A dual-band RF energy harvesting circuit using 4th order dual-band matching network

Abstract

A novel compact rectifier for dual-band operation in the RF energy harvesting is presented. The circuit comprises a 4th order dual-band impedance matching and a single-series circuit with one double diode, both are integrating into a compact shape to occupy a small area of $30\times 35{\text{mm}}^2$. The merit of the proposed rectifier circuit is that it can be extended to n number of the frequency band by using only $2\times n$ matching elements. To validate the design method experimentally, a prototype of a dual-band rectifier is fabricated for two public telecommunication bands of GSM-900 and 1800. In order to reduce the circuit complexity and sensitivity arising due to lumped elements, the meander line and the open stub are used to realize the proposed circuit. A good agreement is obtained between the simulation and the measurement. The measured results show that the proposed rectifier circuit exhibits the conversion efficiency of 25.7 and 65% for an input power of $-20$ and 0 dBm, respectively. In addition, diode nonlinearity which affects the performance of the rectifier in terms of impedance matching is also investigated.

Keywords:

• RF energy harvesting
• dual band impedance matching
• rectifier
• RF-to-dc-conversion efficiency
• frequency transformation

Public Interest Statement

With rapid growth in wireless communication, a huge amount of radio frequency (RF) energy broadcasted through billions of microwave sources such as mobile phones, handheld radios, and radio broadcast stations. Therefore, it is meaningful to collect and supply it to many electrical devices like mobile headsets, wearable medical sensors through RF energy harvesting. Since the ambient RF energy is distributed in multiple frequency bands, therefore the amount of energy harvested could increase if the circuit is designed for multiple frequency bands. In this work, we present a compact dual-band energy harvesting circuit to harvest energy from two most useful frequency bands, GSM-900 and 1800. The merit of the proposed rectifier circuit is it can be extended to n number of the frequency band by using only $2\times n$ matching elements. A prototype is fabricated, and its performance is evaluated using Vector Network Analyzer (VNA). The total size of the rectifier is about $30\times 35{\text{mm}}^2$.

1. Introduction

A revolutionary growth in wireless technology attracts huge attention from research community to make the self-sustainable device feasible through RF energy harvesting. It exploits ambient electromagnetic energy transmitted from different RF systems to remotely feed the electronic devices (Nintanavongsa, Muncuk, Lewis, & Chowdhury, 2012). Compared to other harvesting techniques, RF energy harvesting provides relatively predictable energy supply owing to the features of easy availability and less dependency on environmental variations. The typical block diagram of RF energy harvesting circuit is shown in Figure 1. It consists of three major blocks viz; antenna, matching network (MN), diode detector followed by an energy storage. The first element, antenna is employed to capture the RF signals of different frequencies and polarization, while second MN is for maximum power transfer, and the last rectifier is used to convert the RF energy to dc voltage. It means harvesting circuit performance can be evaluated in terms of accessible ambient RF energy and its conversion rate (Agrawal, Pandey, Singh,& Parihar, 2014). These parameters are heavily influenced by surrounding terrain conditions as the multiple reflection and dissipation certainly deteriorate the level of available ambient RF energy. As a result, conversion efficiency and dc output voltage may degrade. Previously, the majority of available RF energy harvesting circuits focused on single frequency band hence offer low dc output voltage. As the multiple RF energy sources of different frequency bands are available, thus from an ambient RF harvesting perspective, the output dc voltage could be increased if the circuit is designed for multiple frequency bands rather than a single band. A wide-band energy harvester can also promise a high output voltage by accumulating the number of RF signals at a time. However, due to nonlinear behavior of the diode, harvesting circuit itself exhibits nonlinearity i.e. its input impedance varies with the received RF power. Thus, it is quite difficult to retain the impedance match and high conversion efficiency over a large frequency range (Song, Huang, Zhou, & Carter, 2014). The losses due to impedance mismatch over a large bandwidth can be illustrated in Collado and Georgiadis (2013), where only 8% conversion efficiency is achieved at $-20$ dBm.

Figure 1. Typical block diagram of RF energy harvesting circuit.

To address this, it is preferable to harvest energy from several narrow frequency bands rather than a single large one. In literature, numerous topologies have been proposed to accomplish the multiband energy harvesting (Bergès, Fadel, Oyhenart, Vigneras, & Taris, 2015; Hamano et al., 2016; Ho et al., 2016; Keyrouz, Visser, & Tijhuis, 2013; Kuhn, Lahuec, Seguin, & Person, 2015; Liu, Zhong, & Guo, 2015; Niotaki, Georgiadis, Collado, & Vardakas, 2014; Pinuela, Mitcheson, & Lucyszyn, July 2013; Scheeler, Korhummel, & Popovic, 2014; Shariati, Rowe, Scott, & Ghorban, 2015; Sun, Guo, He, & Zhong, 2013). These topologies can be differentiated in terms of filter functionality i.e. how the antenna or source impedance is matched to the rectifier circuit. For instance, in Pinuela et al. (July 2013) and Keyrouz et al. (2013) several single-band rectennas (combination of antenna and rectifier circuit) were stacked to constitute a multi-band harvesting circuit. In this case, each rectenna was designed for a specific frequency band. Thus, for compact applications, this architecture is not suitable due to the number of antennas used. Moreover, in most of the reported works, the quality assessment of the output voltages combination was not taken into consideration. In Kuhn et al. (2015), the circuit complexity is reduced to a certain extent by replacing the multiple antennas with a single wide-band antenna. However, in this topology too, the number of rectifiers increases with the frequency bands, which leads to prolonging the circuit complexity.

Besides, a multi-band harvesting circuit can also be formed by simply embedding a multi-band matching network between the multi-band antenna and the rectifying circuit (Bergès et al., 2015; Hamano et al., 2016; Ho et al., 2016; Liu et al., 2015; Niotaki et al., 2014; Scheeler et al., 2014; Shariati et al., 2015; Sun et al., 2013). The multi-band matching network can be designed either by distributed or by lumped element. In general, the multi-band rectifier circuit experiences two types of losses: first due to shift in resonance frequency from the optimum frequency point, and second due to the filter complexity. Because of the diode nonlinearity, the input impedance of the circuit varies as a function of power and frequency which causes a shift in resonance frequency. The difficulty due to diode nonlinearity can be observed in Sun et al. (2013) where the dual-band rectifier circuit exhibits impedance matching for a small range of input power. The losses induced because of filter complexity can be observed in the recently reported works on dual band harvesting circuit (Niotaki et al., 2014; Scheeler et al., 2014; Shariati et al., 2015). In Niotaki et al. (2014), for $P_{\text{in}}=-15$ dBm, author achieved the conversion efficiency of 23% at the expense of increased filter complexity consisting two series and two shunt pairs of reactive elements. Thus, for more than dual band applications, the proposed circuit topology is not suitable due to excessive filtering components used. To obtain good conversion efficiency a dual-band rectenna reported in Scheeler et al. (2014). However, the rectenna was large in size and requiring a complex impedance tuning circuit. In Shariati et al. (2015) also, a dual-band matching network consisting nine reactive elements was employed to achieve the dual-band characteristics.

In order to reduce the filter complexity, this work proposed a compact dual-band harvesting circuit for GSM-900 and 1800. It consists of a 4th order dual-band matching network based on $1-n$ frequency transformation, which is optimized for the energy harvesting circuit to reduce the complexity up to $2\times n$ reactive elements (n is the number of frequency bands). Similar to frequency transformation method, the proposed dual-band rectifier circuit can be extended to n number of frequency bands by using the $2\times n$ number of reactive elements. The detailed analysis and design guidelines of dual band rectifier circuit are discussed in Section 2.

Figure 2. (a) Circuit diagram of the proposed dual-band rectifier circuit and (b) optimized dual-band rectifier circuit.

2. Dual band rectifier design and analysis

This section presents the design and analysis of a dual-band harvesting circuit in terms of impedance matching, DC output voltage and RF-to-dc conversion efficiency. The topology of the proposed dual-band RF energy harvesting circuit is shown in Figure 2(a). As seen, the low-cost Schottky diode is used to transform the input RF power to DC voltage. The impedance matching at two frequency is achieved using a series and parallel combination of the LC pair. The main idea underlying the suggested multi-band matching network is $1-n$ frequency transformation (one to many mapping of frequency), which transforms a single-band matching network to multi-band matching network (Nallam & Chatterjee, June 2013). As the name ($1-n$) suggests that for designing a multi-band matching network, primarily a single-band matching network is required whose resonant frequency is dependent on the frequencies for which multi-band matching network proposed to designed.

Figure 3. Conversion of a single-band matching network to dual-band matching network using $1-n$ frequency transformation.

Moreover, this frequency transformation method depends on the type of load impedance, whether it is series or parallel combination of RC or RL. Since the selected diode (HSMS-2852) has capacitive behavior throughout the frequency, it can be represented in a series or parallel combination of R and C. In the case of parallel RC load, the following equations are used to transform the single-band matching network into multi-band matching network.(1) $$\begin{array}{c}\hfill \mathit{\omega }=\frac{{\mathit{\omega }}_t^n+a_m{\mathit{\omega }}_t^{n-m}+a_{m+2}{\mathit{\omega }}_t^{n-(m+2)}+\cdots }{{\mathit{\omega }}_t^{n-1}+a_{m+1}{\mathit{\omega }}_t^{n-(m+1)}+a_{m+3}{\mathit{\omega }}_t^{n-(m+3)}+\cdots }\end{array}$$(1)

where, n is the number of bands and m varies from 2 to n. After substituting the value of n, Equation (1) can be expanded in partial fraction form using the causal foster analysis as:(2) $$\begin{array}{c}\hfill \mathit{\omega }={\mathit{\omega }}_t+\frac{1}{\frac{{\mathit{\omega }}_t}{a_2-a_3}+\frac{1}{\cdots }}\end{array}$$(2)

The coefficients $a_2$ and $a_3$ can be calculated as:(3) $$\begin{array}{cc}\hfill {\mathit{\omega }}_m& =\sum _{i=1}^n{(-1)}^{i-1}{\mathit{\omega }}_i\hfill \end{array}$$(3) (4) $$\begin{array}{cc}\hfill a_m& ={(-1)}^m\sum _{i,j=1,1\&i\ne j}^{n,n}{(-1)}^{i+j}{\mathit{\omega }}_i{\mathit{\omega }}_j\hfill \end{array}$$(4) (5) $$\begin{array}{cc}\hfill a_{m+1}& ={(-1)}^{m+1}\sum _{i,j,k=1,1,1\&i\ne j\ne k}^{n,n,n}{(-1)}^{i+j+k}{\mathit{\omega }}_i{\mathit{\omega }}_j{\mathit{\omega }}_k\hfill \end{array}$$(5) (6) $$\begin{array}{cc}\hfill a_{m+n}& ={(-1)}^{m+n}\sum _{i,j,k\dots =1,1,1\dots i\ne j\ne k}^{n,n,n\dots }{(-1)}^{i+j+k+\cdots }{\mathit{\omega }}_i{\mathit{\omega }}_j{\mathit{\omega }}_k\dots \hfill \end{array}$$(6) (7) $$\begin{array}{cc}\hfill a_n& =\prod _{i=1}^n{(-1)}^n{\mathit{\omega }}_i\hfill \end{array}$$(7)

Equation (6) is similar to that presented in Nallam and Chatterjee (June 2013), except the term ${(-1)}^{m+n}$, which is included here to realize the multi-band matching network for more than three frequency bands i.e. for $n\ge 3$.

With this transformation, the capacitor of the matching network is transformed to the combination of prototype capacitor parallel with inductor whereas, an inductor is transformed into a combination of the same inductor with a series capacitor. Figure 3 shows the circuit schematic of transformation of a single-band matching network to the dual-band matching network. It can be seen that $C_1$ is transformed to $C_1\Vert L_2$ and $L_1$ transformed to $L_1$ series with $C_2$. After successful usage of (1)–(7), the resultant multi-band matching network requires $3n-1$ and $4n-1$ reactive elements for L and $\mathrm{\Pi }$-type topology, respectively.

As the aim is to design a dual-band harvesting circuit, therefore, we require here only 5 or 7 reactive elements with L and $\mathrm{\Pi }$-type topologies, respectively. From Figure 2(a), it can be seen that the resultant matching network consists of five elements, where the inductor $L_3$ and capacitor $C_2$ results after the transformation of capacitor $C_1$ and inductor $L_1$, respectively. Besides, the inductor $L_2$ occurrs due to the diode reactive element, which is generally a capacitor.

In this work, two frequencies 0.9 and 1.8 GHz that correspond to the maximum signal strength are chosen for dual-band harvesting circuit. According to this method, it is necessary to assign the frequencies in descending order e.g. ${\mathit{\omega }}_1=1.8$, ${\mathit{\omega }}_2=0.9$. Therefore, from (3) single-band matching network frequency is equal to ${\mathit{\omega }}_1-{\mathit{\omega }}_2=2\mathit{\pi }(1.8-0.9)\times {10}^9=0.9\times 2\mathit{\pi }\times {10}^9$. In order to match the source impedance with the rectifier at the calculated frequency 0.9 GHz, the chosen matching topology is L-type as shown by the encircled portion in Figure 2(a). The corresponding element values can be approximated using the various methods some of which are described in Pozar (2010). Subsequently, this single-band matching network is transformed to dual-band matching network using (1)–(7). The detailed design steps of the dual-band rectifier circuit are summarized as follows:

(1)	As we are interested in matching the diode to 50 $\mathrm{\Omega }$ at two frequencies (0.9 and 1.8 GHz) so, the order of transformation is equal to 2 or $n=2$.
(2)	In the first step, single-band matching network is designed at the frequency f calculated as: $f=f_2-f_1=1.8-0.9=0.9$ GHz. In this case, any matching topology that matches the diode to 50 $\mathrm{\Omega }$, at 0.9 GHz for an input power $P_{\text{in}}=-20$ dBm, and load resistance 4.7 k$\mathrm{\Omega }$ can be used. The chosen single-band matching network is shown by the encircled portion in Figure 2(a).
(3)	Afterwards, this single-band matching network is transformed into dual-band using the (1)–(7) as shown below:

Since n = 2 therefore, from (2)(8) $$\begin{array}{c}\hfill \mathit{\omega }={\mathit{\omega }}_t+\frac{1}{\frac{{\mathit{\omega }}_t}{a_2}}\end{array}$$(8)

From (4) $a_2$ can be calculated as:(9) $$\begin{array}{cc}\hfill a_2& ={(-1)}^{2+2}\sum {(-1)}^{1+2}{\mathit{\omega }}_1{\mathit{\omega }}_2={\mathit{\omega }}_1{\mathit{\omega }}_2\hfill \end{array}$$(9) (10) $$\begin{array}{cc}\hfill a_2& =-1.62\times 4{\mathit{\pi }}^2\times {10}^8=0.64\times {10}^{20}\hfill \end{array}$$(10)

Thus, inductor $L_1$ (=66 nH) is transformed to impedance as:(11) $$\begin{array}{c}\hfill j66\times {10}^9\mathit{\omega }=j66\times {10}^9{\mathit{\omega }}_t+\frac{1}{j0.23\times {10}^{-12}{\mathit{\omega }}_t}\end{array}$$(11)

Similarly, capacitors (=0.5 pF) are transformed to the admittance as:(12) $$\begin{array}{c}\hfill j5\times {10}^{-13}\mathit{\omega }=j5\times {10}^{-13}{\mathit{\omega }}_t+\frac{1}{j32\times {10}^{-9}{\mathit{\omega }}_t}\end{array}$$(12)

Figure 4. Simulated $|S_{11}|$ vs. frequency for different combination of circuit elements.

The circuit schematic of the dual-band harvesting circuit is shown in Figure 2(a). It can be seen that resultant matching network consists of five reactive elements according to $3n-1$. In order to reduce the circuit complexity and sensitivity due to reactive elements, a parametric study has been carried out to eliminate the elements showing minimum influence on the circuit performance.

Figure 4 shows the simulated $|S_{11}|$ for the different combination of matching elements. The simulated results demonstrate that $|S_{11}|$ experiences maximum change when inductor $L_2$ and capacitor $C_2$ are removed from the circuit, whereas it remains almost unaffected when $L_3$ is not present in the circuit. Therefore, inductor $L_3$ can be extruded from the circuit and the resultant matching circuit requires only 2n and 3n reactive elements in place of $3n-1$ and $4n-1$ elements. In this way, for each topology, the proposed circuit reduces $n-1$ elements compared to the conventional method. Figure 2(b) demonstrates the optimized circuit diagram of the dual-band rectifier. It can be observed that circuit requires large inductors value of 32 and 66 nH. Thus, it is quite difficult to realize the practical rectifier circuit whose response is similar to the response of simulated result. In order to avoid any impedance mismatch due to the small difference in elements value, the meander line inductor and open stub are used to realize the inductors and capacitors, respectively. In this case, not only fabrication and optimization process become so easy but the cost will also reduced.

Figure 5. Layout of the proposed dual-band RF energy harvesting circuit.

Figure 6. Photograph of the fabricated dual-band RF energy harvesting circuit.

Figure 5, shows the layout of the dual-band rectifier circuit. In Nintanavongsa et al. (2012) and Agrawal et al. (2014), it has been demonstrated that the number of rectifying diodes or equivalently voltage multiplier stages are very much sensitive to the RF-to-dc conversion efficiency. In low-power region ($\le -20$ dBm), efficiency decreases if voltage multiplier stages increase, whereas in higher power region ($\ge -20$ dBm), an opposite effect occurs. As the demand is to harvest energy in low-power region, single-series circuit with a double diode is used to convert received RF energy into dc voltage. From the left side of the circuit, the first meander line corresponds to the inductor $L_1$, while the second meander line represents the inductor $L_2$, of the Figure 2(b). The shunt stub is accounted for the shunt capacitor $C_1$ of Figure 2(b). The dimensions of each element are calculated according to their respective reactive element value and the substrate on which circuit has to be fabricated. In Assimonis, Daskalakis, and Bletsas (2016), it has been demonstrated that traces (microstrips) connected to the rectifier terminals (e.g. distance between the diode and via and diode and load) are highly sensitive for RF-to-dc efficiency. Therefore, traces $d_1$, $d_2$ between diode and capacitor $C_1$ and $C_2$, $d_3$ between diode and load and $d_4$ between diode and ground are adjusted to optimize the impedance matching as well as the conversion efficiency of the rectifier. Due to nonlinear behavior of the diode, harvesting circuit itself exhibits nonlinearity i.e. its input impedance varies with received RF power, therefore harmonic-balance (HB) and large signal analysis (LSSP) were employed to take into consideration the nonlinear behavior of the rectifier.

The photograph of the fabricated dual-band rectifier is shown in Figure 6. It is fabricated on a 1.54 mm thick FR-4 substrate with a dielectric constant (${\mathit{ϵ}}_r$) of 4.3 using chemical etching method. The rectifier performance is evaluated in terms of $|S_{11}|$ and output voltage using the Agilent vector network analyzer (VNA). The simulated and measured $|S_{11}|$ is illustrated in Figure 7(a). The measured result shows reasonable agreement with the simulated one; the slight difference can be accounted for the fabrication imperfections. It is well known that impedance matching is a function of frequency and input power, due to the nonlinearity of the diode. Such a characteristic is examined in Figure 7(b), where the measured $|S_{11}|$ is demonstrated as a function of input power level for three different load impedance values. From results, it is clear that impedance matching of the harvesting circuit is greatly affected by the input power and the load impedance. Figure 7(b) demonstrates that as power increases, the impedance matching at 0.9 GHz degraded drastically, while at 1.8 GHz, it improves. Moreover, it is noticed that the impedance matching at higher power level is more sensitive to the variation of load impedance (RL).

Figure 7. (a) Simulated and measured $|S_{11}|$ vs. frequency and (b) measured $|S_{11}|$ for various power levels.

The measured RF-to-dc conversion efficiency and output voltage vs. input power for both frequencies are demonstrated in Figure 8(a). For 0.9 GHz, efficiency is equal to 25.7 and 65.1% for an input power of $-20$ and 0 dBm, respectively. However, at 1.8 GHz the efficiency is relatively small that might be due to the increased parasitic losses in the rectifier diode. Figure 8(b) shows the relation between the output voltage and frequency for various input power levels at fixed load resistance value of 4.7 k$\mathrm{\Omega }$. It can be seen that maximum output voltage is achieved in the frequency range of 860–900 and 1770–1800 MHz, showing the rectifier’s capability to harvest RF energy in the GSM-900 and 1800 bands.

Figure 9, depicts the measured conversion for various values of load resistance. It can be noticed that the circuit yields maximum efficiency when the load impedance is 4.7 k$\mathrm{\Omega }$. It starts decreasing as the load impedance varies from 4.7 k$\mathrm{\Omega }$. Table 1 shows the comparison of the conversion efficiency and the size of the proposed rectifier with the similar works reported previously. Only measured results are compared in Table 1. It can be seen that in low-power condition maximum efficiency is achieved in Sun et al. (2013), but the expense of bulky circuit size. However, the proposed rectifier offers an optimal conversion efficiency with compact circuit size.

Figure 8. (a) Measured output dc voltage and RF-to-dc conversion efficiency and (b) measured dc voltage vs. frequency.

Figure 9. Measured RF-to-dc conversion efficiency for different load impedance.

Table 1. Performance comparison of the proposed dual rectifier with recently published works

Ref.	Measured rectifier efficiency (%)	Input power (dBm)	Rectifier size
Ho et al. (2016)	15.8 @ 0.89 GHz	$-20$	$100\times 65{\text{mm}}^2$
	11.2 @ 1.76 GHz
Hamano et al. (2016)	10 @ 2.15 GHz	$-10$	$37\times 71{\text{mm}}^2$
	15 @ 5.84 GHz
Bergès et al. (2015)	27 @ 0.91/2.4 GHz	$-16$	$78\times 88{\text{mm}}^2$
Sun et al. (2013)	30 @ 2.14 GHz	$-20$	145 mm
	35 @ 1.84 GHz
Liu et al. (15)	20 @ (0.91+1.8) GHz	$-20$	$23\times 37{\text{mm}}^2$
This work	27.5 @ 0.9 GHz	$-20$	$30\times 35{\text{mm}}^2$
	20 @ 1.8 GHz

3. Conclusion

A new compact 4th order dual-band rectifier has been designed to harvest the RF power of GSM-900 and 1800 bands. In order to reduce the circuit complexity and sensitivity due to reactive elements, the meander line and the open stub are used to fabricate the matching network. For $P_{\text{in}}=-20$ dBm, the measured RF-to-dc conversion efficiency of 27.5 and 20% is achieved at 0.9 and 1.8 GHz, respectively. Further, more than 45 and 34% conversion efficiency is maintained from $-10$ to 10 dBm for 0.9 and 1.8 GHz, respectively.

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Sachin Agrawal

Sachin Agrawal did his BE and ME from Jiwaji University and Birla Institute of Technology Pilani, India in 2005 and 2009, respectively. Currently, he is pursuing his PhD from PDPM-Indian Institute of Information Technology Design and Manufacturing Jabalpur, India. His area of interest are; RF energy harvesting circuit, Antenna including planar and dielectric resonator antenna and Power amplifier.