave; γ _i is the complex propagation constant of the dielectric circular waveguide to the TM ₀₁ wave; ω is the resonant circular frequency; k ₀ is the k is the wave number in the medium; Equation (14) is the first solution of the first kind of alternative Bessel function J ₀ (λ _i a )=0.

本发明与现有技术相比具有的有益效果：The present invention has the beneficial effect compared with prior art:

1：测量手续简便：只需测量谐振下的第一个波节到样品表面的距离l₀和电压驻波比s。1: The measurement procedure is simple: only need to measure the distance l ₀ from the first node under resonance to the sample surface and the voltage standing wave ratio s.

在给定频率v_r下，放入介质样品，调节短路器达到腔体谐振，记下同轴线-介质圆波导状态时的可调节短路器的读数L_i。用金属短路板取代样品，再次调节短路器，使在相同频率下重新谐振，记下同轴线-短路板状态时的可调节短路器读数L₀。得出第一个波节到样品表面的距离是：At a given frequency v _r , put in a dielectric sample, adjust the short circuit to achieve cavity resonance, and record the reading L _i of the adjustable short circuit in the coaxial line-dielectric circular waveguide state. Replace the sample with a metal short circuit board, adjust the short circuit device again to resonate at the same frequency, and record the adjustable short circuit device reading L ₀ in the coaxial line-short circuit board state. The distance from the first node to the sample surface is found to be:

l₀＝c/(2v_r)-(L₀-L_i) (1)l ₀ ＝c/(2v _r )-(L ₀ -L _i ) (1)

这里，c是空气中的光速。Here, c is the speed of light in air.

用接到输出探针的传感器-微波功率计，移动测量线上的可移动探针，测定同轴线-介质圆波导状态时、在上述谐振频率v_r下的驻波峰值和谷值的功率计读数P_imax和P_imin，有Use the sensor-microwave power meter connected to the output probe to move the movable probe on the measurement line to measure the power of the standing wave peak value and valley value at the above-mentioned resonant frequency v _r when the coaxial line-dielectric circular waveguide is in the state Gauge readings P _imax and P _imin , with

s_i＝(P_imin/P_imax)^1/2 (2)s _i =(P _imin /P _imax ) ^1/2 (2)

用金属短路板取代样品，调节短路器，使在相同频率下重新谐振，再次移动测量线上的可移动探针，测定同轴线-短路板状态下的驻波峰值和谷值的功率计读数P_0max和P_0min，有Replace the sample with a metal short circuit board, adjust the short circuit device to re-resonate at the same frequency, move the movable probe on the measurement line again, and measure the power meter readings of the peak and valley values of the standing wave in the coaxial line-short circuit board state P _0max and P _0min , with

s₀＝(P_0min/P_0max)^1/2 (3)s ₀ =(P _0min /P _0max ) ^1/2 (3)

得由介质样品引起的电压驻波比为The voltage standing wave ratio induced by the dielectric sample is

s＝s_i-s₀·2v_rl₀/c (4)s＝s _i -s ₀ ·2v _r l ₀ /c (4)

2：被测参数与相对复介电常数

之间有着相对简单得多(比之非谐振状态)、而严格的数学关系式。2: Measured parameters and relative complex permittivity

There is a relatively simple (compared with the non-resonant state) and strict mathematical relationship between them.

该同轴线-介质圆波导之组合结构腔体，当在最低次波模谐振时，在同轴线中存在TEM导行波和TM₀₁(q＝1)消逝波，在介质中只存在TM₀₁(i＝1)消逝波或导行波。解谐振结构的电磁场方程，得到同轴线内导体-圆柱介质界面的归一化输入导纳为The combined structure cavity of the coaxial line-dielectric circular waveguide, when resonating in the lowest wave mode, there are TEM guided waves and TM ₀₁ (q=1) evanescent waves in the coaxial line, and only TM exists in the medium ₀₁ (i=1) Evanescent wave or guided traveling wave. Solving the electromagnetic field equation of the resonant structure, the normalized input admittance of the conductor-cylindrical interface in the coaxial line is obtained as

${y the y}_{e e} = = j j \frac{{22 k k}_{00} a a {\overset{^^}{ϵ ϵ}}_{r r}}{ln ln ((a a / / b b))} (({y the y}_{00} - - {y the y}_{q q} {x x}_{q q})) - - - - - - ((55))$

式中：In the formula:

${y the y}_{00} = = \frac{coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {λ λ}_{i i}^{22} {a a}^{33}} \cdot &Center Dot; \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} - - - - - - ((66))$

${y the y}_{q q} = = - - \frac{coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {a a}^{33} (({λ λ}_{i i}^{22} - - {ξ ξ}_{q q}^{22}))} \cdot &Center Dot; \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} - - - - - - ((77))$

x_q＝y_q/A_qn (8)x _q = y _q /A _qn (8)

${A A}_{qn qn} = = \frac{{λ λ}_{i i}^{22} coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {a a}^{33} {(({λ λ}_{i i}^{22} - - {γ γ}_{q q}^{22}))}^{22}} \cdot &Center Dot; \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} + + \frac{11}{{\overset{^^}{ϵ ϵ}}_{r r}} \cdot &Center Dot; \frac{11}{44 a a {γ γ}_{q q}} [[\frac{{a a}^{22} {Z Z}_{11}^{22} (({ξ ξ}_{q q} a a))}{{b b}^{22} {Z Z}_{11}^{22} (({ξ ξ}_{q q} b b))} - - 11]],, ((n no = = q q)) - - - - - - ((99))$

Z₁(ξ_qb)＝J₁(ξ_qb)-J₀(ξ_qb)N₁(ξ_qb)/N₀(ξ_qb) (11)Z ₁ (ξ _q b)=J ₁ (ξ _q b)-J ₀ (ξ _q b)N ₁ (ξ _q b)/N ₀ (ξ _q b) (11)

上述各式中：2a是同轴线外导体内径，2b是同轴线内导体外径。d是圆柱样品厚度。J₀、J₁和N₀、N₁分别是第一类和第二类另阶、一阶贝塞尔函数。ξ_q是按式Among the above formulas: 2a is the inner diameter of the outer conductor of the coaxial line, and 2b is the outer diameter of the inner conductor of the coaxial line. d is the thickness of the cylindrical sample. J ₀ , J ₁ and N ₀ , N ₁ are the first-order and second-order Bessel functions of the first and second order, respectively. ξ _q is according to the formula

J₀(ξ_qa)N₀(ξ_qb)-ξ_q(ξ_qb)N₀(ξ_qa)＝0 (12)J ₀ (ξ _q a)N ₀ (ξ _q b)-ξ _q (ξ _q b)N ₀ (ξ _q a)＝0 (12)

编写的迭代程序得到的第一个解。并有The first solution obtained by the written iterative program. And a

λ_i＝2.4048/a (14)λ _i =2.4048/a (14)

和and

k₀＝ω/c，

ω＝2πv_r (16)k ₀ =ω/c,

ω＝2πv _r (16)

式(5)左边的归一化导纳可以用测量电压驻波比s和第一个波节到样品表面的距离l₀获得，有The normalized admittance on the left side of formula (5) can be obtained by measuring the VSWR s and the distance l ₀ from the first node to the sample surface, as

${y the y}_{e e} = = \frac{11 - - js js \cdot &Center Dot; tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))}{s the s - - j j tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))} - - - - - - ((1717))$

这样，对于非磁性(μ_r＝1)材料，组合式(5)和式(17)，得Thus, for non-magnetic (μ _r =1) materials, combining formula (5) and formula (17), we get

$j j \frac{{22 k k}_{00} a a {\overset{^^}{ϵ ϵ}}_{r r}}{ln ln ((a a / / b b))} (({y the y}_{00} - - {y the y}_{q q} {x x}_{q q})) = = \frac{11 - - js js \cdot &Center Dot; tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))}{s the s - - j j tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))} - - - - - - ((1818))$

用式(18)编写的迭代程序，就可求值材料的复介电常数

Using the iterative program written in formula (18), the complex permittivity of the material can be evaluated

3：是制造样品容易和测量误差小。3: It is easy to manufacture samples and the measurement error is small.

同轴线与其内导体终端与金属短路板的间隔处充满圆柱介质的闭合腔体，其圆柱样品容易制备。在非谐振状态下，在同轴线中存在TEM模和TM_0q模，在介质中只存在TM_0i模。这不仅克服了在同轴线中制备和插入紧密配合的圆环状样品的困难，而且实现了该处电磁场分布与样品尺寸及工作频率无关，以及样品径向尺寸与金属壁的配合误差不再是引起测量不确定性的主要因素。当在最低次波模谐振时，同轴线中为TEM导行波和TM₀₁(q＝1)消逝波，介质中只存在TM₀₁(i＝1)消逝波或导行波，大大简化了计算。采用测量最低次波模谐振时同轴线-介质圆波导界面前方的驻波比，能进一步抑制高次模对振幅测量的影响，提高tanδ的测量准确性度。The gap between the coaxial line and its internal conductor terminal and the metal short circuit board is filled with a closed cavity of cylindrical medium, and its cylindrical samples are easy to prepare. In the non-resonant state, there are TEM mode and TM _0q mode in the coaxial line, and only TM _0i mode exists in the medium. This not only overcomes the difficulty of preparing and inserting a tight-fitting circular sample in the coaxial line, but also realizes that the electromagnetic field distribution here is independent of the sample size and operating frequency, and the matching error between the radial size of the sample and the metal wall is no longer is the main factor causing measurement uncertainty. When resonating in the lowest sub-mode, there are TEM guided waves and TM ₀₁ (q=1) evanescent waves in the coaxial line, and only TM ₀₁ (i=1) evanescent waves or guided waves exist in the medium, which greatly simplifies calculate. By measuring the standing wave ratio in front of the coaxial line-dielectric circular waveguide interface when the lowest wave mode resonates, the influence of the high-order mode on the amplitude measurement can be further suppressed, and the measurement accuracy of tanδ can be improved.

4：是可以在指定的点频或随机的谐振频率下进行测量。4: It can be measured at the specified point frequency or random resonance frequency.

制造不同尺寸的同轴结构，用调节谐振腔中的可调节短路器，可在1GHz～8GHz范围内您所需的任一恒定频率下实现谐振，因而可采用价廉的点频源。而当谐振腔的可调节短路器在某固定位置时，可改变合成信号源的频率，在1GHz～8GHz范围内找到谐振频率进行测量。不同样品厚度会有不同的ε_r测量范围、测量分辨率和准确度。Manufacture coaxial structures of different sizes, and adjust the adjustable short circuit in the resonant cavity to achieve resonance at any constant frequency you need in the range of 1GHz to 8GHz, so a cheap point frequency source can be used. And when the adjustable short-circuiter of the resonant cavity is at a fixed position, the frequency of the synthesized signal source can be changed, and the resonant frequency can be found in the range of 1GHz to 8GHz for measurement. Different sample thickness will have different ε _r measurement range, measurement resolution and accuracy.

5：应用介质样品中传播消逝波或导行波的特性(加上选择同轴尺寸)，可以在1GHz～8GHz范围内的任一频率，从介电常数接近于1到高达ε_r≈100的材料进行测量。5: The characteristics of propagating evanescent wave or guided wave in the application medium sample (plus the selection of coaxial size), can be at any frequency in the range of 1GHz to 8GHz, from a dielectric constant close to 1 to as high as ε _r ≈ 100 material to be measured.

附图说明 Description of drawings

图1是用于1GHz～8GHz频段电介质测量的同轴线-介质圆波导谐振腔示意图；Figure 1 is a schematic diagram of a coaxial line-dielectric circular waveguide resonator used for dielectric measurement in the 1GHz to 8GHz frequency band;

图2是MPC-14系统在消逝波下(ε_r＜28.7)的ε_r～l₀曲线：3GHz，s＝0.001，d＝3mm(蓝)和d＝1mm(粉红)；Figure 2 is the ε _r ~ l ₀ curve of the MPC-14 system under evanescent wave (ε _r <28.7): 3GHz, s=0.001, d=3mm (blue) and d=1mm (pink);

图3是MPC-14系统在导行波下(ε_r＞28.7)的ε_r～l₀曲线：3GHz，s＝0.001，d＝8mm(蓝)，d＝10mm(粉红)。Fig. 3 is the ε _r ~ l ₀ curve of the MPC-14 system under the guided wave (ε _r >28.7): 3GHz, s=0.001, d=8mm (blue), d=10mm (pink).

具体实施方式 Detailed ways

如图1所示，1GHz～8GHz频段用于电介质测量的同轴线-介质圆波导谐振腔的测量装置包括同轴线外导体1、同轴线内导体2、可移动探针3、可调节短路器4、输入耦合环5、圆柱介质样品6、金属短路板7、微波输入信号8和输出驻波信号9；同轴线外导体1和同轴线内导体2为同轴结构、同轴线外导体1上设有轴向缝隙，在轴向缝隙上设有可移动探针3构成空气同轴测量线；空气同轴测量线的一端设有行程为100mm的可调节短路器4，可调节短路器4上设有输入耦合环5；空气同轴测量线另一端端部设有金属短路板7，同轴线内导体2与金属短路板7之间设有间隔，在间隔内充满圆柱介质样品6，圆柱介质样品6、金属短路板7与同轴线外导体1构成介质圆波导；输入耦合环5与微波输入信号8相接，从可移动探针3探测到谐振时的输出驻波信号9振幅，得到电压驻波比，与输出驻波信号9相位有关的长度由可调节短路器4的刻度读出。As shown in Figure 1, the measurement device for the coaxial-dielectric circular waveguide resonator used for dielectric measurement in the 1GHz to 8GHz frequency band includes a coaxial outer conductor 1, a coaxial inner conductor 2, a movable probe 3, an adjustable Short circuit 4, input coupling ring 5, cylindrical dielectric sample 6, metal short circuit board 7, microwave input signal 8 and output standing wave signal 9; coaxial outer conductor 1 and coaxial inner conductor 2 are coaxial structure, coaxial An axial gap is arranged on the outer conductor 1, and a movable probe 3 is arranged on the axial gap to form an air coaxial measurement line; one end of the air coaxial measurement line is provided with an adjustable short circuit 4 with a stroke of 100mm, which can An input coupling ring 5 is provided on the adjusting short circuit 4; a metal short circuit board 7 is provided at the other end of the air coaxial measurement line, and a gap is set between the inner conductor 2 of the coaxial line and the metal short circuit board 7, and the gap is filled with cylinders The dielectric sample 6, the cylindrical dielectric sample 6, the metal short circuit board 7 and the coaxial outer conductor 1 form a dielectric circular waveguide; the input coupling ring 5 is connected to the microwave input signal 8, and the output station when the movable probe 3 detects the resonance The amplitude of the wave signal 9 is used to obtain the voltage standing wave ratio, and the length related to the phase of the output standing wave signal 9 is read by the scale of the adjustable short circuiter 4 .

所述的同轴线外导体1内径与同轴线内导体2外径之比为2.3～3.5。所述同轴线外导体1上的轴向缝隙长度为200mm、宽度为1mm、离圆柱介质样品6表面的距离为10mm。所述的圆柱介质样品6的厚度为1～12mm。The ratio of the inner diameter of the coaxial outer conductor 1 to the outer diameter of the coaxial inner conductor 2 is 2.3-3.5. The axial slit on the coaxial outer conductor 1 has a length of 200 mm, a width of 1 mm, and a distance from the surface of the cylindrical dielectric sample 6 of 10 mm. The thickness of the cylindrical medium sample 6 is 1-12 mm.

在给定频率v_r下，放入介质样品6，调节短路器4达到腔体谐振，记下同轴线-介质圆波导状态时可调节短路器4的读数L_i，用金属短路板7取代样品6，再次调节短路器4，使在相同频率下重新谐振，记下同轴线-短路板状态时可调节短路器4读数L₀，得出第一个波节到样品表面的距离为：At a given frequency v _r , put in the dielectric sample 6, adjust the short circuit 4 to achieve cavity resonance, record the reading L _i of the short circuit 4 when the coaxial line-dielectric circular waveguide is in the state, and replace it with a metal short circuit board 7 For sample 6, adjust the short-circuiter 4 again to resonate at the same frequency, record the reading L ₀ of the short-circuiter 4 when the coaxial line-short-circuit board is in state, and obtain the distance from the first node to the sample surface as:

l₀＝c/(2v_r)-(L₀-L_i) (1)l ₀ ＝c/(2v _r )-(L ₀ -L _i ) (1)

这里，c是空气中的光速，Here, c is the speed of light in air,

用接到输出探针的传感器-微波功率计，移动测量线上的可移动探针3，测定同轴线-介质圆波导状态时在上述谐振频率v_r下驻波峰值和谷值的功率计读数P_imax和P_imin，有Use the sensor-microwave power meter connected to the output probe, move the movable probe 3 on the measurement line, and measure the power meter of the standing wave peak value and valley value at the above-mentioned resonant frequency v _r when the coaxial line-dielectric circular waveguide is in the state Readings P _imax and P _imin , with

s_i＝(P_imin/P_imax)^1/2 (2)s _i =(P _imin /P _imax ) ^1/2 (2)

用金属短路板7取代圆柱介质样品6，调节短路器4，使在相同频率下重新谐振，再次移动测量线上的可移动探针3，测定同轴线-短路板状态下的驻波峰值和谷值的功率计读数P_0max和P_0min，有Replace the cylindrical dielectric sample 6 with a metal short circuit board 7, adjust the short circuit device 4 to resonate at the same frequency, move the movable probe 3 on the measurement line again, and measure the standing wave peak value and the peak value of the coaxial line-short circuit board state Valley power meter readings P _0max and P _0min , with

s₀＝(P_0min/P_0max)^1/2 (3)s ₀ =(P _0min /P _0max ) ^1/2 (3)

s＝s_i-s₀·2v_rl₀/c (4)s＝s _i -s ₀ ·2v _r l ₀ /c (4)

(3)计算材料的复介电常数

编写的复数迭代程序，求解复介电常数

In formula (18):

x_q＝y_q/A_qn (8)x _q = y _q /A _qn (8)

上述各式中：2a是同轴线外导体内径，2b是同轴线内导体外径，d是圆柱样品厚度。J₀、J₁和N₀、N₁分别是第一类和第二类另阶、一阶贝塞尔函数，ξ_q是按式Among the above formulas: 2a is the inner diameter of the outer conductor of the coaxial line, 2b is the outer diameter of the inner conductor of the coaxial line, and d is the thickness of the cylindrical sample. J ₀ , J ₁ and N ₀ , N ₁ are the first and second kind of alternative order and first order Bessel functions respectively, ξ _q is according to the formula

λ_i＝2.4048/a (14)λ _i =2.4048/a (14)

k₀＝ω/c，

ω＝2πv_r (16)k ₀ =ω/c,

ω＝2πv _r (16)

本发明属于低/高介电常数、中/低损耗微波介质材料的相对复介电常数

测量用的同轴线-介质圆波导谐振腔测试系统。可用MPC-14同轴尺寸、APC-7同轴尺寸或另外同轴尺寸(例如：2a＝30.0×10^-3m，2b＝13.0×10^-3m；2a＝50.0×10^-3m，2b＝21.7×10^-3m)来实施。The invention belongs to the relative complex permittivity of low/high dielectric constant, medium/low loss microwave dielectric materials

Coaxial line-dielectric circular waveguide resonator test system for measurement. Available MPC-14 coaxial size, APC-7 coaxial size or other coaxial size (for example: 2a=30.0×10 ^-3 m, 2b=13.0×10 ^-3 m; 2a=50.0×10 ^-3 m, 2b =21.7×10 ^-3 m) to implement.

实施例：表1、图2在介质中传播消逝波的某些情况，和表2、图3在介质中传播导行波的某些情况。表3是聚四氟乙烯样品在MPC-14同轴系统中、两个频率下的测量数据和计算结果。Embodiment: Table 1, Fig. 2 some cases of propagating evanescent wave in the medium, and Table 2, Fig. 3 some cases of propagating traveling wave in the medium. Table 3 is the measurement data and calculation results of PTFE samples in the MPC-14 coaxial system at two frequencies.

表1.γ_i是实数时某些同轴系统可用于测量介电常数情况(s＝0.001)Table 1. When γ _i is a real number, some coaxial systems can be used to measure the dielectric constant (s=0.001)

^*εr_max表示能测量的最大极限值. ^* εr _max indicates the maximum limit value that can be measured.

表2.γ_i是虚数时某些同轴系统可用于测量介电常数情况(s＝0.001)Table 2. When γ _i is an imaginary number, some coaxial systems can be used to measure the dielectric constant (s=0.001)

^*ε_rmin表示能测量的最小极限值. ^* ε _rmin represents the minimum limit value that can be measured.

表3聚四氟乙烯样品(Φ4.25mm×1.5mm)的测量结果Table 3 Measurement results of PTFE samples (Φ4.25mm×1.5mm)

Claims

1. a dielectric parameter test method of a coaxial line-dielectric circular waveguide resonator of 1GHz～8GHz, it is characterized in that: adopt the measuring device of the coaxial line-dielectric circular waveguide resonator that 1GHz～8GHz frequency band is used for dielectric measurement , using the lowest sub-mode resonance, so that there are only TEM guided waves and TM ₀₁ evanescent waves in the coaxial line, and only TM ₀₁ evanescent waves or guided waves exist in the medium; measure the first wave node to the surface of the cylindrical medium sample The distance and VSWR of the material are calculated for the ε _r and tan δ of the material under the TM ₀₁ mode. The specific steps of the method are as follows:

(1) Measure the distance l ₀ from the first wave node under resonance to the surface of the cylindrical medium sample:

At a given frequency ν _r , put a cylindrical dielectric sample (6), adjust the short circuit (4) to achieve cavity resonance, and record the reading L of the adjustable short circuit (4) in the state of the coaxial line-dielectric circular waveguide _i , replace the cylindrical dielectric sample (6) with a metal short circuit board (7), adjust the adjustable short circuit device (4) again to resonate at the same frequency, record the adjustable short circuit device when the coaxial line-short circuit board state ( 4) Reading L ₀ , the distance from the first wave node to the surface of the cylindrical medium sample is obtained as:

l ₀ =c/(2ν _r )-(L ₀ -L _i ) (1)

Here, c is the speed of light in air,

(2) Measure the voltage standing wave ratio s at resonance:

Use the sensor-microwave power meter connected to the output probe to move the movable probe (3) on the air coaxial measuring line, and _measure the standing wave peak value and Valley power meter readings P _imax and P _imin , with

s _i =(P _imin /P _imax ) ^1/2 (2)

Replace the cylindrical dielectric sample (6) with a metal short circuit board (7), adjust the adjustable short circuit device (4) to resonate at the same frequency, move the movable probe (3) on the air coaxial measuring line again, and determine The power meter readings P _0max and P _0min of the standing wave peak value and valley value under the coaxial line-short circuit board state, there are

s ₀ =(P _0min /P _0max ) ^1/2 (3)

The VSWR caused by the cylindrical dielectric sample is obtained as:

s＝s _i -s ₀ 2ν _r l ₀ /c (4)

(3) Calculate the complex permittivity of the material

j j \frac{22 {k k}_{00} a a {\overset{^^}{ϵ ϵ}}_{r r}}{ln ln ((a a / / b b))} (({y the y}_{00} - - {y the y}_{q q} {x x}_{q q})) = = \frac{11 - - js js \cdot &Center Dot; tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))}{s the s - - j j tan the tan ((22 π π {v v}_{r r} {l l}_{00} / / c c))} - - - - - - ((1818))

A complex iterative program written to solve the complex permittivity In formula (18):

{y the y}_{00} = = \frac{coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {λ λ}_{i i}^{22} {a a}^{33}} \cdot &Center Dot; \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} - - - - - - ((66))

{y the y}_{q q} = = - - \frac{coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {a a}^{33} (({λ λ}_{i i}^{22} - - {ξ ξ}_{q q}^{22}))} \cdot \cdot \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} - - - - - - ((77))

x _q = y _q /A _qn (8)

{A A}_{qn qn} = = \frac{{λ λ}_{i i}^{22} coth coth (({γ γ}_{i i} d d))}{{γ γ}_{i i} {a a}^{33} {(({λ λ}_{i i}^{22} - - {γ γ}_{q q}^{22}))}^{22}} \cdot &Center Dot; \frac{{J J}_{00}^{22} (({λ λ}_{i i} b b))}{{J J}_{11}^{22} (({λ λ}_{i i} a a))} + + \frac{11}{{\overset{^^}{ϵ ϵ}}_{r r}} \cdot &Center Dot; \frac{11}{44 a a {γ γ}_{q q}} [[\frac{{a a}^{22} {Z Z}_{11}^{22} (({ξ ξ}_{q q} a a))}{{b b}^{22} {Z Z}_{11}^{22} (({ξ ξ}_{q q} b b))} - - 11]] - - - - - - ((99))

And, the linear combination of Bessel functions

Z ₁ (ξ _q a)＝J ₁ (ξ _q a)+J ₀ (ξ _q a)N ₁ (ξ _q a)/N ₀ (ξ _q a) (10)

Z ₁ (ξ _q b)＝J ₁ (ξ _q b)-J ₀ (ξ _q b)N ₁ (ξ _q b)/N ₀ (ξ _q b) (11)

Among the above formulas: 2a is the inner diameter of the outer conductor of the coaxial line, 2b is the outer diameter of the inner conductor of the coaxial line, d is the thickness of the cylindrical dielectric sample, J ₀ , J ₁ and N ₀ , N ₁ are the first and second types respectively Similar to other order and first order Bessel functions, ξ _q is according to the formula

J ₀ (ξ _q a)N ₀ (ξ _q b)-J ₀ (ξ _q b)N ₀ (ξ _q a)＝0 (12)

The first solution obtained by the written iterative program, and has

{γ γ}_{q q} = = \sqrt{{ξ ξ}_{q q}^{22} - - {k k}_{00}^{22}} - - - - - - ((1313))

λ _i =2.4048/a (14)

{γ γ}_{i i} = = \sqrt{{λ λ}_{i i}^{22} - - {k k}^{22}} - - - - - - ((1515))

{k k}_{00} = = ω ω / / c c,, {k k}^{22} = = {k k}_{00}^{22} {\overset{^^}{ϵ ϵ}}_{r r},, ω ω = = 22 π π {v v}_{r r} - - - - - - ((1616))

In the formula: γ _q is the propagation constant of the coaxial line to the TM ₀₁ wave, which is a real number and propagates the evanescent wave; γ _i is the complex propagation constant of the dielectric circular waveguide to the TM ₀₁ wave; ω is the resonant circular frequency; k ₀ is the k is the wave number in the medium; formula (14) is the first solution of the first kind of alternative Bessel function J ₀ (λ _i a )=0;

The measuring device for the coaxial line-dielectric circular waveguide resonant cavity used for dielectric measurement in the 1GHz to 8GHz frequency band includes a coaxial line outer conductor (1), a coaxial line inner conductor (2), and a movable probe (3) , adjustable short circuit (4), input coupling ring (5), cylindrical dielectric sample (6), metal short circuit board (7), microwave input signal (8) and output standing wave signal (9); coaxial outer conductor (1) and the inner conductor (2) of the coaxial line are of a coaxial structure, and an axial gap is provided on the outer conductor (1) of the coaxial line, and a movable probe (3) is arranged on the axial gap to form an air coaxial Measuring line; one end of the air coaxial measuring line is provided with an adjustable short circuit (4) with a stroke of 100mm, and the adjustable short circuit (4) is provided with an input coupling ring (5); the other end of the air coaxial measuring line A metal short circuit board (7) is provided, and a gap is provided between the inner conductor (2) of the coaxial line and the metal short circuit board (7), and the gap is filled with a cylindrical dielectric sample (6), a cylindrical dielectric sample (6), a metal short circuit The plate (7) and the coaxial outer conductor (1) form a dielectric circular waveguide; the input coupling ring (5) is connected to the microwave input signal (8), and the output standing wave at resonance is detected from the movable probe (3) The amplitude of the signal (9) is used to obtain the voltage standing wave ratio, and the length related to the phase of the output standing wave signal (9) is read from the scale of the adjustable short circuiter (4).

2. A method for testing the dielectric parameters of a 1GHz-8GHz coaxial line-dielectric circular waveguide resonator according to claim 1, characterized in that the inner diameter of the outer conductor (1) of the coaxial line is the same as that of the coaxial line The ratio of the outer diameter of the inner conductor (2) is 2.3-3.5.

3. A method for testing the dielectric parameters of a 1GHz-8GHz coaxial-dielectric circular waveguide resonator according to claim 1, characterized in that the axial slit length on the coaxial outer conductor (1) is 200mm, the width is 1mm, and the distance from the surface of the cylindrical medium sample (6) is 10mm.

4. A method for testing the dielectric parameters of a 1GHz-8GHz coaxial-dielectric circular waveguide resonator according to claim 1, characterized in that the thickness of the cylindrical dielectric sample (6) is 1mm-12mm.