A Quad-Band RF Circuit for Enhancement of Energy Harvesting

Abstract

Radio frequency energy harvesting is one of the new renewable sources that faces some technical challenges, which limit its performance. This study presents two scenarios to enhance the harvested power. The first scenario introduces a quad-band voltage multiplier circuit with a single receiving antenna and four band-pass filters of elliptic type. In this scenario, four frequencies of the Global System for Mobile communications, Universal Mobile Telecommunications System, and Wireless Fidelity frequency bands have been considered for the study. The second scenario proposes a quad-band voltage multiplier circuit with four receiving antennas at the same frequency bands as the first scenario. High conversion efficiencies were achieved for the two scenarios. The proposed quad-band system developed a harvested power level, sufficient for powering up low power micro-devices with no need for an external power supply.

1. Introduction

Portable devices are powered by batteries. Hence, bulky cords and complications related to power interconnections can be eliminated [1,2,3]. However, the traditional battery systems have defects. These defects include the demand for power maintenance, limited life span, requiring periodic replacements, and the processing of the battery wastes. All these are considered to be weak points for traditional batteries. In applications such as wireless sensor networks (WSNs), wireless sensor nodes must be autonomous since battery replacement is not feasible in such applications. Furthermore, battery replacement in the case of thousands of spread embedded nodes will be a complicated and costly process, especially in harsh environments [4,5].

As a result, the concept of power harvesting has been introduced as a technique for reaping energies from the external environment using different resources including thermal energy [6,7,8], solar energy [9,10,11], wind energy [12,13,14], electromagnetic radio frequency (RF) waves [15,16,17], and vibrations excitation and pressure gradients [18,19,20]. Energy harvesting will become a promising technique in the future with tremendous scope instead of replacing small batteries in low-power electrical devices that overcomes the defects related to traditional batteries stated above. Hence, the demand for such energy-harvesting devices is growing. RF energy that belongs to the electromagnetic waves are abundant in space since they are broadcast vastly in the urban ambient environment through RF/microwave frequency bands for instance, the Global System for Mobile communications (GSM 900, GSM 1800) bands [21,22], and Wireless Fidelity (Wi-Fi 2.45 GHz/5.8 GHz) [23,24] bands due to the current applications utilized by societies such as smart medical applications [25], intelligent environment monitoring [26], satellite communications [27,28], mobile telecommunications [29,30], wireless internet [31,32], radar systems [33,34,35], digital multimedia broadcasting [36,37,38], etc.

RF energy harvesting holds vast potential for replacing batteries or increasing their lifespans. Applying RF energy harvesting technologies can make micro-devices self-sustaining concerning the energy required for operation, thereby obtaining an unlimited operating lifespan. As a result, the dependency on traditional batteries can be reduced, which keeps the environment healthy. Therefore, waste is not expected with the harnessing of electromagnetic energy. Moreover, some international foundations such as the Federal Communications Commission (FCC), the International Commission on Non-Ionizing Radiation Protection (ICNIRP), and the Institute of Electrical and Electronics Engineers (IEEE) have recommended regulations for the maximum output power levels. These regulations aim to protect humans against the potential adverse health effects of non-ionizing electromagnetic fields. Hence, these restrictions prevent any health hazards that can result from radiated RF waves. As a result, RF waves are emitted with low power levels in the space, which complies with the maximum output power levels’ regulations [39]. RF is not limited by time, i.e., RF energy is available 24 h, seven days a week, during the whole year [40]. This feature promotes research to realize RF energy harvesting technology through the applications of WSNs [41,42], internet of things (IoT) [43,44], implantable devices and remote patient monitoring [45,46], and radio frequency identification (RFID) [47,48]. Despite the mentioned attractive RF energy source features, it has low power density in the environment. The maximum reported results in the literature for the harvested power of RF energy were in the range of μW to mW, such as the reported in [3,49,50,51,52,53,54], which is considered to be the main challenge of RF energy harvesting to power up any micro-devices efficiently.

The rest of this paper is organized as follows, “Related Work” is summarized in Section 2. “System Modelling” is analyzed in Section 3. “Circuit Design and Simulation” are presented in Section 4. “Simulation Results and Discussion” are given in Section 5. “Conclusions” are summarized in Section 6.

2. Related Work

With reference to the published studies, there are different designs for RF energy harvesters were presented such as single [3,55,56], dual [57,58,59,60], triple [52,61,62,63,64], quad [65,66], six [67], and broad [68,69,70,71,72] bands. For instance, M. Zeng, et al. [55], designed a circuit to harvest signals of GSM-1800 band. A. M. Jie et al. [57], designed a system to work at the dual-band; GSM-900 and (Wi-Fi 2.45 GHz) bands. A. Bakytbekov et al. [61], presented a triple-band rectenna to operate at the GSM-900, GSM-1800, and 2.1 GHz bands. C. Hsu, et al. [65], introduced the quad-band RF harvester for the bands of 1.3, 1.7, 2.4, and 3.6 GHz. A wide-band system was designed [68], to collect power in the frequency range of 1.8 to 2.5 GHz.

The increase of the harvested direct current (DC) power of the RF energy harvester is a goal for researchers by increasing the input frequency ranges or the input powers. However, a rectenna’s high sensitivity is a significant limitation to go through this goal due to the non-linearity of Schottky diodes, which serve as a rectifier for the received RF signals to convert them into DC power. The diode’s non-linearity appears when the received RF signal is varied in power level or frequency. The non-linearity leads to an increase of the reflected power to the receiving antenna and then degrading the RF-DC conversion efficiency, which results in a low harvested DC power [49,62]. Moreover, most of the published work focused on the dual-band design, and limited studies handled the quad-band system.

In this paper, both the mathematical and simulation approaches were used. These approaches were utilized to specify the rectifier input impedance under the variation of input power or frequency. This enabled us to overcome the Schottky diode’s non-linearity challenge by designing a suitable impedance matching network. The authors adopted two scenarios in this study to investigate the quad-band concept to harvest the radiated power of the GSM-900 band, the GSM-1800 band, the Universal Mobile Telecommunications System (UMTS-2100) band, and the Wi-Fi 2.45 band. The first scenario introduced a quad-band voltage multiplier circuit with a single receiving antenna and four band-pass filters (BPFs) of elliptic type. The second scenario presented a quad-band voltage multiplier circuit with four receiving antennas. The proposed quad-band approach can harvest 2 mW DC power; moreover, the optimal RF-DC conversion efficiency of 74.846% was achieved in this study when the four tones were applied. The importance of this study compared to the literature review can be summarized in two points. The first point is to predict the rectifier input impedance theoretically and numerically, unlike most published studies, which took into account the simulation results only for the circuit input impedance. The second point is keeping the RF-DC conversion efficiency acceptable for the interested wide frequency range. Compared to the other published results, the work results are presented in Section 5 to clarify this study’s importance.

3. System Modeling

The output voltage is one of the critical parameters in electronic circuits, especially in energy harvesting circuits. However, the generated output voltage in RF energy harvesting systems is tiny, mainly in using traditional rectifiers. As presented in [59], the output voltage ($V_{out}$) range was reported between 0.38 to 0.75 V. Small value of the output voltage, such as 0.75 V, is insufficient to meet the practical applications’ needs to power up electronic devices. Hence, the voltage doubler circuits are the optimal way for RF energy harvesting applications to overcome the generated output voltage’s limited values. The voltage doubler serves as a rectifier circuit to convert the alternative current (AC) signal into DC power. Furthermore, it multiplies the input signal’s voltage thanks to the doubler’s capacitors. For instance, the output voltage is twice of the input voltage ($V_{in}$), i.e., $V_{out}$ = 2$V_{in}$ in the voltage doubler. However, we should consider that increasing the number of the voltage doubler stages reduces the generated output power, which is not favorable in RF energy harvesting systems. Besides the above-mentioned, it should be noted that the voltage doubler does not increase the output power since the output power totally depends upon the receiving antenna.

In this model, a single-stage voltage doubler was connected to an RF source. The applied input power level ($P_{in}$) varied between −20 dBm to +10 dBm, whereas the frequency was extended between 0.5 GHz to 2.5 GHz.

The equivalent circuit of the single-stage voltage doubler is shown in Figure 1. In this circuit, $C_{J1}$, $R_{S1}$, and $R_{J1}$ are the diode junction capacitance, the series resistance, and the internal diode junction resistance of the first diode ($D_1$), respectively. As well as $C_{J2}$, $R_{S2}$, and $R_{J2}$, are the diode junction capacitance, the series resistance, and the internal diode junction resistance, respectively of the second diode ($D_2$) in the same circuit. The two diodes’ parameters are the same since the two diodes belong to the same model, HSMS-2852. Assuming that the wave has an amplitude ($V_{Max}$), and frequency (F) is applied to the voltage doubler circuit in Figure 1. This figure also depicts a single cycle of the applied RF wave to the voltage doubler. Based on the diode theory with the threshold voltage ($V_{th}$) and according to the single cycle of the applied RF wave in this figure, it can be concluded that there are two operation states in the circuit. The first case when $D_1$ is forward biased and then switched-on during the period ($t_1$: $t_2$) of the negative half while the other diode $D_2$ is reverse biased and switched-off. During the positive half at ($t_3$: $t_4$) the situation is changed so $D_1$ becomes switched-off while $D_2$ goes to be forward biased and switched-on. The circuit impedance at this condition is mentioned as ($Z_{in,F}$).

The second case covers the rest periods of the cycle since both the diodes are reverse biased and switched-off. In this state, the circuit impedance is indicated by ($Z_{in,R}$).

The maximum received voltage ($V_{Max}$) from the antenna, which is considered the input voltage to the voltage doubler circuit ($V_{Max}$ = $V_{input}$) can be calculated as in Equation (1):

$$V_{Max}={10}^{\frac{P_{input}\left(dBm\right)-10}{20}}.$$

(1)

Then, the equivalent input impedance of the rectifier ($Z_{input}$) is a function of the circuit impedance at the two different operation states based on diodes biasing as in Equation (2). Hence, the two impedance can be calculated as in Equations (3) and (4).

$$Z_{input}=f(Z_{in,F},Z_{in,R})$$

(2)

$$Z_{in,R}=\frac{Z_{D,R}^2}{2Z_{D,R}}+\frac{1}{j2\pi F{C}_1}=\frac{Z_{D,R}}{2}+\frac{1}{j2\pi F{C}_1}$$

(3)

$$Z_{in,F}=\frac{Z_{D,R}\times Z_{D,F}}{Z_{D,R}+Z_{D,F}}+\frac{1}{j2\pi F{C}_1},$$

(4)

where $Z_{D,R}$ and $Z_{D,F}$ are the diode impedance at the reverse biasing and forward biasing states, respectively, to find them, a sequence of equations must be followed as expressed in Equations (5)–(12) regarding the HSMS-2852 Schottky diode datasheet.

$$I_{b,F}=I_s\left(e^{\frac{V_{a,F}}{n{V}_T}}-1\right)$$

(5)

$$R_{J,F}=\frac{8.33\times {10}^{-5}nT}{I_{b,F}+I_s}$$

(6)

$$C_{J,F}=\frac{C_{JO}}{{\left(1-\frac{V_{a,F}}{V_J}\right)}^m}$$

(7)

$$Z_{D,F}=R_s+\frac{R_{J,F}}{1+j2\pi F{R}_{J,F}{C}_{J,F}}$$

(8)

$$I_{b,R}=I_s\left(e^{\frac{V_{a,R}}{n{V}_T}}-1\right)$$

(9)

$$R_{J,R}=\frac{8.33\times {10}^{-5}nT}{I_{b,R}+I_s}$$

(10)

$$C_{J,R}=\frac{C_{JO}}{{\left(1-\frac{V_{a,R}}{V_J}\right)}^m}$$

(11)

$$Z_{D,R}=R_s+\frac{R_{J,R}}{1+j2\pi F{R}_{J,R}{C}_{J,R}},$$

(12)

where $I_s$, n, $C_{JO}$, $V_J$, m, $R_s$, $V_T$ and T are the saturation current, the ideality factor, the diode junction capacitance at the zero bias case, the diode junction voltage, the grading coefficient, the series resistance, the thermal voltage, and the temperature in ${}^{\circ }$K, respectively. $I_{b,F}$, $V_{a,F}$, $R_{J,F}$, and $C_{J,F}$ are the externally applied bias current, the applied voltage on the diode, the diode junction resistance, and the diode junction capacitance, respectively when the diode is forward biased. On the other hand, $I_{b,R}$, $V_{a,R}$, $R_{J,R}$ and $C_{J,R}$ are the externally applied bias current, the applied voltage on the diode, the diode junction resistance, and the diode junction capacitance respectively, when the diode is in the reverse case.

Using the power analysis mode for the showed full-cycle in Figure 1, it can be analyzed as follows [73]:

$$P_{input}=\frac{1}{T}{\int }_0^T\frac{V_{input}^2}{Z_{input}}dt,$$

(13)

where T is the periodic time, considering the diode operation theory based on the applied periods of the RF wave, the power integral will be as the following:

$$P_{input}\approx \frac{2}{T}\left({\int }_0^{t_1}\frac{V_{input}^2}{Z_{in,R}}dt+{\int }_{t_1}^{T/4}\frac{V_{input}^2}{Z_{in,F}}dt+{\int }_{T/4}^{T/2}\frac{V_{in}^2}{Z_{in,R}}dt\right).$$

(14)

The second integral in Equation (14) must be from $t_1$ to $t_2$, and $t_2$ is approximately T/4, i.e., $t_2$≈ T/4 (Figure 1, that is why the approximation sign is inserted in Equation (14).

$$V_{input}=V_{Max}sin\left(2\pi Ft\right)$$

(15)

$$P_{input}\approx \frac{V_{Max}^2}{T}\left[\frac{1}{Z_{in,R}}\left[\frac{T}{4}+t_1-\frac{1}{4\pi F}sin\left(4\pi F{t}_1\right)\right]+\frac{1}{Z_{in,F}}\left[\frac{T}{4}-t_1+\frac{1}{4\pi F}sin\left(4\pi F{t}_1\right)\right]\right].$$

(16)

Since

$$P_{input}=\frac{1}{T}{\int }_0^T\frac{V_{input}^2}{Z_{input}}dt=\frac{1}{T{Z}_{input}}{\int }_0^T{V}_{input}^{2}dt$$

(17)

then,

$$Z_{input}=\frac{V_{Max}^2}{2P_{input}}.$$

(18)

Equation (16) is substituted in Equations (18) and (19)

$$Z_{input}\approx \frac{T}{2}\times {\left[\frac{1}{Z_{in,R}}\left[\frac{T}{4}+t_1-\frac{1}{4\pi F}sin\left(4\pi F{t}_1\right)\right]+\frac{1}{Z_{in,F}}\left[(\frac{T}{4}-t_1+\frac{1}{4\pi F}sin\left(4\pi F{t}_1\right)\right]\right]}^{-1}$$

(19)

$$t_1=\frac{1}{2\pi F}{sin}^{-1}\left[\frac{V_{th}+\frac{V_{out}}{2}}{V_{Max}}\right]$$

(20)

$$\begin{array}{cc}{Z}_{input}\approx & 2[\left(\frac{1}{Z_{in,R}}+\frac{1}{Z_{in,F}}\right)+\frac{1}{\pi }(\frac{1}{Z_{in,R}}-\frac{1}{Z_{in,F}})*\hfill \\ & {\left[2{sin}^{-1}\left(\frac{2V_{th}+V_{out}}{2V_{Max}}\right)-sin\left({2sin}^{-1}\left(\frac{2V_{th}+V_{out}}{2V_{Max}}\right)\right)\right]]}^{-1}.\hfill \end{array}$$

(21)

Based on the analyzed model’s extracted formula, the input impedance of the rectifier vs. the frequency at different input power levels is presented in Figure 2. The rectifier input impedance was found under −20 dBm, −10 dBm, 0 dBm, and +10 dBm input powers.

4. Design and Simulation

The voltage multiplier topology is one of the most common topologies used for RF energy harvesting. Single-stage, dual-stage, even different stages were used for this topology [49]. No power biasing is required; enhanced output voltage and simplicity of design are the most important voltage multiplier topology features. In this paper, HSMS-2852 Schottky diodes have been utilized as the main rectifier component. This diode’s selection was due to its low voltage drop, rapid switching at high frequencies, acceptable performance under low input power values, low saturation current, and low junction capacitance. However, the input impedance of the voltage multiplier is dynamic and it depends upon the input power level or the received signal’s frequency due to the non-linear behavior of Schottky diodes [49,62,65,68,69,70,73,74]. This dynamic impedance is not matched to the receiving antenna impedance (often 50 Ohms); therefore, high power loss and low RF-DC conversion efficiency are expected.

Therefore, it is required to know the impedance at each frequency. Advanced Design System (ADS) platform was set and used to evaluate the proposed system. The frequency was adjusted to be varied between 0 and 5 GHz since this range covers the interested quad-bands. Based on the above procedures, the model and simulation results of the rectifier’s input impedance are depicted in Figure 3.

From Figure 3, it can be noticed that the impedance at the GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45 frequency bands under the input power of 0 dBm are 32.94–j546.916, 12.961–j265.774, 11.214–j224.381, and 9.951–j188.295, respectively. The simulation results converge with the model results as shown in Figure 3 under the 0 dBm power level. In the range of frequencies including GSM-1800, UMTS-2100, and Wi-Fi 2.45, the rectifier input impedance variation impedance versus $P_{in}$ is slight, as can be seen from Figure 2. As a result, there will be a small mismatching. At the frequency of GSM-900, the variation of the rectifier input impedance versus $P_{in}$ is significant. Accordingly, a large mismatching will be expected. Figure 2 and Figure 3 show that the model formula and simulation have given close results for the rectifier’s input impedance, which contribute to specifying the impedance of the circuit theoretically and numerically at the same time.

4.1. Single-Band Circuit

The applied input power varied from −40 dBm to 20 dBm. The operating frequency of the RF source was adjusted at each band of the mentioned frequency bands.

L-type matching was inserted, as shown in Figure 4. This matching type has the advantages of simplicity and the limited dimensions the circuit can occupy. The Smith chart was used to determine the suitable lumped elements for matching. As illustrated in Figure 5, lumped elements’ suitable values are determined at each band of the four interested bands. The optimal lumped elements values are as the following: L = 100.9 nH and C = 2.545 pF (for the GSM-900), L = 25.43 nH and C = 2.989 pF (GSM-1800), L = 18.58 nH and C = 2.819 pF (UMTS-2100), and L = 13.52 nH and C = 2.606 pF (Wi-Fi 2.45).

The matching network elements (L and C) were determined by using the Smith chart. The matching between the antenna and the rectifier can be done using transmission line sections (TLs) and lumped elements. TLs are preferably used for the high-frequency bands of UMTS-2100 and Wi-Fi 2.45 in this work to avoid any losses. In contrast, lumped elements are sufficiently used for the GSM-900 and GSM-1800 low-frequency bands to reduce the circuit dimensions. Both the inductance (L) and capacitance (C) are realized using a short-circuited and open-circuited transmission line sections in the high-frequency bands’ circuit.

The lengths of the transmission line sections are found as follows [75]:

$$Z_{in}=Z_O\frac{Z_L+j{Z}_{O}tan\beta \ell }{Z_O+j{Z}_{L}tan\beta \ell },$$

(22)

where $Z_{in}$, $Z_O$, $Z_L$, and $\beta$ are the transmission line’s input impedance, the characteristic impedance, the load impedance, and the phase constant, respectively. The phase constant is calculated as follows:

$$\beta =\frac{2\pi F}{\nu }$$

(23)

where F and $\nu$ are the wave frequency and the speed of light in air. The transmission line’s input impedance is obtained by Equation (24) for the inductance element (L)

$$Z_{in}=j{Z}_{O}tan\beta {\ell }_1,$$

(24)

then, ${\ell }_1$ can be calculated by Equations (25) and (26).

$$j\omega L=j{Z}_{O}tan\beta {\ell }_1$$

(25)

$$L=\frac{Z_{O}tan\beta {\ell }_1}{\omega },$$

(26)

where $\omega$ and ${\ell }_1$ are the angular frequency and the first transmission line’s length. On the other hand, the transmission line’s input impedance for the capacitance (C) is found by Equation (27):

$$Z_{in}=Z_O\frac{1}{jtan\beta {\ell }_2},$$

(27)

therefore, the second transmission line’s length (${\ell }_2$) can be calculated by Equations (28) and (29):

$$\frac{1}{j\omega C}=\frac{Z_O}{jtan\beta {\ell }_2}$$

(28)

$$C=\frac{tan\beta {\ell }_2}{\omega Z_O}.$$

(29)

Equations (30)–(33) are used to find the width of the transmission line (W) [76]:

$$\frac{W}{h}=\frac{2}{\pi }\left\{\{\frac{{\epsilon }_r-1}{2{\epsilon }_r}\left[ln(B-1)-\frac{0.61}{{\epsilon }_r}+0.39\right]+B-1-ln(2B-1)\}\right\},forA>1.52$$

(30)

$$\frac{W}{h}=\frac{8e^A}{e^{2A}-2},forA<1.52$$

(31)

where h, and ${\epsilon }_r$ are substrate thickness and substrate relative permittivity, respectively.

$$A=\frac{Z_O}{60}\sqrt{\{\frac{{\epsilon }_r+1}{2}}{\}}^{1/2}+\frac{{\epsilon }_r-1}{{\epsilon }_r+1}\{\frac{0.11}{{\epsilon }_r}+0.23\}$$

(32)

In this case, A is calculated, and it is found to be <1.52; therefore, Equation (31) is used to find h. Both A and B are variables.

$$B=\frac{529.18}{Z_O\sqrt{{\epsilon }_r}}.$$

(33)

Finally, the dimensions of transmission lines and microstrip lines are calculated and presented in

Table 1. Dimensions of transmission lines and microstrip lines.

Parameter	GSM-900	GSM-1800	UMTS-2100	Wi-Fi 2.45
${\ell }_1$ (mm)	78.56	36.87	31.16	25.92
${\ell }_2$ (mm)	33.10	27.59	24.55	21.64
W (mm)	4.2	4.2	4.2	4.2

.

4.2. Quad-Band Circuit Design

The applied input power of the RF source was set to offer a power of 0 dBm. The frequency was adjusted to be varied between 0 and 5 GHz to cover the interested quad-bands. Power probes were inserted at the input and output points to compute the power and then calculate the RF-DC conversion efficiency. On the other hand, the load resistor ($R_L$) for the two scenarios was selected to be 5 K Ohms since it is a typical value for loads of many applications.

4.2.1. Scenario 1: Quad-Band Circuit with a Single Receiving Antenna

In this scenario, the four-matched single-band voltage multipliers had a single receiving antenna at the input; the output of the four circuits was connected directly via the load resistor [52,74] as illustrated in Figure 6. A band-pass filter (BPF) of the elliptic design was inserted after the receiving antenna for each circuit of the four voltage multipliers. The parameters of BPFs are depicted on the schematic circuit in Figure 6.

4.2.2. Scenario 2: Quad-Band Circuit with Four Receiving Antennas

As shown in Figure 7, each matched single-band voltage multiplier circuit had its receiving antenna. The four channels’ output was connected directly via the load resistor [52,74].

The four channels are connected in parallel with the load resistance. If one channel produces an output voltage higher than the others, the remaining three channels would be off since the diodes will be in reverse bias. A simple solution is proposed here. To investigate this point, the output voltage of each channel was found separately. One channel was connected, and the remaining three channels were disconnected. This step was repeated to find the output voltage of each channel.

Therefore, to ensure that the four channels are active a resistor was added between each channel’s output and the load resistor to avoid the negative effect if one channel of the four channels produces an output voltage higher than the others. The values of these resistors are equal. This modification will enable the output voltage of all channels to be equal, i.e., the output voltage is the same across all branches. The equivalent circuit of the adopted method is shown in Figure 8, whereas the improved circuit of the second scenario is presented in Figure 9. The resistors have a small value of less than 1 $\mathsf{\Omega }$, which will not significantly affect the RF-DC conversion efficiency or system performance.

5. Simulation Results and Discussion

S-parameters ($S_{11}$) for the frequencies GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45 bands are shown in Figure 10. Excellent matching can be noticed from this figure, a very small $S_{11}$ is found. Therefore, in light of S-parameters, the obtained RF-DC conversion efficiency has high values, as presented in Figure 11. The RF-DC conversion efficiency ($\eta$) can be calculated as follows:

$$\eta (\%)=\frac{P_{out}\left(DC\right)}{P_{in}\left(RFpower\right)}\times 100=\left(\frac{V_{out}^2}{R_L}\times \frac{1}{P_{in}}\right)\times 100$$

(34)

where $P_{out}$ is the harvested DC power across the load resistor.

From Figure 11, maximum efficiencies of 82.345% at 6 dBm, 78.165% at 8 dBm, 75.72% at 8 dBm, and 74.622% at 9 dBm were obtained for the GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45 bands, respectively. The output voltage was 1.489 V, 1.276 V, 1.22 V, and 1.163 V, respectively, for the mentioned bands at 0 dBm. The highest output voltage obtained at 20 dBm for the Wi-Fi 2.45 band was 3.579.

For the first scenario of the quad-band circuit with a single receiving antenna, Figure 12 shows S-parameters for the four bands. Figure 13 and Figure 14 illustrate RF-DC conversion efficiency and output voltage versus the input frequency under the input power of 0 dBm. For this scenario, the recorded results for the RF-DC conversion efficiency and output voltage are presented in

Table 2. Recorded results for the first scenario under 0 dBm.

Frequency	RF-DC Conversion Efficiency (%)	Output Voltage (V)
GSM-900	74.846	1.662
GSM-1800	66.974	1.422
UMTS-2100	64.486	1.333
Wi-Fi 2.45	61.407	1.587

. The highest value for the output voltage that could be received was 3.648 V at the Wi-Fi 2.45 band under input power of +20 dBm for the first scenario.

Figure 15 shows S-parameters vs. frequency regarding the proposed quad-band circuit with four receiving antennas as the second proposed scenario. It can be observed that the reflected power is as follows: −30 dB, −24.5 dB, −3.5, and −30 dB at the bands GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45, respectively. Figure 16 and Figure 17, and

Table 3. Recorded results for the second scenario under 0 dBm.

Frequency	RF-DC Conversion Efficiency (%)	Output Voltage (V)
GSM-900	71.194	1.373
GSM-1800	64.944	1.421
UMTS-2100	62.363	1.594
Wi-Fi 2.45	65.096	1.896

depict the conversion efficiency and output voltage vs. the second scenario’s input frequency for the input power of 0 dBm. The maximum output voltage of 3.66 V was noticed under input power of 20 dBm at the Wi-Fi 2.45 band for this scenario.

The output voltage of each channel is illustrated in Figure 18 and Figure 19 under 0 and +10 dBm input powers at the case of connecting one channel and disconnecting the remaining channels. Under 0 dBm, the output voltage varied between 1.23 to 1.387, whereas it varied between 3.307 to 3.328 under + 10 dBm. The output Voltage across all branches ($V_{Out}^{\prime }$) for the improved circuit in Figure 9 can be calculated according to Millman’s theorem [77] as shown below:

$$V_{Out}^{\prime }=\frac{\frac{V_{Branch1}}{R_1}+\frac{V_{Branch2}}{R_2}+\frac{V_{Branch3}}{R_3}+\frac{V_{Branch4}}{R_4}+\frac{V_{Branch5}}{R_L}}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4}+\frac{1}{R_L}},$$

(35)

where $V_{Branch1},V_{Branch2},V_{Branch3},$ and $V_{Branch4}$ are the output voltage of the four channels of GSM-900, GSM-1800, UMTS-2100, and Wi-Fi 2.45, respectively. Applying Equation (35) to the case of 0 dBm input power, the expected output Voltage ($V_{Out}^{\prime }$) is 1.27 V. For the +10 dBm power level’s variations, $V_{Out}^{\prime }$ is expected to be 3.32 volt. The proposed modification to the quad-band circuit has little effect on the RF-DC conversion efficiency which is clearly illustrated in Figure 20. The peak efficiency of 70.4% was obtained at the 900 MHz band under 0 dBm power.

The results are summarized by Figure 21, Figure 22 and Figure 23. Figure 21 shows the maximum received output voltage, output power, and conversion efficiency for the single four bands. Figure 22 describes the maximum received output power at single-band, dual-band, triple-band, and quad-band. Finally, the peak received conversion efficiency at single-band, dual-band, triple-band, and quad-band are depicted in Figure 23. Considering Figure 22, it can be observed clearly concerning the importance of the multi-band concept. In this work, 0.443 mW, 0.8 mW, 1.45 mW, and 2 mW are the highest DC power levels were harvested at the circuits of single-band, dual-band, triple-band, and quad-band, respectively, at the input power of 0 dBm.

To study the effect of load variation on the RF-DC conversion efficiency, a range for the load varied between 1 k$\mathsf{\Omega }$ to 50 k$\mathsf{\Omega }$ was applied and simulated at three input power levels of −10 dBm, 0 dBm, and +10 dBm, respectively. The relevant results for this parameter are illustrated in Figure 24, which introduced conversion efficiency ($\eta$) greater than 40% under - 10 dBm at the range of 5 k$\mathsf{\Omega }$ to 50 k$\mathsf{\Omega }$, $\eta$> 70% under 0 dBm at the range of 5 k$\mathsf{\Omega }$ to 35 k$\mathsf{\Omega }$, and $\eta$ > 70% under +10 dBm at the range of 1 k$\mathsf{\Omega }$ to 15 k$\mathsf{\Omega }$. However, 54.953%, 78.866%, and 78.527% were the optimal values that received at 15 k$\mathsf{\Omega }$, 20 k$\mathsf{\Omega }$, 5 k$\mathsf{\Omega }$ under input power levels of −10 dBm, 0 dBm, +10 dBm, respectively. Finally,

Table 4. A comparison with the related reported results.

Ref.	Frequency	Rectifier Topology	Diode used	Peak $\mathit{\eta }$ at ${\mathit{P}}_{\mathbf{in}}$	${\mathit{V}}_{\mathbf{Out}}$ (V)	${\mathit{R}}_{\mathit{L}}$ (k$\mathsf{\Omega }$)
[49]	Single-band GSM-900	2 stages Dickson VD + LE	HSMS-2852	a 45% at 0 dBm	2.1	10
[79]	Single-band 900 MHz	7 stages Cockcroft VD + LE	HSMS 285-C	a 25.83% at +20 dBm	17.58	10
[80]	Single-band 2.45 GHz	VD + LE	HSMS 2850	a 49% at −5 dBm	1.85 at 0 dBm	3.3
[81]	Single-band 915 MHz	VD + LE	HSMS 2852	a 78.7% at 8 dBm	7.2 at 10:20 dBm	10
[55]	Single-band GSM-1800	Full-wave Greinacher + microstrip TLs	SMS7630	b 61% at 10 W/cm2 power density	1.8	12
[3]	Single-band 2.45 GHz	Single-stage Cockcroft VD + L-shaped IMN	HSMS-2850	a 75.5% at 5 dBm	3.24	5
[57]	Dual-band GSM-900 Wi-Fi 2.45	Single-stage VD + CRLH IMN (microstrip TLs + LE)	SMS7630	b43% and 39% at 0 dBm	NR	1
[58]	Dual-band 2.1 GHz 5.8 GHz	VD + IMN (microstrip stub and microstrip TL)	HSMS-282E	a 79% at 20 dBm and 86% at 5 dBm	3.3 and 4.52	1
[59]	Dual-band UMTS-2100 Wi-Fi 2.45	Greinacher VD + Multi stubs IMN	HSMS-285C	b 24% and 18%	1.9 and 1.7	NR
[68]	Broadband 1.8–2.5 GHz	7 stage Dickson VD	HSMS 2850	b 24% at -20 dBm	0.55–1.8	499
[82]	Dual-band GSM900 GSM1800	Latour VD + LE	Avago HSMS285x	a 68% at 985 MHz, 55% at 1900 MHz under −10 dBm	NR	15
[78]	Dual-band GSM-900 Wi-Fi 2.1	Half-wave rectifier + Lumped elements	HSMS-2852	b 42% and 38% at 3 dBm	2.6 at 10 dBm	4.7
[69]	Wide-band 1.8–2.6	4 wideband rectifiers + A nonuniform TL filter	SMS7630-079LF	b 50% at 26.6 W/cm2 power density	1	3
[61]	Triple-band: GSM-900, GSM-1800, 3 G2.1 GHz,	Half-wave rectifier+ inductor and stubs	SMS7630	b 29.5% and 34% and 19% and (56%: 3 tones) at −10 dBm	0.38 and 0.41 and 0.305 and (0.75:3 tones)	11
[52]	Triple-band: GSM-1800 UMTS-2100 Wi-Fi 2.45	Single-stage Villard VD for each band + Modified Hypred Junction IMN	SMS7630	b 61.7% and 45.3% and 44.5% at 9 dBm	3.9 and 3.335 and 3.4	8.2
This work	★ Single-band: GSM-900 GSM-1800 UMTS-2100 Wi-Fi 2.45 $★★$ Quad-band: 900 + 1800 + 2.1 + 2.45	★ Single-stage VD + simple IMN for each band. $★★$ 4Single-stage VD + 4 simple IMN for each band combined. together	HSMS-2852	$a★$ 82.3% and 78.1% and 75.7% and 74.6% at 0 Bm. $★★$ 74.846% for the first scenario whereas 71.194% for the second scenario at 0 Bm.	★ 1.49 and 1.28 and 1.22 and and 1.16. $★★$1.9	5

TL: Transmission Line, LE: lumped Elements, IMN: Impedance Matching Network, VD: Voltage Doubler, NR: Not Reported, a: Simulation results, b: Measurement results, ★: Simulation results of single-band circuits in this work, $★★$: Simulation results of quad-band circuits in this work.

shows the results of this work compared to related published results.

Based on the number of the utilized frequency bands, the proposed work harvests the number of bands more than the published results [3,52,55,57,58,59,61,69,74,78]. On the other side, the proposed design achieved conversion efficiency higher than the reported in [52,55,57,59,61,69,74,78] whereas it is close to the reported in [3]. Moreover, in [66], the efficiency is 40% if there is a single frequency incident upon the antenna. The efficiency is doubled when there are 4 frequencies whereas in our work the efficiency is nearly stable. It is 80% when there is a single frequency available as shown in Figure 23. Furthermore, in [67] the measured results showed that the maximum harvested DC power in typical outdoor and indoor environments was 26 W and 8 W, respectively. This comparison clearly shows the importance of this work since the conversion efficiency and output power have been enhanced beside the number of harvested frequency bands. In our study, the output power is 2 mW = 2000 W, as shown in Figure 22.

6. Conclusions

The non-linearity of the Schottky diodes is due to the variation of the input powers or frequency. The non-linearity degrades the RF-DC conversion efficiency significantly. Hence, this work’s novelty is to overcome the negative effect of the Schottky diodes’ non-linearity issue. Thereby, the following procedures were done: First, the dynamic rectifier input impedance due to the Schottky diode’s non-linearity was found at each frequency band by the proposed theoretical model and ADS simulator. A simple impedance matching network by utilizing the Smith chart utility was designed for each frequency band according to the impedance found at each band. Two scenarios to combine the four circuits in one circuit called “Quad-band circuit” were adopted to harvest the radiated power of each band of the four frequency bands mentioned in this study (900 MHz, 1800 MHz, 2100 MHz, 2450 MHz). The first scenario introduced a quad-band voltage multiplier circuit with a single receiving antenna and four band-pass filters (BPFs) of elliptic type. The output voltage and conversion efficiency under this approach are 1.662 V and 74.846% for the GSM-900 band, 1.422 V, 66.974% for the GSM-1800 band, 1.333 V, 64.486% for the UMTS 2100 band, and 1.587 V, 61.407% for the Wi-Fi 2.45 band. The second scenario presented a quad-band voltage multiplier circuit with four receiving antennas. The output voltage and conversion efficiency obtained were 1.373 V and 71.194%, 1.421 V and 64.944%, 1.594 V and 62.363%, and 1.896 V and 65.096% for the four frequency bands. The proposed quad-band approach can harvest 2 mW DC power. Hence, harvesting the power of RF waves with high RF-DC conversion efficiency at the four bands under the negative effect of the Schottky diodes’ non-linearity conditions is the novelty of this study.