Given the rapid development of wireless power transfer (WPT) technologies in recent decades, WPT has been employed in a wide range of applications, including portable electronic devices, medical devices, electronics in space environments, and industrial robots [1–3]. These WPT technologies are generally classified into three methods: magnetic induction, magnetic resonance, and microwave power transmission (MPT) [4].

MPT not only enables long-distance power transmission but can also deliver power to various locations through electronic beam steering techniques. Research on transmitting antennas for MPT, which can improve transmission efficiency and enable various beam steering, has been widely conducted [5, 6]. However, in terms of overall power transmission efficiency, the performance of the receiving antenna is as critical as that of the transmitting antenna [7–9]. For example, even a slight misalignment of the receiver antenna can significantly reduce the transmission efficiency of the overall system. To overcome these receiver problems, various studies have been conducted to improve power conversion efficiency by optimizing rectifier circuits, including a full-bridge rectifier [10, 11] and an auto-adaptive impedance matching rectifier [12]. In addition, to resolve this issue from a receiving antenna perspective, extensive studies have been carried out to derive the high-gain characteristics of receiver antennas using higher-order modes [13, 14], a metamaterial superstrate [15], and flexible reflectors [16]. However, these types of antennas cannot be fundamental solutions to the degradation in power transmission efficiency caused by misalignment.

In this paper, we propose a receiving array antenna with a trapezoidal configuration that can be equipped with multiple rectifier circuits for wide-angle reception to resolve misalignment. The proposed receiving antenna system is composed of three individual antenna elements operating at 5.8 GHz and the same number of rectifier circuits. Each antenna is designed to have a half-power beamwidth (HPBW) of 65°, and the angles of the trapezoidal configuration are determined to achieve wideangle reception. To increase the gain and obtain the required beamwidth, a quasi-air substrate is utilized between the radiator and the ground plate, and the designed antennas are connected separately to each rectifier circuit. The rectifier circuits are printed on the circuit board and designed to have a power conversion efficiency of 60% at 20 dBm input power. The outputs of each rectifier circuit are combined in parallel to reliably harvest power into the receiver system.

The proposed receiving array antenna is investigated using the CST Studio Suite full electromagnetic (EM) simulator [17] and is fabricated to verify the antenna performance, including radiation patterns and reflection coefficients. With an optimized angle of the trapezoidal configuration, overall beam coverages of 195° (= 65° × 3) by simulation and 205° by measurement are achieved. We also measure the output power of the three rectifier circuits connected in parallel. The measured power range is from 48.14 mW to 168.75 mW at a distance of 1 m and from 12.74 mW to 40.51 mW at a distance of 2 m. These results demonstrate that the proposed receiving antenna system can harvest stable power even when there is misalignment between the transmitter and receiver.

Fig. 1 shows the geometry of the proposed wireless power receiving array antenna system for wide-angle reception. The system is designed to be mounted on the back of a health monitoring chair; thus, the target reception angle is set to 200° to cover the entire chairback.

Fig. 1(a) illustrates the geometry of the receiving array antenna system with a trapezoidal configuration that can be equipped with multiple rectifier circuits for wide-angle reception. The system consists of three individual antenna elements operating at 5.8 GHz. To overcome the issue of misalignment between the transmitting antenna and the receiving antenna, the receiving array antenna has a trapezoidal configuration. α represents the angle between the adjacent ground plates; it is set at 115° to obtain a total reception angle of 200°.

Fig. 1(b) shows the isometric view of the proposed single element, which is designed by adopting a quasi-air substrate (ɛ_r = 1.05) to improve the gain and the required beamwidth. In general, a conventional single patch antenna with a dielectric substrate has a gain of less than 8 dBi. However, by using a quasi-air substrate, which sustains very low losses, a higher gain can be achieved [18]. The dimensions (width w × length l) of the radiator are 22 mm × 22 mm, and the quasi-air substrate thickness (h) is 3.5 mm. Each square ground plate has a side length (g) of 70 mm.

Fig. 1(c) presents the top view of the receiving array antenna system, including the rectifier circuits. The receiving array antenna is connected to the rectifier circuit through an SMA connector. This antenna receives the transmitted power and delivers RF power to the rectifier circuit. Each antenna is designed to have an HPBW of 65° (= 180° – α) in the zx-plane. The HPBW of each element is an important factor in obtaining wide-angle reception. Rectifier circuits that convert RF power to DC power are designed using microstrip lines, which are printed on the circuit board (RO4350B, ɛ_r = 3.66, tanδ = 0.0037).

Fig. 2(a) presents a photograph of the fabricated receiving array antenna. The radiator and ground plate are fabricated using copper plates, and the quasi-air substrate is manufactured using a foam board, which has a dielectric constant similar to that of air. During the assembly process, three individual grounds are made by bending a 210 mm × 70 mm copper plate. In addition, triangular-shaped plates are inserted between the ground plates to ensure the trapezoidal configuration. The total dimensions (width w × length l × height h) of the fabricated receiving antenna are 129 mm × 63 mm × 70 mm.

Fig. 2(b) shows a photograph of the receiving antenna mounted on a health monitoring chair. The proposed antenna is located on the back of the health monitoring chair to receive RF power wirelessly and supply power to the bio-signal measurement sensor.

Fig. 3 presents the performance of the proposed antenna elements. The measured reflection coefficients of each antenna (Ant. 1, 2, and 3) operating at 5.8 GHz are −19.05 dB, −18.14 dB, and −25.57 dB, respectively, as shown in Fig. 3(a). The simulated reflection coefficient of the center element (Ant. 2) is −31.67 dB at 5.8 GHz, and the measured and simulated reflection coefficients are both less than −10 dB.

Fig. 3(b) shows the measured and simulated 2D radiation patterns. The blue and red lines indicate the measured and simulated results, respectively. At 5.8 GHz, each antenna element has a HPBW of 65° in both simulation and measurement, with a measured gain of more than 11 dBi. The overall beam coverage of this system is 195° in simulation and 205° in measurement. These results show that a wide reception angle is achieved by adopting the trapezoidal configuration.

Fig. 4(a) presents a schematic of the proposed multiple rectifiers. Three rectifiers are connected in parallel to the power management integrated circuit (PMIC). The PMIC has a maximum power point tracking (MPPT) function, which adjusts the output voltage to half of the open circuit voltage, ensuring maximum power transfer.

Fig. 4(b) shows the equivalent circuit of multiple rectifiers. The n-th rectifier, which received the RF power of P_R,n, is represented by a serial connection of V_oc,n and R_Th,n [19]. The open-circuit voltage of the array antenna system is biased toward that of the rectifier receiving the highest RF power. V_DC is expressed as follows:

If one or more rectifiers face a condition in which their V_DC is higher than their open-circuit voltage, those rectifiers cannot harvest power and are excluded from the circuit [20]. The current from the n-th rectifier is defined as follows:

The rectified power P_DC of the proposed system is calculated as follows:

Fig. 5(a) illustrates a schematic diagram of the rectifier circuit combined with the proposed receiving antenna. The rectifier consists of a matching network, DC block capacitor, diode, harmonic suppression structure, smoothing capacitor, and load. A single stub is employed as the matching network, and the DC block capacitor is used to block the effect of the DC bias voltage when the RF source is directly connected to the rectifier input port. For energy harvesting, the system employs the PMIC (SPV1050; STMicroelectronics, Coppell, TX, USA) as the load, which supports the MPPT function to handle open-circuit voltages up to 18 V. The rectifier is designed with a single shunt diode structure using an Advanced Design System (ADS) simulator. A harmonic suppression structure is employed to increase power conversion efficiency by terminating the second and third harmonics [21]. The components of the rectifier are summarized in Table 1.

Fig. 5(b) shows the input impedance of the rectifier circuit at 5.8 GHz with varying input power from −20 dBm to 30 dBm. The rectifier is confirmed to be closely matched to 50 Γ for input powers ranging from 17 dBm to 25 dBm due to the matching network. Fig. 5(c) presents a photograph of the fabricated rectifier, which is printed on a RO4350B board (16.4 mm × 41.6 mm × 0.508 mm).

Fig. 6(a) represents the measured and simulated results of a single rectifier circuit. The input power range is determined to span from 8 dBm to 25 dBm, considering the cold start minimum input voltage of 2.6 V of the PMIC and the MPT system to be used in the experiment. In the experimental setup, the PMIC is used as the load, and a load of 200 Γ is utilized in the simulation. The diode model under large signals in ADS has modelling inaccuracy in the junction capacitance and series resistance due to variations in frequency and power, resulting in simulation errors [22, 23]. The rectifier with the MPPT function achieves over 60% efficiency for input powers ranging from 17 dBm to 24 dBm. In addition, Fig. 6(b) shows the V_oc and R_Th values, which are determined by measuring the voltage and current of the rectifier and then extracting the input power. It has an open-circuit voltage value below the maximum allowable value (18 V) of SPV1050.

Fig. 7 shows the measured power of the proposed receiving antenna system, with measurements obtained under a transmitting antenna gain of 20 dBi and a transmit power of 16 W. The measured power levels at distances of 1 m and 2 m are represented by the blue and red lines, respectively. The output power is measured at 5° intervals within the beam coverage range, as shown in Fig. 7(a). The three rectifier circuits are connected in parallel, as shown in Fig. 7(b). Each rectifier circuit has a conversion efficiency of 60% when the input power is about 20 dBm. The measured power is between 48.14 mW and 168.75 mW at a distance of 1 m, and between 12.74 mW and 40.51 mW at a distance of 2 m. From the boresight direction, the received power at a distance of 1 m is measured to be 168.75 mW, resulting in a WPT efficiency of 1.05%. At a distance of 2 m, the received power decreases to 40.51 mW, with a WPT efficiency of 0.25%, as shown in Fig. 7(c). These results validate that power is reliably received through the proposed receiving antenna system, even with potential misalignment.

A receiving array antenna with a trapezoidal configuration was proposed for wide-angle reception. The receiving antenna system consisted of three individual antenna elements, each paired with a corresponding rectifier circuit. A trapezoidal configuration was utilized for wide-angle reception and designed with an angle of 115° between adjacent antennas. This configuration had a wide-angle reception range of 205° through the measurement of 2D radiation patterns. To achieve high-gain characteristics and the required HPBW, a quasi-air substrate was used for each antenna element. The measured reflection coefficients for the individual antenna elements were less than −10 dB. Furthermore, the measured power recorded at 1 m and 2 m distances ranged from 48.14 mW to 168.75 mW and 12.74 mW to 40.51 mW, respectively. These measurements of the receiving power within the beam coverage demonstrated that the system can reliably receive MPT signals, even in cases of potential misalignment.