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

foam with a low dielectric constant (ε<sup>r</sup> ¼ 1:06). Substrate dimensions are

Rectenna Systems for RF Energy Harvesting and Wireless Power Transfer

2h πaε<sup>r</sup>

communication systems (f2 = 2.45 GHz).

DOI: http://dx.doi.org/10.5772/intechopen.89674

radiating losses.

Figure 15.

163

determined from Eq. (3):

calculated from Eqs. (4) and (5) [47, 48].

Equivalent lumped-elements circuit for antenna in ADS.

ae ¼ a 1 þ

50 mm � 50 mm. The designated antenna resembles good candidate for RF energy harvesting from mobile radio waves (f1 = 1.95 GHz) and from WLAN wireless

> fr <sup>¼</sup> <sup>1</sup>:8412v<sup>0</sup> 2πae

ln <sup>π</sup><sup>a</sup> 2h � � <sup>þ</sup> <sup>1</sup>:<sup>7726</sup> � � � �0:<sup>5</sup>

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 f1 and f2. 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 (f1), whereas R2, L2, and C2 represent the second resonant frequency (f2). 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

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

> fr <sup>¼</sup> <sup>1</sup> 2π ffiffiffiffiffiffi

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

ffiffiffiffi εr

p (1)

LC <sup>p</sup> (3)

(2)

This section introduces a dual-band rectenna with maximum measured conversion efficiency of 63 and 69% at f1 = 1.95 and f2 = 2.5 GHz, respectively, over wide band of the input power, 14 and 15.5 dBm for conversion efficiency above 50% at f1 and f2, 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 ε<sup>r</sup><sup>1</sup> ¼ ε<sup>r</sup><sup>2</sup> ¼ 3:55, thickness h1 = h2 = 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 λ0=8 to improve the antenna gain as well as enhance the front to back ratio. The reflector is built on 0.8 mm thick FR4 substrate with dielectric constant of 4.4 and a loss tangent of 0.02. The reflector is supported by a 15 mm thick layer of lightweight

#### Rectenna Systems for RF Energy Harvesting and Wireless Power Transfer DOI: http://dx.doi.org/10.5772/intechopen.89674

foam with a low dielectric constant (ε<sup>r</sup> ¼ 1:06). Substrate dimensions are 50 mm � 50 mm. The designated antenna resembles good candidate for RF energy harvesting from mobile radio waves (f1 = 1.95 GHz) and from WLAN wireless communication systems (f2 = 2.45 GHz).

$$f\_r = \frac{1.8412v\_0}{2\pi a\_\varepsilon \sqrt{\varepsilon\_r}}\tag{1}$$

$$a\_e = a \left[ 1 + \frac{2h}{\pi a \varepsilon\_r} \left( \ln \left( \frac{\pi a}{2h} \right) + 1.7726 \right) \right]^{0.5} \tag{2}$$

#### 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 f1 and f2. 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 (f1), whereas R2, L2, and C2 represent the second resonant frequency (f2). 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):

$$f\_r = \frac{1}{2\pi\sqrt{LC}}\tag{3}$$

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].

Figure 15. Equivalent lumped-elements circuit for antenna in ADS.

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

This section introduces a dual-band rectenna with maximum measured conversion efficiency of 63 and 69% at f1 = 1.95 and f2 = 2.5 GHz, respectively, over wide band of the input power, 14 and 15.5 dBm for conversion efficiency above 50% at f1 and f2, 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

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 ε<sup>r</sup><sup>1</sup> ¼ ε<sup>r</sup><sup>2</sup> ¼ 3:55, thickness h1 = h2 = 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 λ0=8 to improve the antenna gain as well as enhance the front to back ratio. The reflector is built on 0.8 mm thick FR4 substrate with dielectric constant of 4.4 and a loss tangent of 0.02. The reflector is supported by a 15 mm thick layer of lightweight

matching network

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bands is discussed in Section 3.7.

3.1 Antenna design

Figure 14.

162

3D geometry, perspective view and side view of the proposed disc antenna [45].

$$C\_p = \frac{5f\_c}{\pi \left[f\_0^{\frac{2}{2}} - f\_c^{\frac{2}{2}}\right]} \text{ pF} \tag{4}$$

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

Rectenna Systems for RF Energy Harvesting and Wireless Power Transfer

DOI: http://dx.doi.org/10.5772/intechopen.89674

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

are depicted in Table 2.

Figure 17.

2.45 GHz.

165

<sup>R</sup> <sup>¼</sup> <sup>1</sup>

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

2D measured and simulated results of radiation pattern for the antenna: (a) at 1.95 GHz and (b) at

BW <sup>¼</sup> <sup>1</sup>

RC (7)

BW � <sup>C</sup> (8)

$$L\_p = \frac{250}{C\_p \left[\pi f\_0\right]^2} nH \tag{5}$$

where Cpis the capacitance in picofarads and Lpis the inductance in nanohenrys. Table 1 summarizes the initial values of R and L at the two operating frequencies.

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

$$Q = \frac{a\nu\_0}{BW} = a\nu\_0 RC\tag{6}$$


#### Table 1.

Initial values of L and C for the two resonators.


#### Table 2.

Elements values of the equivalent circuit model for the dual band antenna.

Figure 16. Reflection coefficient of the proposed antenna.

Rectenna Systems for RF Energy Harvesting and Wireless Power Transfer DOI: http://dx.doi.org/10.5772/intechopen.89674

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

$$BW = \frac{1}{RC} \tag{7}$$

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

$$R = \frac{1}{BW \times C} \tag{8}$$

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.

Figure 17. 2D measured and simulated results of radiation pattern for the antenna: (a) at 1.95 GHz and (b) at 2.45 GHz.

Cp <sup>¼</sup> <sup>5</sup> fc π f <sup>0</sup>

> Lp <sup>¼</sup> <sup>250</sup> Cp π f <sup>0</sup>

<sup>Q</sup> <sup>¼</sup> <sup>ω</sup><sup>0</sup>

π f <sup>0</sup> 2 � f <sup>c</sup>

At fc = 2.25 GHz and f0 = 2.45 GHz, then: Cp = 3.8 pF

At fc = 1.65 GHz and f0 = 1.95 GHz, then: Cp = 2.4 pF

Elements values of the equivalent circuit model for the dual band antenna.

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

bandwidth relationship (BW) as:

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Resonator 1 (f0 = 2.45 GHz & fc = 2.25 GHz)

Resonator 2 (f0 = 1.95 GHz & fc = 1.65 GHz)

Table 1.

Table 2.

Figure 16.

164

Reflection coefficient of the proposed antenna.

f0 and fc <sup>C</sup>! (Cp <sup>¼</sup> <sup>5</sup> fc

Initial values of L and C for the two resonators.

<sup>2</sup> � <sup>f</sup> <sup>c</sup>

where Cpis the capacitance in picofarads and Lpis the inductance in nanohenrys. Table 1 summarizes the initial values of R and L at the two operating frequencies. The losses resistance can be determined from the quality factor (Q)-frequency

<sup>2</sup> pF (4)

<sup>2</sup> nH (5)

BW <sup>¼</sup> <sup>ω</sup>0RC (6)

Cp <sup>π</sup> <sup>f</sup> ½ � <sup>0</sup>

At f0 = 2.45 GHz and Cp = 3.8 pF, then: Lp = 1.11 nH

At f0 = 1.95 GHz and Cp = 2.4 pF, then: Lp = 2.8 nH

<sup>2</sup> nH)

<sup>2</sup> ½ � pF) <sup>L</sup> ! (Lp <sup>¼</sup> <sup>250</sup>
