## 1 Introduction
Nonlinear models of microwave devices and circuits [14] can be categorized either as Compact/Physical (based on the physics governing the device) or Black-Box/Behavioral (based on the characteristics of the device from its terminals) [15]. When the internalstructure of the Device Under Test (DUT) is not disclosed or is of no interest to the system designer, black-box modeling is the most suitable approach, with various alternatives available [16; 17; 18; 19; 20; 21]. The X parameters [22] stand out among the available behavioral modeling choices. They are an appealing option given some of their features such as extraction stability, time-invariance, convergence to the S parameters in the small-signal regime, and their integration into simulation software. Albeit the nonlinear behavior of the PIN diode is widely reported and mostly attributed to its nonlinear resistance characteristic [23; 24; 25], and SPICE models suitable for the microwave range have been proposed [26; 27], most manufacturers do not provide the parameters and values needed to be used in compact models at high frequencies. Consequently, X parameters are proposed in this work to experimentally obtain a behavioral model of a PIN diode commonly used for mmW applications. The extracted diode model is validated through independent S parameters and harmonic distortion measurements. Reconfigurable antennas in general and parasitic layer based reconfigurable antennas [11] presenting compact size, low complexity, low power consumption, and small nonlinearities, in particular, are an appealing alternative for the deployment of the 5G-NR usage scenarios (Ultra-Reliable and Low Latency Communications (URLLC), Enhanced Mobile Broadband (EMB), and Massive Machine Type Communications (MMTC)). The extracted nonlinear model of the PIN diode switch is a useful input to gain insight into the nonlinear behavior of reconfigurable antennas using PIN diode switches like the one illustrated in Figure 1, based on [28], which is taken as a case of study in this work to demonstrate a new methodology for the design of minimum nonlinearity reconfigurable antennas and parasitic layers suitable for BS and Customer-Premises Equipment (CPE) in 5G EMB scenarios. The nonlinear behavior of RAs is scarcely reported in the literature, and design strategies considering nonlinearities are non-existent. Two recent experimentally-oriented works are [29], where Third Order Intercept (TOI) and 1 dB Compression Point (1 dB CP) are presented, and [30] which focuses on EVM and IMP measurements. Nevertheless, both cases lack an analytical formulation to explain or estimate the nonlinear behavior of the antenna, which would be required to calculate the measured effects or to consider the nonlinearities in the design stage. This is precisely the gap that this work intends to fill, opening new possibilities for the well-balanced design of reconfigurable antennas for the rigorous 5G performance requirements. Notwithstanding the lack of theoretical approaches and the scarcity of experimental works studying nonlinear effects in RA, the case of nonlinearly loaded basic antennas and arrays has been tackled to some extent. With few exceptions that deal with the  
Figure 1: Exploded view of the Parasitic-Layer-based Reconfigurable-antenna used as case study. (Units in mm). nonlinear problem entirely within the electromagnetic solution, which proves useful in cases where nonlinearities are inherent to the antenna or propagation medium materials, the most reasonable approach to the analysis of nonlinearly loaded antennas is to split the problem into an electromagnetic (linear) and a circuital (nonlinear) problem. The former is commonly dealt with by Full-Wave Electromagnetic (FWEM) numerical techniques, whereas the latter can be tackled by formulations such as the Harmonic Balance (HB) analysis [31].