## 3 System-Level SPICE Modeling of EMP Coupling on Wireless RF Circuits
### SPICE Model of Wireless Antenna
#### 3.2.3 Response Result of Antenna SPICE Model  
The frequency range of the equivalent circuit to be fitted is limited by the frequency range of the simplified RF channel and the potential HPEM it suffers from. Because the excessively wide frequency band will cause the VF fitting order to be too high, leading to higher fitting complexity. Hence, the frequency range of the antenna is limited within 3 GHz. The rational approximation of the input impedance and admittance of the antenna port has been derived by the VF method based on the EM simulated data of impedance and admittance. The basic parameters of the VF method are set as: the order of rational function is 10, and VF iteration is 20. As illustrated in Figure 10, the fitted results have enough accuracy to be used for equivalent circuit modeling.  
Figure 9: Forms of circuit model for admittance: (**a**) entire circuit model; (**b**) basic sub-circuit model.  
According to the rational functions of antenna input impedance and admittance, the equivalent circuits of \(\text{Z}_{\text{in}}\) and \(\text{Y}_{\text{in}}\) in the SPICE models are computed according to Equations (7)-(10). In addition, the excitation sources in the SPICE circuit are set as OC voltage and SC current for the Thevenin model and Norton model, respectively. Then, finally, the entire equivalent Thevenin and Norton SPICE models have been built for antenna coupling response with load 50 ohms connected to the antenna port after HEMP illumination.  
The response results of the two SPICE models with HEMP excitation waves are computed in this subsection and validated with the comparison of the EM simulations. For the Thevenin SPICE model, the SC current and load current results of EM simulation are selected to validate the SPICE simulation results, the curves of which are illustrated in Figure 11. From the consistency of the wave oscillation period and peaks of the curves, it is obviously shown that the accuracy of the Thevenin SPICE model for antenna response is close to that of the EM simulations, so it can be considered that this SPICE modeling of antenna response after HPEM illumination does not reduce the accuracy requirement compared to the original response. The slight difference between the curves should be caused by the cut off of the impedance frequency range and the fitting error of the rational approximation, which can be considered as negligible from the perspective of equivalence.  
Figure 11: Validation of Thevenin SPICE model: (**a**) SC current; (**b**) Load current.  
Figure 10: Fitting result of impedance and admittance of antenna with VF method: (**a**) admittance; (**b**) impedance.  
Furthermore, the comparison of the Norton SPICE model and EM simulation are also provided, where the curves of the OC voltages and load currents of the SPICE and EM simulation are illustrated in Figure 12. The consistency of these curves in Figure 12 also proves the validations of the Norton SPICE model.  
Considering that the parameter of SC current is easier to measure in the HPEM illumination tests, the Norton SPICE model is adopted for the simplified linear RF channel in the following section.