## 4 Response Analysis of EMP Coupling on RF Front-End Circuits-Based Norms
### Response Analysis with Norm Theory  
In this subsection, in order to analyze the risk degree of the HPEM risk faced by the RF channel with a pyramid horn antenna, we utilize three typical time domain norms to represent the waveform characteristics from the electric field to the conducted response of the RF channel. Table 2 illustrates the norm results of the HPEM and the responses. Because this paper mainly focuses on the three typical HPEM environments, we define the risk ranks of HPEM faced by the RF channel as I, II and III. Rank I is the highest risk, and rank III is the lowest. Considering the convenience of the comparison for these HPEMs used in this paper, the amplitude (50 kV/m) of the electric field is set to represent the HPEM  
Figure 16: Coupling response excited by UWB: (**a**) Isc current; (**b**) Responses. Figure 17: Coupling response excited by HPM: (**a**) SC current; (**b**) Responses. pulse strength. However, radiation power or energy may be used as the representation of the pulse intensity in practice. Hence, we compute the ratio of the antenna response versus the electric field and the ratio of the response after BPF versus the electric field for each norm to normalize the selectivity of the pyramid horn antenna and the linear RF channel to the HPEMs. In practice, some sensitive modules such as LNA are always connected at the back end of the RF channel. Therefore, if the RF channel has better frequency selectivity to a certain HPEM, the RF channel faces greater damage EM risk in this HPEM. Table 3 provides the risk rank results of the HPEMs for the linear RF channel according to the results of Table 2. For the antenna response, HPM is the highest EM risk for the pyramid horn antenna, the reason of which is that the center frequency of HPM is located in the pass band frequency range of the antenna. HEMP is the lightest EM risk because this main energy frequency range of below 300 MHz is much lower than the antenna frequency range. In addition, the HPM is also the highest EM risk for the linear RF channel, the main reason is that the frequency range of the antenna and BPF are consistent with the HPM. Of course, the HPM environment has a very wide frequency band and most flexibility compared to other HPEMs. Hence, the carrier frequency needs to be set within the frequency range of the targeted electronic system to produce the most significant effect. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Norms**} & **HPEM Type** & **Electric Field** & \
\begin{tabular}{c} **Response of** \\ **Antenna Port** \\ \end{tabular} &
\begin{tabular}{c} **Response** \\ **after BPF** \\ \end{tabular} \\ \hline \multirow{3}{*}{\(\left|f(\text{t})\right|_{\text{max}}\)} & HEMP & \(5.0\times 10^{4}\) & 0.84 & 0.49 \\ \cline{2-5}  & UWB & \(5.0\times 10^{4}\) & 46.23 & 31.58 \\ \cline{2-5}  & HPM & \(5.0\times 10^{4}\) & 142.96 & 44.64 \\ \hline \multirow{3}{*}{\(\left|\frac{\partial f(\text{t})}{\text{dt}}\right|_{\text{max}}\)} & HEMP & \(3.47\times 10^{13}\) & \(1.38\times 10^{10}\) & \(1.14\times 10^{10}\) \\ \cline{2-5}  & UWB & \(4.61\times 10^{14}\) & \(5.36\times 10^{11}\) & \(4.16\times 10^{11}\) \\ \cline{2-5}  & HPM & \(4.71\times 10^{14}\) & \(1.40\times 10^{12}\) & \(4.60\times 10^{11}\) \\ \hline \multirow{3}{*}{\(\left\{\int_{0}^{\infty}\left|f(\text{t})\right|^{2}dt\right\}^{1/2}\)} & HEMP & \(6.57\) & \(3.10\times 10^{-5}\) & \(1.39\times 10^{-5}\) \\ \cline{2-5}  & UWB & \(0.69\) & \(0.0012\) & \(0.0010\) \\ \cline{1-1} \cline{2-5}  & HPM & \(10.41\) & \(0.029\) & \(0.0090\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Norm results of the HPEM and the responses.