Analysis of twisted pair coupling lightning electromagnetic impulse

Abstract

For the problem of twisted pair coupling lightning electromagnetic impulse, using a combination of test and theory, established a experimental model of twisted pair coupled lightning electromagnetic impulse, get the twisted pair coupling lightning electromagnetic impulse voltage and spectrum characteristics, test results: (1) The situation of twisted pair link matching resistance (100 $\Omega$ ): the coupling voltage increases with the addition of the impulse current; Meanwhile, there is not much impact when increase the height of the coupling voltage. (2) The situation of twisted pair link ground electric resistance: the coupling voltage was positively correlated with the ground electric resistance value in the same height; The coupling voltage increases with increasing height when the resistance value remains the same. (3) Spectral characteristics of the coupling voltage: The frequencies are mainly concentrated around the two frequencies of 8 kHz and 2.3 MHz and the magnitude of the coupling voltage is proportional to the ground electric resistance and the impulse current. The experimental results are in good agreement with the theoretical analysis. The results have some guiding significance.

Keywords

Twisted pair coupling lightning electromagnetic impulse frequency spectrum

1. Introduction

Lightning electromagnetic impulse is a kind of electromagnetic radiation associated with the lightning discharge and a wide frequency range and large energy [1, 2, 3]. It invasive lines by induction and coupling, causing great harm to nearby electronic equipment. In recent years, with the improvement of people’s living standards and use of electronic devices more and more widespread, damage caused by lightning more serious, 80% of which is caused by lightning electromagnetic impulse. Twisted pair is the most commonly used transmission medium for integrated wiring engineering. It is an important part of the telecommunications system used to carry the information signal, along with the provisions of the twisted-pair routing from one point to another point. They all occupy an important place in daily life. So the study of the two is very necessary [4].

Many scholars have done a lot of research work on the lightning electromagnetic coupling. Li et al. obtained different circumstances that study from a variety of cables through the transmission cable coupled with the lightning electromagnetic pulse to do a lot of research [5, 6, 7]. Agrawal et al. research found that the assumptions made in the derivation of the transmission-line equations and the boundary conditions at the terminations are discussed. For numerical calculations, the transmission-line equations are represented by finite-difference techniques, and numerical examples are included [8]. Boumaiza and Labed study the coupling of a lightning wave with an overhead power distribution lines. By the classic method poses a problem of digital heaviness linked to the spatial discretization and taking into account the electrical conditions at the ends of nodes and connections [9]. Rizk comprises the first systematic investigation into the factors that render ultra-high voltage and double-circuit extremely high voltage transmission lines more vulnerable to direct lightning strikes by shielding failure and addresses the effects of the upward connecting leader onset of conductor proximity, ground field due to cloud charges prior to negative leader descent, positive space-charge generation at ground wires, as well as the operating voltage during the positive half cycle [10]. which has important guiding significance for study twisted pair coupling lightning electromagnetic impulse.

Most of the above researchers calculated the pattern in the coupling of transmission lines through simulation models, however, it lacks of experimental results. On the physical conditions, there are differences between the cable coupling on lightning electromagnetic fields and the theoretical model. Especially in the near field, the cable coupling would not be the standard plane wave excitation source for the most of time. In this paper, we analysis the coupling characteristic by scale model discussed, obtain that: (1) the coupling voltage increases with the addition of the impulse current; Meanwhile, there is not much impact when increase the height of the coupling voltage. (2) The situation of twisted pair link ground electric resistance: the coupling voltage increases with increasing height when the resistance value remains the same. (3) Spectral characteristics of the coupling voltage: The frequencies are mainly concentrated around the two frequencies of 8 kHz and 2.3 MHz and the magnitude of the coupling voltage is proportional to the ground electric resistance and the impulse current.

Figure 1.

Multi-conductor transmission line.

2. Analysis of theoretical

Consider a multi-conductor transmission line consisting of uniform conductors parallel to the z-axis, as illustrated in Fig. 1. We may draw a rectangular region $S_{i}$ bounded by $L_{i}$ between the reference conductor and conductor $i$ . It follows from Maxwell equations and Stokes theorem that

$\displaystyle\mathop{\int}\limits_{S_{i}}\nabla\times E\cdot u_{n}dS=\mathop{% \int}\limits_{L_{i}}E\cdot u_{l}dl=-\frac{\partial}{\partial t}\mathop{\int}% \limits_{S_{i}}B\cdot u_{n}ds$ (1)

Where $u_{l}$ is the unit tangent vector along $L_{i}$ in the anti-clockwise direction, and $u_{b}$ is the unit vector pointing out of the page. The above equation can be written as

$\displaystyle\mathop{\int}\limits_{ab}E\cdot u_{l}dl+\mathop{\int}\limits_{bc}% E\cdot u_{l}dl+\mathop{\int}\limits_{cd}E\cdot u_{l}dl+\mathop{\int}\limits_{% da}E\cdot u_{l}dl=-\frac{\partial}{\partial t}\mathop{\int}\limits_{S_{i}}B% \cdot u_{b}dS,(i=1,2,\cdot\cdot\cdot,n)$ (2)

The total field may be decomposed as the sum of the incident field and the scattered field

$\displaystyle E=E_{in}+E_{s},B=B_{in}+B_{s}.$

The scattered field $E_{s}$ is generated by the induced currents and charges on the line conductors. If we assume that the currents on the line conductors are $z$ -directed, the scattered magnetic field $B_{s}$ will be transverse to the $z$ -direction. As a result, a voltage corresponding to the scattered field may be uniquely defined between the conductor $i$ and the reference conductor

$\displaystyle V_{si}(z,t)=-\mathop{\int}\limits_{ad}E_{s}\cdot u_{l}dl,V_{si}(% z+\Delta z,t)=-\mathop{\int}\limits_{bc}E_{s}\cdot u_{l}dl.$ (3)

Figure 2.

Cross-section of multi-conductor transmission line.

Referring to Fig. 2, the current on $i$ th conductor is defined by the line integral of surface current $J_{s}=u_{n}\times H$ as follows

$\displaystyle I_{i}(z,t)=\mathop{\int}\limits_{\Gamma_{i}}J_{s}\cdot u_{z}d% \Gamma=\mathop{\int}\limits_{\Gamma_{i}}H\cdot u_{\Gamma}d\Gamma.$ (4)

Where $\Gamma_{i}$ is the boundary of $i$ th conductor. Since the scattered magnetic field is transverse it may be written as

$\displaystyle\mathop{\lim}\limits_{z\to 0}\frac{1}{\Delta z}\mathop{\int}% \limits_{S_{i}}B_{S}\cdot u_{b}ds=-\mathop{\sum}\limits_{j=1}^{n}l_{ij}I_{j}(z% ,t)$ (5)

Where $l_{ij}(j=1,2,\cdots,n)$ are inductances per unit length. The electric resistance per unit length $r_{i}$ on the lines is defined by

$\displaystyle\mathop{\int}\limits_{ba}E\cdot u_{l}dl=r_{0}\Delta z\sum\limits_% {j=1}^{n}{I_{j}(z,t)},\mathop{\int}\limits_{dc}E\cdot u_{l}dl=r_{i}\Delta zI_{% i}(z,t)$ (6)

Substituting Eqs (3), (5) and (6) into Eq. (2), we obtain

$\displaystyle\mathop{\sum}\limits_{j=1}^{n}r_{0}I_{j}(z,t)+r_{i}I_{i}(z,t)+% \frac{V_{st}(z+\Delta z,t)}{\Delta z}+\mathop{\sum}\limits_{j=1}^{n}l_{ij}% \frac{\partial}{\partial t}I_{j}(z,t)$ $\displaystyle\quad=\frac{1}{\Delta z}\frac{\partial}{\partial t}\mathop{\int}% \limits_{S_{i}}B_{in}\cdot u_{b}dS+\frac{1}{\Delta z}\mathop{\int}\limits_{bc}% E_{in}\cdot u_{l}dl+\frac{1}{\Delta z}\mathop{\int}\limits_{da}E_{in}\cdot u_{% l}dl,$ (7) $\displaystyle i=1,2,\cdot\cdot\cdot,n.$

As $\Delta z\to 0$ , this becomes

$\displaystyle\frac{\partial}{\partial z}V_{si}(z,t)+\mathop{\sum}\limits_{j=1}% ^{n}r_{0}I_{j}(z,t)+\frac{\partial}{\partial z}\mathop{\sum}\limits_{j=1}^{n}l% _{ij}I_{j}(z,t)$ $\displaystyle\quad=\frac{\partial}{\partial t}\mathop{\int}\limits_{ad}B_{in}% \cdot u_{b}dl+\frac{\partial}{\partial z}\mathop{\int}\limits_{ad}B_{in}\cdot u% _{l}dl,$ (8) $\displaystyle i=1,2,\cdot\cdot\cdot,n.$

Note that Eq. (2) also holds for the incident fields

$\displaystyle\mathop{\int}\limits_{ab}E_{in}\cdot u_{l}dl+\mathop{\int}\limits% _{bc}E_{in}\cdot u_{l}dl+\mathop{\int}\limits_{cd}E_{in}\cdot u_{l}dl+\mathop{% \int}\limits_{da}E_{in}\cdot u_{l}dl=-\frac{\partial}{\partial t}\mathop{\int}% \limits_{S_{i}}B_{in}\cdot u_{b}dS$ (9)

which yields

$\displaystyle-\frac{\partial}{\partial t}\mathop{\int}\limits_{S_{i}}B_{in}% \cdot u_{b}dS-\mathop{\int}\limits_{bc}E_{in}\cdot u_{l}dl-\mathop{\int}% \limits_{da}E_{in}\cdot u_{l}dl$ (10) $\displaystyle\quad=-\Delta zE_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{% conductor i}}+E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor 0}}$

As $\Delta z\to 0$ , Eq. (2) becomes

$\displaystyle\frac{\partial}{\partial t}\mathop{\int}\limits_{ad}B_{in}\cdot u% _{b}dl+\frac{\partial}{\partial z}\mathop{\int}\limits_{ad}E_{in}\cdot u_{l}dl$ (11) $\displaystyle\quad=E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor i}}% -E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor 0}}$

Thus Eq. (2) can be rewritten as

$\displaystyle\frac{\partial}{\partial z}V_{si}(z,t)+\mathop{\sum}\limits_{j=1}% ^{n}r_{0}I_{j}(z,t)+\frac{\partial}{\partial z}\mathop{\sum}\limits_{j=1}^{n}l% _{ij}I_{j}(z,t)$ $\displaystyle\quad=E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor i}}% -E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor 0}},$ (12) $\displaystyle i=1,2,\cdot\cdot\cdot,n.$

The above equation can be written in matrix form as

$\displaystyle\frac{\partial}{\partial z}\left[{V_{S}}\right]+\left[R\right]% \left[I\right]+\left[L\right]\frac{\partial}{\partial t}\left[I\right]=\left[{% \Delta E_{in}\cdot u_{z}}\right]$ (13)

Where

$\displaystyle\left[{V_{s}}\right]=\left[{V_{s1},V_{s2},\cdot\cdot\cdot,V_{sn}}% \right]^{T},\left[I\right]=\left[{I_{1},I_{2},\cdot\cdot\cdot,I_{n}}\right]^{T},$ $\displaystyle\left[{\Delta E_{in}\cdot u_{z}}\right]=\left[{\begin{array}[]{c}% E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor 1}}-E_{in}(z,t)\cdot% \left.{u_{z}}\right|_{\textit{conductor 0}}\\ E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor 2}}-E_{in}(z,t)\cdot% \left.{u_{z}}\right|_{\textit{conductor 0}}\\ \vdots\\ E_{in}(z,t)\cdot\left.{u_{z}}\right|_{\textit{conductor n}}-E_{in}(z,t)\cdot% \left.{u_{z}}\right|_{\textit{conductor 0}}\\ \end{array}}\right]$ (14) $\displaystyle\left[R\right]=\left[{{\begin{array}[]{*{20}c}{r_{0}+r_{1}}&{r_{0% }}&\cdots&{r_{0}}\\ {r_{0}}&{r_{0}+r_{2}}&\cdots&{r_{0}}\\ \vdots&\vdots&\ddots&\vdots\\ {r_{0}}&{r_{0}}&\cdots&{r_{0}+r_{n}}\\ \end{array}}}\right],\left[L\right]=\left[{{\begin{array}[]{*{20}c}{l_{11}}&{l% _{12}}&\cdots&{l_{1n}}\\ {l_{21}}&{l_{22}}&\cdots&{l_{2n}}\\ \vdots&\vdots&\ddots&\vdots\\ {l_{n1}}&{l_{n1}}&\cdots&{l_{nn}}\\ \end{array}}}\right].$

We now enclose the $i$ th conductor with a cylinder of length $\Delta z$ , as illustrated in Fig. 3.

Figure 3.

Multi-conductor transmission line.

The side surface of the $i$ th cylinder is denoted by $S_{\rho i}$ and the two ends are denoted by $S_{zi}$ . It follows from the continuity equation that

$\displaystyle\int\limits_{S_{pi}+S_{zi}}{J\cdot u_{n}}ds=-\frac{\partial Q_{i}% }{\partial t},i=1,2,\cdots n.$ (15)

where $u_{n}$ is the unit outward normal of the cylinder, and $Q_{i}$ is the net charge contained in the cylinder. Evidently, we have

$\displaystyle\int\limits_{S_{zi}}{J\cdot u_{n}}ds=I_{i}(z+\Delta z,t)-I_{i}(z,t)$ (16)

Figure 4.

Cross-section of multi-conductor transmission line.

The transverse conduction current $I_{ti}(z,t)$ between the $i$ th conductor and all other conductors is given by

$\displaystyle I_{ti}(z,t)=\mathop{\lim}\limits_{\Delta z\to 0}\frac{1}{\Delta z% }\int\limits_{S_{\rho i}}{J\cdot u_{n}}ds=g_{i1}(V_{si}-V_{s1})+\cdots+g_{ii}V% _{si}+\cdots+g_{in}(V_{si}-V_{sn})=-g_{i1}V_{s1}-\cdots+V_{si}\sum\limits_{j=1% }^{n}{g_{ij}}-\cdots-g_{in}V_{sn}.$ (17)

where $g_{ti}$ is the conductance per unit length between $i$ th conductor line and $j$ th conductor line. The net charge per unit length can be expressed as

$\displaystyle\mathop{\lim}\limits_{\Delta z\to 0}\frac{Q_{i}}{\Delta z}=c_{i1}% (V_{si}-V_{s1})+\cdots+c_{ii}V_{si}+\cdots+c_{in}(V_{si}-V_{sn})=-c_{i1}V_{s1}% -\cdots+V_{si}\sum\limits_{j=1}^{n}{c_{ij}}-\cdots-c_{in}V_{sn}.$ (18)

Substituting Eqs (16)–(18) into Eq. (15) yields

$\displaystyle\frac{\partial}{\partial z}I_{i}(z,t)-g_{i1}V_{s1}(z,t)-\cdots+V_% {si}(z,t)\sum\limits_{j=1}^{n}{g_{ij}}-\cdots-g_{in}V_{sn}(z,t)$ (19) $\displaystyle\quad+\frac{\partial}{\partial t}\left[{-c_{i1}V_{s1}(z,t)-\cdots% +V_{si}(z,t)\sum\limits_{j=1}^{n}{c_{ij}}-\cdots-c_{in}V_{sn}(z,t)}\right],i=1% ,2,\cdots,n.$

This can be written in matrix form as

$\displaystyle\frac{\partial}{\partial z}\left[I\right]+\left[G\right]\left[{V_% {s}}\right]+\left[C\right]\frac{\partial}{\partial t}\left[{V_{s}}\right]=0,$ (20)

Where

$\displaystyle\left[G\right]=\left[{{\begin{array}[]{*{20}c}{\sum\limits_{j=1}^% {n}{g_{1j}}}&{-g_{12}}&\cdots&{-g_{1n}}\\ {-g_{21}}&{\sum\limits_{j=1}^{n}{g_{2j}}}&\cdots&{-g_{2n}}\\ \vdots&\vdots&\ddots&\vdots\\ {-g_{n1}}&{-g_{n1}}&\cdots&{\sum\limits_{j=1}^{n}{g_{nj}}}\\ \end{array}}}\right],\left[C\right]=\left[{{\begin{array}[]{*{20}c}{\sum% \limits_{j=1}^{n}{c_{1j}}}&{-c_{12}}&\cdots&{-c_{1n}}\\ {-c_{21}}&{\sum\limits_{j=1}^{n}{c_{2j}}}&\cdots&{-c_{2n}}\\ \vdots&\vdots&\ddots&\vdots\\ {-c_{n1}}&{-c_{n1}}&\cdots&{\sum\limits_{j=1}^{n}{c_{nj}}}\\ \end{array}}}\right],$ (21)

The multi-conductor transmission line (Fig. 4) is characterized by Eqs (13) and (20), which are summarized below

$\displaystyle\frac{\partial}{\partial z}\left[{V_{S}}\right]+\left[R\right]% \left[I\right]+\left[L\right]\frac{\partial}{\partial t}\left[I\right]=\left[{% E_{in}\cdot u_{z}}\right],$ (22) $\displaystyle\frac{\partial}{\partial z}\left[I\right]+\left[G\right]\left[{V_% {s}}\right]+\left[C\right]\frac{\partial}{\partial t}\left[{V_{s}}\right]=0.$

These are a set of 2 $n$ first-order partial differential equations, which are coupled by electric resistance matrix [R], conductance matrix [G], inductance matrix [L], and the capacitance matrix [C]. All these matrices consist of parameters per unit length. The scattered voltages can be replaced by the total voltages through the relation

$\displaystyle V_{i}(z,t)=V_{si}-\int\limits_{ad}{E_{in}\cdot\left.{u_{l}}% \right|_{\textit{conductor i}}}.$ (23)

Figure 5.

Experimental model.

Figure 6.

(a) Twisted pair any two lines link 100 $\Omega$ resistor coupling voltage; (b) Twisted pair any two lines link 100 $\Omega$ resistor coupling voltage waveform.

Figure 7.

(a) coupling voltage of different electric resistance at 1 m; (b) coupling voltage of different electric resistance at 2 m; (c) coupling voltage of different electric resistance at 3 m.

Figure 8.

(a) the different height correspond the coupling voltage when 100 $\Omega$ electric resistance; (b) the different height correspond the coupling voltage when 1 k $\Omega$ electric resistance; (c) the different height correspond the coupling voltage when 10 k $\Omega$ electric resistance.

Substituting this into Eq. (2) gives

$\displaystyle\frac{\partial}{\partial z}\left[V\right]+\left[R\right]\left[I% \right]+\left[L\right]\frac{\partial}{\partial t}\left[I\right]=\left[{E_{in}% \cdot u_{z}}\right]+\frac{\partial}{\partial z}\left[{V_{in}}\right],$ (24) $\displaystyle\frac{\partial}{\partial z}\left[I\right]+\left[G\right]\left[V% \right]+\left[C\right]\frac{\partial}{\partial t}\left[V\right]=\left[G\right]% \left[{V_{in}}\right]+\left[C\right]\frac{\partial}{\partial t}\left[{V_{in}}% \right].$

where

$\displaystyle\left[V\right]=\left[{V_{1},V_{2},\cdots,V_{n}}\right]^{T},$ $\displaystyle\left[{V_{in}}\right]=\left[{-\int\limits_{ad}E_{in}\cdot\left.{u% _{l}dl}\right|_{\textit{conductor 1}},-\int\limits_{ad}E_{in}\cdot\left.{u_{l}% dl}\right|_{\textit{conductor 2}},\cdots,-\int\limits_{ad}{E_{in}\cdot\left.{u% _{l}dl}\right|_{\textit{conductor n}}}}\right]^{T}.$

3. Experimental model and data results and analysis

3.1 Experimental model establishment

In order to test the characteristics of twisted pairs coupling lightning electromagnetic waves, the experiment uses the impulse current generator (ICG) to simulate 8/20 $\mu$ s lightning current. The simulated lightning wave is applied to a transmission line that Hanging on a 24 meters high buildings. The transmission line functions as an antenna that simulated lightning channel and emitted lightning electromagnetic impulse [11, 12]. The experimental model is shown in Fig. 5. The object was composed of the twisted pair with matching electric resistance 100 $\Omega$ , height 1 m, 2 m, 3 m, ground electric resistance 100 $\Omega$ , 1 k $\Omega$ , 10 k $\Omega$ . Cable-cable connect 100 $\Omega$ , 1 k $\Omega$ , 10 k $\Omega$ . Then observe the coupling characteristics. The Tektronix TDS3012 digital storage oscilloscope is used to collect the voltage waveforms. Impact the line with 5–40 kV, the step length of 5 kA [13, 14, 15, 16].

3.2 Analysis of test data

Twisted-pair transmission line with different heights is coupled lightning radiated electromagnetic pulse with different impulse currents. It will be described below [17, 18, 19, 20].

3.2.1 Coupling voltage analysis

Analysis of Fig. 6a, when the cable-cable link 100 $\Omega$ (twisted pair characteristic impedance), the coupling voltage increases as the impulse current increases, but increasing the cable height (changing the ground area of the cable) does not have much impact on the coupling voltage. The straight line is obtained by fitting the three coupling voltage curves. According to the theory, change the height of the cable is actually to change the ground area of the cable, twisted pair connect electric resistance but not grounded. So the coupling voltage and cable height do not matter. Theory fits well with practice. From Fig. 6b can be seen the damped oscillatory waves which is the graph of cable coupled to the lightning electromagnetic impulse.

Figure 7a–c is the coupling voltage curve that obtained by the cable-ground link the different ground electric resistance when the same height. It can be seen that the coupling voltage has a positive correlation with the ground electric resistance at the same height. According to the theory, the reflection coefficient is positive correlation with that difference of the electric resistance value and the characteristic impedance, and vice versa. Theory fits well with practice.

Figure 8a–c shows the coupling voltage obtained by changing the cable height. Not other conditions are changed. By comparison, the height is proportional to the coupling voltage. It can be seen from the theory, the higher the cable height (the greater the area) coupled to the more electromagnetic waves. Theory fits well with practice.

Figure 9.

(a) The spectrogram of impulse current is 5 kA; (b) The spectrogram of impulse current is 20 kA; (c) The spectrogram of impulse current is 40 kA.

3.2.2 Spectrogram analysis

This experiment uses the FFT (Fast Fourier Transform) function in the origin software to convert the coupled voltage waveform data into a spectrogram. As shown in Fig. 9a–c, keep the other parameters unchanged, select the impulse current of 5 kA, 20 kA, 40 kA spectrogram analysis. It was found that the coupling voltage was mainly concentrated at 8 kHz (the first peak) and 2.3 MHz (second peak) and the magnitude of the voltage is proportional to the magnitude of the impulse current. In addition, when the cable height constant and the ground electric resistance unchanged, the voltage amplitude is also a positive correlation with the impulse current, so the following will no longer repeat this.

As shown in Fig. 10a–c, keep the other parameters constant and analyze the spectrogram with the ground electric resistance of 100 $\Omega$ , 1 k $\Omega$ , 10 k $\Omega$ . By comparing Fig. 10a–c, with the same height of the twisted pair, analysis of the effect of changing the ground electric resistance on the coupling voltage and frequency. We can find out that the coupling voltage frequency is mainly concentrated in the 8 kHz (the first peak) and 2.3 MHz (second peak) and the voltage amplitude increases with the ground electric resistance increases.

Table 1
Peak-to-peak analysis

Impulse	Wire-to-wire connection			Wire-to-ground connection
current	electric resistance			electric resistance
(kA)	1 m	2 m	3 m	1 m			2 m			3 m
	100 $\Omega$	100 $\Omega$	100 $\Omega$	100 $\Omega$	1 k $\Omega$	10 k $\Omega$	100 $\Omega$	1 k $\Omega$	10 k $\Omega$	100 $\Omega$	1 k $\Omega$	10 k $\Omega$
5	17.2	13.2	14.4	29.8	92.0	112.0	22.4	97.0	120.0	29.6	102.0	124.0
10	26.0	19.6	20.4	37.0	142.0	186.0	40.0	166.0	208.0	45.6	166.0	208.0
15	36.0	34.0	32.4	56.8	194.0	276.0	57.6	224.0	284.0	60.0	244.0	300.0
20	43.6	39.2	40.4	62.5	234.0	328.0	61.6	274.0	264.0	94.6	292.0	368.0
25	50.8	46.8	46.8	73.0	288.0	400.0	76.8	336.0	416.0	110.4	366.0	468.0
30	60.0	51.6	51.6	89.0	332.0	456.0	96.0	380.0	476.0	128.0	420.0	504.0
35	60.4	50.8	59.6	96.8	352.0	516.0	134.0	316.0	512.0	142.2	440.0	540.0
40	67.2	56.0	66.0	135.2	380.0	556.0	154.0	432.0	544.0	164.8	472.0	424.0

Figure 10.

(a) The spectrogram of ground electric resistance is 100 $\Omega$ ; (b) The spectrogram of ground electric resistance is 1 k $\Omega$ ; (c) The spectrogram of ground electric resistance is 10 k $\Omega$ .

3.2.3 Coupling voltage peak-to-peak analysis

From Table 1: (1) Twisted pair link 100 $\Omega$ , the same height under the coupling voltage increases with the impact of the current increases, but the same impulse current, the height of the change between the peak and peak there is no significant law. (2) In the twisted pair and ground link a ground electric resistance: when the twisted pair height and the ground electric resistance unchanged, the peak and peak with the impulse current increases. when the other conditions are the same, cable-ground link electric resistance are positively correlated with the peak-to-peak and the height.

4. Conclusions

By analyzing the characteristics of twisted pair coupled lightning electromagnetic waves, it is found that:

The situation of twisted pair link matching resistance (100 $\Omega$ ): the coupling voltage increases with the addition of the impulse current; Meanwhile, there is not much impact when increase the height of the coupling voltage.

The situation of twisted pair link ground electric resistance: the coupling voltage was positively correlated with the ground electric resistance value in the same height; The coupling voltage increases with increasing height when the resistance value remains the same.

Spectral characteristics of the coupling voltage: The frequencies are mainly concentrated around the two frequencies of 8 kHz and 2.3 MHz and the magnitude of the coupling voltage is proportional to the ground electric resistance and the impulse current.

Coupling voltage peak-to-peak analysis: peak-to-peak is positively correlated with the resistance and the height. The experimental results are in good agreement with the theoretical analysis.

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20.

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