## 1 Introduction  
Nowadays, Wireless Power Transfer (WPT) and energy scavenging have been attracting researchers and industry due to the ever-growing need for flexible, sustainable, and unfailing sources of energy. In addition, with recent advances in wireless sensor networks (WSN), e.g., the Internet of Things (IoT), such intelligent systems are further highlighting this necessity [1, 2]. The aim of wireless power transfer is to allow devices to operate for an extended period of time without having to charge/replace their batteries, a critical issue because of the inherent costs and difficulties of reaching inaccessible areas. Furthermore, WPT is seen as an environmental solution and a cost-effective approach since it drastically reduces the need to recycle dead batteries [2]. WPT techniques can be classified into two main classes: (i) inductive and magnetic resonant coupling methods to transfer power over short distances (a few centimeters); and (ii) RF electromagnetic techniques utilized to transport the energy over long distances (a few meters) [3, 4]. RF electromagnetic techniques are considered in this work due to their benefits in powering portable devices over longer distances. In order to estimate the power levels that can be transmitted, received, and harvested as well as the maximum distance that can be reached, a power link budget is essential. The common method to calculate the capability of power transmission is the power link. The propagation in the free space between a transmitter and a receiver can be expressed via the well-known Friis equation where the received power available to the rectifier can be estimated as in (1)  
\[P_{r}=P_{t}G_{t}G_{r}\left(\frac{\lambda}{4\pi R}\right)^{2} \tag{1}\]  
where \(\lambda\) is the signal wavelength. (\(P_{t}\), \(G_{t}\)) and (\(P_{r}\), \(G_{r}\)) state, respectively, the transmitted and received power and gain of antennas separated by a distance \(R\). In the following calculations, we used the Federal Communication Commission (FCC) regulations with a maximum transmitting power of 30 dBm and an Effective Isotropic Radiated Power (EIRP) of 36 dBm at the UHF ISM band. Therefore, the applied transmitted power was set as 23 dBm and the gains of the transmitted and received antennas were set as 6 dBi and 2 dBi, respectively. Table 1 summarizes the received power link budget of the proposed adaptive rectifier and trade-off between distance and efficiency. Note that the system using the concept of an adaptive rectifier reaches an efficiency greater than 40% for distances up to 2 m and 49% of efficiency at 1 m.  
WPT through an electromagnetic technique has been applied in a diverse range of applications and fields, such as Radio Frequency Identification (RFID) [5], Wireless Sensor Networks (WSN), Wearable and Implantable Medical Devices (WIMD) [6], Structural Health Monitoring (SHM) [7], and the Internet of Things (IoT) [8]. Such applications can involve a wide range of power levels depending on the targeted applications and the distance from the controlled source: RFID (\(\mu\)W to mW), bio-implants (mW to W), wirelessly charging systems for user electronic devices (a few W). Consequently, the WPT process is accomplished through a rectenna, which mostly contains an antenna, a rectifier, a matching network, and an output load as illustrated in Figure 1. Once the RF wave is received by the receiving antenna, it will be converted to direct current (DC) voltage to either directly power devices or store the energy in batteries [3]. Several approaches have been explored to improve the efficiency of WPT systems. The rectifier is one of the most widely used sub-circuits in a WPT system to optimize its performance for maximum Power Conversion Efficiency (PCE). Numerous rectifier configurations have been suggested to improve system efficiency, including conventional configurations, such as series/shunt diodes configurations, voltage doublers, and bridge diode rectifiers [4].