Introduction
Wireless power transmission (WPT) systems have garnered significant attention due to their various applications, including medical sensors, implanted devices, immortal sensor networks, wireless charging electric vehicles, and wireless powering of single-chip systems [Reference Shinohara1–Reference Wang, Cheng and Gu3]. In the WPT system, the radio frequency-to-direct current (RF-to-DC) rectifier plays an important role as it determines the overall efficiency of the system. Therefore, it is essential to have a rectifier that exhibits both high power conversion efficiency (PCE) and wide operating bandwidth. This ensures coverage for frequency shifts caused by fabrication errors and enables the harvesting of more energy in wireless power harvesting applications.
In order to achieve wideband and high-efficiency performance of a rectifier, the design of the wideband input-matching-network is crucial. Effective impedance matching results in reduced reflected power at the input port. Consequently, a greater proportion of RF power can be converted to DC power, leading to higher efficiency. However, matching a rectifier over a wideband is a challenge because the diode impedance varies with the operating frequency and input power [Reference Du, Cheng and Gu4]. To address this issue, much research has been carried out recently [Reference Zhang, Du and Xue5–Reference Long, Cheng, Yu, Yu and Huang20]. Most works have focused on the wideband input-matching-network, such as branch-line coupler [Reference Zhang, Du and Xue5], multistage transmission line [Reference Wu, Huang, Zhou, Yu, Liu, Chen and Liu6], series-connected coupled-line [Reference Lin, Zhang, Du and Lin7], nonuniform transmission line [Reference Kimionis, Collado, Tentzeris and Georgiadis8], L-section matching network [Reference Mansour and Kanaya9], series dual-inductive lumped element [Reference Mansour and Kanaya10], T-type matching network [Reference Liu, Huang, Wang, Zhang and Hou11, Reference Yu, Cheng, Gu and Huang17], tapered microstrip line [Reference Joseph, Huang and Hsu12], and open/short stub matching network [Reference He and Liu13]. In papers [Reference Kimionis, Collado, Tentzeris and Georgiadis8] and [Reference Mansour and Kanaya9], lumped elements were adopted in the rectifier design to reduce the circuit size. Minimizing circuit size leads to lower fabrication costs and reduced weight. In contrast to the above methods, Wu et al. proposed a multi-diode structure to realize the wideband rectifier [Reference Wu, Huang, Zhou and Liu14]. Each diode can cover a frequency band, and with more diodes, a wider bandwidth may be realized. In paper [Reference Gyawali, Thapa, Barakat, Yoshitomi and Pokharel19], a broadband and efficient rectifier was realized with minimal interstage matching, which consists of a single short-circuit stub and a virtual battery.
In this paper, a compact multi-octave rectifier with high efficiency is proposed. The asymmetric coupled-line transformer is adopted as the input impedance matching network. It exhibits the merits of compact size and broadband matching. Compared with the design in [Reference Yu, Cheng, Gu and Huang17], the proposed rectifier has better reflection coefficient at low frequency. When the rectifier is connected to a receiving antenna with an input impedance of 50 Ω, the rectifier would get more energy when its reflection coefficient is low. For example, if |S 11| = −10 dB and −15 dB, the signals reflected to the receiving antenna are 10% and 3%, respectively. This implies that approximately 7% more energy can be delivered to the rectifier. For verification, a broadband rectifier is fabricated and measured. The rectifier has dimensions of 19 mm × 18 mm, which is much smaller than those in the previous works. The measured results agree well with the simulated ones. The measured frequency range for |S 11| ≤ −10 dB is from 0.54 to 3 GHz with a relative bandwidth of 139% when the input power is 14 dBm. The measured PCE is exceeding 60% from 0.3 to 2.9 GHz with an input power of 18 dBm. The relative bandwidth for efficiency over 60% is 162.5%. In contrast, the majority of previous works, with the exception [Reference Mansour and Kanaya10] and [Reference Gyawali, Thapa, Barakat, Yoshitomi and Pokharel19], exhibit a relative bandwidth below 100%. Moreover, the measured maximum PCE of the proposed rectifier is 79.8% at 0.9 GHz.
Design and analysis of the wideband rectifier
Compared to the single-diode rectifier topology, the voltage-doubler configuration not only improves the power handling capabilities but also is suitable for achieving broadband performance [Reference Kimionis, Collado, Tentzeris and Georgiadis8]. Therefore, the Schottky diode BAT15-04W with a series connected pair of diode chips in one package is selected for this design [21]. The design procedure of the proposed broadband rectifier includes two parts, as shown in Fig. 1. In Fig. 1(a), the rectifier is matched by four uncoupled transmission lines labeled TL1-TL4. Each transmission line has a characteristic impedance of Z 0i and an electrical length of θi (i = 1–4). The capacitors C 1 and CL are used to block the DC and filter the RF signal, respectively. In Fig. 1(b), TL1 and TL4 are coupled. The asymmetric coupled-line impedance transformer not only enhances the compactness of the rectifier but also widens its bandwidth. The rectifier is designed to operate from fL to fH with a load of 500 Ω, where fL and fH indicate the lowest and highest working frequencies, respectively.
Figure 1. Schematic diagram of the proposed broadband rectifier: (a) without the coupled-line and (b) with the coupled-line.
The design strategy of the input impedance matching network is shown in Fig. 2. The start and end frequencies are fL = 0.3 GHz and fH = 3 GHz, respectively. First, the load impedance ZL is evaluated by the following equation [Reference Zheng, Liu and Pan18]:
\begin{equation}{Z_L} = \frac{{\pi {R_s}}}{{2{\theta _{on}} - \sin 2{\theta _{on}} + j\omega {R_s}{C_j}(2\pi - 2{\theta _{on}} + \sin 2{\theta _{on}})}}\end{equation}
\begin{equation}\tan {\theta _{on}} - {\theta _{on}} = 2\pi \left( {{{{R_s}} \mathord{\left/
{\vphantom {{{R_s}} {{R_L}}}} \right.
} {{R_L}}}} \right)/(1 + {{2{V_{bi}}} \mathord{\left/
{\vphantom {{2{V_{bi}}} {{V_o}}}} \right.
} {{V_o}}})\end{equation}
Figure 2. The input and load impedance on the Smith chart.
where Rs is the series resistance of the diode, Cj is the diode junction capacitance, and θon is the turn-on angle of the diode. In Fig. 2, from 0.1 to 3.2 GHz, ZL is outside the circle where VSWR = 2. Our target is to compress the input impedance trajectory into the circle where VSWR = 2 over a wide frequency range.
To simplify the design process, the coupling between the transmission lines TL1 and TL4 is not considered in the initial stage. The total electrical length of the transmission lines TL1–TL4 is 180° @ 3 GHz, equivalent to 18° @ 0.3 GHz, and its effect at lower frequencies can be neglected. The electrical lengths of the transmission lines θ 1 and θ 2 are set to be 22.5° and 67.5° @ 3 GHz, respectively. To achieve a proper weak coupling, θ 1 is chosen to be shorter than θ 2. In our design, the coupling is approximately −30 dB at low frequencies and −20 dB at high frequencies, respectively. Consequently, it exerts a more pronounced impact on the high-frequency matching of the rectifier. By setting those electrical lengths to be constant, the number of unknown variables can be reduced, and we can solve the characteristic impedance of each transmission line by following procedures.
The transmission lines TL1 and TL2 convert the impedance at the center frequency to be 50 Ω:
\begin{equation}{Z_{L1}}\left( {{{\left( {{f_H} + {f_L}} \right)} \mathord{\left/
{\vphantom {{\left( {{f_H} + {f_L}} \right)} 2}} \right.
} 2}} \right) = 50\end{equation}By solving Equation (3), we can get Z 01 = 98.48 Ω, and Z 02 = 87.39 Ω, respectively. After this step, the curve of ZL 1 from 0.59 to 2.3 GHz is within the VSWR = 2 circle. Then, the trajectory of Zin 1 is further compressed to the center of the Smith chart. By solving
\begin{equation}\left| {{\Gamma _{in}}\left( {{f_L},\;{f_H}} \right)} \right| = 2\end{equation}we can get Z 03 = 98.48 Ω, and Z 04 = 87.39 Ω, respectively. The bandwidth is broadened to 0.39–2.72 GHz.
Finally, the coupling between TL1 and TL4 is considered to broaden the bandwidth of the rectifier. The coupling has the effect of rotating the trajectory of Zin 1 anticlockwise on the Smith chart, as shown in Fig. 2. Thus, the impedance at around 3 GHz can be rotated and compressed into the circle where VSWR = 2. When TL1 is close to TL4, the coupling between them is stronger, and weaker when they are farther apart. By using simulation to vary their distance and observing the bandwidth of S11, we can obtain the final design parameters. Figure 3 compares the simulated |S 11| and PCE of the rectifier with and without TL1 and TL4 coupled. As shown, with the coupling, the higher frequency edge for |S 11| < −10 dB can be extended from 2.73 to 3.05 GHz, while the lower frequency edge remains nearly unchanged. Meanwhile, the higher frequency edge for efficiency over 70% is extended from 2.7 to 3 GHz with the same lower frequency edge. The electrical lengths of TL1 and TL4 are 22.5° @ 3 GHz, which is 2.25° @ 0.3 GHz. At low frequencies, the electrical lengths of TL1 and TL4 are very short, leading to weaker coupling between them. However, at high frequencies, their electrical lengths are longer, resulting in stronger coupling. Therefore, the coupling between TL1 and TL4 has a smaller impact on the rectifier at low frequencies.
Figure 3. Comparison of |S 11| and PCE with and without TL1 and TL4 coupled.
In order to further investigate the effect of electrical lengths θ 1 and θ 2 on the input matching, the return loss performance is simulated by changing θ 1 and θ 2 in Fig. 4. As shown, with the increment of θ 1 and θ 2, the higher operating frequency edge moves towards the lower frequency. Compared with θ 2, although θ 1 only changes slightly for low frequencies, the lower operating frequency changes more noticeably. Here, the coupling plays an important role.
Figure 4. Comparison of |S 11| changing with different electrical lengths, (a) θ 1, (b) θ 2.
Implementation and measurement results
According to the above analysis, the initial dimensions of the rectifier can be obtained. Then, all the dimensions for the rectifier are optimized in ADS. The ultra-wideband rectifier, using Infineon BAT15-04 W Schottky diode, is fabricated on a 0.8 mm thick F4B substrate with a relative permittivity of 2.6 and a loss tangent of 0.002. Figure 5 depicts the layout and photograph of the fabricated rectifier with dimensions of 19 mm × 18 mm. The DC-blocking capacitor C 1 is 47 pF, the by-pass capacitor CL is 180 pF, and the load RL is 500 Ω.
Figure 5. Layout and photograph of the fabricated ultra-wideband rectifier.
The Agilent N5230A network analyzer with a maximum power of 14 dBm was used for |S 11| measurement. The simulated and measured |S 11| under power levels of 0, 5, 10, and 14 dBm are plotted in Fig. 6(a). The simulated |S 11| is better than −10 dB at 14 dBm from 0.51 to 2.88 GHz, while the measured one is from 0.54 to 3 GHz. The measured results agree well with the simulated ones, except for a slight frequency shift, which may be attributed to fabrication and tolerance errors. Figure 6(b) depicts the simulated and measured PCEs changing with the frequency from 0.1 to 3.2 GHz when the input power is 0, 5, 10, and 18 dBm, respectively. These results confirm a good correlation between simulation and measurement. At an input power of 18 dBm, the simulated PCE is over 60% from 0.1 to 2.92 GHz, while the measured one is from 0.3 to 2.9 GHz. When the input power is reduced to 10 dBm, the measured PCE is still over 50% from 0.3 to 2.9 GHz.
Figure 6. Simulated and measured |S 11| and PCE versus frequency at different input power, (a) |S 11|, (b) PCE.
Figure 7 shows simulated and measured PCEs and output DC voltage versus the input power at four typical frequencies, 0.3, 0.9, 1.6, and 3 GHz, respectively. The simulation and measurement agree well with each other, except for the best PCE point, which shows a notable discrepancy. This difference could be attributed to the breakdown voltage of the diode model being larger than the actual one. Also, the marginal difference observed between the measured and simulated results may be ascribed to the package parasitic effects, particularly notable at higher frequencies. In Fig. 7, at the four frequencies, the measured PCE reaches its maximum value of 65.8%, 79.8%, 75.2%, and 56.2%, respectively. At 0.9 GHz, the measured PCE is over 50% when the input power ranges from 5 to 22 dBm, with a dynamic range of 18 dB. Figure 8 shows the simulated and measured PCE changing with the load at 0.9 GHz when the input power is 0, 5, 10 and 18 dBm. As shown, the optimal load resistance of the rectifier is about 500 Ω. The measured PCE is slightly lower than the simulated PCE. When the load is larger than 1500 Ω, and the input power is 18 dBm, the measured PCE is much lower than the simulated one. In the simulation, the diode operates before breakdown, whereas in the measurement, the diode has undergone breakdown, leading to a significant drop in efficiency. It should be noted that the breakdown voltage specified in the model is higher than the diode’s actual breakdown voltage.
Figure 7. Simulated and measured PCE and output DC voltage versus input power: (a) 0.1 GHz, (b) 0.9 GHz, (c) 1.6 GHz, (d) 3.1 GHz.
Figure 8. Simulated and measured PCE changing with the load resistances under different input power levels.
The performance comparison of the proposed ultra-wideband rectifier and the recently published works in the literature is listed in Table 1. As shown, the proposed rectifier has a broader bandwidth than the majority of rectifiers, surpassing all except for those in papers [Reference Mansour and Kanaya10] and [Reference Gyawali, Thapa, Barakat, Yoshitomi and Pokharel19]. Notably, the efficiency over bandwidth in paper [Reference Mansour and Kanaya10] is 45%, while our design achieves 60%. Additionally, the rectifier in paper [Reference Gyawali, Thapa, Barakat, Yoshitomi and Pokharel19] operates at a much lower frequency of 0.06 GHz compared to our rectifier’s 0.3 GHz. Moreover, our design has a smaller size compared to the other works. In summary, our design showcases the merits of high efficiency, broad bandwidth, and compact size.
Table 1. Comparison between the proposed rectifier and the references
BW: bandwidth.
Conclusion
This paper presents a compact and ultra-wideband microwave rectifier using an asymmetric coupled-line as the input impedance matching network. The rectifier, with dimensions of 19 mm × 18 mm, has a measured PCE of over 60% from 0.3 to 2.9 GHz (162.5% relative bandwidth) at an input power of 18 dBm. The high performance is attributed to the asymmetric coupled-line impedance transformer. The proposed rectifier can be applied in WPT applications where compact size and wide bandwidth are required.
Author contributions
Fei Cheng and Li Wu derived the theory and Chun-Hong Du performed the simulations. All authors contributed equally to analyzing data and reaching conclusions, and in writing the paper.
Funding statement
This work was supported by the foundation of National Key Laboratory (Grant No. 2023-JCJQ-LB-051-06).
Fei Cheng received the B.S. degree from Xidian University, Xi’an, China, in 2009, and the Ph.D. degree from University of Electronics Science and Technology of China, Chengdu, China, in 2015. From 2013 to 2015, he was a visiting PhD student at the University of Birmingham, UK. From 2015 to 2017, he was with Chengdu Jiuzou Dfine Technology Co. Ltd. as a microwave engineer. Since July 2017, he joined Sichuan University as an assistant professor. His main research interests are microwave components such as filter, antenna, and rectifier.
Chun-Hong Du received the B.Sc. degree from Chengdu University of Information Technology in 2022. He is currently pursuing the M.S. degree at Sichuan University. His current research interests include wireless power transfer and microwave rectifier.
Li Wu received the B.Sc. degree in electronic information engineering from Sichuan University, Chengdu, China, in 2010. She then went to further her study in the Institute National Polytechnique de Toulouse (INPT) in France and obtained the Ph.D. degree in microwave, electromagnetic and photoelectron in 2016. Her current research interests include microwave plasma discharge theory and its industrial applications, and permittivity measurement.
Chao Gu received the B.S. and M.S. degrees from Xidian University, Xi’an, China, in 2009 and 2012, respectively, and the Ph.D. degree from the University of Kent, Canterbury, U.K., in 2017. He is currently with the Centre for Wireless Innovation, ECIT Institute, School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Belfast, U.K. His research interests include phased array antennas, reconfigurable antennas, and frequency selective surfaces.
