Initial values of L and C for the two resonators.

## Abstract

With the rapid development of the wireless systems and demands of low-power integrated electronic circuits, various research trends have tended to study the feasibility of powering these circuits by harvesting free energy from ambient electromagnetic space or by using dedicated RF source. Wireless power transmission (WPT) technology was first pursued by Tesla over a century ago. However, it faced several challenges for deployment in real applications. Recently, energy harvesting and WPT technologies have received much attention as a clean and renewable power source. Rectenna (rectifying antenna) system can be used for remotely charging batteries in several sensor networks at internet of things (IoT) applications as commonly used in smart buildings, implanted medical devices and automotive applications. Rectenna, which is used to convert from RF energy to usable DC electrical energy, is mainly a combination between a receiving antenna and a rectifier circuit. This chapter will present several designs for single and multiband rectennas with different characteristics for energy harvesting applications. Single and multiband antennas as well as rectifier circuits with matching networks are introduced for complete successful rectenna circuit models. At the end of the chapter, a dual-band rectenna example is introduced with a detailed description for each section of the rectenna.

### Keywords

- dedicated RF source
- directive radiation pattern
- high gain antenna
- rectenna (rectifying antenna)
- RF energy harvesting
- wireless power transmission (WPT)

## 1. Introduction

Wireless power transmission (WPT) can be categorized into three different categories as depicted in Figure 1: near-field inductive or resonant coupling, far-field directive powering, and far-field ambient wireless energy harvesting. For the first category, it usually takes place between two coils, one is the primary and the other is the secondary. The main goal is to transfer the power from the primary coil to the secondary coil for several of centimeter as a separation distance between them [1, 2, 3]. Many defected ground structure (DGS)-based designs are proposed for this type of the wireless power transfer [4, 5, 6] to give a high efficiency coupled system.

The second category of WPT is far-field directive powering that is used with directive power transmission which means the transmission occurs in the far-field zone but with well-defined direction of the source. This sort of WPT is useful for solar power satellites (SPS) applications [7, 8, 9] or with intentional powering such as using a dedicating source with well-known direction to power a network of wireless sensors, each sensor has built-in rectenna which is used as a renewable power source to power the connected sensor. The third type is far-field energy harvesting. The receiver does not know the direction of the received power. So, one of the main goals in this type is how to increase the probability of reception by designing antennas with wide beam-width and multiple or wideband resonance frequencies.

Near-field WPT offers a solution to short range powering for electronic devices, it becomes widely commercialized for several wireless applications [10, 11, 12]. Near-field transmission can also be useful with wireless implantable devices [13, 14, 15]. Nevertheless, near-field WPT suffers from severe issue with regard to the transmitting distance, it covers only very short range distances (few centimeters); therefore this limits its applications. On the other hand, the powering scheme of far-field dedicated source or free ambient powering technique can overcome this problem because of the long-distance charging capability. Several studies are introduced in wireless energy harvesting [16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. Although, the great focusing on the wireless energy harvesting, there are many obstacles in the way of free source energy harvesting. One of the main issues is that low input power levels of the ambient energy. Consequently, there are many research papers introduced for rectennas at low input power levels. However, single band rectennas have a simple structures, many research studies [26, 27, 28, 29, 30, 31] have investigated the multi-band rectennas as a trial for increasing the scavenging received power with the same rectenna device; various single and multi-band rectennas are presented. Also, there are big challenges with respect to working the rectenna with fixed conversion efficiency values over a wide range of the received signal. Thus, Section 2 introduces a literature survey about single and multiband frequency operation of different rectennas; also, various rectennas’ designs working at low input power and over wide input power range are discussed. Finally, in Section 3, dual-band rectenna using voltage doubler rectifier and four-section matching network is discussed as an example for a dual-band operation to illustrate the different stages of the whole rectenna system elaborately. The dual-band antenna, firstly, is designed, fabricated and measured separately to check the antenna performance. Then, the rectifier and the matching network between the antenna and the rectifying circuit are also designed and tested independently. After that the integration between the antenna and rectifier is done on the same PCB substrate.

## 2. Literature review on rectennas

### 2.1 Low input received power rectennas

In [32], a compact dual-band rectenna is proposed as depicted in Figure 2. The rectenna has a conversion efficiency of 37 and 30% at 915 MHz and at 2.45 GHz, respectively, at input power of −9 dBm with resistive load of 2.2 kΩ. A dual-band rectenna using Yagi antenna for low input power applications shown in Figure 3 is introduced in [33]. The rectenna offers an acceptable values for the conversion efficiencies, it reaches up to 34% at 1.84 GHz and 30% at 2.14 GHz for input power level of −20 dBm. A combination between the solar energy and RF energy harvesting is discussed in [34]. This solar rectenna, displayed in Figure 4, achieves RF-DC conversion efficiency of 15% with input power of −20 dBm at 850 MHz and 2.45 GHz. In [35], a 130 nm CMOS rectifier is proposed for ultra-low input power. Figure 5 shows the rectenna structure. It consists of 10 stages to give the maximum efficiency of 42.8% at −16 dBm input power and output DC voltage of 2.32 V at resistive load of 0.5 MΩ. A compact co-planar waveguide-fed rectenna using single stage Cockcroft Walton rectifier and L-shaped impedance matching network, shown in Figure 6, is presented in [16]. The RF-DC conversion efficiency is 68% with a received input signal power of 5 dBm at 2.45 GHz. This rectenna also gives conversion efficiencies around 48 and 19% at −10 and −20 dBm, respectively.

### 2.2 Single and multi-band rectennas

The simplest way in energy harvesting is to harvest from single frequency band; this in turn makes the design of matching circuit, which is used for maximum power transmission between the receiving antenna part and the rectifying circuit, is a little bit easier. In [36], a pentagonal antenna is used with series connection single diode to produce a single band rectenna at 5 GHz. The rectenna has maximum conversion efficiency of 46% at resistive load of 2 kΩ. In [37], a 3 × 2 rectangular patch array with a gain of 10.3 dBi is used with three-stage Dickson charge pump circuit for energy harvesting. The rectenna works at 915 MHz. Figure 7 shows the antenna array as well as the rectifying circuit. The maximum rectifier efficiency is 41% at input power of 10 dBm. A semicircular slot antenna was presented for X-band planar rectenna (at 9.3 GHz) as depicted in Figure 8 [38]. The rectenna gives RF-to-DC conversion efficiency of about 21% at an input power density of 245 μW/cm^{2}. 35 GHz rectenna using 4 × 4 patch antenna array, displayed in Figure 9, is proposed in [39]. The maximum RF-to-dc conversion efficiency is 67% with input RF received power of 7 mW.

Due to the variety in transmission bands for different wireless systems, there is a large ambient wasted energy at different frequencies. Consequently, the demand for harvesting from different bands increases. In [40], triple-band implanted rectenna is discussed. It works at 402 MHz, 433 MHz and 2.45 GHz with antenna has a stacked and spiral structure. Figure 10 shows the antenna structure in addition to the rectifier design. It gives a conversion efficiency of 86% at input power of 11 dBm with 5 kΩ load resistor. A compact reconfigurable rectifying antenna has been presented in [41] for dual-band rectification at 5.2 and 5.8 GHz. The measured maximum conversion efficiencies of the proposed rectenna are 65.2 and 64.8% at 4.9 and 5.9 GHz, respectively, with 15 dBm input power. The rectenna fabricated prototype is shown in Figure 11. A dual frequency band rectenna has been developed in [42]. A planar inverted F-antenna is used with a voltage doubler circuit to configure a dual band rectenna.

With increasing the number of frequencies at which rectenna can harvest, the complexity of the matching circuit and the size of the rectenna increase. Therefore, dual-band is the best choice in the designing of rectenna systems because it combines between the simplicity and the scavenging from more than one frequency band.

### 2.3 Wide input received power rectennas

There are several studies that are proposed to guarantee stable fixed RF-DC conversion efficiency over a wide band of the input power. In [43], dual-band rectifier with extended input power range is proposed. The rectifier schematic circuit and the fabricated design is displayed in Figure 12. The rectifier offers above 30% conversion efficiency with input power range from −15 to 20 dBm and the maximum value is 60% from 5 to 15 dBm. Impedance compression network (ICN) techniques is discussed in [44] to fix RF-dc conversion efficiency over a wide band of input power by maintaining the value of input impedance for the rectifier fixed regardless the value of the input power. Figure 13 shows the rectifier configuration. The rectifier has a maximum conversion efficiency of 56% at 31.8 dBm and the input power range for efficiency over than 50% is 6.7 dBm.

## 3. Dual-band Rectenna using voltage doubler rectifier and four-section matching network

This section introduces a dual-band rectenna with maximum measured conversion efficiency of 63 and 69% at f_{1} = 1.95 and f_{2} = 2.5 GHz, respectively, over wide band of the input power, 14 and 15.5 dBm for conversion efficiency above 50% at f_{1} and f_{2}, respectively. The section arrangements are as follows: in Section 3.1, the antenna design is introduced. Then, the equivalent circuit of the antenna is discussed in Section 3.2. Antenna results (reflection coefficient as well as radiation characteristics) is discussed in Section 3.3. The rectifier-antenna matching network for the dual band is described in Section 3.4. The rectifier structure with the geometrical parameters is illustrated in Section 3.5. The rectenna experiment setup is revealed in Section 3.6. While, the rectenna performance including RF-DC conversion efficiency in addition to the DC output voltage at the two frequency bands is discussed in Section 3.7.

### 3.1 Antenna design

In this section, the enhanced-gain antenna design [45] is introduced to be used to configure the rectenna system. Figure 14 shows the layout of the proposed antenna. As shown in the figure, the antenna includes two substrate layers (substrates 1 and 2). The two layers have the same substrate material with relative dielectric constant _{1} = h_{2} = 0.813 mm and a loss tangent of 0.0027. The antenna design consists of disc antenna printed on the top layer of substrate 1. The resonance frequency of this disc is inversely proportional to the disc radius as shown in Eq. (1) [46] which can be determined from Eq. (2) [46]. This disc is directly fed by a microstrip line with 50Ω through a via with radius of 0.6 mm. Also, this disc feeds (by coupling) a circular slot on the ground plane between the feed line and the radiating patch, a square reflecting plane with defected reflector structure (DRS) placed behind the antenna at a distance of _{1} = 1.95 GHz) and from WLAN wireless communication systems (f_{2} = 2.45 GHz).

### 3.2 Equivalent circuit of the proposed antenna (modeling of patch antenna)

The first challenge of designing the equivalent circuit was to find an accurate model of the proposed antenna at f_{1} and f_{2}. Figure 15 shows the equivalent circuit used to model the electrical behavior of the antenna in response to an incoming RF input signal. It is useful to implement this model using basic components R1, L1, and C1, which represent the influence of the first resonant frequency (f_{1}), whereas R2, L2, and C2 represent the second resonant frequency (f_{2}). Elements L3 and C3 are included in the equivalent circuit model to represent the electrical length of the feed line and slot coupling, respectively. The resistance R1 and R2 correspond to radiating losses.

Each radiator (the disc and the slot) is represented by a resonator. Each resonator consists of parallel RLC circuit, the resonance frequency of each one can be determined from Eq. (3):

Firstly, each resonator is studied separately. S-parameters are calculated from Agilent ADS simulator. Then the resonant and cutoff frequencies (*f0* and *fc* in GHz, respectively) are determined. The initial values of L and C for each one can be calculated from Eqs. (4) and (5) [47, 48].

where

f0 and fc | C→ ( | L → ( |

Resonator 1 ( f0 = 2.45 GHz & fc = 2.25 GHz) | At fc = 2.25 GHz and f0 = 2.45 GHz, then: Cp = 3.8 pF | At f0 = 2.45 GHz and Cp = 3.8 pF, then: Lp = 1.11 nH |

Resonator 2 ( f0 = 1.95 GHz & fc = 1.65 GHz) | At fc = 1.65 GHz and f0 = 1.95 GHz, then: Cp = 2.4 pF | At f0 = 1.95 GHz and Cp = 2.4 pF, then: Lp = 2.8 nH |

The losses resistance can be determined from the quality factor (Q)-frequency bandwidth relationship (BW) as:

where the half power frequency bandwidth is evaluated from Eq. (7).

Then, the loss resistance (R) for each resonator can be determined as:

After combining the two resonators, taking into account the effect of losses resistances (R1 and R2) in addition to making optimization, the final equivalent circuit can be obtained. The corresponding values of the equivalent circuit elements are depicted in Table 2.

Parameter | R1(Ω) | L1(nH) | C1(pF) | R2(Ω) | L2(nH) | C2(pF) | L3(nH) | C3(pF) |
---|---|---|---|---|---|---|---|---|

Value | 750 | 10 | 1.7 | 500 | 1.39 | 4.15 | 10 | 0.2 |

### 3.3 Antenna measurement results

#### 3.3.1 Designed antenna S-parameters

Figure 16 shows the reflection coefficient response of the antenna obtained from CST simulation compared with the calculated response of the equivalent circuit model by using Agilent ADS software in addition to the measured reflection coefficient. Good agreement was between the results of simulated, measured and ADS model. The antenna resonates at two bands 1.95 GHz (f_{1}) and 2.45 GHz (f_{2}). The circular patch is designed to radiate at 2.45 GHz by the direct feed with the transmission line placed behind substrate 2. Whereas, 1.95 GHz resonance frequency is designed to radiate due to the capacitive coupling between the circular patch on the top of substrate 1 and the circular slot located on the ground plane, where in 1.95 GHz case the disc antenna is considered as a feeder for the circular slot. The performance of the proposed antenna was simulated and optimized by commercial EM software CST Microwave Studio. A prototype of the proposed antenna was fabricated and tested. The reflection coefficient of the antenna was measured by R&S ZVA 67 Network Analyzer. It is noted that the simulated and measured results of the input impedances of the antenna are in good agreement. Only, a small shift in the measured S-parameters was observed due to the connector soldering, fabrication tolerance, the adhesive between the two layers of the antenna and the layers alignment in fabrication process.

#### 3.3.2 Radiation characteristics

The simulated and measured results of E-plane and H-plane for the high gain antenna at f_{1} and f_{2} are shown in Figure 17(a) and (b), respectively. The measured values of gain, radiation efficiency, F/B ratio, cross polarization level, 3 dB angular beamwidth at the first resonance frequency (f_{1}) are 8.3 dBi, 90%, 12, −22.3 dB, 73.5^{°}, respectively. While at the second resonance frequency, these values can be summarized as 7.8 dBi, 91.6%, 26, −21.6 dB, 79.5^{°}, respectively. The gain and radiation pattern of the antenna were measured by the Anechoic Chamber shown in Figure 18. There is a good agreement between the simulated and measured results of the radiation characteristics.

### 3.4 Rectifier-antenna matching

In this design, a scheme used in [49] is employed to achieve a dual-band impedance transformation at the two frequency bands (f_{1} and f_{2}). This scheme is used to match between a complex and frequency-dependent rectifier input impedance (Z_{Rec}) and a real impedance of the antenna (Z_{Ant}) by using four different sections (Section 1–4) as shown in Figure 19. The matching technique can be summarized in the following steps:

**Step 1:** Achieve the conjugate matching between the load values at both resonant frequencies, that is, moving the two impedance values of the load (rectifier) on the Smith chart to be located on the same real circle with the imaginary parts are equal on both sides of the Smith chart as shown in Figure 20.

**Step 2:** Cancel the imaginary part of the impedances at f_{1} and f_{2}.

**Step 3:** Real to real impedance transformation.

Each section is characterized by two values Z and _{1} is equal to that of the rectifier input impedance at f_{2} and the imaginary parts are also equal but with opposite signs (one is positive (inductive reactance) and the other one is negative (capacitive reactance)); Section 1 parameters (Z_{1} and _{1}) can be calculated from [50] as:

where n is an arbitrary integer and m = f2/f1. Section 2 is used to cancel the imaginary parts of the admittance Y_{1} at the two frequencies *f1* and *f2*. Section 2 parameters can be determined as [49]:

where p is an integer. Sections 3 and 4 are used for real to real impedance transformation, and their parameters can be calculated from Eqs. (13)–(17) [49, 51]

where q and s are integers.

### 3.5 Rectifier design

Several rectifiers’ topologies are used for energy harvesting, for instance, diodes in parallel connection, diodes in series connection, voltage doubler circuits, multi-stage voltage multiplier and so forth. Voltage multipliers generate high voltages from a low voltage power source. However, in this design a half-wave voltage doubler circuit, which is a special case of voltage multipliers, is used for the rectification to get high voltage with conservation of the design simplicity. The rectifier design as well as the matching network is depicted in Figure 21 [52]. The voltage doubler circuit comprises two Avago HSMS2850 Schottky diodes and two SMD capacitors (C_{s} = C_{p} = 100 pF). The Schottky diode has a built-in voltage (V_{b}) of 0.150 V and a breakdown voltage (V_{br}) of 3.8 V. Due to the small values of the series resistance and the barrier capacitance (R_{s} of 25Ω and C_{b} of 0.18 pF) for the above-mentioned diodes category, so these diodes have a high cutoff frequency and high conversion efficiency. The capacitor C_{s} is used to store the energy in one half cycle to double the charging voltage for C_{p} at the other half cycle, C_{s} also acts as bandpass filter to block the DC voltage generated from the nonlinear diodes. C_{p} has two functions, it is used for bypassing the higher order modes, generated from the nonlinear diode to the ground and getting a smooth DC output voltage as well. Also the shunt connection between C_{p} and the load impedance R_{L} acts as a low pass filter.

The rectifier is designed on Rogers Duroid RO3003 with a relative permittivity (_{r}) of 3, substrate thickness (h) of 0.76 mm, a dielectric loss tangent (tan_{Rec}) at two frequencies are (8 −j × 28.2) and (26.1 −j × 39.7) at f_{1} and f_{2}, respectively, with a resistive load of 1.5 kΩ. The circuit parameters have been optimized to achieve the maximum conversion efficiency at the two frequency bands for the received input power levels. The parameters of the rectifier as well as the matching circuit are illustrated in Figure 21, where each line is defined by the length (L) and width (W). Also, the prototype of the fabricated rectifier is shown in Figure 21.

### 3.6 Rectenna measurements

The rectifying circuit including the matching network is simulated using Keysight advanced design system (ADS), while the antenna was designed using ANSYS high-frequency structure simulator (HFSS). The enhanced-gain antenna described in [45] is used as a receiving antenna in the proposed rectenna to increase the rectifier sensitivity. Hence, increasing rectenna capability to harvest from low input power levels. The receiving antenna and the rectifier are integrated on the same substrate, fabricated and measured in the measurement setup shown in Figure 22. An Agilent Technologies E8257D Analog signal generator is used to send a microwave signal which is connected to a horn antenna with 9 dBi gain at the two frequencies. On the other hand, the rectenna under test (RUT) is connected with a voltmeter to measure the DC output voltage. To take the antenna radiation characteristics into account, the antenna effective area is considered. Hence, the RF-DC conversion efficiency of the proposed rectenna (

where V_{DC} is the measured DC output voltage, Pin is the received RF input power and R_{L} is the resistive load. P_{in} is defined in Eq. (19)

where P_{D} is the RF power density and A_{eff} is the antenna effective area. P_{D} and A_{eff} are calculated using Eqs. (20) and (21), respectively.

P_{t} is the transmitting power, G_{t} is the horn antenna gain and r is the distance between the transmitter and the rectenna all are known. Therefore, the RF-to-DC conversion efficiency can be measured. For far-field measurements, r is chosen of 40 cm. Figure 23 shows the photo of the rectenna measurement setup.

### 3.7 Rectenna results and discussion

The entire system (antenna, matching circuit and rectifier) is tested over different input power levels with different resistive load values at two frequencies (f_{1} and f_{2}); Figure 24(a) and (b) show the comparison between the measured and simulated results of RF-to-DC conversion efficiency and the DC output voltage versus the input power at f_{1} and f_{2}, respectively. The maximum measured conversion efficiency is 63% with input power range of 14 dBm (from −3.5 to 10.5 dBm) at f_{1}, while the measured efficiency at f_{2} is 69% with input power from −4.5 to 11 dBm (15.5 dBm). There is a slight shift between the simulation and measurement results, where the maximum simulated RF-DC conversion efficiency are 66 and 73% at the same two frequencies, respectively. Due to the limitations in the experiments, the received input power is limited only up to 11 dBm.

## 4. Conclusions

This chapter presents a study of rectenna systems for RF energy harvesting and wireless power transfer. A survey about employing rectennas in WPT, low input received power rectennas, single and multi-band rectennas, wide input received power rectennas are introduced. Finally, dual-band rectenna using voltage doubler rectifier and four-section matching network is discussed. The first part of the rectenna design is the dual-band disc antenna with enhanced gain in order to collect a highest amount of RF energy. It radiates at 1.95 and 2.45 GHz. The measured results showed the gain of 8.3 and 7.8 dBi at 1.95 and 2.45 GHz, respectively. The disc antenna is integrated with a dual-band rectifier with four-section matching network to introduce a dual-frequency rectenna with higher conversion efficiency over wide band of the input power for multiband RF energy harvesting. The rectenna gives maximum RF-DC measured conversion efficiency of 63% and 69% at 1.95 GHz and 2.5 GHz, respectively. it also operates over a wide range of the input power; it covers the range of 14 and 15.5 dBm at f_{1} and f_{2}, respectively for a conversion efficiency higher than 50% with load resistance (R_{L}) = 1K. The rectenna is simulated, fabricated and measured. The simulated and measured results show good agreement.