Analysis of voltage doubler

There are several types of topologies in the rectification of RF to DC such as single series, single shunt, full-wave diode rectifiers [Reference Marian, Allard, Vollaire and Verdier21], and voltage double rectifiers. The efficiency of the rectenna depends on frequency, RF diode type, input power level, matching between antenna and rectifier circuit; power losses if rectifier offers minimum losses electrical efficiency is high. Therefore standard voltage doubler is the noble option over half-wave rectifier at ultra-low power levels. Microwave signal arrived at the input of the rectifier v_in = V_AC Sinωt here V_AC is the amplitude and ω is the frequency of the input signal.

Figure 4 explains the rectification of microwave positive and negative half cycle at voltage doubler. The diode D ₁ comes into forward bias to negative half-wave and capacitor C ₁ charges, the diode D ₂ rectifies the positive half-wave, and capacitor C ₂ is charged. Finding the input impedance of the RF (voltage doubler) diode for the design of matching circuit is the vital point since diode has non-linear characteristics. The output DC voltage (V_DC) at the load is given by Eq. (1) and input impedance of the voltage doubler is calculated by using Eq. (2) [Reference Song, Huang, Carter, Zhou, Yuan, Xu and Kod22], where I_S is the diode saturation current, m is the ideality factor, and V_T is the thermal voltage.

(1)$$V_{DC} = 2V_{AC}\sin \omega t-2V_F\comma \;$$

(2)$$Z_D = \displaystyle{{V_{AC}\sin \omega t-0.5V_{DC}} \over {I_S\left[{B_0\left({\displaystyle{{V_{AC}} \over {mV_T}}} \right)\exp \left({\displaystyle{{-0.5V_{DC}} \over {mV_T}}} \right)-1} \right]}}. $$

Fig. 4.

Schematic of the voltage doubler circuit and its operation.

Large-signal S-parameter (LSSP) is a non-linear simulation that accounts for power level-dependent behavior of the diode. The LSSP simulation of the impedance circuits is carried out to measure the degree of matching between source and voltage doubler against microwave input power level.

The voltage doubler circuit, designed in ADS software is shown in Fig. 5, and the same is analyzed with LSSP simulation to verify the power level-dependent and non-linear characteristics behavior of the Schottky diode SMS7630 [23]. The input impedance of the voltage doubler (Z_VD) obtained from ADS simulation is depicted in Fig. 6, at 1.85 GHz the impedance is Z_VD = 43.071-j301.519 and 2.45 GHz it is Z_VD = 28.963-j228.833 with −30 dBm as input power for a load resistance of 7.5 KΩ. It is clear that the real part of the voltage doubler is affected by the frequency, it changes from 43.071 to 28.963 Ω; the imaginary part effected more rapidly changes from 301.519 to 228.833 Ω.

Fig. 5.

Voltage doubler block designed in ADS software.

Fig. 6.

Simulated input impedance of the voltage doubler.

Dual band impedance matching

The primary goal of the matching circuit minimizes the reflection from the voltage doubler, maximizes the received microwave power, and matching is necessary for power transfer from one stage to another [Reference Pavone, Buonanno, D'Urso and Corte24–Reference Wang, Zhang, Xu, Bai, Liu and Shi27].

In the microwave frequency region, filters can be designed using distributed transmission lines. Series inductors and shunt capacitors can be realized with microstrip transmission lines.

There are different kinds of approaches which are used to design dual band filter such as filters operating for each frequency and adding them in parallel. Dual band stub is like a parallel open-shorted stub, simple Tee, Pi circuits, and steeped impedance matching. In case of dual band energy harvesting, rectifier has to be matched with the antenna at both the frequencies to increase the conversion efficiency. Thus, two individual filters are designed for each operating frequency and connected in parallel to match the impedance between the source and voltage doubler.

The microstrip line filter is designed with shunt open and series stubs technique by using smith chart utility in ADS and implemented on jeans textile dielectric substrate with a relative dielectric constant of 1.6 and thickness of 1 mm. The ADS model of the matching filter is shown in Fig. 7(a) and the simulated and measured return loss plot (S11) of the rectifier circuits is shown in Fig. 7(b) at two resonance frequencies. The matching circuit has the return loss coefficient of −20 dB at both resonance frequencies for a −5 dBm power level, for −10 dBm input power level the S11 magnitude is below −20 dB but slightly shifted from center frequencies but still within the band limits. The rectifier is well matched for input RF power levels from −20 to −5 dBm.

Fig. 7.

(a) Rectifier ADS model. (b) Measured and simulated S ₁₁ plot for three different input power levels at 2.45 and 1.86 GHz.

Fabrication of rectifier

Voltage doubler long with matching circuit was built on jeans textile. Textile material properties such as dielectric permittivity (ε _r=1.67), thickness (t = 1 mm), and loss tangent (tanδ = 0.02) are measured by conducting the dielectric test on 1 m length fabric. Once matching circuit is optimized with voltage doubler in ADS, the printed circuit board (PCB) layout of the design is exported as CAD file to print on copper adhesive foil tap. After printing, the design is transferred onto jeans fabric and components of the voltage doubler are assembled with the help a low temperature soldering paste. Solder paste is a mixture of minute solder spheres held within a specialized form of solder flux. As the name indicates it has the texture of a paste, and hence the name. The rectifier circuit Simulink model and fabricated are shown in Fig. 8.

Fig. 8.

(a) Rectifier ADS model exported to print. (b) Fabricated rectifier on jeans textile.

Antenna performance

The key-sight microwave analyzer is used to measure the return loss parameters of the antenna in both bent and flat conditions. The measured return loss for the bent antenna (R = 11 cm) with the help of microwave analyzer is shown in Fig. 9(a). In order to demonstrate the effect of radiating element on the amorphous silicon solar cell, the output voltage was measured with an integrated antenna. As can be seen in Fig. 9(b) multimeter reading shows the rated open-circuit voltage of the solar cell, which means the electrical performance of the solar cell is unaffected by the radiating element.

Fig. 9.

Measuring return loss of flexible antenna (a) H-plane bending (R = 11 cm). (b) Measuring output voltage of the solar cell.

The measured result shows that the antenna has dual band nature; the energy harvesting frequencies are 2.45 and 1.85 GHz with bandwidths of 1.70–1.90 GHz (200 MHz) and 2.35–2.48 GHz (130 MHz). The primary band center resonance frequency is 1.85 GHz with return loss magnitude of −27 dB and the resonance frequency of the second band is 2.45 GHz with the return loss magnitude of −28 dB. The simulated and measured comparative return loss plot is shown in Fig. 10. The antenna return loss in bent formats has no effect in lower band, whereas at upper band the return loss character has two resonance frequencies [Reference Amaro, Mendes and Pinho28–Reference Montero, Espí, Cordero and Martínez Rojas30]. Furthermore, antenna has maintained the dual band nature in bent conditions with return loss less than −20 dB though it has multiple layers of substrates. In case of stacked layers there may be some air gaps in between layers, however in encapsulation process air between layers is removed and a high pressure is applied on multilayer so that they all become single layer; as a result, the proposed flexible antenna has better performance in flat as well as bent condition.

Fig. 10.

Comparative simulated and measured return loss (S ₁₁) in dB.

In order to examine the effect of solar cell on the antenna performance, two models of the antenna with and without solar cell (p-i-n silicon layers) were designed in CST Microwave studio. The flexible solar cell consists of a p-i-n silicon layer of thickness 0.4 μm and dielectric constant (ɛ _r) = 11.7 sandwiched between two zinc oxide (ZnO) layers of thickness 1.5 μm and the simulation results are shown in Fig. 11. However, there is a slight shift of resonance frequencies towards the higher frequency side is observed due to incorporation of p-i-n silicon layers. But still the operating frequencies are in the band limits. Therefore, solar cell under illumination has a negligible effect on resonance frequencies of the proposed antenna.

Fig. 11.

Solar cell effect on antenna performance.

Figures 12 and 13 show the simulated surface current distribution of the proposed antenna in both the resonating bands. It is observed that radiating patch has more current at lower resonance frequency compared to upper resonance frequency which in turn validate gain.

Fig. 12.

Simulated surface current distribution of the proposed antenna at 1.85 GHz, 0^o.

Fig. 13.

Simulated surface current distribution of the proposed antenna at 2.45 GHz, 0^o.

The E- and H-plane radiation patterns measured at both the frequencies in flat and bend (R = 11 cm) format are shown in Figs 14 and 15. The nature of the H-plane radiation pattern is closely Omni-directional with small reductions at 1.85 GHz and 2.45 GHz multiple depreciations are observed. The nature of E-plane measured and simulated radiation pattern is a figure of eight. There is no much change in antenna radiation patterns in flat and bent conditions.

Fig. 14.

Simulated and measured radiation pattern of principale planes at 1.85 GHz.

Fig. 15.

Simulated and measured radiation pattern of principale planes at 2.45 GHz.

RF to DC rectification

The conversion efficiency of the voltage doubler at resonance frequencies is studied for different input power levels. Two zero-bias Schottky diode (SMS7630), the bypass capacitors (C ₁, C ₂) were chosen to be 100 pF and storage capacitors (C ₃) 100 μF. The distance (D_{r .}) between the transmitting horn antenna with the gain of G_tX = 11 dBi and the rectenna is 1 m. The Friis transmission Eq. (4) is used to find out the micro power available at rectenna terminals.

(3)$$P_{rX} = P_{tX}G_{tX}G_{rX}\left({\displaystyle{C \over {4\pi D_rf_o}}} \right)^2\comma \;$$

where P_tX is the transmitting power at a given field strength E (mV/m) G_rX is the receiving antenna gain (4.82 dBi) the constant C and f ₀ are the velocity of light and frequency of the microwave. The output DC voltage (V_outDC) and overall efficiency (η _EH) of the rectenna against power density are calculated by Eq. (4).

(4)$$\eta _{EH} = \displaystyle{{P_{outDC}} \over {P_{rX}}} = \displaystyle{{{{V^2_{outDC} } \over {R_L}}} \over {P_{rX}}}.$$

The RF to DC conversion efficiency of the rectifier as a function of input power (in dBm) and frequency are shown in Fig. 8. The voltage doubler conversion efficiency at 1.85 and 2.45 GHz are 57.8 and 42.6%, respectively, for a load of 7.5 kΩ is shown in Fig. 16(a). In Fig. 16(b) conversion efficiency is plotted against power levels, at −5 dBm a maximum efficiency of 57.8%, at −10 dBm 42.4% and at −20 dBm the maximum efficiency is 11.2% is obtained at 1.85 GHz.

Fig. 16.

(a) Simulated and measured rectifier RF–DC conversion efficiency with load resistance 7.5 kΩ. (b) Simulated and measured rectifier RF–DC conversion efficiency for different load resistances.

The load-dependent conversion efficiency measured at 1.85 GHz frequency for input power levels is depicted in Fig. 17(a) and it can be seen that the efficiency is greater than 50 and 40%, respectively, for the load resistance between 7.5 and 10 kΩ. The effect of load resistance on power conversion efficiency is studied at both operating frequencies. The power conversion efficiency of the rectifier is increased up to 7.5 kΩ and later it is decreased significantly from 7.5 to 50 kΩ with respect to change in load and the graph is shown in Fig. 17(b). The proposed flexible antenna performance and a comparison of proposed work with other reported rectenna designs is illustrated in Tables 3 and 4, respectively. The fabricated solar cell rectenna is depicted in Fig. 18(a) as a flat energy harvesting system and in Fig. 18(b) it is bent on polyvinyl chloride (PVC) pipe with a diameter of 11 cm.

Fig. 17.

(a) Conversion efficiency for input power variation for fixed load. (b) Conversion efficiency for load resistance variation.

Fig. 18.

(a) Wearable rectenna on thin film solar cell flat position. (b) Wearable rectenna on thin film solar cell bent position (D = 11 cm).

Table 3.

Flexible rectenna performance

Table 4.

Comparison of proposed work with other rectenna designs

Hybrid energy harvesting system

The output voltage of the rectenna circuit is determined by the level of electromagnetic energy available at the receiving antenna. These energy levels are irregular in the environment, thus sometimes rectenna is inadequate to generate required DC voltage. Thus, hybrid energy harvesting is an alternative solution to this problem, where energy from different energy sources like solar, wind, temperature, and vibration. In this paper, the selected solar cells are flexible thin film amorphous silicon, with open-circuit voltage of V_OC = 2 V and short circuit current of I_SC = 420 mA. In this hybrid energy harvesting system, the DC output of the solar cell is integrated with voltage double rectifier and the schematic of the proposed DC combining circuit is shown in Fig. 19(a).

Fig. 19.

(a) Solar cell rectenna ADS simulink model. (b) Solar cell connected to RF energy harvesting system.

The RF energy harvesting system and solar cell were connected via an inductor (L ₁) in parallel. The values of the L ₁, is selected by using an optimization technique in ADS software and the aim of this optimization is minimizing the effect of variations produced by changing solar irradiation on rectifier efficiency. The current generated from solar enters onto the rectifier through the inductor (L ₁), because an inductor acts as a short circuit for DC current and at the same time the capacitor (C ₁) blocks the DC currents entering into matching circuit. In the prototype, solar cell connections are designed at the backside of cotton jeans and inductor (L ₁) and capacitor (C ₁) are connected via hole through jeans textile which is illustrated in Fig. 19(b).

The Fig. 20(a) shows the optioned DC output voltage of the combining circuit for different irradiance with an input power level of −5 dBm and for a resistive load of 7.5 kΩ. In practice solar cell is considered as a current source the terminal voltage variation is less effected by irradiation, thus the output voltage is above 1 V at low irradiation conditions (as shown in Fig. 14 600 W/m²).

Fig. 20.

(a) Measured DC output voltage versus frequency for change in irradiation. (b) Measured power conversion efficiency versus irradiation.

However, the current regenerated by the solar cell is much affected with change in irradiation, so that the power conversion efficiency is less under low irradiation conditions that are depicted in Fig. 20(b). The power conversion efficiency is above 70% for solar cell rectenna with 1.85 GHz RF input and is 65% for solar cell rectenna with 2.45 GHz RF input. Finally, the DC combining circuit performance for different combinations of RF signal is presented in Table 5.

Table 5.

Solar cell Rectenna performance