基于微带谐振结构的新型液体介电常数测量探头研究
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摘要
物质的介电常数作为麦克斯韦方程组的本构参数之一，具有重要的物理意义。介电常数描述了介质的电极化特性，是电磁学应用中不可缺少的知识，因而研究介电常数的测量方法成为了基础而关键的问题。
微带线由于具有成本低、体积小、重量轻、易于共形等优点得到了广泛应用。在介电常数测量领域，利用微带线已经设计了多种测量结构，这些结构大致可分为谐振型和非谐振型两类。当介质的复介电常数在一定范围内随频率变化不敏感时，相对于非谐振结构而言，谐振结构可以达到相对更高的测量精度。本文针对微带谐振结构在测量中、高损耗液体的介电常数上存在的不足，展开相关研究得到了一些结果，希望可以对该领域的研究有所帮助。
本文改进了半波长、终端开路的微带线谐振器，设计了基于交指结构的耦合电容，并采用Rogers公司出品的RT／Duroid 5880材料进行加工制作。在微带线基板一侧的上方3mm处覆盖接地的金属盖，避免微带谐振器与待测样品直接接触；在接地板上腐蚀出一条与谐振器等长，位于谐振器正下方中心位置的辐射缝，待测样品通过辐射缝影响谐振器的谐振频率和品质因数。实验研究表明：即使将该结构置于中、高损耗的待测液体中用于测量介电常数时，也可以正常谐振。
分析了该测量探头的等效电路模型，得到了电路描述方程。研究了基于加权最小二乘曲线拟合技术的品质因数提取算法，并采用Fortran语言编程实现。该方法利用测量得到的反射系数，计算出探头置于待测样品中的谐振频率、有载品质因数、空载品质因数及耦合系数。研究表明：基于加权最小二乘法的品质因数提取算法计算精度高，可以自动消除测量噪声，加权函数能够提取出测量数据中变化最敏感的部分。
研究了传输线特征参数计算中使用的二维时域有限差分法2D-FDTD，并采用该方法分析了设计的测量探头，用Fortran语言编程实现。从理论上解释了待测样品的介电常数和电导率对探头的谐振频率和空载品质因数影响的原因。研究表明：2D-FDTD法具有计算速度快、内存需求低的优点；探头的谐振频率随样品介电常数的升高而降低，随电导率的升高而降低；探头的空载品质因数随样品介电常数的升高而升高，随电导率的升高而降低。
结合加权最小二乘品质因数提取算法和2D-FDTD法，提出了校准方法和基于三次样条插值的迭代算法。通过测量探头置于待测样品中的反射系数，计算样品的复介电常数。对甲醇／L醇混合溶液的等效复介电常数进行了测量，验证了探头和算法的有效性。
当待测液体的复介电常数在一定范围内随频率变化不敏感时，本文设计的探头及提出的相关算法在对中、高损耗液体的复介电常数的在线测量上具有一定的优势。
The permittivity of dielectrics has extremely important physical meanings sinceit is one parameter of the constitute relations in Maxwell's equations. Thepermittivity describes the characteristics of the electric polarization in materials,which is a key parameter in electromagnetics. Therefore, the accurate permittivitymeasurements are important fundamental subjects.
Microstrip transmission lines are widely applied in radio frequency andmicrowave circuit design because it is low cost, compact, light weight and easilyconformal. At present, various structures of permittivity measurements have beenproposed by using microstrip transmission lines, which can be categorized to eitherresonant or non-resonant type. When the permittivity of a material is non-sensitivewith respect to the frequency, the measurement accuracy of the resonant structure isgenerally higher than that of the non-resonant structure, but it is difficult to measuremedium or high loss materials. Thus, the thesis aims at solving the problem.
An improved half-lambda open-circuit microstrip resonator with interdigitalcoupling capacitors has been designed and fabricated on RT/Duroid 5880 substrate.A 3mm height metallic cover is welded on the top side of the substrate for protectingthe resonator from directly contacting to materials under test. On the bottom side, aslot is etched on the ground, which is just located beneath the resonant microstripline on the top layer. The permittivity of materials under test will influence theresonant frequency and the quality factor of the microstrip resonator through the etched slot. Experimental results showed that the proposed sensor could be appliedto measure the permittivity of medium or high loss liquids.
The equivalent circuit model and description equation of the sensor areobtained. The weighted least-square curve fitting procedure is applied to extract theresonant frequency, the loaded/unloaded quality factor and the coupling coefficientfrom the measured S parameters of the sensor. Results showed that the algorithmprovided high calculation accuracy and could automatically suppress the noise inmeasurements. The weighted function could extract the most sensitive part of themeasured data.
The proposed sensor is analyzed by a two dimensional finite difference timedomain (2D-FDTD) method, which is suitable for calculating the intrinsicparameters of a transmission line. Numerical simulations showed that the 2D-FDTDmethod was fast and required less memory. The resonant frequency of the sensordecreases when the permittivity or conductivity of materials under test increases.The unloaded quality factor of the sensor increases when the permittivity ofmaterials under test increases, and it also decreases when the conductivity ofmaterials under test increases.
Combined with the 2D-FDTD method and the weighted least-square curvefitting procedure for quality factor calculation, a calibration procedure and apermittivity reconstruction algorithm based on iterative cubic spline interpolationare proposed in this thesis. The complex permittivity can be obtained from themeasured reflection coefficients of the sensor immerged in liquid materials undertest at different frequencies. The proposed sensor and corresponding algorithms arevalidated by measuring the equivalent complex permittivity of a CH_3OH/C_2H_5OHmixture. Results showed that the novel sensor was Suitable for the on-linepermittivity measurements of medium or high loss liquids whose permittivity werenon-sensitive with respect to the frequency.
微带线由于具有成本低、体积小、重量轻、易于共形等优点得到了广泛应用。在介电常数测量领域，利用微带线已经设计了多种测量结构，这些结构大致可分为谐振型和非谐振型两类。当介质的复介电常数在一定范围内随频率变化不敏感时，相对于非谐振结构而言，谐振结构可以达到相对更高的测量精度。本文针对微带谐振结构在测量中、高损耗液体的介电常数上存在的不足，展开相关研究得到了一些结果，希望可以对该领域的研究有所帮助。
本文改进了半波长、终端开路的微带线谐振器，设计了基于交指结构的耦合电容，并采用Rogers公司出品的RT／Duroid 5880材料进行加工制作。在微带线基板一侧的上方3mm处覆盖接地的金属盖，避免微带谐振器与待测样品直接接触；在接地板上腐蚀出一条与谐振器等长，位于谐振器正下方中心位置的辐射缝，待测样品通过辐射缝影响谐振器的谐振频率和品质因数。实验研究表明：即使将该结构置于中、高损耗的待测液体中用于测量介电常数时，也可以正常谐振。
分析了该测量探头的等效电路模型，得到了电路描述方程。研究了基于加权最小二乘曲线拟合技术的品质因数提取算法，并采用Fortran语言编程实现。该方法利用测量得到的反射系数，计算出探头置于待测样品中的谐振频率、有载品质因数、空载品质因数及耦合系数。研究表明：基于加权最小二乘法的品质因数提取算法计算精度高，可以自动消除测量噪声，加权函数能够提取出测量数据中变化最敏感的部分。
研究了传输线特征参数计算中使用的二维时域有限差分法2D-FDTD，并采用该方法分析了设计的测量探头，用Fortran语言编程实现。从理论上解释了待测样品的介电常数和电导率对探头的谐振频率和空载品质因数影响的原因。研究表明：2D-FDTD法具有计算速度快、内存需求低的优点；探头的谐振频率随样品介电常数的升高而降低，随电导率的升高而降低；探头的空载品质因数随样品介电常数的升高而升高，随电导率的升高而降低。
结合加权最小二乘品质因数提取算法和2D-FDTD法，提出了校准方法和基于三次样条插值的迭代算法。通过测量探头置于待测样品中的反射系数，计算样品的复介电常数。对甲醇／L醇混合溶液的等效复介电常数进行了测量，验证了探头和算法的有效性。
当待测液体的复介电常数在一定范围内随频率变化不敏感时，本文设计的探头及提出的相关算法在对中、高损耗液体的复介电常数的在线测量上具有一定的优势。
The permittivity of dielectrics has extremely important physical meanings sinceit is one parameter of the constitute relations in Maxwell's equations. Thepermittivity describes the characteristics of the electric polarization in materials,which is a key parameter in electromagnetics. Therefore, the accurate permittivitymeasurements are important fundamental subjects.
Microstrip transmission lines are widely applied in radio frequency andmicrowave circuit design because it is low cost, compact, light weight and easilyconformal. At present, various structures of permittivity measurements have beenproposed by using microstrip transmission lines, which can be categorized to eitherresonant or non-resonant type. When the permittivity of a material is non-sensitivewith respect to the frequency, the measurement accuracy of the resonant structure isgenerally higher than that of the non-resonant structure, but it is difficult to measuremedium or high loss materials. Thus, the thesis aims at solving the problem.
An improved half-lambda open-circuit microstrip resonator with interdigitalcoupling capacitors has been designed and fabricated on RT/Duroid 5880 substrate.A 3mm height metallic cover is welded on the top side of the substrate for protectingthe resonator from directly contacting to materials under test. On the bottom side, aslot is etched on the ground, which is just located beneath the resonant microstripline on the top layer. The permittivity of materials under test will influence theresonant frequency and the quality factor of the microstrip resonator through the etched slot. Experimental results showed that the proposed sensor could be appliedto measure the permittivity of medium or high loss liquids.
The equivalent circuit model and description equation of the sensor areobtained. The weighted least-square curve fitting procedure is applied to extract theresonant frequency, the loaded/unloaded quality factor and the coupling coefficientfrom the measured S parameters of the sensor. Results showed that the algorithmprovided high calculation accuracy and could automatically suppress the noise inmeasurements. The weighted function could extract the most sensitive part of themeasured data.
The proposed sensor is analyzed by a two dimensional finite difference timedomain (2D-FDTD) method, which is suitable for calculating the intrinsicparameters of a transmission line. Numerical simulations showed that the 2D-FDTDmethod was fast and required less memory. The resonant frequency of the sensordecreases when the permittivity or conductivity of materials under test increases.The unloaded quality factor of the sensor increases when the permittivity ofmaterials under test increases, and it also decreases when the conductivity ofmaterials under test increases.
Combined with the 2D-FDTD method and the weighted least-square curvefitting procedure for quality factor calculation, a calibration procedure and apermittivity reconstruction algorithm based on iterative cubic spline interpolationare proposed in this thesis. The complex permittivity can be obtained from themeasured reflection coefficients of the sensor immerged in liquid materials undertest at different frequencies. The proposed sensor and corresponding algorithms arevalidated by measuring the equivalent complex permittivity of a CH_3OH/C_2H_5OHmixture. Results showed that the novel sensor was Suitable for the on-linepermittivity measurements of medium or high loss liquids whose permittivity werenon-sensitive with respect to the frequency.
引文
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[2] S. R. Robert, A. Von Hippel, "A new method for measuring dielectric constant and loss in the range of centimeter waves" [J], J. Appl. Phys., 1946, 17(7): 610-616.
[3] H. Zheng, and C. E. Smith, "Permittivity measurement using a short open-ended coaxial line probe" [J], IEEE Microw. Guided Wave Lett., 1991, 1(11): 337-339.
[4] D.V. Blackham, and R. D. Pollard, "An improved technique for permittivity measurements using a coaxial probe" [J], IEEE Trans. Instrum. Meas., 1997, 46(5): 1093-1099.
[5] S. Hoshina, Y. Kanai, and M. Miyakawa, "A numerical study on the measurement region of an open-ended coaxial probe used for complex permittivity measurement" [J], IEEE Trans. Magn., 2001, 37(5): 3311-3314.
[6] 金钦汉，戴树栅，黄卡玛，微波化学[M]，北京：科学出版社，1999年，第一版。
[7] 董树义，微波测量[M]，北京：北京理工大学出版社，1991年，第二版。
[8] 唐宗熙，张彪，“用自由空间法测试介质电磁参数”[J]，电子学报，2006，34(1)：189-192。
[9] K. Preis, et al., "Time-domain analysis of quasistatic electric fields in media with frequency-dependent permittivity" [J], IEEE Trans. Magn., 2004, 40(2): 1302-1305.
[10] Y. Kantor, "Dielectric constant measurements using printed circuit techniques at microwave frequency" [J], Electrotechnical Conference, 1998, 1: 101-105.
[11] P. Queffelec, et al., "A microstrip device for the broad band simultaneous measurement of complex permeability and permittivity" [J], IEEE Trans. Magn., 1994, 30(2): 224-231.
[12] P. Queffelec, and P. Gelin, "Influence of higher order modes on the measurements of complex permittivity and permeability of materials using a microstrip discontinuity" [J], IEEE Trans. Microw. Theory Tech., 1996, 44(6): 816-824.
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