## 2 Nonlinear Switch Characterization
### Nonlinear Assessment of RA and PL  
The extracted diode model based on the X-parameters measurements, once validated, becomes a fundamental input to assess the possible nonlinear behavior of reconfigurable antennas and parasitic layers from an analytical viewpoint, and ultimately, a valuable piece of information to be further used as a design tool in the case of minimum nonlinearities reconfigurable antennas and parasitic layers. To illustrate the use of the X-parameters in a particular case, the antenna reported in [30] and reproduced in simplified manner in Figure 6a is taken as case of study. This antenna uses a total of 17 switches based on the MA4 AGFCP910 PIN diode, of which the most critical is the one located in the main feed path (\(S_{6}\) in the diagram); likewise, the set of 12 diodes in the intermediate PL (\(S_{5}\)) are jointly (de)activated, hence, although individually not as significant as \(S_{6}\), when combined, their impact on nonlinearity is similar or can be even larger. The switches \(S_{1-4}\) providing beam-steering are loosely coupled to the fed power, therefore, their impact on antenna nonlinearity is marginal. Notwithstanding that this antenna has 6 diverse modes of operation allowing for beam-steering and bandwidth reconfigurability, given the antenna symmetries and the expected small contribution to nonlinearity of the switches on the upper PL, only modes \(M_{1},M_{4}\) providing bandwidth reconfigurability are considered for analysis. Switch states for these modes are summarized in Table 1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Mode** & \(S_{1}\) & \(S_{2}\) & \(S_{3}\) & \(S_{4}\) & \(S_{5}\) & \(S_{6}\) \\ \hline \(M_{1}\) & 0 & 0 & 0 & 0 & 0 & 1 \\ \(M_{4}\) & 0 & 0 & 0 & 0 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Switch states for the antenna modes of interest. Figure 5: \(S\)- and \(X\)- parameters small signal convergence. Figure 6: Parasitic-Layer-based Reconfigurable-antenna and antenna equivalent circuit. As mentioned in the introduction, a common approach for the analysis of nonlinearly loaded antennas is to split the problem into an electromagnetic (linear) and a circuital network (nonlinear) problem. The first one can be dealt by numerical techniques such as MoM, Finite Elements Method (FEM), Finite-Differences Time-Domain (FDTD), whereas the second one can be tackled by nonlinear formulations like the Harmonic Balance (HB). The internal multi-port method, illustrated in Figure 5(b), which proceeds by replacing each switch location by a simulation port that can be later loaded with the proper switch parameters, and that has been extensively used for the analysis and design of RA and PL, is naturally fitted to translate the electromagnetic problem into a circuital one, in which the use of X-Parameters models of the loads, in combination with nonlinear circuital simulation, allow to calculate the nonlinear metrics of interest. After performing the FWEM simulation using the time domain solver in CST Studio, Keysight ADS is used to carry on the corresponding circuital S-parameters and harmonic balance simulations. Figure 7 shows that in the small-signal regime, the antenna port matching predicted by the X-parameters is quite similar to that predicted by the S-Parameters, ratifying the validity of the approach. Afterwards, two relevant metrics to assess the nonlinearity of the antenna are determined by means of an HB simulation in which the input power is swept from \(-10\) to \(30\) dBm. Figure 8 shows the harmonic components generated by the switches as seen from the antenna input port. From this variation of fundamental and harmonics with input power, the TOI of the antenna can be estimated to be \(IP_{3}=55\) dBm and \(41\) dBm for the \(M_{1}\) and \(M_{4}\) operation modes, respectively. One step further, the Error Vector Magnitude can also be derived with the aid of the X-parameters nonlinear model.