Introduction
The widespread use of technologies such as the Internet of Things (IoT) has significantly impacted our daily lives. The increasing number of IoT sensor nodes and end devices presents a considerable challenge in providing them with sustainable power. Consequently, wireless power transmission wireless power transfer (WPT) has garnered considerable attention in recent years as a potential solution to address this formidable challenge [Reference Wang, Cheng and Gu1–Reference Cheng, Xiao and Gu4]. As the integral component of wireless power transfer (WPT), the rectifier plays a pivotal role in converting the microwave energy received by the receiving antenna into direct current (DC) [Reference Cheng and Gu5]. In the WPT system, the utilization of rectifiers that operate across multiple bands is advantageous, enabling the collection of a greater amount of energy for DC conversion [Reference Du, Cheng and Gu6], thereby enhancing overall energy utilization efficiency. Dual-band rectifiers, as a result, assume critical importance in their capability to extract radio frequency (RF) energy across two distinct frequency bands [Reference Liang and Yuan7–Reference Dubey, Srivastava, Singh and Meshram19].
Once the load section of the rectifier is determined, the dual-band performance of the rectifier primarily depends on the input matching network (IMN). The impedance of the diode, being a function of frequency, presents the main challenge in the design of dual-band rectifiers. Over the past years, several IMNs have been proposed for the design of dual-band rectifiers. For instance, in reference [Reference Chang, Ma, Han, Xue, Liu and Li8], dual-band impedance matching was achieved by two independent matching networks. A metamaterial adaptive frequency switch was utilized to enable independent regulation of a single rectifier circuit at different bands, thereby achieving dual-band matching. Reference [Reference Huang9] proposed a rectifier array that realized dual-band matching by coupling lines using a T-junction power divider. However, the design of the rectifier array leads to an increase in both the circuit size and the quantity of load resistors and diodes present, which elevates both the complexity and loss of circuit. References [Reference Bui, Nguyen and Seo10–Reference Nguyen, Bui, Nam and Seo12] introduced a harmonic termination network for obtaining high power conversion efficiency (PCE) at two frequencies simultaneously. Furthermore, various simplified dual-band matching networks, such as the T-type network [Reference Nguyen and Seo13, Reference Liu, Huang and Du14], L-type network [Reference Li, Cheng, Gu, Yu and Huang15], and π-type network [Reference Liu, Zhang and Xue16], have been proposed to configure dual-band rectifiers. However, high-Q and low-loss matching networks make it challenging to extend the bandwidths. In reference [Reference Liu, Zhang and Yang17], a novel dual-band rectifier with cascaded L-type and π-type matching network was introduced for 0.915 and 2.45 GHz working. Reference [Reference Lee and Oh18] proposed a dual-band matched voltage doubler network that extends the bandwidth. Furthermore, Reference [Reference Dubey, Srivastava, Singh and Meshram19] reported a rectifier working at 1.4 and 2.45 GHz for low RF power harvesting. However, lumped elements are lossy at high frequencies, which degrade the rectifier’s PCE performance.
In this paper, a universal dual-band input matching method has been proposed for dual-band rectifier design. The proposed rectifier utilizes only three section transmission lines to achieve broad dual-band input matching. Compared with the previous works, a significant expansion on the bandwidth has been achieved in this rectifier and only three microstrip lines for the IMN are used in this work, which reduce the complexity of the circuit. Moreover, according to theoretical analysis, the frequency ratio of the operating frequencies can be adjusted by controlling the characteristic impedance and electrical length of the transmission lines. To validate our design, the rectifier was fabricated and measured which agree well with each other. The measured results show that the PCEs are 75.7% and 76.3% at 0.915 and 2.45 GHz, respectively, when the input power is 16 dBm. The proposed design shows a good potential of this rectifier for application in practical wireless power transfer systems.
Design and analysis of the wideband rectifier
Figure 1 depicts the block diagram and layout of the proposed dual-band rectifier, which comprises a DC block capacitor, an IMN, two Schottky diodes (BAT15-04W), a DC-pass filter, and a load. The DC block capacitor serves the purpose of preventing the rectified DC current from flowing back to the signal source. The IMN is constructed from three series-connected transmission lines, where Z 0i and θ 0i (i = 1, 2, 3) denote the characteristic impedance and electric length of the ith microstrip transmission line, respectively. The voltage doubler topology was selected for its ability to facilitate an increase in the output DC voltage and extend the bandwidth [Reference Long, Cheng, Yu and Huang20]. The DC-pass filter, comprising two filtering capacitors and a series transmission line, is employed to suppress the higher harmonics.
Schematic and layout of the broad dual-band rectifier (a) Schematic and (b) Layout.
Design of DC-pass filter
The DC-pass filter, shown in Fig. 1(a), is designed to reflect the RF signals back to the diodes and extract the DC power. The electric length of the series microstrip line in this DC-pass filter is approximately 1/8λg @ 2.45 GHz. Parallel connected lumped capacitors C 2 and C 3 are selected as 68 pF. This π-type filter can effectively suppress high-frequency signals and their higher harmonics. The simulated S-parameters of the DC filter are depicted in Fig. 2. As shown, the return loss is nearly 0 dB which indicates that the RF signal is totally reflected. The fundamental signal is suppressed to −30 dB at 0.915 GHz and −60 dB at 2.45 GHz. The second and third harmonics are suppressed by more than 50 dB at 0.915 GHz and more than 70 dB at 2.45 GHz. Thus, the use of the DC-pass filter circuit yields an excellent harmonic suppression effect.
Simulated S-parameters of the DC-pass filter.
Design of multi-section transmission line impedance matching network
The following design procedure is carried out as shown in Fig. 3. In this design, the load impedance is 1000 Ω, and the input power level is 16 dBm. In the multi-section transmission line impedance matching network, ZL (f 1 and f 2) is transformed to Zin 1 (f 1 and f 2) through two series transmission lines TL2 and TL3, where ZL (fi) = RL (fi) + XL (fi), i = 1, 2, which are 129.73 − j81.13 and 47.9 − j71.08 Ω. The ABCD matrix of those two transmission lines can be expressed as
\begin{equation}\left[ {{A_{in1}}} \right] = \left[ {{A_2}} \right]\left[ {{A_3}} \right] = \left[ {\begin{array}{*{20}{c}}
a&b \\
c&d
\end{array}} \right],\end{equation}Design principle of the input impedance matching network. (a) Simulation diagram of matching process. (b) 0.915 GHz. (c) 2.45 GHz.
where,
\begin{equation}a = \cos {\theta _{02}}\cos {\theta _{03}} - \frac{{{Z_{02}}\sin {\theta _{02}}\sin {\theta _{03}}}}{{{Z_{03}}}},\end{equation}
\begin{equation}b = j\left( {{Z_{03}}\cos {\theta _{02}}\sin {\theta _{03}} + {Z_{02}}\cos {\theta _{03}}\sin {\theta _{02}}} \right),\end{equation}
\begin{equation}c = j\left( {\frac{{\sin {\theta _{02}}\cos {\theta _{03}}}}{{{Z_{02}}}} + \frac{{\cos {\theta _{02}}\sin {\theta _{03}}}}{{{Z_{03}}}}} \right),\end{equation}
\begin{equation}d = \cos {\theta _{02}}\cos {\theta _{03}} - \frac{{{Z_{03}}\sin {\theta _{02}}\sin {\theta _{03}}}}{{{Z_{02}}}},\end{equation}And the input impedance of the ABCD matrix of those two transmission lines can be expressed as
\begin{equation}{Z_{in1}}\left( {{f_i}} \right) = \frac{{a{Z_L}\left( {{f_i}} \right) + b}}{{c{Z_L}\left( {{f_i}} \right) + d}},i = 1,2,\end{equation}The characteristic impedance and electric length are properly designed to satisfy the condition that the imaginary part of Zin 1 (f 2) is zero. So, take equation (1) into equation (3) and separate its imaginary part, we can obtain the follow equation
\begin{equation}bd + j{X_L}\left( {{f_2}} \right)\left( {ad + bc} \right) - ac\left[ {{R^2}_L\left( {{f_2}} \right) + {X^2}_L\left( {{f_2}} \right)} \right] = 0,\end{equation}Here, the input impedance of the rectifier at two operating frequencies has changed to (63.448 − j46.26) Ω and 201.29 Ω. Then, through a series transmission line TL1 whose electric length is 1/4λg @ 2.45 GHz, the rectifier can be matched to 50 Ω at two operating frequencies. The ABCD matrix of the IMN can be expressed as
\begin{align}\left[ A \right] &= \left[ {{A_1}} \right]\left[ {{A_{in1}}} \right] = \left[ {\begin{array}{*{20}{c}}
{{A_{11}}}&{{A_{12}}} \\
{{A_{21}}}&{{A_{22}}}
\end{array}} \right] \nonumber\\
&= \left[ {\begin{array}{*{20}{c}}
{a{\text{cos}}{\theta _{01}} + jc{Z_{01}}\sin {\theta _{01}}}&{b{\text{cos}}{\theta _{01}} + jd{Z_{01}}\sin {\theta _{01}}} \\
{c{\text{cos}}{\theta _{01}} + \frac{{ja\sin {\theta _{01}}}}{{{Z_{01}}}}}&{d{\text{cos}}{\theta _{01}} + \frac{{jb\sin {\theta _{01}}}}{{{Z_{01}}}}}
\end{array}} \right],\end{align}The input impedance of the ABCD matrix of the matching network can be expressed as
\begin{equation}{Z_{in}}\left( {{f_i}} \right) = \frac{{{A_{11}}{Z_L}\left( {{f_i}} \right) + {A_{12}}}}{{{A_{21}}{Z_L}\left( {{f_i}} \right) + {A_{22}}}},i = 1,2,\end{equation}Bring ZL (f 1 and f 2), θ 01 (f 1 and f 2) and Zin (f 1 and f 2) = 50 Ω into equation (6), we can get 4 equations with 5 unknowns. And combine these equations with equation (4), we can get a system of equations that contains 5 equations and 5 unknowns. Therefore, these unknowns can be uniquely solved. In the analysis of the matching network, the derived equation (4) does not need to be solved separately, it should be combined with the subsequent equations to form a system of equations for solving. Therefore, the design parameters of the multi-section transmission line IMN can be solved.
The proposed multi-section transmission line IMN can successfully achieve impedance matching across different frequency ratios. To verify the applicability of this method, the dual-band rectifier with three different frequency ratios for model I, II, and III were simulated, in these simulations, the high frequency was fixed at 2.45 GHz, while the low frequency was adjusted to 0.6, 0.915, and 1.2 GHz, respectively, resulting in corresponding frequency ratios of 4.08, 2.68, and 2.04. The simulation results, including |S 11| and PCE, are illustrated in Fig. 4. Evidently, |S 11| consistently performs better than −20 dB at the working frequencies, indicating a favorable matching. Moreover, the peak PCEs of the rectifier exceed 80% at the operating frequencies. Since the proposed rectifier is wide dual-band, only the PCE near the working frequency of the rectifier needs to be considered here, and the PCE between the two working frequencies of the rectifier does not need to be considered. Overall, the proposed matching network can be suitably employed in the design of dual-band rectifiers with frequency ratios from 2.04 to 4.08.
Simulated |S 11| and PCE versus frequency for dual-band rectifiers at different frequency ratios, (a) |S 11|, (b) PCE. In model I, (Z 01, Z 02, Z 03, θ 01, θ 02, θ 03) = (134.58 Ω, 75.59 Ω, 57.27 Ω, 90°, 118.58°, 21.41°). In model II, (Z 01, Z 02, Z 03, θ 01, θ 02, θ 03) = (100.95 Ω, 68.76 Ω, 145.12 Ω, 90°, 43.13°, 51.39°). In model III, (Z 01, Z 02, Z 03, θ 01, θ 02, θ 03) = (30.37 Ω, 50.68 Ω, 90.81 Ω, 90°, 127.25°, 74.26°).
Implementation and measurement results
The design employs a 0.8 mm F4B substrate with a relative dielectric constant of 2.6 and a loss tangent of 0.001. The Infineon BAT15-04W Schottky diode [21] is utilized in the design due to its low series resistance and zero-bias junction capacitance, which significantly contribute to PCE. Murata capacitors with a value of 68 pF are deployed for both the DC block capacitors (C 1) and the filter capacitors (C 2 and C 3), while the output load R L is set to 1000 Ω. To reduce the circuit size, the IMN is folded, resulting in the rectifier circuit dimensions of 23 mm × 14 mm.
To verify the dual-band characteristics of the rectifier, the simulated and measured |S 11| and PCE across 0.5–3 GHz at 16 dBm input power are plotted in Fig. 5(a). The simulated and measured result has a small shift, this may result from the parasitic of the capacitors. The measured |S 11| at 0.915 and 2.45 GHz are −17.58 and −15.61 dB, while the simulated ones are −23.38 and −27.69 dB at the operating frequencies. The measured |S 11| is below −15 dB from 0.845 to 1 GHz and 2.44 to 2.57 GHz, whereas the corresponding simulated ones are 0.78 to 0.95 GHz and 2.35 to 2.54 GHz. The measured PCEs are 75.7% and 76.3% at 0.915 and 2.45 GHz, which is slightly lower than the simulated values of 82.9% and 77.5%. The measured PCEs exceed 70% over the ranges of 0.78–1.16 GHz and 2.4–2.6 GHz, respectively. It manifests that good impedance matching is achieved by using the multi-section transmission line IMN, and high PCEs can be achieved in a broad frequency range.
Simulation and measurement, (a) |S 11| and PCE versus frequency and (b) PCE and output voltage versus input power. (Solid line: measurement, dash line: simulation).
Figure 5(b) shows the rectifier’s simulated and measured PCE and output DC voltage changing with input power. The measured PCE is greater than 70% when the input power increases from 11 to 18 dBm at 0.915 and 2.45 GHz, while the simulated input power dynamic range extends from 8 to 20 dBm for 0.915 GHz and from 9 to 20 dBm for 2.45 GHz. The measured output voltage at 0.915 and 2.45 GHz is 5.49 and 5.51 V, respectively, at an input power of 16 dBm. There appears to be a disparity between the outcomes obtained from simulations and actual measurements, which could be attributed to discrepancies between the breakdown voltage specified by the simulation model and the actual diode. Table 1 summarizes this work alongside previously reported dual-band rectifier works. The proposed rectifier outperforms other works regarding bandwidth and PCE while maintaining a smaller footprint.
Comparison between the proposed rectifier and the references
Note: NA: not applicable; λ0 is the wavelength referring to the lowest frequency of rectifier operation.
Conclusion
This paper has presented an efficient broad dual-band rectifier using a multi-section matching network for WPT applications. In comparison to other dual-band rectifiers that have been reported, this rectifier expands the bandwidth and adapts to a variety of frequency ratios. Additionally, this rectifier exhibits the advantages of possessing a simple structure and a compact circuit size. The dual-band rectifier is fabricated and measured to validate the performance of the proposed topology. The maximum PCEs are 75.7% and 76.3% at 0.915 and 2.45 GHz, respectively, when the input power is 16 dBm. The rectifier is suitable for applications in a WPT system due to its excellent performance.
Author contributions
Fei Cheng, Li Wu and Chao Gu 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 in part by the Sichuan Science and Technology Program (Grant No. 2022YFH0097), in part by the State Key Laboratory of Millimeter Waves (Grant No. K202206), and in part by the Fundamental Research Funds of Shaanxi Key Laboratory of Artificially-Structured Functional Materials and Devices (Grant No. AFMD-KFJJ-21202).
Competing interests
The authors report no conflict of interest.
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.
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.
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.
