CN108345753B - A crosstalk noise prediction method for non-parallel cables - Google Patents

Abstract

The invention discloses a crosstalk noise prediction method for non-parallel cables. A wire-wound crosstalk model is established according to actual cable parameters, a segmented cascade method is used to analyze the non-parallel cables, and segments are compared to multi-conductors under straight conditions. The non-parallel multi-conductor electromagnetic coupling model is established; according to the common solution method of cable crosstalk, the non-parallel cable equation is established, and an equivalent electromagnetic parameter matrix is proposed to predict the near-end and far-end of the non-parallel cable Electromagnetic Crosstalk. By predicting the magnitude of electromagnetic crosstalk and the actual degree of harm, it has important theoretical and engineering significance for the efficient operation of electrical equipment. Accurately predicting crosstalk is helpful to quickly predict and discover potential crosstalk problems in the early stage of design, preventing problems from At the same time, as a basis for designing crosstalk suppression measures, it can also provide a theoretical basis for implementing crosstalk suppression remedial measures in the testing stage after the electrical equipment is manufactured, thereby improving the stability of the equipment system.

Description

A crosstalk noise prediction method for non-parallel cables

technical field

The invention relates to the technical field of electromagnetic compatibility, in particular to a crosstalk noise prediction method for non-parallel cables.

Background technique

In electromagnetic compatibility, the interference of electronic equipment to itself is generally called crosstalk. Cable crosstalk refers to the interference between cables to the original signal due to the conversion of energy through electromagnetic coupling. In engineering use, cables exist in large numbers. In recent years, industrial development requires power devices to have the characteristics of high efficiency, high reliability, and high performance. Then it is bound to require "high integration" and "high frequency" of electrical equipment. Cables as connectors must be placed in a small space and still need to transmit extremely fast power or signals, so the crosstalk of cables within the device is often not negligible. of.

Existing solutions to crosstalk caused by field-line coupling include directly solving Maxwell's equations or their equivalent second-order equations, and specific mainstream methods include time-domain finite difference method, finite element method, and moment-of-moment method. The time-domain finite difference method is to approximate the first-order partial differential quotient of time and space with the central difference quotient of the field quantity, and to obtain the field distribution by recursively simulating the time-domain propagation process of the wave. The finite element method is to transform the given Laplace equation solution problem into the extreme value problem of solving the functional. The method of moments is a method for solving linear differential equations, which discretizes continuous equations into algebraic equations, and solves them with matrix changes as its mathematical basis.

At present, the research on cable crosstalk has become a system, and the electromagnetic mechanism and worst state of cable crosstalk have been deeply studied. However, most of the researches take cable bundles with ideal spatial layout (straight arrangement) as the research object, and there are a large number of unconventional layout cable bundles in practical projects. In conclusion, there is a lack of research on non-parallel cables. In addition, the Chinese invention patent (CN104007326A) discloses a "method for rapidly predicting the dynamic characteristics of vehicle wire harness crosstalk in frequency domain", which can realize rapid prediction of the dynamic characteristics of vehicle cable crosstalk in frequency domain, but the patented technology cannot Prediction of crosstalk in non-parallel cables.

SUMMARY OF THE INVENTION

Purpose of the Invention: The purpose of the present invention is to provide a method for predicting crosstalk noise between non-parallel cables.

Technical solution: The crosstalk noise prediction method for non-parallel cables of the present invention includes the following steps:

Step 1: Obtain the spatial position parameters between non-parallel cables;

The second step: establish a multi-conductor model of unit length, and list the impedance matrix Z and admittance matrix Y of the corresponding unit length of the cable. The analytical formula for the basic electromagnetic matrix of the cable, combined with the theory of multi-conductor transmission lines, proxy space parameters, deduce Analytical formula of basic electromagnetic matrix elements of cables;

The third step: the non-parallel multi-conductor crosstalk prediction method based on the segmented cascade, using the analogy method, differentiate the non-parallel cables, that is, segmented cascade, and use the non-parallel electromagnetic parameter matrix to be equivalent to the parallel electromagnetic parameter matrix. , solve the electromagnetic equivalent matrix;

Step 4: Combine the boundary condition matrix to solve the non-parallel cable crosstalk.

Wherein, the spatial location parameters in the first step include tilt angle, near-end distance, far-end distance, cable length, and ground clearance.

In the second step, the analytical formulas of the impedance matrix Z and the admittance matrix Y are:

Among them, R is the resistance matrix, L is the inductance matrix, G is the conductance matrix, C is the capacitance matrix, ω=2πf, f is the frequency, and R, L, G, and C are the basic parameter matrices of the cable. The G matrix is very small and is generally ignored directly. When the R, L, and C matrices are calculated, the Z and Y matrices can also be solved.

The element calculation formula of the resistance matrix R is:

Formula (2) is divided into two parts according to the relationship between the radius of the solid core wire and the skin depth, where σ is the electrical conductivity of the wire core conductor, rw is the radius of the solid core circular conductor, and δ is the skin depth; , which can be considered as a parallel connection of multiple solid core wires with a radius of rws (rws is the radius of one wire core).

The element calculation formula of the inductance matrix L is:

Among them, h _i and h _j are the heights of the cables from the ground, and s _ij is the actual distance between the two cables;

s _ij =b+z·tan(a)

Among them, a is the intersection angle of cables, b is the minimum distance between cables, and z is the lateral distance.

The third step is to substitute the electromagnetic matrix elements obtained in the second step into the analytical expressions of the resistance matrix R and the inductance matrix L, wherein the analytical expressions of the resistance matrix R and the inductance matrix L are:

After obtaining the inductance matrix L, substitute it into the analytical formula of the capacitance matrix C:

C=μεL ^-1 (6)

Among them, ε is the dielectric constant, μ is the permeability coefficient;

Substitute the obtained resistance matrix R, inductance matrix L and capacitance matrix C into the analytical formulas of impedance matrix Z and admittance matrix Y in the second step, to obtain Z and Y, by first integrating the distance z, and then dividing by the total length d, find the electromagnetic equivalent matrix Z _d and Y _d , as follows:

Among them, z is the lateral distance, and d is the cable length.

The fourth step is specifically:

Solving the first-order differential equations from equation (1), we get:

According to formula (8), the electromagnetic matrix equivalent to the parallel cable is solved;

List the boundary condition equations:

和

为传输线两端z＝0和z＝d的戴维南等效电压源，同时

为非平行线缆远端串扰矩阵；该式显示了端口的戴维南等效，线缆两端的端口连接的各种电路都可以等效为电源和内电阻的形式，从而简化分析过程，in,

and

is the Thevenin equivalent voltage source with z=0 and z=d at both ends of the transmission line, while

is the non-parallel cable far-end crosstalk matrix; this formula shows the Thevenin equivalent of the port, and various circuits connected to the ports at both ends of the cable can be equivalent to the form of power supply and internal resistance, thus simplifying the analysis process,

Combining the equivalent electromagnetic parameter matrix with the second-order method of moments to solve the crosstalk of parallel cables, the equations (8) and (9) are used to obtain:

where d is the cable length, e is a natural constant, γ is a diagonal matrix, and its diagonal elements are the eigenvalues of the matrix (YZ), and P is a matrix composed of the eigenvectors corresponding to the eigenvalues of the matrix (YZ);

According to formula (10), formula (11), formula (12) and formula (13), the crosstalk matrix is obtained by solving in sequence

Beneficial effects: Compared with the prior art, the advantages of the present invention are: firstly, the present invention establishes a non-parallel cable model based on segmented cascade, and proposes an equivalent electromagnetic parameter matrix, which uses the non-parallel electromagnetic parameter matrix as The parameters of parallel cables are equivalent, so as to solve the problem of predicting the crosstalk of non-parallel wire bundles; secondly, by predicting the magnitude of electromagnetic crosstalk and the actual degree of harm, it has important theoretical and engineering significance for the efficient operation of electrical equipment. In the early stage of design, it can quickly predict and discover potential crosstalk problems and prevent them from happening. At the same time, as the basis for designing crosstalk suppression measures, it can also be used to implement crosstalk suppression remedial measures in the testing stage after the electrical equipment is fabricated. Provide theoretical basis to improve the stability of the equipment system.

Description of drawings

FIG. 1 is a schematic diagram of obtaining spatial position parameters between non-parallel cables;

Figure 2 is a schematic diagram of a parallel cable crosstalk analysis model;

3 is a schematic diagram of a non-parallel cable segment cascade model;

FIG. 4 is a schematic diagram of boundary conditions of cable crosstalk.

Detailed ways

The technical solution of the invention will be further described below with reference to the accompanying drawings.

A method for predicting crosstalk noise for non-parallel cables, comprising the following steps:

The first step: As shown in Figure 1, use the position sensor to obtain the spatial position information between the cables, including the inclination angle, the near-end distance, the far-end distance, the cable length, and the height above the ground. The specific sensor model depends on the predicted cable type, which is not described in detail in the present invention, but only needs to be able to measure the relevant spatial parameters;

The second step: establish a multi-conductor model of unit length, and list the impedance matrix Z and admittance matrix Y of the corresponding unit length of the cable. The analytical formula for the basic electromagnetic matrix of the cable, combined with the theory of multi-conductor transmission lines, proxy space parameters, deduce The basic electromagnetic matrix element analytical formula of the cable; on the basis of satisfying the engineering accuracy, the electromagnetic matrix of each section can be solved by the analytical expression. In the parallel cable crosstalk model shown in Figure 2, r _ii and r _jj represent the resistance per unit length of the cable, l _ii and l _jj represent the self-inductance per unit length of the cable, and l _ij represent the mutual inductance between the cables per unit length ; c _ii , c _jj and g _ii , g _jj represent the self-capacitance and self-conductance per unit length of the cable, respectively, and c _ij and g _ij represent the corresponding mutual capacitance and mutual conductance. Z represents the total length of the cable spanning, dz represents the differential length of the MTLs in this section, and the corresponding voltage and current phasors of each cable are also output.

The analytical formulas of the impedance matrix Z and the admittance matrix Y are:

Among them, R is the resistance matrix, L is the inductance matrix, G is the conductance matrix, C is the capacitance matrix, ω=2πf, f is the frequency, and R, L, G, and C are the basic parameter matrices of the cable. The G matrix is very small and is generally ignored directly. When the R, L, and C matrices are calculated, the Z and Y matrices can also be solved.

The element calculation formula of the resistance matrix R is:

Formula (2) is divided into two parts according to the relationship between the radius of the solid core wire and the skin depth, where σ is the electrical conductivity of the wire core conductor, rw is the radius of the solid core circular conductor, and δ is the skin depth; , which can be considered as a parallel connection of multiple solid core wires with a radius of rws (rws is the radius of one wire core).

The element calculation formula of the inductance matrix L is:

Among them, h _i and h _j are the heights of the cables from the ground, and s _ij is the actual distance between the two cables;

s _ij =b+z·tan(a)

Among them, a is the intersection angle of cables, b is the minimum distance between cables, and z is the lateral distance

The third step: the non-parallel multi-conductor crosstalk prediction method based on the segmented cascade, using the analogy method, differentiate the non-parallel cables, that is, segmented cascade, and use the non-parallel electromagnetic parameter matrix to be equivalent to the parallel electromagnetic parameter matrix. , solve the electromagnetic equivalent matrix; as shown in Figure 3, cut the cable into m parts. If the value of m is infinite, then each section of the conductors can be parallel to each other. It can be seen that the equation of the parallel multi-conductor transmission line for each segment is still valid.

Substitute the electromagnetic matrix elements obtained in the second step into the analytical expressions of the resistance matrix R and the inductance matrix L, where the analytical expressions of the resistance matrix R and the inductance matrix L are:

After obtaining the inductance matrix L, substitute it into the analytical formula of the capacitance matrix C:

C=μεL ^-1 (6)

Among them, ε is the dielectric constant, μ is the permeability coefficient;

Substitute the obtained resistance matrix R, inductance matrix L and capacitance matrix C into the analytical formulas of impedance matrix Z and admittance matrix Y in the second step, to obtain Z and Y, by first integrating the distance z, and then dividing by the total length d, find the electromagnetic equivalent matrix Z _d and Y _d , as follows:

where z is the lateral distance and d is the cable length

Step 4: Combine the boundary condition matrix to solve the non-parallel cable crosstalk.

Solving the first-order differential equations from equation (1), we get:

According to formula (8), the electromagnetic matrix equivalent to the parallel cable is solved;

According to the boundary condition matrix shown in Figure 4, the boundary condition equations are listed:

和

为传输线两端z＝0和z＝d的戴维南等效电压源，同时

为非平行线缆远端串扰矩阵；该式显示了端口的戴维南等效，线缆两端的端口连接的各种电路都可以等效为电源和内电阻的形式，从而简化分析过程，in,

and

is the Thevenin equivalent voltage source with z=0 and z=d at both ends of the transmission line, while

is the non-parallel cable far-end crosstalk matrix; this formula shows the Thevenin equivalent of the port, and various circuits connected to the ports at both ends of the cable can be equivalent to the form of power supply and internal resistance, thus simplifying the analysis process,

Combining the equivalent electromagnetic parameter matrix with the second-order method of moments to solve the crosstalk of parallel cables, the equations (8) and (9) are used to obtain:

where d is the cable length, e is a natural constant, γ is a diagonal matrix, and its diagonal elements are the eigenvalues of the matrix (YZ), and P is a matrix composed of the eigenvectors corresponding to the eigenvalues of the matrix (YZ);

According to formula (10), formula (11), formula (12) and formula (13), the crosstalk matrix is obtained by solving in sequence

Claims (1)

1. A method for predicting crosstalk noise for non-parallel cables, characterized by comprising the following steps: Step 1: Obtain the spatial position parameters between non-parallel cables; The second step: establish a multi-conductor model of unit length, and list the analytical formula of the impedance matrix Z and admittance matrix Y of the corresponding unit length of the cable about the basic electromagnetic matrix of the cable, and deduce the analytical formula of the basic electromagnetic matrix element of the cable; The third step: the non-parallel electromagnetic parameter matrix is equivalent to the parallel electromagnetic parameter matrix, and the electromagnetic equivalent matrix is solved; Step 4: Combine the boundary condition matrix to solve the non-parallel cable crosstalk; In the first step, the spatial position parameters include the inclination angle, the near-end distance, the far-end distance, the cable length and the height above the ground; In the second step, the analytical formulas of the impedance matrix Z and the admittance matrix Y are:

Among them, R is the resistance matrix, L is the inductance matrix, G is the conductance matrix, C is the capacitance matrix, ω=2πf, and f is the frequency; The element calculation formula of the resistance matrix R is:

Among them, σ is the electrical conductivity of the wire core conductor, r _w is the radius of the solid core circular conductor, and δ is the skin depth; The element calculation formula of the inductance matrix L is:

Among them, h _i and h _j are the heights of the cables from the ground, and s _ij is the actual distance between the two cables; s _ij =b+z·tan(a) Among them, a is the intersection angle of cables, b is the minimum distance between cables, and z is the lateral distance; The third step is to substitute the electromagnetic matrix elements obtained in the second step into the analytical expressions of the resistance matrix R and the inductance matrix L, wherein the analytical expressions of the resistance matrix R and the inductance matrix L are:

After obtaining the inductance matrix L, substitute it into the analytical formula of the capacitance matrix C: C=μεL ^-1 (6) Among them, ε is the dielectric constant, μ is the permeability coefficient; Substitute the obtained resistance matrix R, inductance matrix L and capacitance matrix C into the analytical formulas of impedance matrix Z and admittance matrix Y in the second step, obtain Z and Y, and then obtain electromagnetic equivalent matrix Z _d and Y _d , as follows:

Among them, z is the lateral distance, d is the cable length; The fourth step is specifically: Solving the first-order differential equations from equation (1), we get:

According to formula (8), the electromagnetic matrix equivalent to the parallel cable is solved; List the boundary condition equations:

in,

and

is the Thevenin equivalent voltage source with z=0 and z=d at both ends of the transmission line, while

is the non-parallel cable far-end crosstalk matrix; Combining the equivalent electromagnetic parameter matrix with the second-order method of moments to solve the crosstalk of parallel cables, the equations (8) and (9) are used to obtain:

where d is the cable length, e is a natural constant, γ is a diagonal matrix, and its diagonal elements are the eigenvalues of the matrix (YZ), and P is a matrix composed of the eigenvectors corresponding to the eigenvalues of the matrix (YZ);

According to formula (10), formula (11), formula (12) and formula (13), the crosstalk matrix is obtained by solving in sequence

Images