CN1828314A

CN1828314A - Substrate-integrated waveguide measurement method for dielectric constant of microwave dielectric substrate

Info

Publication number: CN1828314A
Application number: CN 200610039507
Authority: CN
Inventors: 洪伟; 颜力
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2006-04-13
Filing date: 2006-04-13
Publication date: 2006-09-06

Abstract

The invention discloses a method for measuring the dielectric constant of a microwave and millimeter wave dielectric substrate. The method is to manufacture two substrate-integrated waveguides with different lengths on the same dielectric substrate, and connect the same microstrip- The substrate-integrated waveguide converter is connected to the vector network analyzer through a high-frequency SMA connector. After the scattering parameters are measured by the vector network analyzer, a section of pure substrate-integrated waveguide is extracted by using the cascading method of the transfer matrix. A single transmission parameter, and thus obtain the relative permittivity of the medium sample. Compared with the prior art, the invention has the following advantages: the accuracy of the method for measuring the dielectric constant of the medium is improved, the operation is simple and reliable, and the measurement result is accurate.

Description

Substrate-integrated waveguide measurement method for dielectric constant of microwave dielectric substrate

技术领域Technical field

本发明涉及一种精确测量微波毫米波介质基片介电常数的方法，从而为集成微波毫米波电路的设计提供精确的介电常数参数，最终提高集成微波毫米波电路设计精度和成品率。The invention relates to a method for accurately measuring the dielectric constant of a microwave and millimeter wave dielectric substrate, thereby providing accurate dielectric constant parameters for the design of integrated microwave and millimeter wave circuits, and finally improving the design accuracy and yield of integrated microwave and millimeter wave circuits.

背景技术 Background technique

随着微波毫米波技术的不断发展，人们研制出了各种各样的微波毫米波集成工艺和器件。PCB工艺、LTCC工艺制作的印刷微带电路、印刷天线等，其电气性能同介质基片的相对介电常数密切相关，这使得准确测量介质基片的相对介电常数变得愈发重要。过去半个世纪中，人们广泛使用基于传输线技术的单端口和双端口测量方法来测量介电常数。这种方法的核心是Nicolson-Ross和Weir(NRW)过程。在这个过程中，用介质样本填满一段波导或者同轴线，然后通过测得的散射参数显式地求出媒质的介电常数。然而，当样本长度为半波长整数倍时这一显式过程不再稳定，且在低损耗媒质中这种不稳定尤为明显。为此，Baker-Jarvis提出了一种求取介电常数的迭代方法，他同时分析了测量过程中误差的来源。几年后，Boughrie等在详尽地分析了NRW公式的基础上增加了一个中间步骤，从而获得了一种不需要迭代的、稳定的介电常数测量方法。上述几种方法都仅仅考虑了波导中的基模，这是一种理想的情况。由于很难用介质样本完全填满波导，因此在介质样本和导体边界之间必然存在空隙。这种空隙将激励出高阶模式，给测量的结果带来误差。With the continuous development of microwave and millimeter wave technology, various microwave and millimeter wave integrated processes and devices have been developed. The electrical properties of printed microstrip circuits and printed antennas produced by PCB technology and LTCC technology are closely related to the relative dielectric constant of the dielectric substrate, which makes it more important to accurately measure the relative dielectric constant of the dielectric substrate. Over the past half century, one-port and two-port measurement methods based on transmission line technology have been widely used to measure dielectric constant. At the heart of this approach is the Nicolson-Ross and Weir (NRW) process. In this process, a section of waveguide or coaxial line is filled with a medium sample, and then the dielectric constant of the medium is explicitly obtained from the measured scattering parameters. However, this explicit process is no longer stable when the sample length is an integer multiple of half-wavelength, especially in low-loss media. For this reason, Baker-Jarvis proposed an iterative method to obtain the dielectric constant, and he also analyzed the sources of errors in the measurement process. A few years later, Boughrie et al. added an intermediate step to the exhaustive analysis of the NRW formula, resulting in a stable method of permittivity measurement that did not require iteration. The above methods only consider the fundamental mode in the waveguide, which is an ideal situation. Since it is difficult to completely fill the waveguide with the dielectric sample, there must be a gap between the dielectric sample and the conductor boundary. Such voids will excite higher-order modes, causing errors in the measured results.

在现代微波毫米波工业中，对介质基片的相对介电常数的精度要求很高。于是，几种新的介电常数测量方法应运而生。为避免产生空隙，可以直接把介质样本放入自由空间中进行测量。Afsar回顾并比较了几种常用的自由空间方法，这些方法的原理是测量样本所构成的天线系统的远场，并由此求出介电常数。显然它需要样本具有很大的截面以减小色散影响。后来Ghodgaonkar等采用聚焦喇叭透镜天线系统测量自由空间中介质样本的介电常数。这种方法可以用于较小截面的样本，但由于参考平面不确定，他的方法很难进行很好的校准。In the modern microwave and millimeter wave industry, the accuracy of the dielectric constant of the dielectric substrate is very high. As a result, several new dielectric constant measurement methods emerged as the times require. To avoid voids, the medium sample can be directly placed in free space for measurement. Afsar reviews and compares several commonly used free-space methods, which are based on measuring the far field of an antenna system composed of a sample and deriving the permittivity from it. Obviously it requires the sample to have a large cross-section to reduce the effects of dispersion. Later, Ghodgaonkar et al. used a focusing horn-lens antenna system to measure the dielectric constant of a medium sample in free space. This method can be used for samples with smaller cross-sections, but his method is difficult to calibrate well due to the uncertain reference plane.

解决空隙问题的另一类方法是仅让介质样本部分填充波导结构，从而避免空隙效应的出现。Bahl和Somlo使用部分介质填充的H平面开缝的短路波导作为测试系统；York则在矩形金属波导宽边的中心线上开出径向缝隙，然后把介质样本填入缝隙，以此作为测试系统。这些方法的公式中都存在不确定性，而且在计算介电常数时需要一个猜测初始值的过程。近来Catalá-Civera[13]采用迭代的方法从测试所得的散射矩阵中求得部分填充的介质样本的复介电常数，这样做确保了公式中不存在不确定性。但是他的方法过于复杂，限制了其适用范围。Another way to solve the void problem is to only partially fill the waveguide structure with the dielectric sample, thus avoiding the void effect. Bahl and Somlo used a partially dielectric-filled H-plane slotted short-circuit waveguide as a test system; York opened a radial slot on the center line of the wide side of a rectangular metal waveguide, and then filled the gap with a dielectric sample as a test system . There are uncertainties in the formulas of these methods, and the process of guessing the initial value is required when calculating the permittivity. Recently Catalá-Civera [13] used an iterative method to obtain the complex permittivity of a partially filled medium sample from the scattering matrix obtained from the test, which ensures that there is no uncertainty in the formula. But his method is too complex, which limits its scope of application.

发明内容Contents of Invention

本发明提供一种能够提高测量精确性的微波介质基片介电常数的基片集成波导测量方法。The invention provides a method for measuring the dielectric constant of a microwave dielectric substrate and a substrate integrated waveguide capable of improving measurement accuracy.

本发明所述微波介质基片介电常数的基片集成波导测量方法，在同一块介质基片上制作两个不同长度的基片集成波导，在其两端连接有相同的微带—基片集成波导转换器，再通过高频SMA接头与矢量网络分析仪相连，分别用矢量网络分析仪测得其散射参数后，利用转移矩阵的级联方法提取出一段纯的基片集成波导的单次传输参数，并由此获得介质样本的相对介电常数。The substrate-integrated waveguide measurement method for the dielectric constant of a microwave dielectric substrate according to the present invention is to manufacture two substrate-integrated waveguides of different lengths on the same dielectric substrate, and to connect the same microstrip-substrate-integrated waveguide at both ends thereof. The waveguide converter is connected to the vector network analyzer through a high-frequency SMA connector. After the scattering parameters are measured by the vector network analyzer, the single transmission of a pure substrate integrated waveguide is extracted by using the cascading method of the transfer matrix. parameters, and thus obtain the relative permittivity of the medium sample.

本发明所述的用于实施上述微波介质基片介电常数的基片集成波导测量方法的装置，包括表面设有金属贴片的介质基片和微带传输线在介质基片上设有两个不同长度的介质基片集成波导，介质基片集成波导的两端分别与微带传输线连接。The device for implementing the substrate-integrated waveguide measurement method for the dielectric constant of the microwave dielectric substrate described in the present invention includes a dielectric substrate with a metal patch on the surface and a microstrip transmission line on the dielectric substrate. Two different The length of the dielectric substrate integrated waveguide, and the two ends of the dielectric substrate integrated waveguide are respectively connected with the microstrip transmission line.

与现有技术相比，本发明具有如下优点：Compared with prior art, the present invention has following advantage:

1)基片集成波导(SIW)结构在波导壁和填充介质之间几乎不存在空隙，使用这种结构作为测试对象可以使介质介电常数测量方法的精确性得以提高。1) The substrate-integrated waveguide (SIW) structure has almost no gap between the waveguide wall and the filling medium. Using this structure as a test object can improve the accuracy of the dielectric constant measurement method of the medium.

2)测试系统的设计制作完全基于成熟的印刷电路板(PCB)或低温共烧结陶瓷(LTCC)工艺和常规的微波矢量网络分析仪，简单可靠。2) The design and manufacture of the test system is completely based on the mature printed circuit board (PCB) or low temperature co-sintered ceramic (LTCC) process and conventional microwave vector network analyzer, which is simple and reliable.

3)测量结果准确，传统基于介质填充波导的测量方法由于存在介质同波导壁之间的空气间隙和需要制作精确的介质样片，从而导致测量过程复杂，测量结果精度不高。本发明的微波介电常数测量方法由于利用了基片集成波导的类波导特性及其导体介质之间的无缝隙特性，因而测量结果准确。仿真和实际测试结果都验证了该方法的准确性。3) The measurement result is accurate. The traditional measurement method based on the dielectric-filled waveguide has an air gap between the medium and the waveguide wall and the need to make an accurate dielectric sample, which leads to a complicated measurement process and low accuracy of the measurement result. The microwave dielectric constant measuring method of the invention utilizes the waveguide-like characteristic of the substrate integrated waveguide and the seamless characteristic between conductor media, so the measurement result is accurate. Both simulation and actual test results verify the accuracy of the method.

附图说明Description of drawings

图1是本发明实施例的主视图。Fig. 1 is a front view of an embodiment of the present invention.

图2是本发明实施例的俯视图。Fig. 2 is a top view of an embodiment of the present invention.

图3是本发明实施例的仰视图。Fig. 3 is a bottom view of an embodiment of the present invention.

图4是本发明金属化通孔结构示意图。FIG. 4 is a schematic diagram of the metallized via structure of the present invention.

图5是在X波段介质基片的介电常数测量结果图。Fig. 5 is a graph showing the results of dielectric constant measurement of the X-band dielectric substrate.

图6是基片集成测试系统的配置图。Fig. 6 is a configuration diagram of a substrate integration test system.

图7是基片集成测试系统的三个部分分离图。Fig. 7 is an isolated view of three parts of the substrate integrated test system.

具体实施方式 Detailed ways

实施例1Example 1

一种微波介质基片介电常数的基片集成波导测量方法，其特征在于在同一块介质基片上制作两个不同长度的基片集成波导，在其两端连接有相同的微带—基片集成波导转换器511，512，521，522，再通过高频SMA接头与矢量网络分析仪相连，分别用矢量网络分析仪测得其散射参数后，利用转移矩阵的级联方法提取出一段纯的基片集成波导的单次传输参数，并由此获得介质样本的相对介电常数。A substrate-integrated waveguide measurement method for the dielectric constant of a microwave dielectric substrate, which is characterized in that two substrate-integrated waveguides of different lengths are fabricated on the same dielectric substrate, and the same microstrip-substrate is connected at both ends. The integrated waveguide converters 511, 512, 521, 522 are connected to the vector network analyzer through the high-frequency SMA connector. After the scattering parameters are measured by the vector network analyzer, a section of pure The substrate integrates the single transmission parameter of the waveguide, and thus obtains the relative permittivity of the medium sample.

实施例2Example 2

一种用于实施上述微波介质基片介电常数的基片集成波导测量方法的装置，包括表面设有金属贴片2、3的介质基片1和微带传输线511，512，521，522，其特征在于在介质基片1上设有两个不同长度得介质基片集成波导41，42，介质基片集成波导41，42的两端分别分别与微带传输线511，512和521，522连接。上述介质基片集成波导41，42各由设在介质基片1上的两行金属化通孔6构成；微带传输线为50欧姆微带传输线。A device for implementing the above-mentioned substrate-integrated waveguide measurement method for the dielectric constant of a microwave dielectric substrate, comprising a dielectric substrate 1 with metal patches 2 and 3 on the surface and microstrip transmission lines 511, 512, 521, 522, It is characterized in that two dielectric substrate integrated waveguides 41, 42 with different lengths are arranged on the dielectric substrate 1, and the two ends of the dielectric substrate integrated waveguides 41, 42 are respectively connected to microstrip transmission lines 511, 512 and 521, 522 . The dielectric substrate integrated waveguides 41 and 42 are each composed of two rows of metallized through-holes 6 arranged on the dielectric substrate 1; the microstrip transmission line is a 50 ohm microstrip transmission line.

实施例3Example 3

一种用于微波毫米波介质基片的介电常数测量装置，包括表面设有金属贴片2、3的介质基片1，在介质基片1上设有介质基片集成波导41，42，上述介质基片集成波导41，42各由两行金属化通孔6构成，在本实施例中，介质基片集成波导41，42的两端分别连接到50欧姆微带线511，512和521，522，两边的微带线再连接到SMA接头，金属化通孔是在介质基片上开设通孔，在通孔壁上设置金属套6并将金属套与覆于介质基片双侧的金属贴片连接起来。A dielectric constant measuring device for microwave and millimeter wave dielectric substrates, comprising a dielectric substrate 1 with metal patches 2 and 3 on the surface, dielectric substrate integrated waveguides 41, 42 are arranged on the dielectric substrate 1, The dielectric substrate integrated waveguides 41, 42 are each composed of two rows of metallized through holes 6. In this embodiment, the two ends of the dielectric substrate integrated waveguides 41, 42 are respectively connected to 50 ohm microstrip lines 511, 512 and 521 , 522, the microstrip lines on both sides are connected to the SMA connector, the metallized through hole is to open a through hole on the dielectric substrate, set the metal sleeve 6 on the wall of the through hole and connect the metal sleeve with the metal covering both sides of the dielectric substrate The patches are connected.

如图1所示，在待测基片上分别制作有四行金属通孔，它们组成了两个不同长度的基片集成波导，所有金属通孔的外径d＝1mm，周期长度p＝2mm，基片厚度b＝1.5mm。基片上印刷的两个基片集成波导的宽度都为a＝15.65mm，两个基片集成波导的长度分别为40mm和20mm。As shown in Fig. 1, four rows of metal through holes are respectively made on the substrate to be tested, and they form two substrate integrated waveguides of different lengths, the outer diameter of all metal through holes is d=1mm, and the period length p=2mm, The substrate thickness b=1.5 mm. The widths of the two substrate-integrated waveguides printed on the substrate are both a=15.65mm, and the lengths of the two substrate-integrated waveguides are 40mm and 20mm respectively.

我们用矢量网络分析仪、高频同轴电缆、高频SMA接头等组成测试系统分别测出这两个基片集成波导的散射参数。然后通过去除不连续性获得一段不含不连续性的基片集成波导的单次传输参数，最后再通过一些数学计算得到该基片在X波段的相对介电常数，结果见附图5。很明显，基片的相对介电常数和标称值2.2有很大不同，在10GHz处，测量所得的εr≈2.4。我们按照测得的相对介电常数设计了基片集成波导缝隙阵列天线，测试结果和仿真结果符合得很好，这也证明了这种基片集成的介电常数的测量方法的正确性和有效性。We use a vector network analyzer, high-frequency coaxial cable, high-frequency SMA connector and other test systems to measure the scattering parameters of the two substrate-integrated waveguides. Then, the single transmission parameters of a substrate-integrated waveguide without discontinuities are obtained by removing the discontinuities, and finally the relative permittivity of the substrate in the X-band is obtained through some mathematical calculations. The results are shown in Figure 5. Obviously, the relative permittivity of the substrate is very different from the nominal value of 2.2. At 10 GHz, the measured εr≈2.4. We designed the substrate-integrated waveguide slot array antenna according to the measured relative permittivity, and the test results and simulation results are in good agreement, which also proves the correctness and effectiveness of this substrate-integrated permittivity measurement method sex.

参照图6，现有技术在SMA接头和微带的连接处以及微带—波导转换两处地方都存在不连续性。矢量网络分析仪测得的散射参数是整个测试系统(包括SMA接头、微带—波导转换和基片集成波导)的散射参数，由于不连续性引起的反射，难以直接从这个散射参数中提取出基片集成波导的传输参数。为此，本发明提出了一种解决方案，采用两块不同长度的基片集成波导进行测试，利用转移矩阵的级联方法准确地提取出一段纯的基片集成波导的单次传输参数，并由此获得介质样本的相对介电常数。Referring to Figure 6, prior art discontinuities exist both at the junction of the SMA connector and the microstrip and at the microstrip-to-waveguide transition. The scattering parameter measured by the vector network analyzer is the scattering parameter of the entire test system (including SMA joints, microstrip-waveguide conversion and substrate integrated waveguide), and it is difficult to extract directly from this scattering parameter due to the reflection caused by the discontinuity Transmission parameters of substrate-integrated waveguides. For this reason, the present invention proposes a solution, using two substrate integrated waveguides of different lengths for testing, using the cascading method of the transfer matrix to accurately extract a single transmission parameter of a pure substrate integrated waveguide, and The relative permittivity of the dielectric sample is thus obtained.

参照图7，本发明把基片集成波导测试系统分成三个部分。I和III包含了所有的不连续性，这样第II部分中仅仅含有纯粹的基片集成波导结构，因此可以认为第II部分的单次传输参数T＝exp(-γl_d)，其中γ表示基片集成波导的复传播常数。我们将分别对两个不同长度的基片集成波导分别进行测试，第一个测试对象仅有I和III这两个部分；第二个测试对象包括长为l_d的基片集成波导。两个测试对象的I、III两部分保持不变。假设测量获得的两个测试对象的散射参数分别为[S]⁽¹⁾和[S]⁽²⁾，则我们可以推导出基片集成波导的复传播常数满足的公式。Referring to FIG. 7, the present invention divides the substrate integrated waveguide test system into three parts. I and III include all discontinuities, so that part II only contains pure substrate-integrated waveguide structures, so it can be considered that the single transmission parameter T of part II is T=exp(-γl _d ), where γ represents the base The complex propagation constant of the chip-integrated waveguide. We will test two substrate-integrated waveguides with different lengths respectively. The first test object only has two parts I and III; the second test object includes substrate-integrated waveguides with a length of l _d . Parts I and III of the two test subjects remained unchanged. Assuming that the measured scattering parameters of the two test objects are [S] ⁽¹⁾ and [S] ⁽²⁾ respectively, we can derive the formula that the complex propagation constant of the substrate-integrated waveguide satisfies.

首先，第一个测试对象的I，III两部分相互对称，因此第一个测试对象为对称可逆网络。它的散射参数满足条件S₁₁ ⁽¹⁾＝S₂₂ ⁽¹⁾，S₁₂ ⁽¹⁾＝S₂₁ ⁽¹⁾，由此可以得到第一个测试对象的归一化转移矩阵First, the I and III parts of the first test object are symmetrical to each other, so the first test object is a symmetric reversible network. Its scattering parameters satisfy the conditions S ₁₁ ⁽¹⁾ ＝S ₂₂ ⁽¹⁾ , S ₁₂ ⁽¹⁾ ＝S ₂₁ ⁽¹⁾ , thus the normalized transfer matrix of the first test object can be obtained

${[A]}^{(1)} = [\begin{matrix} A_{11}^{(1)} & A_{12}^{(1)} \\ A_{21}^{(1)} & A_{11}^{(1)} \end{matrix}],$ 其中 $A_{11}^{(1)} = \frac{1}{{2 S}_{21}^{(1)}} (1 - {| [S]}^{(1)} |),$ ${[A]}^{(1)} = [\begin{matrix} A_{11}^{(1)} & A_{12}^{(1)} \\ A_{twenty one}^{(1)} & A_{11}^{(1)} \end{matrix}],$ in $A_{11}^{(1)} = \frac{1}{{2 S}_{twenty one}^{(1)}} (1 - {| [S]}^{(1)} |),$

${A A}_{1212}^{((11))} = = \frac{11}{{22 S S}_{21 twenty one}^{((11))}} ((11 + + {| | [[S S]]}^{((11))} | | + + {S S}_{1111}^{((11))} + + {S S}_{22 twenty two}^{((11))})),, {A A}_{21 twenty one}^{((11))} = = \frac{11}{{22 S S}_{21 twenty one}^{((11))}} ((11 + + {| | [[S S]]}^{((11))} | | - - {S S}_{1111}^{((11))} - - {S S}_{22 twenty two}^{((11))})) \cdot \cdot - - - - - - ((11))$

不妨设第I部分的的归一化转移矩阵为Let us assume that the normalized transition matrix in Part I is

$[[{T T}_{I I}]] = = [\begin{matrix} {a a}_{1111} & {a a}_{1212} \\ {a a}_{21 twenty one} & {a a}_{22 twenty two} \end{matrix}],, - - - - - - ((22))$

由于第III部分和第I部分的结构完全对称，而且都满足可逆性条件。这样第III部分的归一化转移矩阵可以写成Since the structures of Part III and Part I are completely symmetric, and both satisfy the reversibility condition. Thus the normalized transition matrix of Part III can be written as

$[[{T T}_{III III}]] = = [\begin{matrix} {a a}_{22 twenty two} & {a a}_{1212} \\ {a a}_{21 twenty one} & {a a}_{1111} \end{matrix}] - - - - - - ((33))$

第一个测试对象的归一化转移矩阵可以写成第I部分和第III部分的归一化转移矩阵的矩阵乘积，即The normalized transfer matrix of the first test subject can be written as the matrix product of the normalized transfer matrices of Part I and Part III, namely

${[[A A]]}^{((11))} = = [\begin{matrix} {a a}_{1111} {a a}_{22 twenty two} + + {a a}_{1212} {a a}_{21 twenty one} & 22 {a a}_{1111} {a a}_{1212} \\ 22 {a a}_{22 twenty two} {a a}_{21 twenty one} & {a a}_{1111} {a a}_{22 twenty two} + + {a a}_{1212} {a a}_{21 twenty one} \end{matrix}] \cdot &Center Dot; - - - - - - ((44))$

将等式(1)和等式(4)进行比较，再加上第I部分所满足的互易性条件，就能得到一个关于a₁₁、a₁₂、a₂₁、a₂₂的方程组：Comparing Equation (1) with Equation (4), plus the reciprocity condition satisfied in Part I, yields a system of equations for a ₁₁ , a ₁₂ , a ₂₁ , a ₂₂ :

$\{\begin{matrix} {a a}_{1111} {a a}_{22 twenty two} + + {a a}_{1212} {a a}_{21 twenty one} = = {A A}_{1111}^{((11))} \\ 22 {a a}_{1111} {a a}_{1212} = = {A A}_{1212}^{((11))} \\ 22 {a a}_{22 twenty two} {a a}_{21 twenty one} = = {A A}_{21 twenty one}^{((11))} \\ {a a}_{1111} {a a}_{22 twenty two} - - {a a}_{1212} {a a}_{21 twenty one} = = 11 \end{matrix} - - - - - - ((55))$

在分析第二测试对象时需要引入图2中的第II部分。显然第II部分满足对称可逆条件，这样它的归一化转移矩阵为Part II in Figure 2 needs to be introduced when analyzing the second test object. Obviously Part II satisfies the symmetric invertibility condition, so its normalized transition matrix is

$[[{T T}_{II II}]] = = [\begin{matrix} {b b}_{1111} & {b b}_{1212} \\ {b b}_{21 twenty one} & {b b}_{1111} \end{matrix}],, - - - - - - ((66))$

其中b₁₁ ²-b₁₂b₂₁＝1。I、II、III三个部分级联得到的总的转移矩阵为：Where b ₁₁ ² -b ₁₂ b ₂₁ =1. The total transfer matrix obtained by cascading the three parts I, II, and III is:

${[[A A]]}^{((22))} = = [\begin{matrix} (({a a}_{1111} {a a}_{22 twenty two} + + {a a}_{1212} {a a}_{21 twenty one})) {b b}_{1111} + + {a a}_{1212} {a a}_{22 twenty two} {b b}_{21 twenty one} + + {a a}_{1111} {a a}_{21 twenty one} {b b}_{1212} & 22 {a a}_{1111} {a a}_{1212} {b b}_{1111} + + {a a}_{1212}^{22} {b b}_{21 twenty one} + + {a a}_{1111}^{22} {b b}_{1212} \\ 22 {a a}_{21 twenty one} {a a}_{22 twenty two} {b b}_{1111} + + {a a}_{22 twenty two}^{22} {b b}_{21 twenty one} + + {a a}_{21 twenty one}^{22} {b b}_{1212} & (({a a}_{1111} {a a}_{22 twenty two} + + {a a}_{1212} {a a}_{21 twenty one})) {b b}_{1111} + + {a a}_{1212} {a a}_{22 twenty two} {b b}_{21 twenty one} + + {a a}_{1111} {a a}_{21 twenty one} {b b}_{1212} \end{matrix}] - - - - - - ((77))$

与此同时根据第二个测试对象的散射参数的测量值所得的转移矩阵At the same time the transfer matrix obtained from the measured values of the scattering parameters of the second test object

${[A]}^{(2)} = [\begin{matrix} A_{11}^{(2)} & A_{12}^{(2)} \\ A_{21}^{(2)} & A_{11}^{(2)} \end{matrix}],$ 其中 $A_{11}^{(2)} = \frac{1}{{2 S}_{21}^{(2)}} (1 - | {[S]}^{(2)} |),$ ${[A]}^{(2)} = [\begin{matrix} A_{11}^{(2)} & A_{12}^{(2)} \\ A_{twenty one}^{(2)} & A_{11}^{(2)} \end{matrix}],$ in $A_{11}^{(2)} = \frac{1}{{2 S}_{twenty one}^{(2)}} (1 - | {[S]}^{(2)} |),$

${A A}_{1212}^{((22))} = = \frac{11}{{22 S S}_{21 twenty one}^{((22))}} ((11 + + | | {[[S S]]}^{((22))} | | + + {S S}_{1111}^{((22))} + + {S S}_{22 twenty two}^{((22))})),, {A A}_{21 twenty one}^{((22))} = = \frac{11}{{22 S S}_{21 twenty one}^{((22))}} ((11 + + | | {[[S S]]}^{((22))} | | - - {S S}_{1111}^{((22))} - - {S S}_{22 twenty two}^{((22))})) \cdot &Center Dot; - - - - - - ((88))$

把公式(5)代入公式(7)得到关于b₁₁，b₁₂，b₂₁的矩阵方程为Substituting formula (5) into formula (7) to get the matrix equation about b ₁₁ , b ₁₂ , b ₂₁ is

$[\begin{matrix} A_{11}^{(1)} & A_{12}^{(1)} / 2 & A_{21}^{(1)} / 2 \\ A_{12}^{(1)} & A_{12}^{{(1)}^{2}} / 2 (A_{11}^{(1)} + 1) & (A_{11}^{(1)} + 1) / 2 \\ A_{21}^{(1)} & (A_{11}^{(1)} + 1) / 2 & A_{21}^{{(1)}^{2}} / 2 (A_{11}^{(1)} + 1) \end{matrix}] [\begin{matrix} b_{11} \\ {tb}_{21} \\ {(1 / t) b}_{12} \end{matrix}] = [\begin{matrix} A_{11}^{(2)} \\ A_{12}^{(2)} \\ A_{21}^{(2)} \end{matrix}],$ 其中t＝a₂₂/a₁₁。 $[\begin{matrix} A_{11}^{(1)} & A_{12}^{(1)} / 2 & A_{twenty one}^{(1)} / 2 \\ A_{12}^{(1)} & A_{12}^{{(1)}^{2}} / 2 (A_{11}^{(1)} + 1) & (A_{11}^{(1)} + 1) / 2 \\ A_{twenty one}^{(1)} & (A_{11}^{(1)} + 1) / 2 & A_{twenty one}^{{(1)}^{2}} / 2 (A_{11}^{(1)} + 1) \end{matrix}] [\begin{matrix} b_{11} \\ {tb}_{twenty one} \\ {(1 / t) b}_{12} \end{matrix}] = [\begin{matrix} A_{11}^{(2)} \\ A_{12}^{(2)} \\ A_{twenty one}^{(2)} \end{matrix}],$ where t=a ₂₂ /a ₁₁ .

(9)(9)

我们知道第一个测试对象是可逆的，因此它的转移矩阵满足条件[A₁₁ ⁽¹⁾]²-A₁₂ ⁽¹⁾A₂₁ ⁽¹⁾＝1。根据这个条件我们可以求出在公式(9)中的系数矩阵的行列式：We know that the first test object is reversible, so its transition matrix satisfies the condition [A ₁₁ ⁽¹⁾ ] ² -A ₁₂ ⁽¹⁾ A ₂₁ ⁽¹⁾ =1. According to this condition, we can find the determinant of the coefficient matrix in formula (9):

$|\begin{matrix} {A A}_{1111}^{((11))} & {A A}_{1212}^{((11))} / / 22 & {A A}_{21 twenty one}^{((11))} / / 22 \\ {A A}_{1212}^{((11))} & {A A}_{1212}^{{((11))}^{22}} / / 22 (({A A}_{1111}^{((11))} + + 11)) & (({A A}_{1111}^{((11))} + + 11)) / / 22 \\ {A A}_{21 twenty one}^{((11))} & (({A A}_{1111}^{((11))} + + 11)) / / 22 & {A A}_{21 twenty one}^{{((11))}^{22}} / / 22 (({A A}_{1111}^{((11))} + + 11)) \end{matrix}| = = {- - A A}_{1111}^{{((11))}^{22}} + + {A A}_{1212}^{((11))} {A A}_{21 twenty one}^{((11))} = = - - 11,, - - - - - - ((1010))$

同时at the same time

$|\begin{matrix} {A A}_{1111}^{((22))} & {A A}_{1212}^{((11))} / / 22 & {A A}_{21 twenty one}^{((11))} / / 22 \\ {A A}_{1212}^{((22))} & {A A}_{1212}^{{((11))}^{22}} / / 22 (({A A}_{1111}^{((11))} + + 11)) & (({A A}_{1111}^{((11))} + + 11)) / / 22 \\ {A A}_{21 twenty one}^{((22))} & (({A A}_{1111}^{((11))} + + 11)) / / 22 & {A A}_{21 twenty one}^{{((11))}^{22}} / / 22 (({A A}_{1111}^{((11))} + + 11)) \end{matrix}| = = - - {A A}_{1111}^{((11))} {A A}_{1111}^{((22))} + + (({A A}_{1212}^{((11))} {A A}_{21 twenty one}^{((22))} + + {A A}_{21 twenty one}^{((11))} {A A}_{1212}^{((22))})) / / 22 \cdot &Center Dot; - - - - - - ((1111))$

再根据克莱姆法则，可以解得According to Cramer's rule, we can get

${b b}_{1111} = = {A A}_{1111}^{((11))} {A A}_{1111}^{((22))} - - (({A A}_{1212}^{((11))} {A A}_{21 twenty one}^{((22))} + + {A A}_{21 twenty one}^{((11))} {A A}_{1212}^{((22))})) / / 22 \cdot &Center Dot; - - - - - - ((1212))$

根据公式(12)，我们可以推导出第II部分的b₁₁仅与这一部分的单次传输系数T有关，和这一部分的单次反射系数Γ无关。实际上可以简单地导出b₁₁＝(1+T²)/2T。如果经过前面的计算已经求出了b₁₁，我们就可以解得According to formula (12), we can deduce that the b ₁₁ of Part II is only related to the single transmission coefficient T of this part, and has nothing to do with the single reflection coefficient Γ of this part. In fact b ₁₁ =(1+T ² )/2T can be simply derived. If b ₁₁ has been obtained through the previous calculation, we can solve

$T T = = {b b}_{1111} &PlusMinus; &PlusMinus; \sqrt{{b b}_{1111}^{22} - - 11} - - - - - - ((1313))$

在T的两个解中选择幅度小于1的那个，再根据Choose the one whose amplitude is less than 1 among the two solutions of T, and then according to

γ＝-ln(T)/l_d (14)γ=-ln(T)/l _d (14)

求出第II部分基片集成波导的复传播常数γ，其中γ＝α+jβ，α和β分别表示基片集成波导的衰减常数和相位常数。Obtain the complex propagation constant γ of the substrate-integrated waveguide in Part II, where γ=α+jβ, α and β represent the attenuation constant and the phase constant of the substrate-integrated waveguide respectively.

我们知道宽度为a的基片集成波导可以等效成为宽度为aRWG的矩形金属波导，其厚度b不变，归一化等效波导宽度的公式We know that a substrate-integrated waveguide with width a can be equivalent to a rectangular metal waveguide with width aRWG, and its thickness b remains unchanged. The formula for normalizing the equivalent waveguide width

$\overset{&OverBar;}{a} = ξ_{1} + \frac{ξ_{2}}{\frac{p}{d} + \frac{ξ_{1} + ξ_{2} - ξ_{3}}{ξ_{3} - ξ_{2}}},$ TM_x ^On模式， (15) $\overset{&OverBar;}{a} = ξ_{1} + \frac{ξ_{2}}{\frac{p}{d} + \frac{ξ_{1} + ξ_{2} - ξ_{3}}{ξ_{3} - ξ_{2}}},$ TM _x ^On Mode, (15)

其中in

${ξ ξ}_{11} = = 1.0198 1.0198 + + \frac{0.3465 0.3465}{\frac{a a}{p p} - - 1.0684 1.0684},, {ξ ξ}_{22} = = - - 0.1183 0.1183 - - \frac{1.2729 1.2729}{\frac{a a}{p p} - - 1.2010 1.2010},, {ξ ξ}_{33} = = 1.0082 1.0082 - - \frac{0.9163 0.9163}{\frac{a a}{p p} + + 0.2152 0.2152} \cdot \cdot - - - - - - ((1616))$

这里a、p、d分别是基片集成波导的宽度、金属化孔周期和直径。Here a, p, d are the width of the substrate-integrated waveguide, the metallized hole period, and the diameter, respectively.

算出基片集成波导的等效矩形波导宽度a_RWG之后，就可以进一步获得基片集成波导所在的介质基片的相对介电常数ε_r：After calculating the equivalent rectangular waveguide width a _RWG of the substrate-integrated waveguide, the relative permittivity ε _r of the dielectric substrate where the substrate-integrated waveguide is located can be further obtained:

${ϵ ϵ}_{r r} = = {((\frac{c c}{22 πf πf}))}^{22} {k k}^{22},, {k k}^{22} = = {β β}^{22} + + {((\frac{π π}{{a a}_{RWG RWG}}))}^{22} \cdot &Center Dot; - - - - - - ((1717))$

需要注意的是，为使上式成立，我们必须保证基片集成波导工作在主模工作区。也就是说，我们必须精心选择被测的基片集成波导的宽度以使得在指定的频带范围内，波导内仅能传播TE₁₀模式。It should be noted that, in order to make the above formula valid, we must ensure that the substrate-integrated waveguide works in the main mode working area. That is to say, we must carefully select the width of the substrate-integrated waveguide under test so that only the TE ₁₀ mode can propagate in the waveguide within the specified frequency band.

Claims

1. A substrate-integrated waveguide measurement method for the dielectric constant of a microwave dielectric substrate, which is characterized in that two substrate-integrated waveguides of different lengths are made on the same dielectric substrate, and the same microstrip- The substrate-integrated waveguide converters (511, 512, 521, 522) are connected to the vector network analyzer through a high-frequency SMA connector, and after the scattering parameters are measured by the vector network analyzer, the cascading method of the transfer matrix is used to extract The single transmission parameter of a pure substrate integrated waveguide is obtained, and the relative permittivity of the dielectric sample is obtained from it.