# Shielding Grounding Optimization Method for Spaceborne Multi-Cable
## 2 Shielding Grounding Optimization Method
### MATLAB Transformation Truth Table  
The CST simulation results were automatically judged and binary-coded using MATLAB and ultimately converted into a truth table, as shown in Table 3. The left input of the truth table is the state of each variable of the CST model: \"1\" means the resistance is 0 \(\Omega\), i.e., the shield is grounded on this side; \"0\" means the resistance is \(10^{8}\)\(\Omega\), i.e., the shield is not grounded on this side. The interference voltages obtained from the simulation of \(4^{i}\) cases are sorted from small to large and divided into \(n\) voltage levels, i.e., the right-hand side of the truth table output \(Y_{1}Y_{2}\ldots Y_{n}\), corresponding to an \(n\) shielding effect. The smaller the subscript number of \(Y\), the smaller the interference voltage induced on the target cable and the better the shielding effect. The reason for this grading is that, in \(4^{i}\) cases, there are several cases with close interference voltage results, i.e., the simulation results will be graded, resulting in \(n\ \leq\ 4^{i}\).  
For each row of the truth table, only one of the bits in \(Y_{1}Y_{2}\ldots Y_{n}\) is \"1\", representing the level of the shielding effect of this state, and the rest of the bits are \"0\". For example, \"No.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & **Parameter Sweep** & & & **Results** \\ \hline
**No.** & \(R_{\text{IN}}\) & \(R_{\text{IF}}\) & \(\ldots\) & \(R_{iN}\) & \(R_{iF}\) &
\begin{tabular}{c} **Other Parameters** \\ **(If Required)** \\ \end{tabular} & \(\boldsymbol{U}\) \\ \hline
0 & \(10^{8}\) & \(10^{8}\) & \(10^{8}\) & \(10^{8}\) & \(10^{8}\) & \(\ldots\) & \(U_{0}\) \\
1 & \(10^{8}\) & \(10^{8}\) & \(10^{8}\) & \(10^{8}\) & \(0\) & \(\ldots\) & \(U_{1}\) \\
2 & \(10^{8}\) & \(10^{8}\) & \(10^{8}\) & \(0\) & \(10^{8}\) & \(\ldots\) & \(\ldots\) \\
3 & \(10^{8}\) & \(10^{8}\) & \(10^{8}\) & \(0\) & \(0\) & \(\ldots\) & \(\ldots\) \\ \(\cdots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\ \(4^{i}-2\) & 0 & 0 & 0 & 0 & \(10^{8}\) & \(\ldots\) & \(U_{4^{i}-2}\) \\ \(4^{i}-1\) & 0 & 0 & 0 & 0 & 0 & \(\ldots\) & \(\ldots\) \\ \(\cdots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) & \(\ldots\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: CST simulation results (resistance unit: \(\Omega\)).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & \(R_{\text{2N}}\) & \(R_{\text{2F}}\) & \(\boldsymbol{U}\) (V) \\ \hline
0 & \(10^{8}\) & \(10^{8}\) & \(3.183\) \\ \hline
1 & \(10^{8}\) & 0 & 3.097 \\ \hline
2 & 0 & \(10^{8}\) & 3.090 \\ \hline
3 & \(10^{8}\) & \(10^{8}\) & \0\" corresponds to the truth table output \(Y_{1}Y_{2}\ldots Y_{n}=100\,\ldots\,\,00\), meaning that, when all the cables are shielded without grounding, the interference voltage is in the first level, i.e., the best shielding effect. \"No. 1\" corresponds to the truth table output \(Y_{1}Y_{2}\ldots Y_{n}=010\,\ldots\,\,00\), meaning that, when the shield of cable \(C_{i}\) is grounded at the far end and the shield of the rest of the cable is not grounded, the interference voltage is in the second level, i.e., the shielding effect is second best.  
With Table 2 used as an example, the results obtained after MATLAB transformation are shown in Table 4. It can be seen that, although \(U\) has four results, the shielding effect is classified into three levels because the results of No. 1 and No. 2 are very close.