1. Introduction

In the past few decades, substantial research efforts have been devoted to wireless power transfer (WPT) applications from both dedicated [1] and ambient RF sources [2, 3]. The sensitivity of the receiver and the energy transfer efficiency are the main concerns in any WPT system, and they eventually dictate the RF energy harvesting (EH) system's performance, its range, and the overall reliability. The sensitivity depends on the minimum power that is required in order to power up the semiconductor devices used [4] in the EH circuit. On the other hand, RF-to-DC efficiency depends on the receiving antenna performance, the impedance matching network between the antenna and the rectifying circuit, and the overall

power conversion efficiency of the rectifier's subsequent stage, that is, the voltage multiplier. Traditionally, the efficiency of any rectifying circuit is controlled and improved by optimizing the circuit design [5, 6]. Additionally, it can be further improved by using a high peak-to-average power ratio (PAPR) multi-sine signals that have demonstrated improved efficiency performance compared to the conventional sinusoidal signals [7, 8]. Usually, the available ambient RF power is very low and therefore the harvested power is not sufficient to support any immediate application, although, it can be utilized to directly control the external supply dynamically [9–11]. Recently, one of the key developments in wireless communication is the exploitation of the same RF signal for information and energy harvesting. This refers to the concept of simultaneous wireless information and power transfer (SWIPT) [12] systems. Finally, RF EH is widely used in RFID tags that are used for tracking and identification [13]. With the development and integration of a low cost compact, energy harvesting circuit on the RFID tag, the conventional passive tags [14–16] can be converted into "active-equivalent" tags with improved life time and increased read range through RF energy harvesting coming from designated power beacons without relying on the reader to activate the RFID oscillating circuit [17].

works as a low pass filter to smoothen the output DC voltage. The third topology (Figure 1c) is the voltage multiplier (multi-stage), which is a full-wave rectifier that further increases the output voltage with a network of capacitors and diodes. It has a similar operation principle to the voltage doubler. The voltage of each stage is used as a reference for the next stage, and the maximum output voltage depends on the overall number of stages. The undesired effect of the multi-stage rectifiers is the decrease in the overall efficiency which degrades for every additional stage since the efficiency of every single stage is a multiplying factor smaller than one (1). It is important to note that the overall RF-to-DC conversion efficiency depends directly on the selected topology. Where the available AC power is high, the use of multi-stage rectifiers results in an increased DC voltage level, although the overall power efficiency is decreased. For RF EH systems though, the available input power is usually very low. For relatively low input power situations where the available power is comparable to the amount of power that is required to switch on the rectifying diodes, the lower the number of diodes is, the higher the overall

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power…

The use of the voltage doubler circuit implemented with Schottky diodes appears often in the literature. The voltage doubler circuit consists of a combination of two diodes and two capacitors connected in the topology presented in the schematic of Figure 2a. Several types of diodes can be used for the implementation of a

voltage doubler. Figure 2b presents the equivalent circuit for the Skyworks SMS7630 Schottky diode, which was used for many of the rectifiers which are

Figure 2a illustrates the schematic of a voltage double topology with the preceding antenna and the required matching network. The antenna and rectifier, including the intermediate matching network, are commonly referred to as a rectenna. The presented voltage doubler implementation consists of the clamper stage formed by the capacitor C1 and the diode D1, the rectifying diode (D2), and the RC low pass filter (C2 and RL). The preceding matching network illustrated here as a box, is usually part of the rectifier circuit and it assures the maximum power transfer by reducing the impedance mismatch loss between the preceding antenna and the rectifier circuit. Often, the matching network is built with reactive lumped or distributed components, optimized for the intended operation frequency and

RF energy harvesting systems (a) voltage doubler circuit (b) equivalent model for Schottky diodes in voltage

RF-to-DC efficiency is.

DOI: http://dx.doi.org/10.5772/intechopen.89271

2. Voltage doubler

discussed in this chapter.

Figure 2.

197

doubler topology.

To convert RF to DC power, the RF energy harvesting circuits are generally implemented using semiconductor-based rectifying elements such as CMOS diodes with transistors [18] or Schottky diodes, due to their low cost and low power requirements [4]. The most common Schottky diodes include Skywork's SMS [19] and Broadcom's HSMS [20] series of surface mount devices (SMD). Figure 1 illustrates the basic RF-to-DC rectifier topologies. The first one (Figure 1a) is a single diode half-wave rectifier (envelope detector) that consists of a series diode with shunt capacitor and performs half-wave rectification by passing either the negative or the positive half of the AC current while the remaining half is blocked. Single diode, half-wave rectifiers have large rectified voltage ripples compared to fullwave rectifiers, hence, additional filtering is required to remove the harmonics from the DC output. The use of Schottky diodes with lower built-in threshold voltage, such as the SMS7630, contributes toward improved RF-to-DC conversion efficiency for the lower input power signals. This happens because a fixed amount of power is consumed for biasing the diodes, which for lower power signals, it is high percentage of the original RF power. The second rectifier topology (Figure 1b) is the voltage doubler, or single stage voltage multiplier, that works as a full-wave rectifier and converts the incident AC signal to a constant polarity voltage at its output. Compared to the half-wave rectifier, it results in a higher average DC voltage. It consists of a one-stage clamper with a pumping capacitor at the input of a shunt diode and a series rectifying diode along a shunt capacitor at the output stage, which

Figure 1.

Rectifier topologies, (a) single diode (single-stage), (b) voltage doubler, and (c) voltage multiplier (multi-stage).

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power… DOI: http://dx.doi.org/10.5772/intechopen.89271

works as a low pass filter to smoothen the output DC voltage. The third topology (Figure 1c) is the voltage multiplier (multi-stage), which is a full-wave rectifier that further increases the output voltage with a network of capacitors and diodes. It has a similar operation principle to the voltage doubler. The voltage of each stage is used as a reference for the next stage, and the maximum output voltage depends on the overall number of stages. The undesired effect of the multi-stage rectifiers is the decrease in the overall efficiency which degrades for every additional stage since the efficiency of every single stage is a multiplying factor smaller than one (1). It is important to note that the overall RF-to-DC conversion efficiency depends directly on the selected topology. Where the available AC power is high, the use of multi-stage rectifiers results in an increased DC voltage level, although the overall power efficiency is decreased. For RF EH systems though, the available input power is usually very low. For relatively low input power situations where the available power is comparable to the amount of power that is required to switch on the rectifying diodes, the lower the number of diodes is, the higher the overall RF-to-DC efficiency is.

#### 2. Voltage doubler

power conversion efficiency of the rectifier's subsequent stage, that is, the voltage multiplier. Traditionally, the efficiency of any rectifying circuit is controlled and improved by optimizing the circuit design [5, 6]. Additionally, it can be further improved by using a high peak-to-average power ratio (PAPR) multi-sine signals that have demonstrated improved efficiency performance compared to the conventional sinusoidal signals [7, 8]. Usually, the available ambient RF power is very low and therefore the harvested power is not sufficient to support any immediate application, although, it can be utilized to directly control the external supply dynamically [9–11]. Recently, one of the key developments in wireless communication is the exploitation of the same RF signal for information and energy harvesting. This refers to the concept of simultaneous wireless information and power transfer (SWIPT) [12] systems. Finally, RF EH is widely used in RFID tags that are used for tracking and identification [13]. With the development and integration of a low cost compact, energy harvesting circuit on the RFID tag, the conventional passive tags [14–16] can be converted into "active-equivalent" tags with improved life time and increased read range through RF energy harvesting coming from designated power beacons without relying on the reader to activate

To convert RF to DC power, the RF energy harvesting circuits are generally implemented using semiconductor-based rectifying elements such as CMOS diodes with transistors [18] or Schottky diodes, due to their low cost and low power requirements [4]. The most common Schottky diodes include Skywork's SMS [19] and Broadcom's HSMS [20] series of surface mount devices (SMD). Figure 1 illustrates the basic RF-to-DC rectifier topologies. The first one (Figure 1a) is a single diode half-wave rectifier (envelope detector) that consists of a series diode with shunt capacitor and performs half-wave rectification by passing either the negative or the positive half of the AC current while the remaining half is blocked. Single diode, half-wave rectifiers have large rectified voltage ripples compared to fullwave rectifiers, hence, additional filtering is required to remove the harmonics from the DC output. The use of Schottky diodes with lower built-in threshold voltage, such as the SMS7630, contributes toward improved RF-to-DC conversion efficiency for the lower input power signals. This happens because a fixed amount of power is consumed for biasing the diodes, which for lower power signals, it is high percentage of the original RF power. The second rectifier topology (Figure 1b) is the voltage doubler, or single stage voltage multiplier, that works as a full-wave rectifier and converts the incident AC signal to a constant polarity voltage at its output. Compared to the half-wave rectifier, it results in a higher average DC voltage. It consists of a one-stage clamper with a pumping capacitor at the input of a shunt diode and a series rectifying diode along a shunt capacitor at the output stage, which

Rectifier topologies, (a) single diode (single-stage), (b) voltage doubler, and (c) voltage multiplier

the RFID oscillating circuit [17].

Recent Wireless Power Transfer Technologies

Figure 1.

196

(multi-stage).

The use of the voltage doubler circuit implemented with Schottky diodes appears often in the literature. The voltage doubler circuit consists of a combination of two diodes and two capacitors connected in the topology presented in the schematic of Figure 2a. Several types of diodes can be used for the implementation of a voltage doubler. Figure 2b presents the equivalent circuit for the Skyworks SMS7630 Schottky diode, which was used for many of the rectifiers which are discussed in this chapter.

Figure 2a illustrates the schematic of a voltage double topology with the preceding antenna and the required matching network. The antenna and rectifier, including the intermediate matching network, are commonly referred to as a rectenna. The presented voltage doubler implementation consists of the clamper stage formed by the capacitor C1 and the diode D1, the rectifying diode (D2), and the RC low pass filter (C2 and RL). The preceding matching network illustrated here as a box, is usually part of the rectifier circuit and it assures the maximum power transfer by reducing the impedance mismatch loss between the preceding antenna and the rectifier circuit. Often, the matching network is built with reactive lumped or distributed components, optimized for the intended operation frequency and

Figure 2. RF energy harvesting systems (a) voltage doubler circuit (b) equivalent model for Schottky diodes in voltage doubler topology.

the expected power levels, since rectifiers are non-linear devices. Several different matching topologies are discussed in the subsequent sections.

#### 2.1 Voltage doubler operation principle

As the first voltage doubler stage following the matching network, the clamper is used to enhance the input voltage to the rectifying diode (D2), as can be seen in Figure 2a. Clamping circuits are mostly used to implement the voltage multiplier [8]. For a time-varying sinusoidal input signal, the clamping circuit uses the peak of the negative voltage of the input signal to produce a positive shift in the signal during its positive part, as explained below.

From Figure 2a, Vi is the voltage at the input of the capacitor C1, i1 is the current passing through C1, Vd is the voltage on diode D1, and i2 is the current on D1. The clamper is activated during the negative cycle of Vi, and C1 is charging with D1 in ON state. During the positive cycle, C1 acts as a voltage source of -Vc1 with D1 in OFF state. According to Kirchhoff's law at the relevant loop, Vd is associated with VC1 and Vi through (1)

$$V\_i = V\_{C1} + V\_d \tag{1}$$

VDC <sup>¼</sup> <sup>1</sup>

of n periods of the output signal [8].

DOI: http://dx.doi.org/10.5772/intechopen.89271

2.2 Implemented rectifier circuits

various power levels of the UHF rectifiers investigated.

Figure 3b.

Figure 3.

199

percentage vs. input power and termination load.

T � t

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power…

ðT t

where t is the steady state charging starting time, and T ¼ nτ is the total number

The non-linear response of the diode is represented by a varying ohmic load Rj (see Figure 2b). A real diode requires a combination of parasitic capacitors and inductors, which are needed to accurately model the package of the semiconductor device. The non-linear nature of the Schottky diodes used is reflected in the matching of the rectifier device (|S11|) and also on the resulting RF-to-DC efficiency. Figure 3a presents the simulated reflection coefficient for a single-port voltage doubler rectifier. The reflection coefficient resonance shifts when the input power is varied and therefore a wideband matching network is needed in order to maintain the |S11| below �10 dB, despite the shift of the resonance. The achieved RF-to-DC efficiency also depends non-linearly on the termination load and the input RF power, as can be seen in the simulated efficiency surface presented in

A thorough study of voltage-doubler rectifiers in the UHF frequency range is presented in this section, considering possible variations on (a) the diode model (b) the substrate type, and (c) several alternative matching configurations. In particular, the Broadcom HSMS2850 and the Skyworks SMS7630 Schottky diodes were investigated. The use of low-cost, lossy FR4 substrate (ε<sup>r</sup> = 4.3, tanδ = 0.016) was compared with the higher-cost and less lossy Duroid 5880 substrate (ε<sup>r</sup> = 2.2, tanδ = 0.0009). Finally, a wide range of matching circuits that consisted of one or more lumped inductors, one or more radial and custom shaped open and shorted stubs, and the use of tapered microstrip lines for bandwidth enhancement were considered in an attempt to enhance the bandwidth and the bandwidth stability for

For this study, 11 rectifier variations were fabricated and measured. The fabricated rectifiers labeled A to K with a short description of their characteristics, matching networks, and diodes used are presented in Table 1. The first comparison between a voltage-doubler rectifier (Rectifier A) and a single-stage rectifier (Rectifier B) presented in Figure 4 suggests that for input power levels higher than �15 dBm, the voltage doubler topology exhibits a higher RF-to-DC efficiency. For most wireless power transfer applications and due to the unavoidable free-space

Non-linearity of the rectifying circuit (a) simulated |S11| versus frequency and input power (b) efficiency

Voutð Þt dt (8)

$$
\dot{\mu}\_1 = \mathbf{C}\_1 \frac{dv\_{C\_1}}{dt} = -\dot{\mathbf{e}}\_2 = -\mathbf{I}\_s \left( e^{V\_{d\_{\parallel}V\_T}} - \mathbf{1} \right) \tag{2}
$$

where Vd ¼ VD<sup>1</sup> � Is, VT,Is, and n show the thermal voltage, the saturation current, and the ideality factor, respectively. The voltage enhancement factor is defined as the ratio of input voltage to rectifying diode voltage Vd with peak input voltage to clamper circuit Vi [8]. For the ideal continuous wave excited voltage doubler, the voltage enhancement factor is two, if the clamper moves perfectly the input signal to the DC offset, equal to the peak of Vi during the negative input cycle.

It can be seen in Figure 2a that the rectifying circuit consists of the diode D2 and the low pass RC filter with capacitor C2 and termination load RL. Vd is the input voltage and i3 is current through the diode D2, while the current though the capacitor C2 and load resistor RL is denoted by i4 and i5, respectively, and the output voltage is Vout. According to Kirchhoff's law, the voltage across diode D2 is:

$$V\_{D2} = V\_d - V\_{out} \tag{3}$$

$$\text{where}$$

$$\begin{array}{ll}\text{where} & i\_3 = i\_4 + i\_5 \end{array} \tag{4}$$

$$i\_3 = I\_t \left( e^{V\_{d\_{\sqrt{l}V\_T}}} - 1 \right) \tag{5}$$

$$i\_1 = C\_2 \frac{dV\_{out}}{dt}, i\_5 = {}^{V\_{out}}\!/\_{RL} \tag{6}$$

The ordinary differential equation (ODE) by proper transformation of nonlinear behavior of the diode described in Eqs. (5) and (6) is:

$$\frac{dV\_{\rm out}}{dt} = {}^{i\_{\prime}}\!/\_{C\_{2}} = I\_{s} \left(e^{V\_{d} - V\_{\rm out}/}{}\_{nV\_{T}} - \mathbf{1}\right) - {}^{V\_{\rm out}}\!/\_{R\_{L}C\_{2}}\tag{7}$$

Equation (7) is a nonlinear form of an ODE, and a closed form solution for the general case is not available. Though, its numerical solution is possible using the ODE solver [8], the calculated DC output voltage is

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power… DOI: http://dx.doi.org/10.5772/intechopen.89271

$$V\_{DC} = \frac{1}{T - t} \int\_{t}^{T} V\_{out}(t)dt\tag{8}$$

where t is the steady state charging starting time, and T ¼ nτ is the total number of n periods of the output signal [8].

The non-linear response of the diode is represented by a varying ohmic load Rj (see Figure 2b). A real diode requires a combination of parasitic capacitors and inductors, which are needed to accurately model the package of the semiconductor device. The non-linear nature of the Schottky diodes used is reflected in the matching of the rectifier device (|S11|) and also on the resulting RF-to-DC efficiency. Figure 3a presents the simulated reflection coefficient for a single-port voltage doubler rectifier. The reflection coefficient resonance shifts when the input power is varied and therefore a wideband matching network is needed in order to maintain the |S11| below �10 dB, despite the shift of the resonance. The achieved RF-to-DC efficiency also depends non-linearly on the termination load and the input RF power, as can be seen in the simulated efficiency surface presented in Figure 3b.

#### 2.2 Implemented rectifier circuits

the expected power levels, since rectifiers are non-linear devices. Several different

As the first voltage doubler stage following the matching network, the clamper is used to enhance the input voltage to the rectifying diode (D2), as can be seen in Figure 2a. Clamping circuits are mostly used to implement the voltage multiplier [8]. For a time-varying sinusoidal input signal, the clamping circuit uses the peak of the negative voltage of the input signal to produce a positive shift in the signal

From Figure 2a, Vi is the voltage at the input of the capacitor C1, i1 is the current passing through C1, Vd is the voltage on diode D1, and i2 is the current on D1. The clamper is activated during the negative cycle of Vi, and C1 is charging with D1 in ON state. During the positive cycle, C1 acts as a voltage source of -Vc1 with D1 in OFF state. According to Kirchhoff's law at the relevant loop, Vd is associated with

dt ¼ �i<sup>2</sup> ¼ �Is <sup>e</sup>

where Vd ¼ VD<sup>1</sup> � Is, VT,Is, and n show the thermal voltage, the saturation current, and the ideality factor, respectively. The voltage enhancement factor is defined as the ratio of input voltage to rectifying diode voltage Vd with peak input voltage to clamper circuit Vi [8]. For the ideal continuous wave excited voltage doubler, the voltage enhancement factor is two, if the clamper moves perfectly the input signal to the DC offset, equal to the peak of Vi during the

It can be seen in Figure 2a that the rectifying circuit consists of the diode D2 and the low pass RC filter with capacitor C2 and termination load RL. Vd is the input voltage and i3 is current through the diode D2, while the current though the capacitor C2 and load resistor RL is denoted by i4 and i5, respectively, and the output voltage is Vout. According to Kirchhoff's law, the voltage across diode

where <sup>i</sup><sup>3</sup> <sup>¼</sup> <sup>i</sup><sup>4</sup> <sup>þ</sup> <sup>i</sup><sup>5</sup> (4)

dVout

Vd=nVT � 1 

dt , <sup>i</sup><sup>5</sup> <sup>¼</sup> Vout

The ordinary differential equation (ODE) by proper transformation of nonlinear

Vd�Vout=nVT � 1 

Equation (7) is a nonlinear form of an ODE, and a closed form solution for the general case is not available. Though, its numerical solution is possible using the

=

i<sup>3</sup> ¼ Is e

i<sup>1</sup> ¼ C<sup>2</sup>

behavior of the diode described in Eqs. (5) and (6) is:

ODE solver [8], the calculated DC output voltage is

dVout dt <sup>¼</sup> is =<sup>C</sup><sup>2</sup> ¼ Is e

Vi ¼ VC<sup>1</sup> þ Vd (1)

VD<sup>2</sup> ¼ Vd � Vout (3)

� Vout=

RL (6)

RLC<sup>2</sup> (7)

(2)

(5)

Vd=nVT � 1 

matching topologies are discussed in the subsequent sections.

2.1 Voltage doubler operation principle

Recent Wireless Power Transfer Technologies

during its positive part, as explained below.

i<sup>1</sup> ¼ C<sup>1</sup>

dvC<sup>1</sup>

VC1 and Vi through (1)

negative input cycle.

D2 is:

198

A thorough study of voltage-doubler rectifiers in the UHF frequency range is presented in this section, considering possible variations on (a) the diode model (b) the substrate type, and (c) several alternative matching configurations. In particular, the Broadcom HSMS2850 and the Skyworks SMS7630 Schottky diodes were investigated. The use of low-cost, lossy FR4 substrate (ε<sup>r</sup> = 4.3, tanδ = 0.016) was compared with the higher-cost and less lossy Duroid 5880 substrate (ε<sup>r</sup> = 2.2, tanδ = 0.0009). Finally, a wide range of matching circuits that consisted of one or more lumped inductors, one or more radial and custom shaped open and shorted stubs, and the use of tapered microstrip lines for bandwidth enhancement were considered in an attempt to enhance the bandwidth and the bandwidth stability for various power levels of the UHF rectifiers investigated.

For this study, 11 rectifier variations were fabricated and measured. The fabricated rectifiers labeled A to K with a short description of their characteristics, matching networks, and diodes used are presented in Table 1. The first comparison between a voltage-doubler rectifier (Rectifier A) and a single-stage rectifier (Rectifier B) presented in Figure 4 suggests that for input power levels higher than �15 dBm, the voltage doubler topology exhibits a higher RF-to-DC efficiency. For most wireless power transfer applications and due to the unavoidable free-space

#### Figure 3.

Non-linearity of the rectifying circuit (a) simulated |S11| versus frequency and input power (b) efficiency percentage vs. input power and termination load.


similar matching networks that consist of shorted and radial matching stubs. The |S11| resonance remains rather stable as the input power varies, but it is narrowband (25 MHz). The different diode models have minimum effect on the matching, but

Voltage-Doubler RF-to-DC Rectifiers for Ambient RF Energy Harvesting and Wireless Power…

Voltage doubler (A) and single stage rectifier (B) comparison; (a) Rectifier A |S11|, (b) Rectifier B |S11|,

Rectifier (C) and rectifier (D) comparison; (a) Rectifier C |S11|, (b) Rectifier D |S11|, (c) |S11| at 10 dBm

(c) |S11| at 10 dBm comparison, and (d) RF-to-DC efficiency.

DOI: http://dx.doi.org/10.5772/intechopen.89271

Figure 4.

Figure 5.

201

comparison, and (d) RF-to-DC efficiency.

#### Table 1. Implemented rectifiers labeled A to K.

loss, the available power at the receiver is rather low. However, the received power level is random and cannot be predicted, and the efficiency plots for Rectifiers A and B cross at the 15 dB input power mark (Figure 4d), therefore a direct comparison of the efficiency performance is not straight forward. The improved average efficiency performance over the entire power range is the main reason why the voltage doubler was preferred over the single stage rectifier and was further studied in detail. The free-space loss is inversely proportional to λ<sup>2</sup> and this is the reason why the UHF frequency (relatively low frequency) was preferred for the presented study.
