Research on Crosstalk Coupling of Trackside Cable in High Speed Railway

The signal and power supply of trackside equipment in Chin’s high-speed railway is usually placed in the trackside trunking to avoid the influence of external harassing signals on the cable. However, due to the different voltage levels of the cables in the trough, strong and weak current cables will produce crosstalk coupling problems, which will affect the quality of train communication and running efficiency, and even endanger the safety of train running. Therefore, it is necessary to accurately analyze the crosstalk coupling problem between the cables in the trough. In this paper, the crosstalk coupling model of trackside cable is established. The Green function method simplifies the trackside trunking model, the crosstalk coupling of the cable in the trackside trunking and the electromagnetic field distribution in the trackside trunking are analyzed by using the method of moments (MOM), and the results of theoretical calculation are verified by simulation experiments.


INTRODUCTION
There are many sources of disturbance and various coupling ways in the AC 25 kV urban railway system, which bring unpredictable electromagnetic disturbance to the signal system of the urban railway.Specifically, the axle-counting equipment and wireless communication system of the urban railway under the AC 25 kV traction system may not work properly due to harassment.The lowfrequency electromagnetic noise beside the track may interfere with the signal cables arranged beside the track in the way of crosstalk coupling.Different from the railway line that uses the track circuit as the inspection equipment of the occupied status of the track section, the urban railway mostly uses the axle meter installed beside the rail to record and compare the number of wheel shafts passing through the two axle points on the line to judge that the train occupies or clears the track section.The signal cable connecting the shaft meter will have a crosstalk coupling with the strong electric cable used for the power supply, which may affect the normal operation of the shaft meter and even endanger the safety of train operation.To ensure information transmission and power supply, the signal line and power supply line of trackside equipment of high-speed railway are placed in the U-shaped trunking beside the track.The influence of the external electromagnetic environment on the signal line is ensured, What's more, it reduces the induced electromotive force (EMF) on the line.However, due to the limitation of space, cables with different operating frequencies and voltage levels are inevitably placed in the same or adjacent trunking.The electromagnetic interference caused by the inter-line crosstalk in the trunking becomes one of the key problems affecting the good electromagnetic compatibility of trackside equipment.
A couple of researchers have conducted a lot of research on the inter-line crosstalk [1][2][3][4][5] .A variety of numerical calculation methods can be used to deal with cable crosstalk [6][7][8][9] .Kapora et al. used the transmission line method to study the induced current and voltage on the internal wires of the Ushaped conduit under plane wave excitation, but the influence of the boundary of the conduit was not considered enough.When there were multiple wires in the conduit, the calculation error of crosstalk coupling between them was large [10] .Tan et al. proposed an effective method to calculate periodic Green's function, but it can only solve the formula for the periodic Green's function in one and two dimensions, lacking the computation of periodic Green's function in three dimensional space [11] .Wu et al. proposed a method combining cylindrical Green's function to analyze and optimize antennas conformal with the MOM, but the analysis object was limited to line antennas, and the calculation time was long and the memory consumption was large [12] .
In addition, the rail side trough is mostly U-shaped, its structure is a three-sided metal trough structure, the upper end is open, and the cable is placed in it.In this complex structure, it is difficult to extract the distribution parameters by using the classical transmission line method.By using the MOM on the basis of free space Green's function, a simple cable model can be obtained, but the multiple scattering effects of the metal trunking wall on the electromagnetic wave in the wire trunking and the induced current on the metal trunking wall have a powerful influence on the cable in the wire trunking.In this paper, a coupling modeling method is on the basis of dyadic Green's function method and MOM is proposed for interline crosstalk in the rail side trunking.The influence of substituting Green's function for the U-shaped trunking metal boundary, the crosstalk coupling and electromagnetic field distribution of the U-shaped trunking are calculated by the MOM to accurately analyze the crosstalk coupling between the lines in the trunking, and according to the electromagnetic field distribution in the trunking, the suggestions for the wiring in the U-shaped trunking are put forward.

TRACKSIDE CABLE CROSSTALK COUPLING MODEL
The rail side cable model is shown in Figure 1.Two parallel cables are placed in the U-shaped wire trunking with the upper-end opening.The length, width and height of the metal trough are 1 m , a m and b m respectively.The distance between the interference line and the disturbed line from the side wall of the trough is 1 a m and 2 a m respectively, and the distance between the top of the trough is 1 b m and 2 b m respectively.The length of the cable is the same as that of the trough.If the commonmode disturbance exists interference line current, a common-mode disturbance current is induced in the adjacent signal line (the disturbed line). .U-shaped cavity and intra-cavity rail side cable model The analysis of cross-talk coupling of trackside cable consists of the following steps.Firstly, Green's function of the U-shaped trunking is derived according to the mirror method, and then Green's function is substituted into the electric field integral formula, excitation, and solved by using the MOM under the action of track side trunking of current distribution on the cable.Furthermore, the scattering field generated in the induced-current in-line trunking is solved to achieve the purpose of crosstalk analysis.Finally, the crosstalk analysis results obtained by electromagnetic numerical simulation software are compared with those obtained by the analytical formula method to verify the results.
The electric field near the cable is the sum of the incident electric field and the scattered electric field.The scattered electric field can be expressed as where A is the vector magnetic potential,  is the scalar electric potential, and their expressions are respectively: where  is the permeability of the cable,  is the dielectric constant of the medium around the cable, J is the cable surface current density,  is the cable surface charge density, A G and G  is Green's function.The boundary condition that the tangential total electric field is zero is satisfied on the surface of the cable conductor: where E i is the incident electric field.Then, the continuous expression of surface current density and surface charge density is correlated, The distribution of the current () J r' on the cable in the U-shaped trunking could be obtained by substituting the sum of Green's function corresponding A G and G  to trunking U into Formula (6).

Derivation of dyadic Green's function for U-shaped trunkings
Due to the waveguide structure formed by the metal wall of the U-shaped trunking, the calculation of crosstalk between lines at the boundary is more complicated.Therefore, by using Green's function of the U-shaped trunking to replace the influence of the metal wall of the U-shaped trunking, which greatly simplifies the calculation process of crosstalk between lines.In addition, in the boundary conditions of U-shaped trunkings, the same point source generates different fields in different directions, so dyadic Green's function can be used to study the distribution of electromagnetic fields in different directions.
The dyadic Green's function of the U-shaped trunking represents the relationship between the source and the field in the U-shaped trunking, while the trunking is a metal cavity composed of three sides of ideal conductive materials.To solve the dyadic Green's function of the U-shaped trunking, five mirror images of the current source in the cavity can be used to replace the effect of the three metal surfaces of the cavity by the mirror principle.The cavity field produced by a current source in the cavity can be expressed as a current source and its image field is generated by the sum, the mirror current is used to replace the influence of the metal wall, thus obtaining Green's function based on the mirror method.The calculated cell is shown in Figure 2.
where A qq K represents the direction of the unit current source or its mirror image, where a is the width of the waveguide cavity, m is the periodic coefficient in the direction Y .
x y z J J J 、 、 represents the distance from the source to the site in the mirror image in each region, which concrete numerical value, as shown in Table 2.
Table 1.Direction coefficient of unit current source and its mirror image The distance from the source to the site in the mirror image in each term

The coupling current of the cable in the trunking
The roof function is selected as the basis function, in addition to the Galerkin method is used to solve Formula (6), which defined as The current on the upper surface of the wire can be obtained by expanding by the MOM where f n is the basis function, M is the amount of unknown conductor surface currents.By substituting Formula ( 11) with Formula (6), we get The first term of ( 12) on the left could be where p l and q l are the length of each cable after the segment.The second term of Formula ( 12) on the left could be The integral formula of the electric field can be written as Applying a discrete voltage source to the cable can be equivalent to adding an external electric field between nodes p and q , according to the Figure 3.

Equivalence of discrete voltage sources
According to Formula (19), the average equivalent voltage point p and q of the voltage source S V are calculated, i.e. /2 . Finally, by solving the matrix, it is possible to get the current distribution on the cable in the U-shaped trunking.

Calculation of electromagnetic field distribution in U-shaped trunking
When the current distribution of the cable in the U-shaped trunking is known, the scattering electric field in the U-cavity can be calculated The first integral term is written as The integral of the second term with respect to the gradient is written as , and the U-shaped trunking is a covered rectangular waveguide structure with a length, width and height of 1 0.1 0.1


. A common-mode voltage source with an amplitude of 1V is set on the interference cable.The frequency is 100MHz , the distance between the interference line and the disturbed line is 0.04 m and 0.07 m from the side wall of the line trunking, and 0.06 m and 0.03m from the top of the line trunking The current distribution and electromagnetic field distribution of cables in U-shaped trunkings are studied in the following sections.

Coupling current of the cable in the U-shaped trunking
This section presents the current distribution results of the disturbed line and the disturbed line in the U-shaped trunking under the two algorithms.The current distribution results as shown in Figure 4.
the voltage source frequency is 100MHz , the distributed current of two lines in the wire trunking is shown in Figure 4.The current on the interference line in the U-shaped trunking as shown in Figure 4 (a).Compared with the traditional MOM calculation, the calculated surface current at both ends of are compared with commercial software.In other words, the electric field distribution inside the U-shaped trunking and at the opening of the U-shaped trunking are studied respectively.20 and 10 field observation points were selected along the X , Y directions on the Z -plane in the U cavity, and the electromagnetic field distribution at each observation point was calculated respectively.The comparison of results as follow in Figure 5.

EEICE-2023 Journal of Physics: Conference Series 2625 (2023) 012055
In Figure 5, the field diagram in the U-shaped trunking presents a symmetrical structure, and the positions with large electric field intensity are mainly concentrated near the cable model, and the change of electric field intensity shows an increasing trend from the center of the cable to both ends of the cable, and the calculation results of commercial software are consistent with the analytical formula.In Figure 6, the field distribution diagram at the opening of the U-cavity still presents a symmetrical structure, and the electric field intensity is still increasing from the center of cable to both ends of the cable, but the locations with large electric field intensity are scattered, the calculation results of commercial tools are consistent with those of the analytical formula, which proves that the above algorithm is effective in calculating the field distribution in the U-cavity.

CONCLUSIONS
In this paper, a coupling model of cable crosstalk in the U-shaped cavity is proposed, and the crosstalk coupling and electromagnetic field distribution of cable in the U-shaped cavity are calculated with the MOM.The results show that this method can accurately and effectively calculate and analyze the crosstalk coupling problem of cable in the U-shaped cavity, and provide a theoretical basis for better engineering routing schemes of rail side cables.

Figure 1
Figure 1.U-shaped cavity and intra-cavity rail side cable modelThe analysis of cross-talk coupling of trackside cable consists of the following steps.Firstly, Green's function of the U-shaped trunking is derived according to the mirror method, and then Green's function is substituted into the electric field integral formula, excitation, and solved by using the MOM under the action of track side trunking of current distribution on the cable.Furthermore, the scattering field generated in the induced-current in-line trunking is solved to achieve the purpose of

Figure 2 .
Figure 2. Cell calculated by waveguide Green function, source term (0) and its five image terms

Figure. 4
Figure. 4 Comparison results of common mode current on the wire in the U-shaped trunking 4.2 Electromagnetic field distribution in U-shaped trunking This section presents the comparison of results of electric field distribution on planes at different heights in the U-shaped trunking.The final results of electric field distribution at 0.05 m z  and

Figure. 5 Figure 6 .
Figure. 5 The distribution of the field in the U cavity )