# Dual-Band RF Wireless Power Transfer System with a Shared-Aperture Dual-Band Tx Array Antenna
## 2 Implementation of a Dual-Band RF Wireless Power Transfer (WPT) System
### Design of a Shared-Aperture Dual-Band Tx Array Antenna  
To merge a 2.4 GHz array and a 5.8 GHz array into a dual-band RF Tx system, a shared-aperture dual-band array based on the configuration of a thinned array is proposed as a Tx antenna [24; 25]. This shared-aperture dual-band array is composed of a 2.4 GHz thinned array with 2.4 GHz radiating elements and a 5.8 GHz thinned array with 5.8 GHz radiating elements. As these two different array antennas are employed in a single planar structure, an aperiodic array configuration such as thinned array is necessary [26; 27]. The configuration of the thinned array is derived by optimization, and optimization of the array is usually performed to ensure that desired far-field characteristics (such as the gain, beam width and side-lobe) are achieved [28; 29; 30]. However, when optimizing a thinned array for WPT, the transmission efficiency should be considered above all. The transmission efficiency (in other words, the WPT efficiency) is defined as \(P_{R}/P_{T}\) (here, \(P_{R}\) is the total received power and \(P_{T}\) is the total transmitted power) and achieving high WPT efficiency is the ultimate goal of WPT technology. Therefore, in this paper, optimization of the thinned array for WPT is conducted with the aim of improving the transmission efficiency considering various power transmission scenarios. We assume a square aperture 50 cm \(\times\) 50 cm in size with a grid of 31.23 mm spacing (equal to 0.26 \(\lambda\) for 2.482 GHz and 0.60 \(\lambda\) for 5.73 GHz), as shown in Figure 2. Here, \(\lambda\) is the wavelength of the operating frequency. We are supposed to arrange 32 elements for 2.4 GHz and 32 elements for 5.8 GHz on this aperture, constructing 2.4 and 5.8 GHz thinned arrays, respectively. Both the 2.4 GHz and 5.8 GHz thinned arrays are strategically determined by optimization. When the center of this Tx aperture in Figure 2 is considered to be the origin and the position of the Rx is \((x^{\prime},y^{\prime},z^{\prime})\), optimization of the thinned array is carried out with the aim of maximizing the evaluation function following Equation (1). In other words, an optimized arrangement of 32 elements for each frequency is derived to achieve maximum transmission efficiency, taking into account 25 WPT scenarios of transmitting power to a Rx position at \(x^{\prime}=0.5n,\ y^{\prime}=0.5n\), and \(z^{\prime}=2\) (when \(n=-2\), \(-1\), 0, 1, and 2). Evaluation Function \(=\sum\limits_{n}\frac{P_{R}}{P_{T}}\{\)when transmitting power to Rx position\((x^{\prime},y^{\prime},z^{\prime})|x^{\prime}=0.5n,y^{\prime}=0.5n,z^{\prime}=2\}\) (1)  
Figure 2: Arrangement of radiating elements in the optimized shared-aperture dual-band array. In this equation, \(z^{\prime}=2\) denotes a distance of 2 m in the \(+z\)-direction between the Tx and Rx antennas; this distance is in not a far-field region but in the Fresnel region for the 2.4 and the 5.8 GHz arrays [31]. When \(\beta_{m}\) and \(\left(x_{m},y_{m},z_{m}\right)\) are defined as the excited phase and position of the \(m\)-th element of the Tx array, by feeding the phase calculated by Equation (2) into the \(m\)-th element, the beam can be formed in a desired direction (here, it is the direction to Rx (\(\theta^{\prime}\),\(\phi^{\prime}\))) and power can be transmitted. This is known as beam-forming, and it is usually the method used for beam-steering. On the other hand, if the phase according to Equation (3) is applied as the excited phase of the \(m\)-th element, the transmitted beam is concentrated to a specific point (here, it is the location of Rx (\(x^{\prime}\),\(y^{\prime}\),\(z^{\prime}\))), known as beam-focusing. According to the literature [7; 32; 33; 34], in the Fresnel region, using beam-focusing rather than beam-forming as a beam-steering method can improve the received power. Thus, we assume that the beam is sequentially formed to the 25 Rx position in Equation (1) by applying the beam-focusing method.