In this section, an attempt has been made to increase rectenna efficiency by loading it with a frequency selective surface (FSS). The concept is to design an FSS that is highly reflective at 2.45 GHz and place it at an optimized distance below the ground so that the backscattered field can be reflected by it and add with the broadside field at the same phase to increase the broadside gain. The increased gain will increase received RF voltage at the base of the antenna and hence efficiency of rectenna system.
A. Design of Frequency Selective Surface
The unit cell of the proposed FSS is shown in Fig. 9(a). Size of the unit cell is 12.9×12.9 mm2 (0.105λ0 × 0.105λ0, where λ0 is free space wavelength at 2.45 GHz). Optimized dimensions of the unit cell are, d1 = 10.2 mm, d2 = 5.6 mm, and G = 0.65 mm. The FSS unit cell was simulated using CST Microwave studio (Version 14) with periodic boundary conditions (Fig. 9(b)) and incident EM wave from z-direction. For unit cell simulation the required boundaries are PEC on yz-planes and PMC on xz-plane. Wave ports are used on the plane of FSS (xy-plane). The final FSS structure is a 7×7 element periodic array of the unit cell and has dimensions 90×90 mm2. 1.6 mm thick FR4 substrate with copper thickness 0.035 mm and εr = 4.4 is used to design the FSS. The FSS is four-fold symmetric and exhibits similar stop band response for TE and TM polarizations, as shown in Fig. 9(c). Transmission coefficient of the FSS has been simulated for TE and TM polarizations and are plotted in Fig. 10(a) and Fig. 10(b), respectively. They show angular insensitive performance of the FSS for both the polarizations. It is observed that both resonances are insensitive up to 700 incidence angle with a maximum frequency shift of 7.9 % only.
Equivalent circuit of the FSS is shown in Fig. 11(a). Values of the lumped elements can be found using [27] equations (2) and (3) and simulated |S11| response of the unit cell in Fig. 11(b). In the equivalent circuit, inductances represent metallic strips whereas the capacitances represent gap of the structure. Transmission line with characteristic impedance Z0 represents the free space.
where ω0 is angular resonance frequency, B3dB is the 3 dB bandwidth, S11(jω0) is the value of S11 at ω0, and η0 is the free space impedance. The values of the lumped elements can be found as L1 = 0.47651 nH, C1 = 8.8559 pF, L2 = 0.11989 nH, and C2 = 2.2134 pF. The simulated |S11| responses of the unit cell and of its equivalent circuit are also plotted in Fig. 11(b) for comparison purpose.
B. FSS Loaded Circular Shaped Antenna
The FSS is placed below the antenna using four Bakelite rods, as shown in Fig. 12(a). Distance between the FSS and the antenna was determined using parametric analysis, shown in Fig. 12(b). It reveals that as H decreases from 35 mm to 20 mm, the antenna gain response improves till H = 25 mm and after that it deteriorates. Therefore, optimized distance ‘H’ is considered as 25 mm (or 0.204λ0). Radiation efficiencies of the antenna, with and without FSS loading, are plotted in Fig. 12(c) and is found to be 80.5% for unloaded antenna and 85% for loaded antenna. Comparison of the |S11| responses of the antenna with and without the FSS layer is shown in Fig. 13(a). It reveals that the loading of the FSS layer has minor effect on the |S11| response. The 10 dB RL bandwidth of the antenna covers 2.34–2.66 GHz. S-parameter and far field measurements of the antenna are done using a calibrated Keysight N5221A VNA. Comparison of the simulated and measured |S11| responses is provided in Fig. 13(a). They are in close agreement. The slight discrepancies at the higher frequencies are due to the parasitic effects of soldier joint of connector with antenna. Figure 13(a) reveals a 10 dB RL bandwidth of 2.20–2.51 GHz (around 6.58% on each side of the center frequency). Comparison of the gains of the antennas (with and without FSS layer) are provided in Fig. 13(b). It shows that within the 10 dB RL bandwidth, the gain of the FSS loaded antenna remains almost constant around 6 dBi with a maximum of 7.7 dBi at 2.45 GHz. It also reveals that the antenna gain is almost 3.34 times higher than that of antenna without FSS layer.
The normalized radiation patterns of the antenna, with and without FSS loading, on both the orthogonal planes at 2.45 GHz are provided in Fig. 14. Suppression of the back lobe is observed, as expected. Simulated half-power beamwidths at xz and yz planes are found to be 840 and 680, respectively. It also reveals that the cross-pol is more than 35 dB down than the co-pol at the broadside direction on both the orthogonal planes.
C. Development of the rectenna circuit
The fabricated rectenna is shown in Fig. 15. Efficiency of the fabricated rectenna can be calculated using the relation
$$\eta \left(\%\right)=\frac{{V}_{dc}^{2}}{{R}_{L}\times {P}_{r}}\times 100 \%$$
4
where RL is the load, Pr is the power received by the receiving antenna, and Vdc is the output DC voltage across load. The received power Pr can be calculated using the relation
$${ P}_{r}={\left(\frac{\lambda }{4\pi R}\right)}^{2}{P}_{t}{G}_{t}{G}_{r}$$
5
where Pt is the power at the input of the transmitting antenna, Gt is the transmitting antenna gain, Gr is the receiving antenna gain, λ is the free-space wavelength at 2.45 GHz, and R is the distance between the transmitting and receiving antenna.
The rectenna have been measured in an anechoic chamber to find the output voltage and efficiency variations with the transmitter (pin)/received (Pr) powers. Output voltages of the rectenna was measured by a volt meter across a load resistance 2.7 kΩ for different transmitter powers and measured data are plotted in Fig. 16(a). It reveals that output voltage of the rectenna increases with transmitter power till 7 dBm (output power of the signal generator) and after that it saturates. It further reveals that maximum output voltage of the rectenna is 1.52 V. The efficiencies of the rectenna have been calculated using Eqs. (4) and (5) and are plotted with received powers in Fig. 16(b). It reveals that the maximum efficiency of the rectenna is 66.13% for 1.1 mW received power (incident power at the antenna). This corresponds to a significant improvement in efficiency of the rectenna presented in section III, which has maximum efficiency of only 1.24 %.
Characteristics of the proposed rectifying antenna is compared with few other rectennas, available in literature, in Table I. It reveals that the proposed rectifying antenna has a high conversion efficiency at low input power than others.
Table I: Comparison of the input power and efficiency of the rectifier at frequency 2.45 GHz.
Ref. No
|
Rectifying
element
|
Frequency
(GHz)
|
Pin (dBm)
|
Efficiency
(%)
|
[1]
|
HSMS 2862
|
0.9
|
7
|
60.0
|
[10]
|
HSMS 286C
|
2.45
|
-
|
51.5
|
[21]
|
HSMS 2820
|
2.4
|
10
|
56.7
|
[22]
|
HSMS 286C
|
2.29
|
10
|
< 50
|
[23]
|
MA4E1317
|
2.45
|
23
|
65
|
[24]
|
HSMS 2862
|
2.45
|
24
|
62
|
[25]
|
HSMS 2820
|
2.45
|
33
|
66
|
[26]
|
HSMS 2860
|
2.45
|
10
|
63
|
Proposed
|
SMS 7630
|
2.45
|
7
|
66.13
|