Md. Ahsan Halimi, Taimoor Khan, Merih Palandoken, Ahmed A. Kishk, Yahia M.M. Antar
©SHUTTERSTOCK.COM/HANSS
RF-based wireless energy harvesting (WEH) and wireless power transfer (WPT) are gaining attention due to their capability of powering various sensors and devices. A low-power device can be fed wirelessly by capturing ambient RF energy through a WEH system. In the case of a high-power device, a WPT system can provide the required amount of power using intentional RF sources.
The rectenna is the key device for enabling wireless powering in both WEH and WPT systems. The rectenna, also known as a rectifying antenna, is a combination of a rectifier and an antenna. A rectenna’s performance depends on the rectifier that is used for the RF-to-dc conversion. Hence, a rectifier in these systems is essential because most low-power devices and sensors need dc power to operate appropriately. Therefore, the rectifier contributes significantly to wireless sensors, RF identification tags, wireless charging systems, implantable/wearable biomedical devices, and thus to smart cities and to the RF electronic subcomponents of Internet of Things systems [1], [2], [3].
There are two types of RF sources: intentional and ambient. An intentional source is devoted to providing RF signals for energy transfer for WPT. Ambient sources can be either anticipated or unknown. Several ambient RF signals are freely available in the environment, such as FM, digital TV, code division multiple access, GSM, Universal Mobil Telecommunications System, LTE, and Wi-Fi [2]. The WEH/WPT system is shown in Figure 1. It works as a receiver antenna that captures the RF signal transmitted by the base station, and then the rectifier converts the RF signal into dc, which is either stored in a battery or supplied directly to the low-power device [3]. At the receiver end, the received power can be affected by multiple factors, such as transmitted power, distance from the transmitter, transmission frequency, polarization state, and receiving antenna gain, which can be calculated using the Friis transmission equation in (1): \[\frac{{P}_{r}}{{P}_{t}} = {G}_{r}{G}_{t}{\left({\frac{\lambda}{{4}{\pi}{R}}}\right)}^{2} \tag{1} \]
Figure 1. Wireless energy harvester/power transfer system. LPF, low-pass filter; Rx, receiver; Tx, transmitter.
where ${P}_{r}$ and ${P}_{t}$ are received and transmitted power, respectively; ${G}_{r}$ and ${G}_{t}$ are the gain of the receiving and transmitting antennas, R is the distance between transmitter and receiver, and ${\lambda}$ is the wavelength in the transmitting medium.
The receiving node is a rectenna composed of an antenna and a rectifier. A matching circuit is necessary between the antenna and the rectifying diode to reduce mismatch losses, which are predicted by the maximum power transfer theorem [4]. Also, an output low-pass filter is required to smooth the dc output. Generally, the shunt capacitor is used to smooth the dc output [5]. In [6], a shunt capacitor and Zener diode (which acts as a regulator) are utilized to reduce the ripples that occur across the load resistance. Usually the lumped elements and/or transmission lines (TL) are used to design matching networks (MNs) and dc pass filters. Currently the primary interest is to design a rectifier that maximizes the RF-to-dc power conversion efficiency (PCE). The main cause of inefficiency in a rectenna is impedance mismatch between the receiving antenna and the rectifier. Rectifiers operate at different frequencies of interest, including 0.9 GHz, 1.8 GHz, 2.1 GHz, 2.45 GHz, 5.8 GHz, and above 5.8 GHz [7]. However, these rectifiers are optimized to achieve maximum PCE at a particular frequency of interest and input power level. Hence, these rectifiers can perform efficiently at a particular frequency for a particular input power level, and the performance deteriorates when the frequency shifts and input power fluctuates. This is due to the rectifier circuit utilizing a Schottky diode as a rectifying element, which is nonlinear. Due to the nonlinearity of the rectifying device, the rectifier input impedance changes with a change in RF input power and in the frequency of operation. Hence, the performance of the rectifier in terms of PCE varies with the operating frequency and the fluctuation of the input power level [8]. The variation in the diode impedance causes mismatch and hence the PCE of the rectifier deteriorates.
Various single/multiband rectifiers have been built with maximum PCEs for small spans of the operating frequency and input power level [9], [10], [11]. This article discusses the design challenges of rectifiers that have almost stable PCE for a broad operating frequency range and a wide input power range. The ambient RF energy in the atmosphere is capricious, and there are many closely allocated spectrums available for harvesting. Therefore, this article highlights the fundamental methods to design a broadband rectifier (BBR) and a rectifier operating in a wide power range. In the “Diode Impedence Behavior” section, diode impedance modeling is presented, and BBR and wide power range rectifiers are included in the “BBR Design” and “Rectifier With Wide Power Range” sections, respectively.
The rectifying circuit involves a nonlinear Schottky diode for rectification purposes. Therefore, to design a good matching circuit, knowledge of the impedance behavior of the diode is necessary. Hence, the primary objective is to find the diode’s equivalent circuit model and then the impedance behavior of the selected diode using small-signal analysis. The step-wise procedure to design an efficient rectifier is depicted in Figure 2.
Figure 2. Flow diagram of the rectifier design procedure. VD, voltage doubler.
The selection of an appropriate diode depends mainly on the available power level. Maximum diode efficiency versus. input power is shown in Figure 3 [7]. The diode threshold voltage limits the sensitivity and the breakdown voltage limits the power handling capability of the rectifier. After an appropriate Schottky diode has been selected, the impedance behavior should be examined. The equivalent circuit of a small-signal diode model is shown in Figure 4. The Keysight Advanced Design System (ADS) also provides a small-signal model of a Schottky diode, known as the vendor model. The characteristic of nonlinearity is due to the junction resistance ${(}{R}_{j}{)}$ and junction capacitance $({C}_{j})$, which can be calculated using (2) and (3), respectively. The parasitic series resistance ${R}_{s}$ is the sum of the bond-wire and lead resistance, ${L}_{p}$ is the lead parasitic inductance, and ${C}_{p}$ is the interlead parasitic capacitance: \begin{align*}{R}_{j} & = \frac{{8.33}\,{\times}\,{10}^{5}{nT}}{{I}_{b} + {I}_{s}} \tag{2} \\ {C}_{j} & = {C}_{j0}{\left({{1}{-}\frac{{V}_{d}}{{V}_{j}}}\right)}^{{-}{M}}{.} \tag{3} \end{align*}
Figure 3. Diode maximum efficiency curve [7].
Figure 4. Nonlinear small-signal model of a Schottky diode with parasitic components [9].
The bias current ${I}_{b}$ is shown in (4): \[{I}_{b} = {I}_{s}{\left({e}^{}{-}{1}\right)} \tag{4} \] where n is an ideality factor that depends on the material and fabrication process, T is the temperature in Kelvin, ${I}_{s}$ is the saturation current which depends on the barrier height, ${C}_{j0}$ is zero bias junction capacitance, ${V}_{d}$ is the voltage across ${R}_{j}$, ${V}_{j}$ is the junction potential, M is the grading coefficient that depends on the doping profile of the junction, and ${V}_{t}$ is the thermal voltage [12].
The diode impedance can be calculated as a function of frequency [13]. The diode impedance without and with parasitic components is calculated as ${Z}_{d}{(}{f}{)}$ and ${Z}_{D}{(}{f}{)}$ in (5) and (6), respectively: \begin{align*}{Z}_{d}{\left({f}\right)} & = {R}_{s} + {\left({\frac{1}{{R}_{j}} + {j}{2}{\pi}{fC}_{j}}\right)}^{{-}{1}} \tag{5} \\ {Z}_{D}{\left({f}\right)} & = {\left({\frac{1}{{R}_{s} + {\left({\frac{1}{{R}_{j}} + {j}{2}{\pi}{f}{C}_{j}}\right)}^{{-}{1}}} + {j}{2}{\pi}{f}{C}_{p}}\right)}^{{-}{1}} + {j}{2}{\pi}{f}{L}_{p}{.} \tag{6} \end{align*}
The values of all the parameters except temperature (T) and externally applied voltage ${(}{V}_{d}{)}$ can be found from the corresponding datasheets of the Schottky diodes used. It is clear from (6) that the impedance of diode ${(}{Z}_{D}{)}$ depends on the operating frequency and ${V}_{d}$, as ${R}_{j}$ and ${C}_{j}$ depend on ${V}_{d}$. An externally applied signal in the form of an RF input power is used for the rectifier circuit. Hence, the rectifier’s input impedance also varies in accordance with the input power and frequency. The input impedance of the rectifier versus input power at different frequencies is shown in Figure 5 [8].
Figure 5. The input impedance of different optimal rectifier designs at (a) 0.9 GHz, (b) 1.8 GHz, (c) 2.4 GHz, (d) 5.8 GHz, and (e) a rectifier circuit [8].
The different frequency bands available for wireless communication are also the choices that are available for WEH/WPT systems. To exploit any available frequency band to harvest a particular energy, WEH systems need specific rectifiers that can operate for that particular frequency band. However, most of the rectifiers do not cover the complete span of the band efficiently. Also, many available bands are very close to each other. Therefore, a BBR is expected to operate over a wideband or more than one band efficiently. This improves the amount of power collected by simultaneously harvesting RF energy from different sources and channels. Figure 6 shows the schematic diagram of a BBR. The limitation to obtain broadband matching is introduced by the Fano–Bode criteria [14]. The relation between the minimum achievable reflection coefficient ${(}{\Gamma}_{m}{)}$ and bandwidth (B) can be calculated using (7), where R and C are the equivalent resistance and capacitance value of the rectifier input impedance. It is challenging to obtain high PCE over a broad bandwidth range with high return loss: \[{\left\vert{\Gamma}{m}\right\vert}\,{≥}\,{e}^{\frac{-1}{{2B}\,{\ast}\,{RC}}}{.} \tag{7} \]
Figure 6. Block diagram of a BBR.
Cai et al. [15] have designed a BBR using a series diode and a five sectional TL matching circuit. A similar type of matching circuit optimized using quality factor analysis is designed by Sakaki and Nishikawa in [16]. In [17], a TL-based third-order low-pass matching circuit is utilized with a shunt diode. Shi et al. [18] have designed a BBR in which the matching circuit consists of a 3.3-nH chip inductor and dual stub matching line. Park and Hong [19] have designed a BBR in which the impedance matching is obtained by adding two inductors in series with each diode of the voltage doubler (VD). A wideband resistance compression network (RCN) is combined with VD diode configuration to design a BBR in [20].
A TL, shunt short-circuited stub, and coupled line are used in the MN design to extend the operating bandwidth [21]. As shown in Figure 7, the TL makes the imaginary part of the input impedance odd symmetrical with respect to the center frequency, and the shunt short-circuited stub results in the imaginary part of the input impedance offset. The real part in this process is almost constant and the imaginary part becomes zero. After that, the coupled line is used for wideband impedance transformation.
Figure 7. Wideband rectifier using a coupled line MN [21].
A BBR designed using a low-pass type L-section with inductive L-section [22], a high-pass type L-section with inductive L-section [23], [24], and a bandpass type L-section with inductive L-section [25] is shown in Figure 8(a). Figure 8(b) shows the different L-sections utilized in Figure 8(a). Figure 8(c) shows the BBR proposed by Mansour and Kanaya [23]. Two L-sections are cascaded to realize broadband matching. A high-pass type L-section comprises a shunt inductor and a series capacitor used for the impedance matching in the lower frequency band, while the inductive L-section is used for the impedance matching in the higher frequency band. Series and shunt inductors of the inductive L-section are utilized to adjust the imaginary and real parts of the rectifier impedance at the center frequency of the required band. The approximate value of the inductive L-section inductors can be calculated using (8) and (9) given in [24]: \begin{align*}{L}_{2} & = \frac{1}{{\omega}_{c}} \sqrt{\frac{{R}_{i}{Z}_{0}}{{1}{-} \frac{{R}_{i}}{{Z}_{0}}}} \tag{8} \\ {L}_{1} & = \frac{{X}_{i}}{{\omega}_{c}}{-}\frac{{L}_{2}}{2} {\pm} \sqrt{\frac{{L}_{2}^{2}}{4}{-}\frac{{R}_{i}^{2}}{{\omega}_{c}^{2}}}{.} \tag{9} \end{align*}
Figure 8. (a) BBR using filter-type L-section and inductive L-section. (b) Different L-section. (c) BBR using high-pass L-section and inductive L-section [23].
Here, ${\omega}_{c}$ is the central frequency of the band to be impedance matched.
However, the inductive L-section provides impedance matching only for a narrow bandwidth. Adding a high-pass type L-section improves the operating bandwidth of the rectifier. The series capacitor affects the value and placement of an additional dip in the reflection coefficient and the inductor ${L}_{3}$ adjusts the frequency dip location.
Single-branch multitaper nonuniform TL matching, as shown in Figure 9(a), is utilized to design a one-octave and one-decade bandwidth rectifier in [26]. Multistage TL matching [27], [28], [29], harmonic termination [30], [31], and frequency-selective diode array [Figure 9(b)] [32] techniques have also been utilized to design a BBR. In [33], to achieve broadband impedance matching, a quasi-T–shaped MN of four-stage TLs is utilized. In [34], a BBR was proposed with a matching topology based on a cross-shaped stub of two ${\lambda} / {8}$ TLs. A BBR-based on the harmonic feedback topology is proposed in [35]. Coupled lines and filters are used to build the feedback path. A broadband coplanar waveguide (CPW) rectifier is designed in [36] and [37] using a VD diode configuration. In [38], a broadband CPW rectifier with two series inductors as a matching circuit is proposed. Some BBRs have also been designed in differential [39] and in full-wave Greinacher topology [40]. Table 1 shows the performance comparison of existing BBRs.
Figure 9. (a) Schematic of nonuniform TL based decade-bandwidth rectifier [26], (b) schematic of BBR using frequency selective diode array [32].
Table 1. Performance comparison of BBRs.
Table 2. Performance comparison of single-band rectifier for wide dynamic range.
Table 3. Performance comparison of dual-band rectifier for wide dynamic range.
In the case of an intentional source for WPT, a change in receiver position causes a change in the input power level to the rectenna because the received power is inversely proportional to the square of the distance between transmitter and receiver. On the other hand, in a WEH system, the amount of ambient RF power is unpredictable, and a change in input power may affect the rectifier performance. The critical input power ${(}{P}_{c}{)}$ is inversely proportional to the load resistance ${(}{R}_{L}{)}$, as shown in (10). ${P}_{C}$ is the maximum power handling capability of the rectifier. Above this power level the rectifier will break down and performance will degrade drastically: \[{P}_{c} = \frac{{V}_{br}^{2}}{4{R}_{L}}{.} \tag{10} \]
Hence, the change in the load affects the power handling capability of the rectifier. Since the input impedance of the rectifier depends on the input power and load, impedance mismatch occurs, and PCE degrades. Therefore, there is a need for rectifiers that are less sensitive to input RF power and load so that a significant change in the load and input power causes only a small change in the input impedance of the rectifier. Resistance/impedance compression networks (ICNs) can provide a solution for such a situation.
In [41], a four-way TL-based resistance compression network is connected between the input port of the rectifier and multiple rectifiers in order to minimize the effect of input power on the input impedance. A differential RCN is designed and integrated with a differential rectifier in [42]. A single branch RCN was utilized by Li and Zhang [43] to improve the performance. However, an RCN can only compress either the real or the imaginary part of the input impedance. Therefore, an ICN has been proposed to compress both the real and the imaginary parts of the input impedance and give better stability [44]. In [45], an ICN was utilized before two subrectifiers to get good PCE over a wide range of input power by compressing the complex input impedance. In [46], an integrated ICN is proposed in which two parallel diodes are utilized in a single branch. Figure 10 shows the different compression networks.
Figure 10. Schematic of different RCNs: (a) lumped element-based RCN [43], (b) TL-based RCN [43], (c) differential RCN [42], (d) single-branch RCN [43], (e) ICN [45], and (f) integrated ICN [46].
The same concept has been utilized in dual-band rectifiers using an ICN [45], a lumped component-based RCN [47], and a TL-based RCN [48]. Figure 11 shows the dual-band RCN. Unit cell-1 in Figure 11 shows a negative and positive phase response at the first and second operating frequencies, respectively. Unit cell-2 in Figure 11 mirrors unit cell-1; thus, unit cell-2 exhibits positive and negative phase responses at the first and second operating frequencies.
Figure 11. Schematics of dual-band RCNs: (a) conceptual image [47], (b) lumped component based [47], and (c) TL based [48].
Two-branch topologies with a common load and two separate loads, as shown in Figure 12(a) and (b), respectively, may also be used to design a rectifier that operates over a wide input power range with good PCE. As discussed earlier, the breakdown voltage limits the power handling capability of the diode while the threshold voltage limits its sensitivity. A diode with a low threshold and high breakdown voltage can give better PCE for an extensive input range. However, a diode with a low threshold voltage also exhibits low breakdown voltage. Hence, dividing the input power into multiple subrectifying branches can extend the operable power range.
Figure 12. Schematic of dual branch rectifier with (a) common load [50] and (b) two separate loads [49].
In [49], the input power is divided into a 2:1 ratio using a Wilkinson power divider (WPD) and fed to two branches with different loads. The branch designed to operate at low power has high load resistance (1 kΩ), and the branch designed to operate at high power has low load resistance (300 Ω). In [50], a two-branch topology with a common load is proposed. Two HSMS2860 diodes in series are used in one branch to increase the overall breakdown voltage to handle high power. In the other branch, an HSMS2852 diode is used for low power rectification. Another solution is to design two subrectifiers using different diodes that have different breakdown voltages and then feed the subrectifiers through a ${\lambda} / {4}$ T-junction power divider [51] or with an automatic power distribution (APD) technique [52].
A branch line coupler (BLC) has also been utilized to design a rectifier with a wide input power range. The rectifier consists of a BLC with two identical subrectifying branches with a grounded isolation port [53], 50 Ω termination [54], and power recycling subrectifier [55] designed to enhance the input power range. A power recycling branch (PRB) has been utilized in [55] for recycling reflected power from two main subrectifiers, as shown in Figure 13(a). In [56], two subrectifiers are utilized, one of which is VD for high-power rectification and the other of which is a shunt diode for low-power rectification with the isolation port of the BLC terminated by a ${\lambda} / {4}$ TL stub. In [57], a power recycling network (PRN) is utilized at the input port of two subrectifiers. In the case of mismatch due to a change in the input power level, the PRN can collect some of the reflected power and transmit it back to the subrectifier for recycling. In [58], a cooperative subrectifier is incorporated with the main subrectifier, as shown in Figure 13(b). Only the main subrectifier works at low input power and both subrectifiers work together at high input power. APD for an array of rectifiers designed to rectify different input power levels is proposed as a wide operating range rectifier in [59]. Power is distributed among the array elements adaptively, based on their input impedance for a given input power. Three arrays of different power rectifiers with APD are designed using two subrectifiers utilizing different diodes, two subrectifiers utilizing the same diode, and three subrectifiers utilizing different diodes. In [60], a reflected power compensation network (RPCN) is proposed to widen the rectifier power range by adding a hybrid coupler and phase-shift stub between the original rectifier terminal and the input port. To improve the dynamic power range of the rectifier, a solution using paired diodes for capacitive self-compensation is proposed in [61]. Through impedance transforming, the imaginary part of one diode’s impedance is corrected by utilizing another similar diode with a section of TL.
Figure 13. Schematic of the rectifier with (a) PRB [55] and (b) cooperative structure [58].
In [62], the adaptive matching has been confirmed using a variable capacitor (varactor) with external biasing. The change in capacitance has been achieved by providing suitable biasing voltage, and hence the rectifier adaptively reconfigures its impedance when there is a change in input power. In [63], self-tuning impedance matching is proposed, which provides the output voltage of the rectifier back to the varactor for self-biasing. In [64], a self-matching system based on an artificial TL (ATL) is proposed that can provide autonomous impedance transforming regardless of the input power to design a rectifier with a wide input power range. The output dc voltage is supplied back into the ATL for controlling the varactors, and hence the ATL’s effective electrical length and effective characteristic impedance is increased by tuning the varactors for appropriate impedance transformation according to the input power. In some articles, a field effect transistor (FET) and Schottky diode combination is utilized to design a rectifier with a wide dynamic range, as shown in Figure 14 [65], [66]. The n-channel FET turns ON for low input power, and the low-power diode works for the rectification. On the other hand, a high-power (high breakdown voltage) diode works for the rectification in high input power conditions. In [67], a pseudomorphic high-electron mobility transistor (pHEMT) and Schottky diode combination has been utilized for the same purpose. The performance comparison of single-band and dual-band rectifiers designed for a wide input power range is shown in Tables 2 and 3, respectively.
Figure 14. Schematic of a rectifier designed using FET and a Schottky diode [66].
Rectifier design challenges for wide operating conditions are discussed in this article. Two of the most exciting research trajectories in rectifiers for WEH/WPT are addressed. The design methodologies of broadband and wide input power range rectifiers are introduced. BBRs can be used for harvesting more energy from many closely allocated bands. In contrast, wide operating input power range rectifiers can work efficiently in varying environmental conditions. Both types of rectifiers are designed using different types of matching techniques. In Figure 15(a), matching techniques for the design of BBRs are summarized. Figure 15(b) summarizes the matching techniques involved in the design of rectifiers with a wide operating power range.
Figure 15. Overall organization of (a) BBRs and (b) wide power range rectifiers.
The research on microwave rectifiers is rapidly progressing to improve sensitivity and PCE and to extend their operating conditions, including bandwidth, input power, and load. This article has focused on reviewing BBRs and rectifiers with wide power ranges and load impedances to exploit in WEH/WPT. Many closely allocated bands are available, and the amount of RF power available to harvest is unpredictable. Hence, the authors’ recommendations are: 1) the BBR is the best solution to operate across multiple closely specified bands simultaneously; and 2) multiple subrectifiers optimized for different power levels can be combined through the power divider/branch line coupler/hybrid junction to boost the rectifier immunity in fluctuating power conditions. The authors expect that this article can help researchers working on microwave rectifiers for WEH/WPT. Although we have tried our best to include the important and novel contributions of the available research, the authors apologize if any significant contribution has been unknowingly and unintentionally omitted in this review article.
This work was supported by the Ministry of Human Resource Development under Scheme for Promotion of Academic and Research Collaboration (SPARC), Government of India (Research Grant SPARC/2018–2019/P266/SL/2019).
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Digital Object Identifier 10.1109/MMM.2023.3256379