Introduction

With the increasing development and high frequency of electrical and electronic equipment, as the important component of various equipment connections, the immunity to electromagnetic noise of cables is extremely essential for the stable operation of electrical system [1-3]. Generally, electromagnetic noise can be divided into electromagnetic noise on G-line and new electromagnetic noise on R-line coupled by the electromagnetic noise of G-line, the latter is called crosstalk [4-6]. Because of the serious influence of the far-end electromagnetic noise on the device, we focus on the electromagnetic noise of the far-end multi-conductor cables [7-10]. This paper studies the G-line and R-line electromagnetic noise transfer condition in different situations based on MTL theory.

The Model of Electromagnetic Noise (N+1) Transmission Line

For (n + 1) transmission line systems, "n" refers to wires that transmit electromagnetic energy; "1" refers to a ground reference line, such as the case in a multi-electric aircraft, the body of an electric car, etc. The model of (n+1) transmission lines is shown in Figure 1. The near-end and far-end voltage of G-line are, respectively, ÛG(0) and ÛG(l). K can be called the " transfer coefficient of G-line voltage", which means that the closer the value is to 1.0, the smaller the voltage transfer loss; ÛG(0)and ÛG(l)can be derived by FEKO, then the amplitude of K can be obtained.

$$K=\frac{{\stackrel{\wedge }{{\displaystyle U}}}_G(l)}{{\stackrel{\wedge }{{\displaystyle U}}}_G(0)}\text{ (1)}$$

H_FE(ω) is the ratio of ÛR(l) to ÛG(0) which is called "characteristic of far-end crosstalk".

$$H_{FE}(\omega )=\frac{{\stackrel{\wedge }{{\displaystyle U}}}_R(l)}{{\stackrel{\wedge }{{\displaystyle U}}}_G(0)}\text{ (2)}$$

The far-end voltage of R-line U_R(l) and the near-end voltage of G-line U_G(0) can be erived by FEKO, so that the amplitude of the H_FEcan be obtained.

In fact, K and H_FE are functions of length l of transmission lines and frequency f, for the reason that introduces the L_e which is the ratio of l to wavelength λ.

$$K=K(f,l)\text{ (3)}$$ $$H_{FE}=H_{FE}(f,l)\text{ (4)}$$ $$L_{\text{e}}=l/\lambda \text{ (5)}$$

This comprehensive parameter makes (3) and (4) become

$$K=K(L_{\text{e}})\text{ (6)}$$ $$H_{FE}=H_{FE}(L_{\text{e}})\text{ (7)}$$

Based on this, the changes of K and H_FE with L_e are studied.

Based on this, the changes of K and H_FE with L_e are studied.

For case where the electrical length, L_e, is small, the line can be represented by lumped parameters (inductance, capacitance, resistance). As L_e increases, lumped parameter representation is no longer valid, and distributed parameter model must be used. For large L_e , one convenient representation is with the ABCD parameters, which A, B, C, and D are hyperbolic function of the propagation constant γ = α + β, derived from the line physical parameters (resistance, capacitance, inductance and conductance). This article chooses to use FEKO simulation software to replace these traditional numerical calculation methods.

Electromagnetic noise characteristics at the far-end of (2+1) transmission line

For the frequency range of (0.1~300) MHz, that is, the electrical dimension Le is in the range of (0.0005~1.5) m, the (2+1) conductor transmission line simulation is performed in FEKO.

In Figure 2, the length of the transmission line is l, the source on the interference line is composed of the noise source of G-lineUS and the source resistance RS. RL is the far-end load of the interference line, and RNE and RFE represent the near-end load and far-end load on the R-line, respectively. The cable structure in this section is shown in Table 1.

Figure 3 shows that, when the electrical length, Le= l/λ, is small, the loss of voltage is almost ignorable. As f increases (i.e., λ decreases) or l increases, Le increases, and the effects of distributed line parameters must be considered. Moreover, the number of resonance points increases, and the voltage amplitudes at the near and far ends of the lines are no longer approximately equal, which leads to significant variations of |K|.

As shown in Figure 4 when the electrical length is small, |H_FE| is small, that is, the far-end crosstalk voltage is small at low frequency. As f increases (i.e., λ decreases) or l increases, Le increases, and the effects of distributed line parameters must be considered., |H_FE| increases and when it rises to a certain level, it begins to fall which is caused by resonance point.

Electromagnetic Noise Characteristics of Multilayer Conductor Transmission Lines

For the (n+1, n>2) conductor system, the corresponding inductivecapacitive coupling model is too complicated compared to the (2+1) transmission line. This article takes n=7 and 19 as examples to research, where n=7 is a two-layer transmission line model, and n = 19 is a multi-layer (actually three-layer) transmission line model.

The cables simulated in this section are shown in Figure 5. No.1 conductor is the G-line, and No. (2 ~ 7) conductors are the R-line. The blue circles surround the orange and red circles, represent the wire insulation.

The cable structure in this section is shown in Table 2.

The simulation results show (Figure 6) that the far-end crosstalk voltages of No. (2~7) conductors are almost equal, so No.1 conductor is taken as the research object to study the features of K, and No.2 conductor is taken as the research object to study the features of H_FE.

As shown in Figure7, when the electrical length is small, the loss of voltage is almost ignorable. As f increases (i.e., λ decreases) or l increases, Le increases, and the effects of distributed line parameters must be considered. Moreover, the number of resonance points increases, and the voltage amplitudes at the near and far ends of the lines are no longer approximately equal, which leads to significant variations of |K|. Compared with Figure 3, the amplitude of |K| oscillates violently at high frequency.

As shown in Figure 8, the features of |H_FE| are similar to Figure 4, but resonance is more serious. The magnitude of |H_FE| in Figure 8 is smaller than Figure 4 in that the length of transmission line is smaller.

For the 3-layer transmission line, the simulation analysis is performed in the frequency range of (0.1~200) MHz, that is, Le is in the range of (0.0005~1) m. The (19+1) conductor transmission line is shown in Fig.9, the conductor No. 1 is the G-line, and the No. (2~9) conductors are the R-line.

The cable structure in this section is shown in Table 3

The simulation results show (Figure10) that the crosstalk voltages at the far end of No. (2~7) conductors in the middle layer are almost equal, and the crosstalk voltages of No. (8~19) conductors also has the same characteristics. Therefore, No.1 conductor is taken as the research object to study the features of K, and No.2 and No.8 conductors are the research object to study the features of H_FE, which are called H_FE2 and H_FE8, respectively.

As shown in Figure 11, when the electrical length is small, the loss of voltage is almost ignorable. As f increases (i.e., λ decreases) or l increases, Le increases, the amplitude of |K| oscillates at high frequencies, which overall shows a downward trend.

As shown in Figure 12, when the electrical length is small, |H_FE2| and |H_FE8| are small, that is, the far-end crosstalk voltage is small at low frequency; as the electrical length increases, |H_FE2| and |H_FE8| increase. When it rises to a certain level, it starts to fall because of the resonance point. In addition, in the entire frequency band |H_FE2| is slightly higher than |H_FE2|. It can be seen that as the distance between the G-line and the R-line increases, the crosstalk voltage decreases.