CN103226166A - Shielded twisted pair RLCG model and computational method of transfer characteristic thereof - Google Patents

Abstract

Translated fromChinese

一种屏蔽双绞线RLCG模型及其传输特性的计算方法，将屏蔽双绞线的屏蔽层视为第三根导体,并将其作为屏蔽层内两根导线的参考。则整个屏蔽双绞线有三根导体，由屏蔽双绞线上一小段长度dz的RLCG参数分布的等效RLCG参数模型，根据屏蔽双绞线RLCG模型设定RLCG参数矩阵的形式；分别计算电阻R矩阵、电感L矩阵、电容C矩阵和电导G矩阵；根据各矩阵计算屏蔽双绞线的传输常数矩阵和屏蔽双绞线的特性阻抗矩阵；从而得到屏蔽双绞线上任意位置处与源位置处的电压/电流关系，也即屏蔽双绞线的传输特性矩阵。本发明，数据源是屏蔽双绞线固有的材料参数，避免了烦琐的测量以及由此引入的测量误差。

A calculation method for RLCG model of shielded twisted pair and its transmission characteristics, regards the shielding layer of shielded twisted pair as the third conductor, and uses it as a reference for the two wires inside the shielding layer. Then the entire shielded twisted pair has three conductors, and the equivalent RLCG parameter model of the RLCG parameter distribution of a small section of length dz on the shielded twisted pair is used to set the form of the RLCG parameter matrix according to the shielded twisted pair RLCG model; respectively calculate the resistance R Matrix, inductance L matrix, capacitance C matrix, and conductance G matrix; calculate the transmission constant matrix of the shielded twisted pair and the characteristic impedance matrix of the shielded twisted pair according to each matrix; thus obtain the shielded twisted pair at any position and the source position The voltage/current relationship, that is, the transmission characteristic matrix of the shielded twisted pair. In the present invention, the data source is the inherent material parameter of the shielded twisted pair, which avoids cumbersome measurement and measurement errors introduced thereby.

Description

Translated fromChinese

屏蔽双绞线RLCG模型及其传输特性的计算方法RLCG Model of Shielded Twisted Pair and Calculation Method of Its Transmission Characteristics

技术领域technical field

本发明涉及一种屏蔽双绞线。特别是涉及一种用于1553B屏蔽双绞线的屏蔽双绞线RLCG模型及其传输特性的计算方法。The invention relates to a shielded twisted pair. In particular, it relates to a shielded twisted pair RLCG model for 1553B shielded twisted pair and a calculation method for its transmission characteristics.

背景技术Background technique

电信号的传输是主要的信号传输形式之一，目前航空机载高速数据信号的接入主要基于1553B总线系统上的数字式时分制多路数据传输技术。这是因为早期机载电子设备的设计与安装覆盖范围广泛，综合投资无法估量，充分利用已有的1553B总线系统来提供新的高速数据接入服务，不仅可以减少投资，而且便于成熟技术的延续和拓展（参见：Dennis J.Rauschmayer,杨威,ADSL/VDSL原理,人民邮电出版社,2001.ISBN 7-115-09153-6/TP·2108）。同时，早期在军用机载设备上的成功运用，使得1553B总线在机载/弹载/舰载综合火力控制系统、人造卫星等军事平台上进行了广泛的推广，对于这些不同的运用载体，需要在设计过程中灵活、方便地对信道的传输特性进行准确预测，从而保证数据传输质量（参见：寻建晖.1553B总线系统的建模与仿真[D].西安电子科技大学2011）。此外，新的应用需要更高的带宽资源，适用于长距离、大容量的光纤通信的发展，对基于屏蔽双绞线的1553B总线系统提出了更高的速率要求，而为解决信道扩容过程中的所遇到的多径、串扰等问题也需要清楚地了解信道特性。可见，实现1553B总线系统的灵活设计和运用、完成整个总线系统数据速率的提升，都迫切需要对1553B总线系统的信道传输特性进行准确地描述。The transmission of electrical signals is one of the main forms of signal transmission. At present, the access of high-speed data signals on airborne aircraft is mainly based on the digital time-division multiplex data transmission technology on the 1553B bus system. This is because the design and installation of early airborne electronic equipment cover a wide range, and the comprehensive investment is immeasurable. Making full use of the existing 1553B bus system to provide new high-speed data access services can not only reduce investment, but also facilitate the continuation of mature technologies and expansion (see: Dennis J.Rauschmayer, Yang Wei, ADSL/VDSL Principles, People's Posts and Telecommunications Press, 2001. ISBN 7-115-09153-6/TP·2108). At the same time, the successful application of the early military airborne equipment has made the 1553B bus widely popularized on military platforms such as airborne/missile/shipborne integrated fire control systems and artificial satellites. For these different application carriers, it is necessary to In the design process, it is flexible and convenient to accurately predict the transmission characteristics of the channel, so as to ensure the quality of data transmission (see: Xun Jianhui. Modeling and Simulation of 1553B Bus System [D]. Xidian University 2011). In addition, new applications require higher bandwidth resources, which are suitable for the development of long-distance and large-capacity optical fiber communication, and put forward higher speed requirements for the 1553B bus system based on shielded twisted pair, and in order to solve the channel expansion process Problems such as multipath and crosstalk encountered also require a clear understanding of channel characteristics. It can be seen that to realize the flexible design and application of the 1553B bus system and to improve the data rate of the entire bus system, it is urgent to accurately describe the channel transmission characteristics of the 1553B bus system.

屏蔽双绞线是1553B总线系统的重要组成部分，其传输特性的分析方法有很多种，如应用在HSPICE中的W-element模型法和TLM法(Transmission Lines Matrix)法（参见：T.Starr,J.M.Cioffi and P.J.Silverman,Understanding Digital Subscriber Line Technology[M],PrenticeHall,Upper Saddle River,NJ,1999)。此处介绍的RLCG参数法是用电阻R、电感L、电容C、电导G的分布参数矩阵和电报方程来描述单位长度屏蔽双绞线的传输特性。Shielded twisted pair is an important part of the 1553B bus system. There are many analysis methods for its transmission characteristics, such as the W-element model method and TLM method (Transmission Lines Matrix) method applied in HSPICE (see: T.Starr, J.M.Cioffi and P.J.Silverman, Understanding Digital Subscriber Line Technology [M], Prentice Hall, Upper Saddle River, NJ, 1999). The RLCG parameter method introduced here uses the distribution parameter matrix of resistance R, inductance L, capacitance C, and conductance G and the telegraph equation to describe the transmission characteristics of the shielded twisted pair per unit length.

发明内容Contents of the invention

本发明所要解决的技术问题是，提供一种通过1553B屏蔽双绞线已知的结构参数和材料特性，便可以得到传输线的RLCG参数，并准确地获得屏蔽双绞线的传输特性，进而给出屏蔽双绞线信道模型的屏蔽双绞线RLCG模型及其传输特性的计算方法。The technical problem to be solved by the present invention is to provide a 1553B shielded twisted pair with known structural parameters and material properties, so that the RLCG parameters of the transmission line can be obtained, and the transmission characteristics of the shielded twisted pair can be obtained accurately, and then given The shielded twisted pair RLCG model of the shielded twisted pair channel model and the calculation method of its transmission characteristics.

本发明所采用的技术方案是：一种屏蔽双绞线RLCG模型，将屏蔽双绞线的屏蔽层作为第三根导体，并将该第三根导体作为屏蔽层内两根铜导线的参考，则单位长度dx上屏蔽双绞线RLCG模型包括：第一根铜导线、第二根铜导线和屏蔽层，所述的第一根铜导线上依次串接有电阻R₁dx和电感L₁₁dx，所述的第二根铜导线上依次串接有电阻R₂dx和电感L₂₂dx，所述的屏蔽层上有电阻R₀dx，在第一根铜导线和第二根铜导线之间连接有电感L₁₂dx，第一根铜导线与第二根铜导线之间分别连接有电容C₁₂dx和电导G₁₂dx，第一根铜导线与屏蔽层之间分别连接有电容C₁₁dx和电导G₁₁dx，第二根铜导线与屏蔽层之间分别连接有电容C₂₂dx和电导G₂₂dx，其中，所述的第一根铜导线的输入电流为I₁(x)，输入电压为V₁(x)，输出电流为I₁(x+dx)，输出电压为V₁(x+dx)；所述的第二根铜导线的输入电流为I₂(x)，输入电压为V₂(x)，输出电流为I₂(x+dx)，输出电压为V₂(x+dx)；所述的屏蔽层（2）的输入电流为

输出电流为

The technical solution adopted in the present invention is: a shielded twisted pair RLCG model, the shielding layer of the shielded twisted pair is used as the third conductor, and the third conductor is used as a reference for the two copper wires in the shielding layer, Then the RLCG model of the shielded twisted pair on the unit length dx includes: the first copper wire, the second copper wire and the shielding layer, and the resistance R₁ dx and the inductance L₁₁ dx are sequentially connected in series on the first copper wire , the second copper wire is sequentially connected in series with a resistor R₂ dx and an inductance L₂₂ dx, and the shielding layer has a resistor R₀ dx between the first copper wire and the second copper wire The inductance L₁₂ dx is connected, the capacitance C₁₂ dx and the conductance G₁₂ dx are respectively connected between the first copper wire and the second copper wire, and the capacitance C₁₁ dx is respectively connected between the first copper wire and the shielding layer and conductance G₁₁ dx, capacitance C₂₂ dx and conductance G₂₂ dx are respectively connected between the second copper wire and the shielding layer, wherein, the input current of the first copper wire is I₁ (x), input The voltage is V₁ (x), the output current is I₁ (x+dx), the output voltage is V₁ (x+dx); the input current of the second copper wire is I₂ (x), the input voltage is V₂ (x), the output current is I₂ (x+dx), and the output voltage is V₂ (x+dx); the input current of the shielding layer (2) is

The output current is

一种基于屏蔽双绞线RLCG模型的屏蔽双绞线传输特性的计算方法，包括如下步骤：A kind of calculation method of the shielded twisted pair transmission characteristic based on shielded twisted pair RLCG model, comprises the steps:

1）根据屏蔽双绞线RLCG模型设定RLCG参数矩阵的形式：1) Set the form of the RLCG parameter matrix according to the shielded twisted pair RLCG model:

$\mathrm{<span><span>R</span>R</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>1</span>1</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}\\ {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>r</span><figure-callout\; label="r"\; filenames="HDA00002948008100011.png,HDA00002948008100013.png"\; state="\{\{state\}\}">r</figure-callout></span>}}_{\mathrm{<span><span>2</span>2</span>}}\end{array}\right]<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>1</span>1</span>}}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>2</span>2</span>}}\end{array}\right]<span><span>+</span>+</span>\left[\begin{array}{cc}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}\\ {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}\end{array}\right]$

$\mathrm{<span><span>L</span>L</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>11</span>11</span>}}& {\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>12</span>12</span>}}\\ {\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>12</span>12</span>}}& {\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>22</span>twenty\; two</span>}}\end{array}\right]$

$\mathrm{<span><span>C</span>C</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>11</span>11</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}& <span><span>-</span>-</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}\\ <span><span>-</span>-</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}& {\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>22</span>twenty\; two</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}\end{array}\right]$

$\mathrm{<span><span>G</span>G</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>11</span>11</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}& <span><span>-</span>-</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}\\ <span><span>-</span>-</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}& {\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>22</span>twenty\; two</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}\end{array}\right]$

式中，R₀为屏蔽层单位长度的直流电阻，R₁和R₂分别为两根导体单位长度的直流电阻，对于1553B屏蔽双绞线有R₁=R₂；L₁₁和L₂₂分别为两根导体与屏蔽层之间的互感，且L₁₁=L₂₂，L₁₂为两导体之间的互感；同理，C₁₁、G₁₁与C₂₂、G₂₂分别为两根导体与屏蔽层之间的电容与电导，C₁₂与G₁₂为两根导体之间的电容和电导，这些参数都是屏蔽双绞线的材料特性和结构参数的函数；In the formula, R₀ is the DC resistance per unit length of the shielding layer, R₁ and R₂ are the DC resistance per unit length of the two conductors, and for 1553B shielded twisted pair, R₁ =R₂ ; L₁₁ and L₂₂ are respectively The mutual inductance between two conductors and the shielding layer, and L₁₁ =L₂₂ , L₁₂ is the mutual inductance between the two conductors; similarly, C₁₁ , G₁₁ and C₂₂ , G₂₂ are the two conductors and the shielding layer respectively The capacitance and conductance between, C₁₂ and G₁₂ are the capacitance and conductance between two conductors, these parameters are the function of the material properties and structural parameters of the shielded twisted pair;

2）根据屏蔽双绞线各部分的材料电参数以及尺寸、空间分布参数计算RLCG参数矩阵各元素值；2) Calculate the value of each element of the RLCG parameter matrix according to the material electrical parameters, size and spatial distribution parameters of each part of the shielded twisted pair;

3）根据步骤2）得到的RLCG参数值计算屏蔽双绞线的传输常数矩阵γ和屏蔽双绞线的特性阻抗矩阵Z₀，其中：3) Calculate the transmission constant matrix γ of the shielded twisted pair and the characteristic impedance matrix Z₀ of the shielded twisted pair according to the RLCG parameter values obtained instep 2, where:

$\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>=</span>=</span>\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&beta;</span>j\&beta;</span>}<span><span>=</span>=</span>\sqrt{<span><span>(</span>(</span>\mathrm{<span><span>R</span>R</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;L</span>j\&omega;L</span>}<span><span>)</span>)</span><span><span>(</span>(</span>\mathrm{<span><span>G</span>G</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;C</span>j\&omega;C</span>}<span><span>)</span>)</span>}<span><span>;</span>;</span>$${\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>=</span>=</span>\sqrt{\frac{\mathrm{<span><span>R</span>R</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;L</span>j\&omega;L</span>}}{\mathrm{<span><span>G</span>G</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;C</span>j\&omega;C</span>}}}$

式中，ω是输入信号的角频率，j是虚数单位；In the formula, ω is the angular frequency of the input signal, and j is the imaginary unit;

4）根据步骤3）得到的屏蔽双绞线的传输常数矩阵γ、屏蔽双绞线的特性阻抗矩阵Z₀和基尔霍夫定律，得到屏蔽双绞线上任意位置处与源位置处的电压/电流关系，也即屏蔽双绞线的传输特性矩阵T：4) According to the transmission constant matrix γ of the shielded twisted pair obtained in step 3), the characteristic impedance matrix Z₀ of the shielded twisted pair and Kirchhoff's law, the voltage at any position on the shielded twisted pair and the source position is obtained /current relationship, that is, the transmission characteristic matrix T of the shielded twisted pair:

T=[cosh(γ^Tdx)+sinh(γ^Tdx)Y_tZ₀]^-1T=[cosh(γ^T dx)+sinh(γ^T dx)Y_t Z₀ ]^-1

对应的传输矩阵Φ：The corresponding transmission matrix Φ:

$\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}\mathrm{<span><span>cosh</span>cosh</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&gamma;dx</span>\&gamma;dx</span>}<span><span>)</span>)</span>& \mathrm{<span><span>sinh</span>sinh</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&gamma;dx</span>\&gamma;dx</span>}<span><span>)</span>)</span>{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}\\ \mathrm{<span><span>sinh</span>sinh</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>dx</span>dx</span>}<span><span>)</span>)</span>{{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}& \mathrm{<span><span>cosh</span>cosh</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>dx</span>dx</span>}<span><span>)</span>)</span>\end{array}\right]$

式中，sinh是双曲正弦函数，cosh是双曲余弦函数，γ^T是屏蔽双绞线传输常数矩阵γ的转置矩阵，Z₀^-1是屏蔽双绞线特性阻抗矩阵Z₀的逆矩阵，Y_t是已知的负载的电纳矩阵；In the formula, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, γ^T is the transposition matrix of the shielded twisted pair transmission constant matrix γ, Z₀^-1 is the inverse matrix of the shielded twisted pair characteristic impedance matrix Z₀ , Y_t is the known susceptance matrix of the load;

步骤2）所述的计算RLCG参数矩阵中的电阻R矩阵中的各元素参数值是：Step 2) The parameter value of each element in the resistance R matrix in the calculation RLCG parameter matrix is:

（1）计算出铜导体的趋肤深度δ，单位为米：(1) Calculate the skin depth δ of the copper conductor in meters:

$\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>\&pi;f\&mu;</span>\&pi;f\&mu;</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>Cu</span>Cu</span>}}}}$

式中，σ_Cu是金属铜的电导率，单位为西门子/米；f是输入信号的频率，单位为赫兹；μ是金属铜的介电常数，单位为法拉/米；In the formula, σ_Cu is the electrical conductivity of metallic copper in Siemens/m; f is the frequency of the input signal in Hertz; μ is the dielectric constant of metallic copper in Farad/m;

（2）由（1）得到的

计算出第u根铜导线单位长度上的直流电阻R_u值，也即电阻率，单位为欧姆/米：(2) obtained from (1)

Calculate the DC resistance R_u value per unit length of the uth copper wire, that is, the resistivity, and the unit is ohm/meter:

式中，σ_Cu是金属铜的电导率，单位为西门子/米；r_w是铜导线的半径；In the formula, σ_Cu is the electrical conductivity of metal copper, and the unit is Siemens/m; r_w is the radius of the copper wire;

（3）得到电阻矩阵R中位于u行v列处元素的R_u,v值，单位为欧姆/米：(3) Obtain the R_u,v value of the element at row u and column v in the resistance matrix R, in ohm/meter:

u,v任取1或2

u, v take either 1 or 2

式中，R₀是屏蔽层单位长度上的直流电阻，单位为欧姆/米。In the formula, R₀ is the DC resistance per unit length of the shielding layer, and the unit is ohm/meter.

步骤2）所述的计算RLCG参数矩阵中电感L矩阵各元素的参数值是：对铜导线逐个进行镜像分析，得出电感矩阵L中位于u行v列处元素的值L_u,v，单位为亨利/米：Step 2) The calculation of the parameter values of the elements of the inductance L matrix in the RLCG parameter matrix is as follows: the copper wires are mirrored one by one to obtain the value L_u,v of the element at the u row v column in the inductance matrix L, the unit For Henry/meter:

式中，In the formula,

r_s为屏蔽层的半径，d_u为标号是u的第u根铜导线与屏蔽层中心点之间的距离，r_w是铜导线的半径，θ为第u根铜导线与第v根铜导线之间的夹角，μ是金属铜的介电常数。r_s is the radius of the shielding layer, d_u is the distance between the uth copper wire marked u and the center point of the shielding layer, r_w is the radius of the copper wire, θ is the uth copper wire and the vth copper wire The angle between the wires, μ is the dielectric constant of metallic copper.

步骤2）所述的计算RLCG参数矩阵中电容C矩阵是：Step 2) The capacitance C matrix in the calculation RLCG parameter matrix is:

C=μξL^-1C=μξL^-1

式中，μ是金属铜的介电常数；ξ为金属铜的磁导率，单位为亨利/米；L为电感矩阵，可以得到电容矩阵C，矩阵中各元素的单位为法拉/米。In the formula, μ is the dielectric constant of metallic copper; ξ is the magnetic permeability of metallic copper, in Henry/m; L is the inductance matrix, and the capacitance matrix C can be obtained, and the unit of each element in the matrix is farad/m.

步骤2）所述的计算RLCG参数矩阵中电导G矩阵是：The conductance G matrix in the calculation RLCG parameter matrix described in step 2) is:

$\mathrm{<span><span>G</span>G</span>}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>cu</span>cu</span>}}}{\mathrm{<span><span>\&xi;</span>\&xi;</span>}}\mathrm{<span><span>C</span>C</span>}$

式中，C为电容的参数矩阵，σ_Cu是金属铜的电导率；ξ为金属铜的磁导率；矩阵中各元素的单位为西门子/米。In the formula, C is the parameter matrix of capacitance, σ_Cu is the electrical conductivity of metallic copper; ξ is the magnetic permeability of metallic copper; the unit of each element in the matrix is Siemens/m.

本发明的屏蔽双绞线RLCG模型及其传输特性的计算方法，与一般通过实测的方法来得到屏蔽双绞线的传输特性相比，数据源是屏蔽双绞线固有的材料参数，避免了烦琐的测量以及由此引入的测量误差。同时，本发明基于严格的理论推导，与实测法和经验估算法相比，其结论具有数学和物理意义，并且便于在本发明结果的基础上进行进一步的理论研究和推广。The shielded twisted pair RLCG model of the present invention and the calculation method of its transmission characteristics, compared with the transmission characteristics of the shielded twisted pair obtained by the method of actual measurement, the data source is the inherent material parameters of the shielded twisted pair, which avoids the cumbersome measurement and the resulting measurement error. At the same time, the present invention is based on strict theoretical derivation. Compared with the actual measurement method and empirical estimation method, the conclusion has mathematical and physical significance, and is convenient for further theoretical research and promotion on the basis of the results of the present invention.

通过RLCG参数所表示的屏蔽双绞线的传输特性，可以预测在待传输信号已知时屏蔽双绞线信道传输的可靠性，预测屏蔽双绞线上任意节点之间的信号畸变程度，并据此指导整个1553B高速数据系统的设计，避免产生不可用的终端节点，从而提高整个系统的性能。同时，该方法对其他类似的有线高速传输系统的理论研究和实现具有一定的借鉴意义和参考价值。Through the transmission characteristics of the shielded twisted pair represented by the RLCG parameter, the reliability of the shielded twisted pair channel transmission can be predicted when the signal to be transmitted is known, and the signal distortion degree between any nodes on the shielded twisted pair can be predicted, and according to This guides the design of the entire 1553B high-speed data system to avoid unavailable terminal nodes, thereby improving the performance of the entire system. At the same time, this method has certain reference significance and reference value for the theoretical research and realization of other similar wired high-speed transmission systems.

附图说明Description of drawings

图1是1553B屏蔽双绞线的结构示意图；Figure 1 is a schematic diagram of the structure of the 1553B shielded twisted pair;

图2是屏蔽双绞线的等效RLCG参数模型；Fig. 2 is the equivalent RLCG parameter model of the shielded twisted pair;

图3是屏蔽双绞线镜像分析法的结构示意图。Fig. 3 is a structural schematic diagram of the shielded twisted pair mirror analysis method.

图中in the picture

1：护套                            2：屏蔽层1: Sheath 2: Shielding layer

3：绝缘套                          4：铜导线3: Insulation sleeve 4: Copper wire

5：填充物                          41：第一根铜导线5: Filler 41: The first copper wire

42：第二根铜导线42: Second copper wire

具体实施方式Detailed ways

下面结合实施例和附图对本发明的屏蔽双绞线RLCG模型及其传输特性的计算方法做出详细说明。The shielded twisted pair RLCG model of the present invention and the calculation method for its transmission characteristics will be described in detail below in conjunction with the embodiments and the accompanying drawings.

1553B系统中使用的是标准的屏蔽双绞线，如图1所示，其传输方向上任何截面的结构都相同，可认为其分布参数均匀且不随位置变化。将屏蔽双绞线的屏蔽层2视作为第三根导体，并将其作为屏蔽层内两根铜导线4的参考。则整个屏蔽双绞线有三根导体，屏蔽双绞线上一小段长度dx的RLCG参数分布如图2所示，即本发明的屏蔽双绞线RLCG模型包括：第一根铜导线41、第二根铜导线42和屏蔽层2，所述的第一根铜导线41上依次串接有电阻R₁dx和电感L₁₁dx，所述的第二根铜导线42上依次串接有电阻R₂dx和电感L₂₂dx，所述的屏蔽层2上有电阻R₀dx，在第一根铜导线41和第二根铜导线42之间连接有电感L₁₂dx，第一根铜导线41与第二根铜导线42之间分别连接有电容C₁₂dx和电导G₁₂dx，第一根铜导线41与屏蔽层2之间分别连接有电容C₁₁dx和电导G₁₁dx，第二根铜导线42与屏蔽层2之间分别连接有电容C₂₂dx和电导G₂₂dx，其中，所述的第一根铜导线41的输入电流为I₁(x)，输入电压为V₁(x)，输出电流为I₁(x+dx)，输出电压为V₁(x+dx)；所述的第二根铜导线42的输入电流为I₂(x)，输入电压为V₂(x)，输出电流为I₂(x+dx)，输出电压为V₂(x+dx)；所述的屏蔽层2的输入电流为

输出电流为

The standard shielded twisted pair is used in the 1553B system. As shown in Figure 1, the structure of any section in the transmission direction is the same, and its distribution parameters can be considered to be uniform and do not change with the position. Consider theshield 2 of the shielded twisted pair as the third conductor and use it as a reference for the twocopper wires 4 inside the shield. Then the whole shielded twisted pair has three conductors, and the RLCG parameter distribution of a short length dx on the shielded twisted pair is as shown in Figure 2, that is, the shielded twisted pair RLCG model of the present invention includes: the first copper wire 41, the second A copper wire 42 and a shielding layer 2, the first copper wire 41 is sequentially connected with a resistor R₁ dx and an inductance L₁₁ dx, and the second copper wire 42 is sequentially connected with a resistor R₂ dx and inductance L₂₂ dx, there is resistance R₀ dx on the shielding layer 2, inductance L₁₂ dx is connected between the first copper wire 41 and the second copper wire 42, the first copper wire 41 and Capacitance C₁₂ dx and conductance G₁₂ dx are respectively connected between the second copper wire 42, capacitance C₁₁ dx and conductance G₁₁ dx are respectively connected between the first copper wire 41 and the shielding layer 2, and the second copper Capacitance C₂₂ dx and conductance G₂₂ dx are respectively connected between the wire 42 and the shielding layer 2, wherein the input current of the first copper wire 41 is I₁ (x), and the input voltage is V₁ (x) , the output current is I₁ (x+dx), the output voltage is V₁ (x+dx); the input current of the second copper wire 42 is I₂ (x), and the input voltage is V₂ (x) , the output current is I₂ (x+dx), the output voltage is V₂ (x+dx); the input current of the shielding layer 2 is

The output current is

利用图2所示的等效RLCG参数模型，以得到本发明的基于屏蔽双绞线RLCG模型的屏蔽双绞线传输特性的计算方法，包括如下步骤：Utilize the equivalent RLCG parameter model shown in Fig. 2, to obtain the computing method of the shielded twisted pair transmission characteristic based on the shielded twisted pair RLCG model of the present invention, comprise the steps:

1）根据屏蔽双绞线RLCG模型设定RLCG参数矩阵的形式，由于模型将双绞线和屏蔽层视为三根导体，则RLCG各参数均为一个2×2的矩阵：1) Set the form of the RLCG parameter matrix according to the shielded twisted pair RLCG model. Since the model regards the twisted pair and the shielding layer as three conductors, each parameter of the RLCG is a 2×2 matrix:

$\mathrm{<span><span>R</span>R</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>1</span>1</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}\\ {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>r</span><figure-callout\; label="r"\; filenames="HDA00002948008100011.png,HDA00002948008100013.png"\; state="\{\{state\}\}">r</figure-callout></span>}}_{\mathrm{<span><span>2</span>2</span>}}\end{array}\right]<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>1</span>1</span>}}& \mathrm{<span><span>0</span>0</span>}\\ \mathrm{<span><span>0</span>0</span>}& {\mathrm{<span><span>R</span><figure-callout\; label="R"\; filenames="HDA00002948008100011.png,HDA00002948008100013.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span><span>2</span>2</span>}}\end{array}\right]<span><span>+</span>+</span>\left[\begin{array}{cc}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}\\ {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}& {\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>0</span>0</span>}}\end{array}\right]$

$\mathrm{<span><span>L</span>L</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>11</span>11</span>}}& {\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>12</span>12</span>}}\\ {\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>12</span>12</span>}}& {\mathrm{<span><span>L</span>L</span>}}_{\mathrm{<span><span>22</span>twenty\; two</span>}}\end{array}\right]$

$\mathrm{<span><span>C</span>C</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>11</span>11</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}& <span><span>-</span>-</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}\\ <span><span>-</span>-</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}& {\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>22</span>twenty\; two</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>C</span>C</span>}}_{\mathrm{<span><span>12</span>12</span>}}\end{array}\right]$

$\mathrm{<span><span>G</span>G</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>11</span>11</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}& <span><span>-</span>-</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}\\ <span><span>-</span>-</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}& {\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>22</span>twenty\; two</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>G</span>G</span>}}_{\mathrm{<span><span>12</span>12</span>}}\end{array}\right]$

式中，R₀为屏蔽层单位长度的直流电阻，R₁和R₂分别为两根导体单位长度的直流电阻，对于1553B屏蔽双绞线有R₁=R₂；L₁₁和L₂₂分别为两根导体与屏蔽层之间的互感，且L₁₁=L₂₂，L₁₂为两导体之间的互感；同理，C₁₁、G₁₁与C₂₂、G₂₂分别为两根导体与屏蔽层之间的电容与电导，C₁₂与G₁₂为两根导体之间的电容和电导，这些参数都是屏蔽双绞线的材料特性和结构参数的函数；In the formula, R₀ is the DC resistance per unit length of the shielding layer, R₁ and R₂ are the DC resistance per unit length of the two conductors, and for 1553B shielded twisted pair, R₁ =R₂ ; L₁₁ and L₂₂ are respectively The mutual inductance between two conductors and the shielding layer, and L₁₁ =L₂₂ , L₁₂ is the mutual inductance between the two conductors; similarly, C₁₁ , G₁₁ and C₂₂ , G₂₂ are the two conductors and the shielding layer respectively The capacitance and conductance between, C₁₂ and G₁₂ are the capacitance and conductance between two conductors, these parameters are the function of the material properties and structural parameters of the shielded twisted pair;

从而，单位长度屏蔽双绞线的RLCG参数可用上式中的参数矩阵形式来描述。Therefore, the RLCG parameters of the unit length shielded twisted pair can be described in the form of a parameter matrix in the above formula.

2）根据屏蔽双绞线各部分的材料电参数以及尺寸、空间分布参数计算RLCG参数矩阵各元素值，是分别计算电阻R矩阵、电感L矩阵、电容C矩阵和电导G矩阵，包括：2) Calculate the value of each element of the RLCG parameter matrix according to the material electrical parameters, size and spatial distribution parameters of each part of the shielded twisted pair, which is to calculate the resistance R matrix, inductance L matrix, capacitance C matrix and conductance G matrix respectively, including:

（1）计算RLCG参数矩阵中的电阻R矩阵中的各元素参数值是：(1) Calculate the parameter value of each element in the resistance R matrix in the RLCG parameter matrix:

（a）计算出铜导体的趋肤深度δ，单位为米：(a) Calculate the skin depth δ of the copper conductor in meters:

$\mathrm{<span><span>\&delta;</span>\&delta;</span>}<span><span>=</span>=</span>\frac{\mathrm{<span><span>1</span>1</span>}}{\sqrt{\mathrm{<span><span>\&pi;f\&mu;</span>\&pi;f\&mu;</span>}{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>Cu</span>Cu</span>}}}}$

式中，σ_Cu是金属铜的电导率，单位为西门子/米；f是输入信号的频率，单位为赫兹；μ是金属铜的介电常数，单位为法拉/米；In the formula, σ_Cu is the electrical conductivity of metallic copper in Siemens/m; f is the frequency of the input signal in Hertz; μ is the dielectric constant of metallic copper in Farad/m;

（b）由（a）得到的

计算出第u根铜导线单位长度上的直流电阻R_u值，也即电阻率，单位为欧姆/米：(b) obtained from (a)

Calculate the DC resistance R_u value per unit length of the uth copper wire, that is, the resistivity, and the unit is ohm/meter:

式中，σ_Cu是金属铜的电导率，单位为西门子/米；r_w是铜导线的半径；In the formula, σ_Cu is the electrical conductivity of metal copper, and the unit is Siemens/m; r_w is the radius of the copper wire;

（c）得到电阻矩阵R中位于u行v列处元素的R_u,v值，单位为欧姆/米：(c) Get the R_u,v value of the element at row u and column v in the resistance matrix R, in ohm/meter:

u,v任取1或2

u, v take either 1 or 2

式中，R₀是屏蔽层单位长度上的直流电阻，单位为欧姆/米。In the formula, R₀ is the DC resistance per unit length of the shielding layer, and the unit is ohm/meter.

（2）计算RLCG参数矩阵中电感L矩阵各元素的参数值是：(2) Calculate the parameter values of each element of the inductance L matrix in the RLCG parameter matrix:

可根据镜像法由传输线的横截面参数来计算电感矩阵L中的各元素。如图3所示，每根铜导线的镜像放置在屏蔽层之外，并且与其原铜导线相对应。为使镜像时，两个导体在理想的镜像环境下作用，保证屏蔽层为等电位面，故认为屏蔽层的阻抗可以忽略。镜像铜导线的电流与原铜导线中的电流大小相等、方向相反。在双绞线的任意横截面上，镜像铜导线的中心、原铜导线的中心、屏蔽层的中心三者成一条直线。r_s为屏蔽层的半径，d_u为标号是u的第u根铜导线与屏蔽层中心点之间的距离，则镜像铜导线中心点与屏蔽层中心点的距离为r_s²/d_u。r_w是铜导线的半径，θ为第u根铜导线与第v根铜导线之间的夹角。对铜导线逐个进行镜像分析，得出电感矩阵L中位于u行v列处元素的值L_u,v，单位为亨利/米：Each element in the inductance matrix L can be calculated from the cross-sectional parameters of the transmission line according to the mirror image method. As shown in Figure 3, the mirror image of each copper conductor is placed outside the shield and corresponds to its original copper conductor. In order to make the mirror image, the two conductors act in an ideal mirror image environment to ensure that the shielding layer is an equipotential plane, so it is considered that the impedance of the shielding layer can be ignored. The current in the mirrored copper wire is equal in size and opposite in direction to the current in the original copper wire. On any cross-section of the twisted pair, the center of the mirrored copper wire, the center of the original copper wire, and the center of the shielding layer form a straight line. r_s is the radius of the shielding layer, d_u is the distance between the uth copper wire marked u and the center point of the shielding layer, then the distance between the center point of the mirrored copper wire and the center point of the shielding layer is r_s² /d_u . r_w is the radius of the copper wire, θ is the angle between the uth copper wire and the vth copper wire. The mirror image analysis of the copper wires is carried out one by one, and the value L_u,v of the element at the row u and column v in the inductance matrix L is obtained, and the unit is Henry/meter:

（3）计算RLCG参数矩阵中电容C矩阵，是由电感矩阵L，可以得到电容矩阵C如下：(3) Calculating the capacitance C matrix in the RLCG parameter matrix is derived from the inductance matrix L, and the capacitance matrix C can be obtained as follows:

C=μξL^-1C=μξL^-1

式中，μ是金属铜的介电常数；ξ为金属铜的磁导率，单位为亨利/米；L为电感矩阵，可以得到电容矩阵C，矩阵中各元素的单位为法拉/米。In the formula, μ is the dielectric constant of metallic copper; ξ is the magnetic permeability of metallic copper, in Henry/m; L is the inductance matrix, and the capacitance matrix C can be obtained, and the unit of each element in the matrix is farad/m.

（4）计算RLCG参数矩阵中电导G矩阵，是由电容矩阵C，可以得到电导矩阵G：(4) Calculate the conductance G matrix in the RLCG parameter matrix. From the capacitance matrix C, the conductance matrix G can be obtained:

$\mathrm{<span><span>G</span>G</span>}<span><span>=</span>=</span>\frac{{\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}}_{\mathrm{<span><span>cu</span>cu</span>}}}{\mathrm{<span><span>\&xi;</span>\&xi;</span>}}\mathrm{<span><span>C</span>C</span>}$

式中，C为电容的参数矩阵，σ_Cu是金属铜的电导率；ξ为金属铜的磁导率；矩阵中各元素的单位为西门子/米。In the formula, C is the parameter matrix of capacitance, σ_Cu is the electrical conductivity of metallic copper; ξ is the magnetic permeability of metallic copper; the unit of each element in the matrix is Siemens/m.

3）根据步骤2）得到的RLCG参数值计算屏蔽双绞线的传输常数矩阵γ和屏蔽双绞线的特性阻抗矩阵Z₀，其中：3) Calculate the transmission constant matrix γ of the shielded twisted pair and the characteristic impedance matrix Z₀ of the shielded twisted pair according to the RLCG parameter values obtained instep 2, where:

$\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>=</span>=</span>\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&beta;</span>j\&beta;</span>}<span><span>=</span>=</span>\sqrt{<span><span>(</span>(</span>\mathrm{<span><span>R</span>R</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;L</span>j\&omega;L</span>}<span><span>)</span>)</span><span><span>(</span>(</span>\mathrm{<span><span>G</span>G</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;C</span>j\&omega;C</span>}<span><span>)</span>)</span>}<span><span>;</span>;</span>$${\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>=</span>=</span>\sqrt{\frac{\mathrm{<span><span>R</span>R</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;L</span>j\&omega;L</span>}}{\mathrm{<span><span>G</span>G</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;C</span>j\&omega;C</span>}}}$

式中，ω是输入信号的角频率，j是虚数单位。where ω is the angular frequency of the input signal, and j is the imaginary unit.

4）根据步骤3）得到的屏蔽双绞线的传输常数矩阵γ、屏蔽双绞线的特性阻抗矩阵Z₀和基尔霍夫定律，则单位长度的屏蔽双绞线的电报方程为：4) According to the transmission constant matrix γ of the shielded twisted pair obtained in step 3), the characteristic impedance matrix Z₀ of the shielded twisted pair and Kirchhoff's law, the telegraph equation of the shielded twisted pair per unit length is:

$\frac{\mathrm{<span><span>dV</span>dV</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>dx</span>dx</span>}}<span><span>=</span>=</span>\mathrm{<span><span>RI</span>RI</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>L</span>L</span>}\frac{\mathrm{<span><span>dI</span>iGO</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>dt</span>dt</span>}}$

$\frac{\mathrm{<span><span>dI</span>iGO</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>dx</span>dx</span>}}<span><span>=</span>=</span>\mathrm{<span><span>GI</span>GI</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>+</span>+</span>\mathrm{<span><span>C</span>C</span>}\frac{\mathrm{<span><span>dV</span>dV</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>}{\mathrm{<span><span>dt</span>dt</span>}}$

其中，in,

$\mathrm{<span><span>V</span>V</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\left[\begin{array}{c}{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\\ {\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\end{array}\right]$

$\mathrm{<span><span>I</span>I</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\left[\begin{array}{c}{\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\\ {\mathrm{<span><span>I</span>I</span>}}_{\mathrm{<span><span>2</span>2</span>}}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\end{array}\right]$

由于1553B屏蔽双绞线为对称的均匀传输线，在时谐场时，上述两个式子可简写为：Since the 1553B shielded twisted pair is a symmetrical uniform transmission line, in the time harmonic field, the above two formulas can be abbreviated as:

$\frac{{\mathrm{<span><span>d</span>d</span>}}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>V</span><figure-callout\; label="V\; dx"\; filenames="HDA00002948008100011.png,HDA00002948008100013.png"\; state="\{\{state\}\}">V</figure-callout></span><figure-callout\; label="V\; dx"\; filenames="HDA00002948008100011.png,HDA00002948008100013.png"\; state="\{\{state\}\}"></figure-callout>}}{{\mathrm{<span><span></span></span>}}^{}}<span><span>=</span>=</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>V</span>V</span>}$

$\frac{{\mathrm{<span><span>d</span>d</span>}}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>I</span><figure-callout\; label="I\; dx"\; filenames="HDA00002948008100011.png,HDA00002948008100013.png"\; state="\{\{state\}\}">I</figure-callout></span><figure-callout\; label="I\; dx"\; filenames="HDA00002948008100011.png,HDA00002948008100013.png"\; state="\{\{state\}\}"></figure-callout>}}{{\mathrm{<span><span></span></span>}}^{}}<span><span>=</span>=</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>I</span>I</span>}$

其中，in,

$\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}<span><span>=</span>=</span>\mathrm{<span><span>\&alpha;</span>\&alpha;</span>}<span><span>+</span>+</span>\mathrm{<span><span>jb</span>jb</span>}<span><span>=</span>=</span>\sqrt{<span><span>(</span>(</span>\mathrm{<span><span>R</span>R</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;L</span>j\&omega;L</span>}<span><span>)</span>)</span><span><span>(</span>(</span>\mathrm{<span><span>G</span>G</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;C</span>j\&omega;C</span>}<span><span>)</span>)</span>}<span><span>;</span>;</span>$${\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>=</span>=</span>\sqrt{\frac{\mathrm{<span><span>R</span>R</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;L</span>j\&omega;L</span>}}{\mathrm{<span><span>G</span>G</span>}<span><span>+</span>+</span>\mathrm{<span><span>j\&omega;C</span>j\&omega;C</span>}}}$

ω是输入信号的角频率，j是虚数单位。ω is the angular frequency of the input signal and j is the imaginary unit.

则解上面的两个微分方程，可以得到：Then solving the above two differential equations, we can get:

V(x+dx,t)=cosh(γdx)·V(x,t)+sinh(γdx)Z₀·I(x,t)V(x+dx,t)=cosh(γdx) V(x,t)+sinh(γdx)Z₀ I(x,t)

I(x+dx，t)＝sinh(γ^Tdx)·Z₀^-1·V(x，t)+cosh(γ^Tdx)·I(x，t)I(x+dx,t)=sinh(γ^T dx)·Z₀^-1 ·V(x,t)+cosh(γ^T dx)·I(x,t)

将其写作矩阵形式为：Write it in matrix form as:

$\left[\begin{array}{c}\mathrm{<span><span>V</span>V</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>+</span>+</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>I</span>I</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>+</span>+</span>\mathrm{<span><span>dx</span>dx</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\end{array}\right]<span><span>=</span>=</span>\left[\begin{array}{cc}\mathrm{<span><span>cosh</span>cosh</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&gamma;dx</span>\&gamma;dx</span>}<span><span>)</span>)</span>& \mathrm{<span><span>sinh</span>sinh</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&gamma;dx</span>\&gamma;dx</span>}<span><span>)</span>)</span>{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}\\ \mathrm{<span><span>sinh</span>sinh</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>dx</span>dx</span>}<span><span>)</span>)</span>{{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}& \mathrm{<span><span>cosh</span>cosh</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>dx</span>dx</span>}<span><span>)</span>)</span>\end{array}\right]\left[\begin{array}{c}\mathrm{<span><span>V</span>V</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>I</span>I</span>}<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>,</span>,</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span>\end{array}\right]$

则可以得到其传输矩阵Φ为：Then its transmission matrix Φ can be obtained as:

$\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}<span><span>=</span>=</span>\left[\begin{array}{cc}\mathrm{<span><span>cosh</span>cosh</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&gamma;dx</span>\&gamma;dx</span>}<span><span>)</span>)</span>& \mathrm{<span><span>sinh</span>sinh</span>}<span><span>(</span>(</span>\mathrm{<span><span>\&gamma;dx</span>\&gamma;dx</span>}<span><span>)</span>)</span>{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}\\ \mathrm{<span><span>sinh</span>sinh</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>dx</span>dx</span>}<span><span>)</span>)</span>{{\mathrm{<span><span>Z</span>Z</span>}}_{\mathrm{<span><span>0</span>0</span>}}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}& \mathrm{<span><span>cosh</span>cosh</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&gamma;</span>\&gamma;</span>}}^{\mathrm{<span><span>T</span>T</span>}}\mathrm{<span><span>dx</span>dx</span>}<span><span>)</span>)</span>\end{array}\right]$

从而得到屏蔽双绞线上任意位置处与源位置处的电压/电流关系，也即屏蔽双绞线的传输特性矩阵T：Thus, the voltage/current relationship between any position on the shielded twisted pair and the source position is obtained, that is, the transmission characteristic matrix T of the shielded twisted pair:

T=[cosh(γ^Tdx)+sinh(γ^Tdx)Y_tZ₀]^-1T=[cosh(γ^T dx)+sinh(γ^T dx)Y_t Z₀ ]^-1

式中，sinh是双曲正弦函数，cosh是双曲余弦函数，γ^T是屏蔽双绞线传输常数矩阵γ的转置矩阵，Z₀^-1是屏蔽双绞线特性阻抗矩阵Z₀的逆矩阵，Y_t是已知的负载的电纳矩阵。In the formula, sinh is the hyperbolic sine function, cosh is the hyperbolic cosine function, γ^T is the transposition matrix of the shielded twisted pair transmission constant matrix γ, Z₀^-1 is the inverse matrix of the shielded twisted pair characteristic impedance matrix Z₀ , Y_t is the known susceptance matrix of the load.

可见，屏蔽双绞线的传输特性矩阵T（或传输矩阵Φ）可由γ和Z₀参数矩阵来表达，而γ和Z₀参数矩阵可由RLCG参数矩阵表达。It can be seen that the transmission characteristic matrix T (or transmission matrix Φ) of the shielded twisted pair can be expressed by the γ and Z₀ parameter matrix, and the γ and Z₀ parameter matrix can be expressed by the RLCG parameter matrix.

Claims (6)

1. A shielded twisted pair RLCG model, wherein the shield (2) of the shielded twisted pair is used as the third conductor and the third conductor is used as the reference for two copper conductors in the shield, and wherein the RLCG model for the shielded twisted pair per unit length dx comprises: a first copper wire (41), a second copper wire (42) and a shielding layer (2), wherein a resistor R is connected in series on the first copper wire (41) in sequence₁dx and inductance L₁₁dx and a resistor R is sequentially connected in series on the second copper wire (42)₂dx and inductance L₂₂dx, said screenThe shielding layer (2) is provided with a resistor R₀dx between the first copper wire (41) and the second copper wire (42) is connected an inductance L₁₂dx, capacitors C are respectively connected between the first copper wire (41) and the second copper wire (42)₁₂dx and conductance G₁₂dx, capacitors C are respectively connected between the first copper wire (41) and the shielding layer (2)₁₁dx and conductance G₁₁dx, capacitors C are respectively connected between the second copper wire (42) and the shielding layer (2)₂₂dx and conductance G₂₂dx, wherein the input current of the first copper wire (41) is I₁(x) Input voltage of V₁(x) Output current is I₁(x + dx) and an output voltage V₁(x + dx); the input current of the second copper wire (42) is I₂(x) Input voltage of V₂(x) Output current is I₂(x + dx) and an output voltage V₂(x + dx); the input current of the shielding layer (2) is

Output current of

2. A method for calculating transmission characteristics of a shielded twisted pair based on the RLCG model of the shielded twisted pair as claimed in claim 1, comprising the steps of:

1) setting the form of an RLCG parameter matrix according to a shielded twisted pair RLCG model:

in the formula, R₀Direct current resistance per unit length of the shielding layer, R₁And R₂The direct current resistances of the two conductors per unit length are respectively R for a 1553B shielded twisted pair₁=R₂；L₁₁And L₂₂Are mutual inductance between the two conductors and the shielding layer, respectively, and L₁₁=L₂₂，L₁₂Is the mutual inductance between two conductors; in the same way, C₁₁、G₁₁And C₂₂、G₂₂Capacitance and conductance between two conductors and a shielding layer, C₁₂And G₁₂Capacitance and conductance between the two conductors, which are functions of the material properties and structural parameters of the shielded twisted pair;

2) calculating each element value of the RLCG parameter matrix according to the material electrical parameters, the size and the spatial distribution parameters of each part of the shielded twisted pair;

3) calculating a transmission constant matrix gamma of the shielded twisted pair and a characteristic impedance matrix Z of the shielded twisted pair according to the RLCG parameter value obtained in the step 2)₀Wherein:

where ω is the angular frequency of the input signal and j is the imaginary unit;

4) the transmission constant matrix gamma of the shielded twisted pair and the characteristic impedance matrix Z of the shielded twisted pair obtained according to the step 3)₀And kirchhoff's law to obtain a shield twisted pairVoltage/current relationship at any position to the source position, i.e. the transmission characteristic matrix T of the shielded twisted pair:

T=[cosh(γ^Tdx)+sinh(γ^Tdx)Y_tZ₀]^-1

corresponding transmission matrix Φ:

where sinh is a hyperbolic sine function, cosh is a hyperbolic cosine function, γ^TIs a transposed matrix, Z, of a matrix of transmission constants gamma of a shielded twisted pair₀^-1Is a shielded twisted pair characteristic impedance matrix Z₀Inverse matrix of, Y_tIs known as the load's susceptance matrix.

3. The shielded twisted pair RLCG model-based shielded twisted pair transmission characteristic calculation method of claim 2, wherein the parameter values of each element in the resistance R matrix in the calculated RLCG parameter matrix of step 2) are:

(1) the skin depth δ of the copper conductor was calculated in meters:

in the formula, σ_CuIs the conductivity of metallic copper, in siemens/meter; f is the frequency of the input signal in hertz; μ is the dielectric constant of metallic copper, in farads per meter;

(2) obtained by (1)

Calculating the direct current resistance R of the u-th copper conductor in unit length_uThe value, i.e. the resistivity, is given in ohms/meter:

in the formula, σ_CuIs the conductivity of metallic copper, in siemens/meter; r is_wIs the radius of the copper wire;

(3) obtaining R of the element positioned at u rows and v columns in the resistance matrix R_u,vValues, in ohms/meter:

u, v being either 1 or 2

In the formula, R₀Is the direct current resistance per unit length of the shielding layer, in ohms/meter.

4. The shielded twisted pair RLCG model-based shielded twisted pair transmission characteristic calculation method of claim 2, wherein the parameter values of each element of the inductance L matrix in the calculated RLCG parameter matrix of step 2) are: carrying out mirror image analysis on the copper conductors one by one to obtain the value L of the element positioned in the u rows and v columns in the inductance matrix L_u,vThe unit is henry/meter:

in the formula,

r_sradius of the shielding layer, d_uDistance between u-th copper conductor, denoted by u, and center point of shielding layer, r_wIs the radius of the copper wire, theta is the included angle between the u-th copper wire and the v-th copper wire, and mu is the dielectric constant of the metal copper.

5. The shielded twisted pair RLCG model-based shielded twisted pair transmission characteristic calculation method of claim 2, wherein the capacitance C matrix in the RLCG parameter matrix calculation of step 2) is:

C=μξL^-1

wherein μ is the dielectric constant of metallic copper; xi is the magnetic conductivity of the metal copper, and the unit is Henry/meter; l is an inductance matrix, a capacitance matrix C can be obtained, and the unit of each element in the matrix is Farad/meter.

6. The shielded twisted pair RLCG model-based shielded twisted pair transmission characteristic calculation method of claim 2, wherein the conductance G matrix in the RLCG parameter matrix calculation of step 2) is:

where C is the parameter matrix of the capacitance, σ_CuIs the conductivity of metallic copper; xi is the magnetic conductivity of the metal copper; the units of the elements in the matrix are siemens/meter.

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