While sufficient review articles exist on inductive short-range wireless power transfer (WPT), long-haul microwave WPT (MWPT) for solar power satellites, and ambient microwave wireless energy harvesting (MWEH) in urban areas, few studies focus on the fundamental modeling and related design automation of receiver systems. This article reviews the development of MWPT and MWEH receivers, with a focus on rectenna design automation. A novel rectifier model capable of accurately modeling the rectification process under both high and low input power is presented. The model reveals the theoretical boundary of radio frequency-to-direct current (dc) power conversion efficiency and, most importantly, enables an automated system design. The automated rectenna design flow is sequential, with the minimal engagement of iterative optimization. It covers the design automation of every module (i.e., rectifiers, matching circuits, Antennasae, and dc-dc converters). Scaling-up of the technique to large rectenna arrays is also possible, where the challenges in array partitioning and power combining are briefly discussed. In addition, several cutting-edge rectenna techniques for MWPT and MWEH are reviewed, including the dynamic range extension technique, the harmonics-based retro-directive technique, and the simultaneous wireless information and power transfer technique, which can be good complements to the presented automated design methodology.
In addition to the demand for wireless communication, there is also a demand for wireless power. In fact, the concept of wireless power transfer (WPT) has been brought up since the adoption of electricity, when Heinrich Hertz proved Maxwell’s theory and Tesla attempted to scale up his coil in the early 20th century [1]. Modern WPT research and development emerged from harvesting and transmitting space-based solar power (SSP) to the ground in the 1970s [2], [3] and from remotely powering high-altitude platforms (including unmanned aerial vehicles, UAVs) in the 1980s [4]. Since the wireless medium used was primarily in the microwave regime, this technology was also known as microwave WPT (MWPT).
After some stagnation in the 1990s, the development of MWPT revived, with a renewed interest in powering radio frequency (RF) identifications (RFIDs) by harvesting ambient microwave power/energy [5]. Unlike MWPT for SSP applications, microwave wireless energy harvesting (MWEH) works at short ranges and low frequencies. It is, however, limited by the available ambient microwave power capped at -50 dBm·cm−2 in the frequency range from 500 to 3000 MHz [6]. Fig. 1 shows the ambient power density levels in Singapore. In order to better scavenge weak ambient power, a few approaches have emerged. The most straightforward way involves spatially expanding the harvesting aperture using multiple rectennas or arrays [7], [8], [9]. A similar concept applies to spectral expansion, in which the ambient power over multiple frequency channels is exploited, leading to multi-band [10] and broadband rectennas [11]. Unlike these approaches, the most disruptive way is probably boosting the rectification efficiency at low input power by leveraging low-threshold diodes (backward tunnel diodes, spin-torque diodes, etc.) [12], [13], [14]. A good review on far-field MWEH with a focus on low-power emerging applications can be found in Ref. [15].
Fig. 2 shows a typical MWPT system from the power source in a transmitter all the way to the direct current (dc) load in a receiver. The power source (regardless of being dedicated or ambient) comprises an oscillator, power amplifier, and transmit antenna, while the receiver includes a receive antenna, matching circuit, rectifying circuit, dc-dc converter, and dc load. For mid- and long-haul MWPTs [16], [17], the dc-to-dc power conversion efficiency is the key performance indicator, while for near- and mid-range MWEH, only the RF-to-dc power conversion efficiency of the receiver is of concern. Since receivers exist for both MWPT and MWEH systems, they will be the focus of this article.
The overall RF-to-dc power conversion efficiency of a receiver after the antenna can be decomposed as follows:
where is the efficiency of the matching circuit between the antenna and the rectifier, is the RF-to-dc power conversion efficiency of the rectifier, and is the efficiency of the converter. To maximize , one needs a good match between antenna and rectifier, a high-efficiency rectifier, and a high-efficiency dc-dc converter (usually a boost converter) if the rectifier output is insufficient for the load. Other factors, including the rec-tenna array design [18], power combining strategy [19], and possible power scheduling and management [20], may also affect the overall performance. Nevertheless, the foundation of a receiver is always the rectifier. To achieve a good design, an accurate rectifier model is of the utmost importance.
This article reviews the development of MWPT and MWEH receivers, with a focus on rectenna design automation. A novel model, capable of accurately modeling the rectification process under both high and low input power is presented. It reveals the theoretical boundary of the rectifiers’ RF-to-dc efficiency. Based on the model, a parametric analysis is conducted, which benefits both the device tuning of rectifying diodes and the optimization of rectifier design. More importantly, an automated system design methodology is enabled. Scaling up from a single rectenna element to large rectenna arrays becomes possible, and array partitioning and power combining are thoroughly discussed. Furthermore, several cutting-edge techniques for rectenna design in MWPT and MWEH are introduced, including the dynamic range extension technique, the harmonics-based retro-directive technique, and the simultaneous wireless information and power transfer (SWIPT) technique.
2. Rectifier modeling
2.1. Development of rectifier modeling
Rectifiers are the key building blocks of rectennas. Due to their nonlinear behavior, accurate modeling of rectifiers is desirable for optimal design of rectennas in terms of efficiency, functionality, and cost. Numerical methods such as harmonic balance (HB) are widely used in rectifier design flows; however, such methods often hinder people from obtaining physical insight into the rectification phenomenon. In comparison, analytical models offer good physical insight. In specific, they are helpful in revealing the impact of circuit parameters and topologies on key performance indicators (i.e., conversion efficiency, loading condition, and input impedance). In addition, they can reveal the physical limitation of a rectifier, mainly the conversion efficiency. Most importantly, they allow the design of an MWPT/MWEH receiver system to flow automatically. Therefore, this article deals with analytical rectifier modeling.
There are two main directions for analytical rectifier modeling: ① the time-domain method and ② the harmonic expansion method. The time-domain method analyzes the input and output of a rectifier in the time domain and obtains the frequency-domain results (i.e., power conversion efficiency and input impedance) via Fourier transformation [21], [22], [23]. The time-domain analysis is intuitive, and the results are acceptable for preliminary prototyping [24], [25], [26]. However, the assumption of ideal switching characteristics for the rectifying diodes limits this method’s accuracy under low input power [12]. In comparison, the harmonic expansion method is good at modeling rectifiers under low input power, as it was initially developed for detectors [27], [28], [29]. By expanding the diode current-voltage (IV) characteristics in the square-law (low-power) region [30], the harmonic expansion method provides better accuracy at low input power, making it ideal for MWEH applications [31]. However, it is not suitable for high-power or after-breakdown (BR) situations, nor can it take multi-tone [32] and power-optimized waveform excitations [26] into consideration.
Table 1 summarizes the two modeling methods. Although they complement each other in terms of the power condition, from a design automation perspective, two models serving different scenarios are still inconvenient and the boundary between them is still unclear. A unified model capable of working under both low- and high-input powers is thus desirable.
2.2. A unified rectifier model
Based on the time-domain model, a unified rectifier model that works for both low and high powers is developed. This model preserves the advantages of time-domain models while eliminating their drawbacks at low input power by considering the nonlinear diode IV characteristics. The concept was originally raised in Ref. [33] and will be discussed in detail here. Symbols that appear multiple times in this article are listed in Table 2.
Fig. 3(a) [33] shows the core equivalent circuit of a shunt-diode rectifier. It excludes the matching circuit, implying that . An ideal dc pass filter consisting in the rectifier load capacitance is assumed, resulting in a dc path (denoted by the dashed line) for rectifier load resistance . The rectifying diode (usually a Schottky diode) is represented by a series resistance , a nonlinear junction resistance , and a nonlinear junction capacitance . The package parasitics are ignored for simplicity. and may be described by the IV and capacitance-voltage (CV) characteristics as follows:
where is the diode saturation current; and are the diode junction voltage and current, respectively; is the diode ideality factor; is the thermal voltage, where is the Boltzmann constant, is the junction temperature, and is the charge of an electron; is the diode built-in voltage; is the diode zero-bias junction capacitance; and is the diode grading coefficient.
Fig. 3(b) depicts the typical time-domain behavior of a rectifier, where is the input voltage of rectifier. Due to the self-bias nature of a rectifier [24], consists of a dc term, , and an RF term, :
where is output dc voltage of a rectifier, is the amplitude of RF incidence, is the angular operating frequency, and is time.
is often represented in a piecewise fashion according to the three states of rectification-namely, ON, OFF, and BR-in Fig. 3(b). For gigahertz applications, it is safe to ignore the phase difference between and , leading to , where is the dc component of diode junction voltage and is the RF component of diode junction voltage [33]. Hence, may be expressed as follows:
where is the diode reverse BR voltage and is the diode forward voltage. Based on Eq. (5), the turn-on angle and BR angle can be determined:
Since is voltage-divided from the average of , the relationship between , and may be obtained:
Moreover, the RF input power can be decomposed as follows:
where is the dc output power, and is the dissipated power during rectification, covering the losses due to , and in their respective states.
where is the power loss due to in ON state, is the power loss due to in ON state, is the power loss due to in OFF state, is the power loss due to in BR state, is the power loss due to in BR state, and is the phase angle.
Unlike conventional time-domain models [21], [22], [23], the proposed unified model considers the IV characteristics of a rectifying diode, as follows:
With Eq. (15), becomes a variant, in contrast to being fixed (usually ) in conventional models (Figs. 4(a) and (b)).
Once are solved for any given , the two key performance indicators of a rectifier-the power-conversion efficiency and the rectifier input impedance can be obtained, where is the diode current at the fundamental frequency [33].
Fig. 4(c) [12] compares three rectifier models using the case of SMS7630 at 2.45 GHz, where . While the conventional time-domain model only provides good results at high power and the harmonic expansion method only works for lower power, it is clear that the proposed unified model combines the advantages of both models, working for both high and low powers. This is primarily due to Eq. (15) which incorporates the IV characteristics of a rectifying diode in a simple yet efficient manner.
2.3. Parametric analysis
The unified rectifier model enables parametric analysis, which benefits both the device tuning of rectifying diodes and the diode selection toward an optimal rectifier design. In this article, a study based on HSMS286x is conducted, where the operating frequency and . The Simulation Program with Integrated Circuit Emphasis (SPICE) model parameters of HSMS286x can be found in Table 3.
Fig. 5(a) shows the impact of on rectifier performance. accounts for the carrier recombination as charge carriers cross the depletion layer. It typically ranges from 1 to 2, where a larger value suggests more imperfection in the junction. This is reflected in Eq. (2), where a larger causes lower junction current under the same input power (voltage). Hence, a larger results in a lower , which can be observed from Fig. 5(a).
Fig. 5(b) shows that a higher lowers before BR. Likewise, a higher lowers before BR (Fig. 5(c)). The higher loss due to a larger and/or is explained by Eq. (12). In Fig. 5(d), a larger extends the turning point of (i.e., the maximum efficiency point) to a higher because a higher is supported.
An interesting observation of the is shown in Fig. 5(e), where has little influence on the rectifier performance. This is in stark contrast to the sweep in Ref. [34], where a smaller firmly enhances before BR. The result in Ref. [34] is questionable, because ① the variations in and were ignored in Ref. [34]; and ② is a dependent variable rather than a diode performance indicator. In fact, sweeping but keeping the other diode parameters is not realistic, because is physically related to , , and . For one diode-processing technology, a smaller (larger) is normally accompanied by a smaller (larger) , smaller (larger) , and larger (smaller) .
Therefore, considering these interrelated diode parameters, a smaller (larger) is expected to improve (degrade) the before-BR performance and shift the after-BR performance to a lower (higher) . Furthermore, while only dominates the after-BR performance, , and all have an impact on the before-BR performance. Since does not vary much among diodes, we can use the product of and to characterize the before-BR performance of a diode. The smaller is for a diode, the higher is before BR, and thus the more suitable it is for low-power applications.
Figs. 5(a)-(d) show single-sided parametric studies in the absence of physical interrelation. Introducing the physical interrelation (i.e., constraint) would lead to a more comprehensive conclusion. Fig. 5(f) shows clear impact of the operating frequency on the before-BR performance. This can easily be explained by the power loss due to in the OFF state in Eq. (12). Fig. 5(g) shows that a varying load resistance affects both the level and the horizontal location of the maximum efficiency point, which is of practical use. In general, a larger corresponds to a smaller . Fig. 5(h) shows another interesting phenomenon, in which a low ambient temperature has a positive impact on the rectifier performance. According to Eq. (2), a low ambient temperature causes a low , leading to a higher current under the same input power (voltage). Therefore, in a cold environment, ambient microwave energy harvesting is expected to have better performance.
2.4. Contour maps
Another important application of the unified rectifier model is in the contour maps of key rectifier parameters versus independent parameters . Such contour maps can serve as lookup tables, facilitating rectenna design automation. Although ADS HB is able to model rectifiers well, specifying the power delivered to the rectifier-that is, -is still troublesome in ADS [33]. In contrast, the unified model can take on any specific . This allows for equidistant data generation, which is favored for contour mapping.
Figs. 6(a)-(d) [33] show contour maps of HSMS28600’s key parameters over a two-dimensional (2D) plane of , where the operating frequency is . The maps are built based on data generated by the unified model. A more useful form is the overlapped contour map in Fig. 6(d), where the black contour indicates the desired , and the purple and orange lines denote the real part of and the imaginary part of , , respectively. This contour map directly links the rectifier performance to the design considerations thereby eliminating the need for iterative optimization.
While 2D contour maps facilitate single or narrow-band rectifier designs, three-dimensional (3D) contour maps over can assist in the design of wide- and multi-band rectifiers. Fig. 6(e) shows such a 3D map of the same diode, where the contours are now iso-surfaces of . The horizontal area enclosed by the surface shrinks as the frequency increases, indicating a more stringent design condition at higher frequencies.
2.5. Catering for various rectifier topologies
The above contour maps for a single-shunt rectifier can be easily adapted to the common rectifier topologies [35] shown in Fig. 7. Single-shunt (Fig. 7(a)) and single-series (Fig. 7(b)) topologies share the same contour maps since, theoretically, they have the same behavior [36]. The voltage doublers in Fig. 7(c) are commonly used in MWEH when the dc output voltage is insufficient for the load. Based on a voltage doubler, the Cockcroft-Walton voltage multiplier [37] and Dickson voltage multiplier [38], respectively shown in Figs. 7(d) and (e), were developed. They have similar performance, provided the requirement for capacitances is met. Differential voltage multipliers can also be constructed based on voltage doublers. By combining two voltage doublers, a single-stage differential voltage multiplier is formed as shown in Fig. 7(f).
Fig. 8 shows the decomposition of a voltage doubler circuit into its RF and dc loops, where the two diodes are identical. For RF inputs, the two diodes are in parallel, because the two capacitors are short circuits. Hence, the input impedance at the RF frequency of the voltage doubler is halved compared with a single-diode rectifier , where the superscripts "d" and "s" denote variables of voltage doubler and single-diode rectifier, respectively; they apply throughout the article. At dc, the capacitors are open circuits; thus, the two diodes are in series, with doubled dc output voltage compared with single-diode rectifiers . For a case in which the efficiencies of a voltage doubler and a single-diode rectifier are the same , in order to sufficiently feed the two diodes in the voltage doubler, the input power must be doubled and the load resistance must also be doubled , as the output voltage is doubled. Therefore, without any recalculation, it is possible to adapt the contour maps of single-diode rectifiers to voltage doublers via simple scaling.
In summary, the contour maps of N-stage voltage multipliers can be obtained from those of their single-diode counterparts through the operations below:
where the superscript “N” denotes variables for N-stage voltage multipliers.
From Eq. (16), in addition to a higher dc output, voltage multipliers have a lower input impedance compared with their single-diode counterparts, which may be favorable in a matching circuit design. However, they require higher input power to achieve the same efficiency, which may be unfavorable in MWEH.
3. Rectenna design automation
3.1. Overview
In a MWPT/MWEH receiver system (Fig. 2), the rectifier is always the bottleneck, since its performance is highly sensitive to variation of the input power and load. Thus, it is reasonable to base the design automation of a rectenna or a rectenna array on that of a rectifier. Fig. 9 shows a rectifier-centric design automation flow for rectennas (or a single rectenna element in an array). It consists of four steps (in the middle row), according to the four main receiver modules shown in Fig. 2. The top row indicates the input and output of the steps, and the bottom row shows the resources and techniques required to complete these steps. The power density spectrum and the desired footprint for the system should be available beforehand, from which Pin can be estimated. The load information in terms of the required Pdc and the load variation during operation should also be known.
The flow in Fig. 9 starts with a contour-map-based automated rectifier design. The resulting is used for the successive matching circuit design. Subsequently, the antenna design is carried out while considering the footprint and conjugate matching. It should be noted that the matching circuit may be ignored for the purpose of miniaturization. In the last step, a dc-dc converter is implemented to isolate the volatile dc load from the sensitive rectifier and to boost the output voltage level, if needed. The above flow can be repeated for rectenna array design automation.
3.2. Rectifier and matching circuit design
Rectifier design is an integral part of designing the whole receiver system. It can be divided into four steps: ① select the diode and the rectifier topology according to , the available , the required , and the loading information ; ② determine and ; ③ design a matching circuit between and the desired input impedance of the matching circuit ; and ④ implement the circuit and fine-tune the design. Unfortunately, due to the nonlinear nature of the circuit, rectifier design is often carried out by means of iterative optimization and tuning.
With the contour maps presented in Figs. 7 and 8, however, an automated rectifier (cum matching circuit) design can easily be achieved (Fig. 10 [33]). The use of contour maps as lookup tables helps in identifying suitable diodes and topologies to meet the requirements , and . Furthermore, from overlapped contour maps, it is possible to locate an ideal operating point that fits the application. Three common applications according to regions A, B, and C are shown in Fig. 10. Once the operating point is fixed, is easily read out from the overlapped contour map and used in the subsequent matching circuit design. Closed-form formulae are available for matching circuit prototypes, leading to compact designs.
The whole flow is automated and can be directly integrated into any electronic design automation (EDA) tools or form a standalone widget. Fig. 11 shows the graphic user interface (GUI) of the automated rectifier design studio (Auredest) developed based on the above technology. This tool has been used by the Internet of Things (IoT) startup WaveBoost Pte. Ltd. (Singapore), in their product development.
3.3. Antenna design
In the design flow discussed in the previous section, a matching circuit is available to bridge the gap between the impedances of the antenna and the rectifier. This makes the antenna design easy and allows for the use of off-the-shelf antennas. However, from a miniaturization perspective, it is desirable to eliminate the matching circuit by directly conjugately matching the antenna and rectifier [39], [40]. Such an elimination demands direct mapping from a desired antenna input impedance to an antenna geometry. Iterative forward modeling using full-wave solvers and inverse modeling based on neural networks [41] can do this task; however, the tuning and network training are labor intensive and time consuming. On the other hand, analytical antenna models capable of fast modeling with reasonable accuracy can easily be incorporated into the automated design flow.
Commonly used antennas in rectennas and arrays can be categorized into wire antennas [24], [42], microstrip antennas [43], [44], and slotted waveguide antennas [7], [16]. Rectangular patch antennas can be modeled by means of cavity models [45] or transmission line models [46]. The input impedance of slotted waveguide antennas can be estimated via cascading admittances [47]. In this article, we take dipole antennas as an example. For a center-fed cylindrical dipole antenna with length 2l and radius a (where l is the half-length of the dipole antenna), the antenna input impedance can be predicted by means of the induced electromotive force (EMF) method [48].
where and is the wave number; and are the sine and modified cosine integrals, respectively.
Fig. 12 shows the input impedance of a center-fed cylindrical dipole antenna computed using the induced EMF method for different lengths and radii. It can be seen that the real part of , is independent of (where is the operating wavelength), whereas the imaginary part of is more gently sloped for a larger . The typical half-wave dipoles at have an impedance of 73.13 + j42.51. With lookup tables such as Fig. 12, it is possible to identify suitable antenna physical parameters for a given target impedance (i.e., conjugate matching). The receive antenna gain can then be evaluated analytically or numerically based on the physical parameters. The analytical-model-based antenna design can be easily plugged into the previous automated rectifier design flow.
3.4. dc-dc converter design
There are two issues associated with driving a dc load in a MWPT/MWEH receiver system: ① The rectifier dc output is too low to drive any practical load; and ② the rectifier efficiency performance is sensitive to load variation. A dc-dc converter solves both problems [49].
Among switching converters, both boost converters [20] and buck-boost converters [50] are often used. Fig. 13 shows the schematic of an asynchronous boost converter composed of an inductor , a MOSFET switch, a diode, and a capacitor . When the switch is closed, the inductor stores the input power as magnetic energy. The magnetic energy is released to boost the output voltage when the switch is open. In the continuous-conduction mode, the ideal input-output voltage and current relationships are as follows:
where is the duty cycle ratio between 0 and is the output voltage of a dc-dc converter, is the input voltage of a converter, is the output current of a converter, and is the input current of a converter. It can be seen that is always greater than or equal to . The input-output impedance (resistance) relationship is thus as follows:
where and are the input and output resistance of the converter, respectively.
Due to the switching operation, ripples occur in the input current and output voltage, which can be predicted by these equations:
where is the switching frequency.
Since dc-dc converter technology is mature, commercially available converter chips are often used in an MWPT/MWEH receiver system. The design then includes the determination of , , and . Eqs. (20) and (21) help in determining and also affects the dynamic range of when a rectifier is connected in front, which should be taken into consideration in the rectifier design phase. With careful design, can be greater than 90%.
3.5. Array design and power combining
Mid- and long-range MWPT and MWEH systems present a more complicated design challenge: namely, rectenna array synthesis, which cannot simply be considered as a repetition of a single rectenna design. To ensure a high overall receiver efficiency, at least three key steps must be well addressed: ① the determination of the aperture size of the rectenna array, ② the array partitioning based on the available aperture power density, and ③ power combining at the RF and/or dc stages [18].
The aperture size of a rectenna array can be explained by the relationship below for close to 100% beam collection [2].
where At and Ar are the transmit and receive aperture sizes, respectively; and L is the distance between the transmit and the receive antennas. It is clear that Ar is inversely proportional to At when the rest parameters are fixed. Transmit antenna array synthesis powered by advanced optimization methods is able to focus most of the beam within a small aperture area for the receive antenna, such that both At and Ar can be small [51], [52], [53], [54], [55], [56].
The array partitioning depends on the available power density distribution over the receive aperture. The power density, in general, decreases from center to edge, with a few sidelobes (Fig. 14(a) [55]). Since the rectification efficiency drops sharply as the input power decreases, it is imperative to combine the weak input power at the edge of the receive aperture to form subarrays. A few subarray partitioning schemes for rectangular and circular arrays are shown in Fig. 14(b) [51], though they were originally developed for transmit antenna arrays. The rectifiers behind each subarray can be identical; thus, the number of rectifier designs is roughly equal to the number of subarray partitions. While the above design scheme is sequential (i.e., transmitter first, receiver second), a joint design of the transmit and receive systems may achieve higher overall efficiency at a lower cost.
RF power combining for subarray elements can be relatively easy to achieve; however, dc combining at the system end is a real challenge. Different rectenna subarrays have different ideal dc loads, and a direct connection can potentially degrade the overall performance. A few solutions are available, such as introducing dc power management networks (dc-dc converters) [20] and isolating dc loads with additional diodes [19]. A recent work theoretically analyzed the dc power combination of rectifiers in shunt and series topologies using an equivalent resistance method. It is found that the shunt topology outperforms its series counterpart under uneven power inputs [57].
4. Cutting-edge techniques
While the advances in rectenna design methodology offer new opportunities for microwave MWPT and MWEH technologies, the advent of new rectenna techniques can further strengthen and functionalize the canonical rectennas obtained from the foregoing automated design methodology. Therefore, in this section, three cutting-edge techniques—namely, the dynamic range extension, retro-directive design with harmonics, and SWIPT—will be reviewed.
4.1. Dynamic range extension technique
Due to the nonlinearity of the rectifying diode, the operating dynamic ranges of the frequency, input power, and load value are relatively narrow. To realize a high-efficiency rectifier in multi- or wide-band, some state-of-the-art works are reported here. In Refs. [10], [11], [58], sub-rectifiers working at different frequency bands are stacked to extend the frequency band coverage. A six-band rectifier in Ref. [2] is divided into three branches, and each branch is connected to a dual-band sub-rectifier. This allows for automatic frequency selection toward multi-band rectification.
A matching network that is effective over multi-/wide-bands is another useful technique. Such networks include π-shaped networks [59], coupled lines [60], T-shaped stubs [61], L-shaped stubs [62], cross-shaped networks [63], nonuniform transmission lines [64], multi-stage transmission lines [65], real frequency techniques [66], and frequency selective techniques [67]. By employing these elaborate networks, the frequency-dependent rectifier impedance can be matched to 50 Ω over a wide bandwidth. Moreover, the bandwidth extension can be constructed by directly implementing conjugate matching between an antenna and a rectifier, as shown in Refs. [39], [43], [68].
For input power range extension, the multi-branch stacking technique with adaptive power distribution [69], [70], [71] can be used, where the upper and lower branches are for high and low powers, respectively. Adding a depletion-mode field-effect transistor [72], [73], [74], [75] is another practical way to modify a conventional rectifier for a wide input power range. The modified rectifier automatically switches from low-power to high-power mode, maintaining high efficiency over a wide dynamic input power range.
Furthermore, a maximum power point tracking (MPPT) technique is proposed in Ref. [49] using a dc-dc converter. A stable and high efficiency can be maintained not only in the wide power range but also in the wide load value range. Another useful concept is power recycling [76], [77]. The dynamic ranges of the input power and load value can be extended by improving the matching performance with branch-line and Lange couplers (Fig. 15 [76]).
In recent years, the resistance compression network (RCN) [78] has become popular for extending the ranges of the input power and load value, due to its simplicity and effectiveness. An RCN is able to suppress the resistance variation caused by variation in the rectifier input power and load. Based on the RCN, the impedance compression network (ICN) has been proposed [79] to directly compress the variation range of complex impedance, featuring design flexibility. To extend the frequency range at the same time, wideband RCNs and ICNs have also been developed, as illustrated in Fig. 16 [80], [81]. At the same time, the input power dynamic range can be extended by reducing the input impedance variation by means of self-tuning techniques [82], [83].
Along with the development of wireless communication technologies, the focus of input power dynamic range extension has shifted to the lower power bound, so that the rectenna can better harvest the ambient RF energy. That is to say, an increasing number of studies have reported enhancing the efficiency of the rectenna at a low energy density. The enhancement can be implemented at the rectifier and the antenna sides. For the rectifier part, the nonlinear behavior of the rectifying diode can be improved by means of specific circuit topologies, such as the multi-stage rectifier [84], or by improving the circuit insertion loss at low power input [85]. Low-threshold diodes specifically for low power applications have also been reported in Refs. [13], [14]. For antenna elements, it is desirable to realize a larger effective receiving area at a limited size, such as the Huygens antenna [86].
Apart from the rectifier dynamic range extension, it is also desirable to achieve wide coverage of the incident wave. In wireless power transmission and wireless energy harvesting, a dual-polarized (DP) antenna is a good candidate, since it receives a linearity-polarized incident wave at any polarized tilt angle. In this case, uneven power distribution occurs at the two ports of a DP antenna under different polarized tilt angles, resulting in the efficiency fluctuation of a rectifier. To solve this problem, in Ref. [87], a 3 dB branch-line coupler is employed between the antenna and the rectifier to realize uneven-to-even power distribution.
The abovementioned techniques aim to extend only one or two aspects of the rectifier dynamic ranges, including frequency, input power, load resistance, and polarization tilt angle. In Ref. [88], by introducing a six-port coupling network, simultaneous enhancement of all the above aspects is achieved with great flexibility. This design and its outdoor demonstration are shown in Fig. 17 [88].
4.2. Harmonics-based retro-directive techniques
In radiative MWPT applications, the conversion efficiency often suffers from antenna misalignment between the transmitter and the receiver. In contrast, the unexploited harmonic power level of a rectifier is directly related to the misaligned angle, which can be exploited to realize backscattering and antenna alignment. The second harmonic is generated by a rectifier and enhanced by a power amplifier. It is then transmitted to a dual-band antenna to achieve direction-adaption [89]. However, the overall system is complicated, and such a method eliminates the possibility of recycling the second harmonic, which may take up to 25% of the total input power.
The third harmonic (weaker than its second counterpart) is thus adopted to align transmit (TX) and receive (RX) antennas [90]. A branch-line coupler is used to separate the fundamental and third harmonic powers, acting as a duplexer (Fig. 18(a) [90]). Moreover, a rat-race coupler can be exploited to realize MWPT antenna alignment using the second and third harmonics [91], [92]. Circuit diagrams are depicted in Figs. 18(b) and (c) [91], [92]. To ensure stable wireless links of the fundamental and second/third harmonics between TX and RX, a dual-band dual linearly-polarized (DLP) antenna is critical for allowing both high gain and necessary isolation between the vertical and horizontal polarizations. For a detailed design, interested readers are referred to Ref. [91].
(a) Reproduced from Ref. [90] with permission; (b) reproduced from Ref. [91] with permission; (c) reproduced from Ref. [92] with permission.
The distance-adaptive MWPT based on harmonics plays an important role in micro-unmanned aerial vehicles [93], as demonstrated in Fig. 19 [90], [91], [92].
4.3. SWIPT technique based on rectifying behavior
Conventional SWIPT systems require local oscillators on the receiver side for demodulation. To eliminate the need for additional resources (i.e., hardware and power) in realizing a SWIPT system, it is desirable to exploit the rectifying behavior itself—for example, the dc output, the harmonics, and the intermodulation products—to carry information. For modulation schemes, amplitude-shift keying (ASK), phase-shift keying (PSK), frequency-shift keying (FSK), and pulse-width modulation (PWM) are often used to improve the power-conversion efficiency and transfer the information simultaneously. While high peak-to-average power ratio (PAPR) waveforms can improve the efficiency at low input power levels for far-field radiative MWPT [32], [94], it is also meaningful to combine a high PAPR signal with traditional communication technology in an MWPT system.
To reduce the effect of symbol change on the rectification efficiency, traditional amplitude modulation (AM) is improved to amplitude-phase modulation (AM-PM). This technique considers the nonlinearity of diodes and improves the reliability of SWIPT systems. The combination of amplitude and phase can further improve the communication rate. At the receiver side, data extraction is achieved by measuring the dc voltage and the first intermodulation product. This scheme does not require a local oscillator for demodulation, saving system resources [95]. The system test framework is shown in Fig. 20(a) [95].
In addition to modulating via amplitude and phase, frequency intervals can be used. Such a scheme adopts the FSK modulation of multi-tone signals, which improves the symbol rate to a certain extent. A system block diagram is shown in Fig. 20(b) [96], and the symbol construction is provided in Fig. 20(c) [96]. After the signal is down-converted by the rectifier hardware, a fast Fourier transform (FFT) operation is performed. Since the second-order intermodulation of the input signal changes with different frequency intervals, the symbol can be determined by measuring the second-order intermodulation of the output in FFT. The modulation of this technique does not need a local oscillator [96].
Other modulation techniques used in SWIPT are listed in Table 4 [97], [98], [99], [100] for comparison. It can be seen that a local oscillator is not required for all the techniques. The difference between these techniques lies in the symbol construction scheme (amplitude/phase/frequency) and the corresponding demodulation technique.
Compared with traditional system architecture [101], [102], [103], [104], the novel SWIPT technology described above, based on rectifying behavior, allows for information extraction from the rectifying product without splitting signals before a rectifier, leading to compact and reliable designs at the receive side. It is worth mentioning that, in cases requiring a minimal architecture, such as the on-body scenario, a simple dual-band dual-mode topology is a good candidate for rectenna design [105].
5. Conclusions
This article reviewed the development of MWPT and MWEH receivers, with a focus on the design automation methodology. Starting with a brief review of rectifier models, a novel unified rectifier model that works for both low and high powers was introduced. Based on the unified rectifier model, a rectenna design automation method was presented, covering the design automation of each module (i.e., the rectifier, matching circuit, antenna, and dc-dc converter). The whole flow is sequential, with the least possible involvement of iterative optimization and human intervention; hence, the proposed method can easily be integrated into any electronic design automation (EDA) tools. In addition, several emerging rectenna design techniques for MWPT and MWEH were reviewed, including the dynamic range extension technique, the harmonics-based retro-directive technique, and the simultaneous wireless information and power transfer technique. These can potentially strengthen the canonical designs obtained using the automated design flow.
Acknowledgments
The work is supported by the Singapore Ministry of Education Academic Research Fund Tier 1.
Compliance with ethics guidelines
Si-Ping Gao, Jun-Hui Ou, Xiuyin Zhang, and Yongxin Guo declare that they have no conflict of interest or financial conflicts to disclose.
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