Introduction
With the invention of rectenna (rectifying antenna), microwave energy-harvesting (MEH) and microwave power transfer (MPT) technologies have received wide notice in the research and industry. Rectennas give MEH and MPT systems flexibility in terms of physical wiring, battery charging, and periodic replacement. Such systems have found applications in wireless charging of mobile phones or any electric/electronic equipment, radio-frequency (RF) identification (RFID) tags, Internet of Things, implantable/wearable biomedical devices, wireless sensors, and devices in the smart home [Reference Surender, Halimi, Khan, Talukdar and Rengarajan1–Reference Hussein and Mohammed3]. Wi-Fi, GSM, LTE, and third/fourth/fifth generation (3G/4G/5G) are some wireless communication systems that radiate electromagnetic power in the environment. Radiation from these systems may serve as a source of electromagnetic energy that may harvest using an appropriate rectenna. Rectifying antenna A rectenna consists of an antenna, and rectifier, through a matching circuit. The rectifier is the crucial component of the rectenna for converting microwave energy into electrical direct current (DC). Therefore, several recent studies have been conducted to introduce efficient rectifier circuits [Reference Halimi, Khan, Nasimuddin and Antar4–Reference Surender, Halimi, Khan, Talukdar, Kanaujia, Rambabu and Kishk8]. The popular rectifier topologies are series diode [Reference Halimi, Surender, Khan, Kishk and Rengarajan9], shunt diode [Reference Meher, Mishra and Halimi10], voltage doubler (VD) [Reference Halimi, Khan, Kishk and Rengarajan11], and Greinacher full-wave rectifiers [Reference Gozel, Kahriman and Kasar12]. VD topology doubles the output voltage and improves the power handling capability for low power requirements [Reference Halimi, Surender and Khan13]. The matching circuit is very essential for maximum power transfer from the antenna to the rectifier. To know the input impedance of the rectifier is necessary for proper matching network (MN) design. The operating frequency and input power level affect the input impedance of the rectifier. Hence, it is very difficult to find impedance matching at two or more frequencies simultaneously [Reference Shieh and Kamarei14–Reference Trevisoli, D. Paz, D. Silva, Doria, Casella and Capovilla16]. A dual-band rectifier (DBR) has the potential to utilize two bands simultaneously which can improve the output power levels. In recent years, many techniques have been adopted to design a DBR. In paper [Reference Niotaki, Kim, Jeong, Collado, Georgiadis and Tentzeris17], a rectifier using an impedance matching network (IMN), having three lumped inductors and a radial stub, was designed to work at 0.915 and 2.45 GHz, simultaneously. A dual-band matching was realized using cascaded L-type and π-type networks to design a DBR circuit working at 0.915 and 2.45 GHz bands [Reference Liu, Zhang and Yang18]. In paper [Reference Quddious, Zahid, Tahir, Antoniades, Vryonides and Nikolaou19], two-branch IMN was utilized to match within the 0.9 GHz UHF and 2.45 GHz ISM bands using a T-type MN. In paper [Reference Jiang, Liu, Huang, Huang and Huang20], a DBR circuit consisting of a band-stop filter (BSF), a short-ended quarter-wave transmission line (QWTL) in series with a shunt diode, and a short-ended quarter-wave stub was proposed. Here, BSF and QWTL were applied to block the second harmonic at 2.45 and 5.8 GHz, respectively. A short-ended quarter-wave stub was applied for impedance tuning at the first band. In papers [Reference Wang and Negra21, Reference Huang, Wang, Wu and Liu22], dual-band IMN at 2.45 and 5.8 GHz has been designed by tuning the characteristic impedance (width) of a quarter-wave short-ended stub. A dual-band matching at 0.915 and 2.45 GHz was realized using a stepped impedance stub (SIS) [Reference Li, Cheng, Gu, Yu and Huang23]. The uniform width stub was cut out to form a SIS to find matching at two resonance bands to design a DBR. In paper [Reference Dubey, Srivastava, Singh and Meshram24], a DBR was designed using lumped component-based modified T-section IMN. The DBRs above targeted GSM 0.9 GHz, GSM 1.8 GHz, ISM 2.45 GHz, and ISM 5.8 GHz bands. However, the commercialization of fifth-generation (5G) wireless communication has gained attention to the design of a rectifier operating at sub-6 GHz 5G bands. Some of the DBRs are reported at one of the 5G bands. DBR was reported to operate at 2.45 GHz Wi-Fi and 3.5 GHz 5G using composite left/right-handed-based IMN [Reference Chandrasekaran, Agarwal, Alphones, Mittra and Karim25], short-ended stub IMN [Reference Eltresy, Eisheakh, Abdallah and Elhenawy26], and two-branch IMN [Reference Wang, Fan, Yang, Li, Feng and Shi27]. In [Reference Derbal and Nedil28–Reference Halimi, Khan, Koul and Rengarajan30], DBRs were proposed to work at 3.5 and 5.8 GHz bands. In paper [Reference Bui, Nguyen and Seo31], a rectifier has been designed using π-type dual-band IMN with a dual-band harmonic termination network (HTN). In paper [Reference Noor, Zakaria, Lago and Said32], a DBR using two-branch IMN was utilized to work at 2.45 and 5 GHz. In paper [Reference Patil, Subramanian, Pradhan, Varadharaj, Senthilkumaran and Murugesan33], a three-stage Villard DBR was designed to operate at 2.4 and 5.2 GHz.
All of these rectifiers have relatively low efficiencies. Also, the DBR reported in papers [Reference Chandrasekaran, Agarwal, Alphones, Mittra and Karim25–Reference Patil, Subramanian, Pradhan, Varadharaj, Senthilkumaran and Murugesan33] does not focus on dual 5G bands. In paper [Reference Bougas, Papadopoulou, Boursianis, Nikolaidis and Goudos34], a Greinacher full-wave rectifier circuit was developed to operate at dual 5G bands, and at 12 dBm input, it achieved 22.7% and 30.7% power conversion efficiency (PCE) at 3.5 and 5.0 GHz, respectively. In paper [Reference Yu, Wang, Ju, Zhang, Liu, Tao and Lu35], a transparent and flexible dual-band 5G rectifier was reported, but the achieved PCE at 13 dBm was 54.67% and 7% at N78 and N79 bands, respectively, which is very poor, especially at the N79 band. Hence, it is desirable to develop an efficient and compact rectifier circuit to harvest RF energy of sub-6 GHz dual 5G bands. The 5G bands adopted in some nations are displayed in Table 1 [Reference Halimi, Shome, Khan and Rengarajan36] which is self-explanatory.
Table 1. Sub-6 GHz fifth-generation bands
The short-ended stub [Reference Jiang, Liu, Huang, Huang and Huang20–Reference Huang, Wang, Wu and Liu22], stepped impedance short-ended stub [Reference Li, Cheng, Gu, Yu and Huang23], composite right/left-handed structure [Reference Chandrasekaran, Agarwal, Alphones, Mittra and Karim25], half-wavelength transmission line (TL) [Reference Halimi, Khan, Koul and Rengarajan30], π-type dual-band IMN with dual-band HTN [Reference Bui, Nguyen and Seo31], cross-branch dual-stub [Reference Bougas, Papadopoulou, Boursianis, Nikolaidis and Goudos34], and combination of open and short-ended stub [Reference Guo, Li, Sun, Zhao and Wu37] were utilized in some of the existing designs to achieve dual-band matching. The proposed design uses a novel stepped impedance TL technique to satisfy the matching at two sub-6 GHz fifth-generation (5G) bands. Hence, the novelty of the proposed dual-band 5G rectifier is in terms of (a) dual 5G bands with better performance compared to existing ones and (b) a novel dual-band matching technique using a stepped impedance TL.
This paper demonstrates an efficient DBR circuit covering 3.3–3.7 GHz (N 78 band adopted by India, China, Europe, and Korea) and 4.8–5.0 GHz bands (N 79 band adopted by China). The power/frequency-weighted efficiency (PFE) has been derived to compare the overall circuit performance including frequency of operation and operating power level. The proposed work exhibits the highest PFE. The rest of this paper is arranged as follows. The “Dual-band rectifier” discusses the geometric description and simulated results of the proposed DBR circuit. The “Fabrication, measurement, and comparison” section discusses the fabrication and characterization of the rectifier. Finally, the work is concluded in the “Conclusion” section.
Dual-band rectifier
The design of a DBR is auspicious to operate at sub-6 GHz 5G bands. For this, a dual-band MN is needed. It is very challenging to design an MN satisfying two different operating frequencies because of the diode’s nonlinear nature. One of the methods is to combine two rectifiers operating at two different operating frequencies. The second method is to utilize a single dual-band MN. The proposed design uses a novel stepped impedance TL to satisfy the matching at two sub-6 GHz fifth-generation (5G) bands.
Geometrical description
Figure 1(a) and (b) displays the schematic and layout view of the proposed DBR circuit. The SOT-23 package of HSMS-2862 (VD topology) is used in the proposed rectifier. The substrate used in this design is RO4003 (dielectric constant = 3.55, loss tangent = 0.0027, and thickness = 1.524 mm). The MN is based on stepped impedance TL segments of different lengths. For simplification, the principle of dual-band impedance transformation is analyzed using lossless TL theory [Reference Costantine, Eid, Abdallah, Tawk and Ramadan38]. The impedance 
${Z_{\textrm{a}}}$ across the TL, TL1 can be calculated using (1):
\begin{equation}{Z_{{\textrm{a}}@{f_i}}} = {Z_{0{\textrm{TL}}1}}{{{Z_{{\textrm{L}}@fi}} + j{Z_{0{\textrm{TL}}1}}\tan {\beta _{fi}}{L_{{\textrm{TL}}1}}} \over {{Z_{0{\textrm{TL}}1}} + j{Z_{{\textrm{L}}@fi}}\tan {\beta _{fi}}{L_{{\textrm{TL}}1}}}}\end{equation}
Figure 1. Image of dual-band rectifier: (a) Schematic view and (b) Layout view.
Here, “i” denotes 1 and 2 of the DBR’s first and second bands, f 1 and f 2, respectively. The impedance 
${Z_{\textrm{b}}}$, 
${Z_{\textrm{c}}}$, and 
${Z_{{\textrm{in}}}}$ across the TL2, TL3, and TL4, respectively, can be calculated using (2), (3), and (4), respectively:
\begin{equation}{Z_{{\textrm{b}}@{f_i}}} = {Z_{0{\textrm{TL}}2}}{{{Z_{{\textrm{a}}@fi}} + j{Z_{0{\textrm{TL}}2}}\tan {\beta _{fi}}{L_{{\textrm{TL}}2}}} \over {{Z_{0{\textrm{TL}}2}} + j{Z_{{\textrm{a}}@fi}}\tan {\beta _{fi}}{L_{{\textrm{TL2}}}}}}\end{equation}
\begin{equation}{Z_{{\textrm{c}}@{f_i}}} = {Z_{0{\textrm{TL}}3}}{{{Z_{{\textrm{b}}@fi}} + j{Z_{0{\textrm{TL}}3}}\tan {\beta _{fi}}{L_{{\textrm{TL}}3}}} \over {{Z_{0{\textrm{TL}}3}} + j{Z_{{\textrm{b}}@fi}}\tan {\beta _{fi}}{L_{{\textrm{TL3}}}}}}\end{equation}
\begin{equation}Z_{in@f_i}=Z_{0TL4}\frac{Z_{c@fi}+jZ_{0TL4}\tan\beta_{fi}L_{TL4}}{Z_{0TL4}+jZ_{c@fi}\tan\beta_{fi}L_{TL4}}\end{equation} For matching at two frequencies, f 1 and f 2, the real and imaginary parts of the input impedance 
${Z_{{\textrm{in}}}}$should follow the criteria of (5) and (6).
\begin{equation}{{\rm Re}}\left( {{Z_{{{\rm in}}@{f_1}}}} \right) \approx {{\rm Re}}\left( {{Z_{{{\rm in}}@{f_2}}}} \right) \approx 50\;\Omega \end{equation}
\begin{equation}{{\rm Im}}\left( {{Z_{{{\rm in}}@{f_1}}}} \right) \approx {{\rm Im}}\left( {{Z_{{{\rm in}}@{f_2}}}} \right) \approx 0\;\Omega \end{equation}The matching at two frequency bands is achieved by tuning the TL parameters. The 3.5 and 4.9 GHz dual sub-6 GHz 5G bands are selected as f 1 and f 2, respectively.
Figure 2(a) shows the input impedance of the rectifier circuit without using the MN are Z L@f1 = 157 + j8 Ω and Z L@f2 = 20 – j61 Ω. After introducing a MN using the source pulling technique, Fig. 2(b) shows the input impedance of the rectifier becomes, Z [email protected] GHz = 52-j1 Ω and Z [email protected] GHz = 45 – j9 Ω which satisfies (5) and (6). The optimal dimensions of the TLs (in mm) are; L TL1 = 4.5, L TL2 = 4.2, L TL3 = 5, L TL4 = 3.8, L TL5 = 6, L TL6 = 6.4, L TL7 = 3.8, W TL1 = 1, W TL2 = 8.6, W TL3 = 7, W TL4 = 3.6, W TL5 = W TL6 = 1, W TL7 = 1.1, radius of fan-shaped stub r = 9 and angle θ = 60o.
Figure 2. Input impedance of rectifier (a) without MN (Z L) and (b) with an MN (Z in).
Simulated results and discussion
The rectifier circuit is simulated using Keysight advanced design system. At different values of input power levels, the simulated S 11 vs. frequency is depicted in Fig. 3(a). The result shows that the circuit is well-matched at both 3.5 GHz and 4.9 GHz 5G bands. The PCE in the desired band is simulated for different load values and input power. The PCE vs. P in at 3.5 and 4.9 GHz is displayed in Fig. 3(b). The maximum PCE is 70.6% @6 dBm and 62.9% @ 5 dBm at 3.5 and 4.9 GHz, respectively, for a 3 kΩ load. The simulated PCE is greater than 50% for the input power range from −2.5 to 12.4 and −0.8 to 8.3 dBm for 3.5 and 4.9 GHz, respectively. PCE vs. load is depicted in Fig. 3(c) at 0, 3, and 6 dBm input power levels at both frequencies. With the increase of load value, PCE starts increasing and reached its maximum value, and then starts decreasing. Hence, a 3-kΩ resistor is selected as the optimum load to better perform at an input power level between −10 and 10 dBm.
Figure 3. Simulated performance: (a) S 11 vs. frequency, (b) PCE vs. input power (P in), (c) PCE vs. load (R L). (d) PCE vs. frequency, and (e) V out vs. frequency.
Figure 4. (a) Measurement setup, (b) rectifier prototype.
Figure 3(d) shows the PCE vs. frequency graph. The maximum simulated PCE at two different bands is 72.8% and 67.2% at 3.55 and 4.94 GHz at 6 dBm. PCE is higher than 60%, from 3.35 to 3.83 and 4.83 to 5.09 GHz. At a 3 dBm power level, the PCE is higher than 55% from 3.3 to 3.74 and 4.8 to 5.0 GHz. PCE is 61.4% and 53.5% at 3.45 and 4.8 GHz, respectively, at 0 dBm. The V out vs. frequency at −3, 0, 3, and 6 dBm input power levels are displayed in Fig. 3(e). At 3 dBm, the V out is greater than 1.5 V for both bands from 3.1 to 3.84 and 4.6 to 5.07 GHz. Also, the V out is more than 2.5 V from 3.28 to 3.86 and 4.76 to 5.13 GHz.
Fabrication, measurement, and comparison
For the endorsement of the proposed 5G rectifier, an experimental setup is depicted in Fig. 4(a). Figure 4(b) describes the fabricated prototype of the proposed DBR. The RF signal generator was used for input power feeding to the rectifier circuit, and a digital meter was used for output voltage measurement. The output DC voltage was noted, and the PCE was calculated using (7).
\begin{equation}{\textrm{PCE}} = {{V_{{\textrm{out}}}^2} \over {{R_{\textrm{L}}}*{P_{{\textrm{in}}}}}} \times 100\% \end{equation}Figure 5(a) shows the measured S11 (bottom left negative y-axis), Vout (right y-axis), and PCE (top left positive y-axis) vs. frequency, respectively at 6 dBm input power. Load resistance of 3 kΩ and input power of 0 dBm are applied to the rectifier. The measured value of |S 11| is −28.9 and −16.2 dB at 3.7 and 5.0 GHz respectively. The maximum recorded DC output voltage is 2.96 and 2.77 V at 3.7 and 5.05 GHz, respectively. The PCE is more than 50% for 3.25–3.96 and 4.81−5.15 GHz bands. Figure 5(b) and (c) show the V out and PCE vs. P in, respectively. The measured DC output voltages recorded are 1.32 V @ 0 dBm and 2.53 V @ 5 dBm at 3.5 GHz, respectively. At 4.9 GHz, the output voltages are 1.26 V @ 0 dBm and 2.31 V @ 5 dBm. At 3.5 GHz, the measured PCE is 58.1% @ 0 dBm, 67.3% @ 5 dBm, and the maximum PCE reached 67.6% @ 6 dBm input power. The measured value of PCE at 4.9 GHz is 52.8% at 0 dBm, 56.3% at 5 dBm, and the peak PCE reached 56.8% at 3.5 dBm input power. Measured results show good agreement with the simulated ones. The little difference between simulated and measured performance may be due to diode model inaccuracies and fabrication tolerance.
Figure 5. Measured results of (a) S 11, PCE, V out vs. frequency, (b) V out, vs. P in, (c) PCE vs. P in.
Table 2 describes the comparison of the 5G DBR performance with some existing works. The rectifier achieved 58.1% and 52.8% PCE at 0 dBm for operating frequencies 3.5 and 4.9 GHz, respectively. The PCE at 0 dBm of existing rectifiers presented in papers [Reference Dubey, Srivastava, Singh and Meshram24, Reference Eltresy, Eisheakh, Abdallah and Elhenawy26, Reference Wang, Fan, Yang, Li, Feng and Shi27, Reference Nguyen, Bui, Nam and Seo39] looks better because of the lower operating frequency (band). Because of the skin effect and parasitic effects, the loss increases at a high operating frequency. Therefore, to compare DBRs operating at different bands, a frequency-weighted efficiency (FE) can be calculated using (8) [Reference Nguyen, Bui, Nam and Seo39]. The PCE presented in papers [Reference Bui, Nguyen and Seo31, Reference Nguyen, Bui, Nam and Seo39] looks better because of the higher input power level. As the PCE of the rectifier circuit is also influenced by input power level, a new PFE is presented in (9) to compare the overall circuit performance.
\begin{equation}{{\rm FE}} = \sum\limits_{i = 1}^n {\left[ {{\eta _i}\,f_i^{0.25}} \right]} \end{equation}
\begin{equation}{\textrm{PFE}} = {1 \over {{P_{{\textrm{in}}}}^{0.1}}} \times {\textrm{FE}}\end{equation}Table 2. Comparison with existing works
FE: frequency-weighted efficiency FE. PFE: power/frequency-weighted efficiency.
where n is the number of bands, 
${f_i}$ is the ith frequency band, 
${\eta _i}$ is the PCE at ith frequency band, and 
${P_{{\textrm{in}}}}$ is input power level in mW.
The power factor of input power in the denominator of (9) is decided based on the proposed circuit FOM at two different power levels (0 and 5 dBm). The circuit performance is found approximately equal using this overall PFE (i.e., approximately 158 and 156 at 0 and 5 dBm, respectively).
Conclusion
A rectifier to operate at dual sub-6 GHz 5G band has been designed. An HSMS2862 in the SOT-23 package (VD configuration) has been employed for RF to DC conversion. A stepped impedance TL-based MN has been utilized to transform the rectifier input impedance close to 50 Ω at both operating bands. The rectifier efficiently covers the 3.5 GHz (N78 band) and 4.9 GHz (N79 band) bands of fifth-generation wireless communication. A maximum PCE of 67.6% at 3.5 GHz and 56.8% at 4.9 GHz has been achieved. These characteristics make this rectifier a good candidate for MEH and MPT systems. Future work includes improving the sensitivity of the rectifier and a dual-band 5G antenna design to implement a rectenna circuit.
Funding statement
This work was supported by the Science and Engineering Research Board (SERB), Government of India under VAJRA Scheme (No. VJR/2019/000009, dated July 22, 2020).
Competing interests
The authors report no conflict of interest.
Md. Ahsan Halimi received his B.Tech. and M.Tech. degrees in the stream of Electronics and Communication Engineering from Ajmer Institute of Technology, Ajmer, India, and Pondicherry University, Pondicherry, India, respectively. He is working as a PhD scholar at National Institute of Technology Silchar, India. Currently, he is an assistant professor with the Department of Electronics and Communication Engineering, V R Siddhartha Engineering College, Vijayawada, India. His research interest includes RF energy harvesting, microwave rectifiers, UWB antennas, reconfigurable antennas.
Email: [email protected].
Taimoor Khan received his Ph.D. degree in Electronics and Communication Engineering from National Institute of Technology Patna, India. Presently he is an Assistant Professor in the Department of Electronics and Communication Engineering at the National Institute of Technology Silchar, Assam, since 2014. Before joining NIT Silchar, he served different organizations for around 15 years in different capacities like lab instructor, lecturer, assistant professor, and associate professor, respectively. His active research interest includes printed microwave circuits, electromagnetic bandgap structures, ultrawideband antennas, dielectric resonator antennas, ambient microwave energy harvesting, and artificial intelligence paradigms in electromagnetics.
Corresponding author email: [email protected].
Ahmed A. Kishk received his Ph.D. degree from University of Manitoba, Winnipeg, Canada, in 1986. From 1977 to 1981, he was a research assistant and an instructor at the Faculty of Engineering, Cairo University. From 1981 to 1985, he was a research assistant at the Department of Electrical Engineering, University of Manitoba. From December 1985 to August 1986, he was a research associate fellow in the same department. In 1986, he joined the Department of Electrical Engineering, University of Mississippi, as an assistant professor. He was on sabbatical leave at the Chalmers University of Technology, Sweden, during the 1994−1995 and 2009−2010 academic years. He was a professor at the University of Mississippi (1995−2011). He was the director of the Center for Applied Electromagnetic System Research (CAESR) during the period 2010–2011. Currently, he is a professor at Concordia University, Montréal, Québec, Canada (since 2011) as Tier 1 Canada Research Chair in Advanced Antenna Systems. Email: [email protected].
Yahia M. M. Antar joined the Division of Electrical Engineering, National Research Council of Canada. In 1987, he joined the Department of Electrical and Computer Engineering, Royal Military College of Canada, Canada, where he has been a professor since 1990. He was appointed as a member of the Canadian Defence Advisory Board of the Canadian Department of National Defence in 2011. He is a fellow of the Engineering Institute of Canada, the Electromagnetic Academy, and the International Union of Radio Science. He served as the Chair for Commission B from 1993 to 1999 and for CNC, URSI from 1999 to 2008, and has a cross-appointment at Queen’s University, Kingston. In 2002, he was awarded a Tier 1 Canada Research Chair in electromagnetic engineering, which has been renewed in 2016. He serves as an associate editor for many IEEE and IET journals and as an IEEE-APS Distinguished Lecturer. He was elected by the URSI to the Board as the Vice President in 2008 and 2014 and by the IEEE AP AdCom in 2009. Presently, he is serving as President, IEEE APS (Region 7–10) for the year 2021.
Email: [email protected].
