A Compact and High-Efficiency Design of Triple-Band Rectifier for Wireless Power Transfer

Abstract

This paper proposes a novel method for the design of arbitrary tri-band rectifiers. This method proposes a novel multiband impedance matching network (IMN) consisting of three Transmission Lines (TLINs), which can realise the matching of source and complex impedance matching in any three bands. For the first time, a network is proposed that realises the second harmonic suppression in three bands using only three TLINs. The Harmonic Suppression Network (HSN) is independent of other parts, which reduces the interaction between TLINs and simplifies the derivation process. For demonstration, the three bands are set to 2.45, 3.5 and 5.8 GHz in the theoretical analysis of closed-form equations. The measured results show that the maximum Power Conversion Efficiencies (PCEs) are 75.4%, 71.2%, and 80.9% at a load of 200 Ω, respectively. This approach to designing compact and efficient tri-band rectifiers has great potential for wireless power transfer applications.

1. Introduction

Wireless power transfer (WPT) is a technology that harvests energy from the surrounding environment and converts it into electrical energy [1,2,3]. WPT has a wide range of applications in areas such as the Internet of Things (IoT) [4], wearable devices [5] and wireless sensor networks [6]. The efficient transmission of electrical energy is the purpose of the WPT system. Key system metrics include efficiency, size, distance, and an effective impedance matching scheme. The classification and main applications of WPT systems are shown in Figure 1. The WPT system consists of a receiving antenna and a rectifier circuit, in which the rectifier circuit serves as the key component of the WPT system. It is critical for RF-DC energy conversion [7,8]. Based on the conventional power supply model, the conversion efficiency to obtain 1 mW of DC energy from residential AC power is only 6% and the cost of the converter is high. The production of electronic devices is moving towards low power, miniaturisation and low cost. The output DC voltage of the rectifier is usually in the range of 1.2–3.5 V and has a high rectification efficiency. It can effectively solve the power supply problem of low-power electronic devices [9,10].

At present, single- and dual-band rectifier circuit design methods are relatively well developed. Various rectifiers operate at different frequency bands in mobile communication such as GSM900 [11], GSM1800 [12], GSM1900 [13], UMTS2100 [14] and in wireless networks [15,16,17,18]. A rectifier with a broad input power range has been proposed in Reference [19]. It uses a pseudomorphic High-Electron-Mobility Transistor (pHEMT) with a Schottky diode to achieve dual-band rectification at 0.915 and 1.8 GHz. Reference [20] designed a dual-band rectifier circuit that can operate in the Industrial, Scientific and Medical (ISM) band using a T-type Impedance Matching Network (IMN). A rectifier proposed in Reference [21] operates at 3.5 and 5.8 GHz. The Power Conversion Efficiency (PCE) is divided into 54.5% and 41.2% when the input power is 5 dBm. It may include several frequency bands due to the wide distribution of electromagnetic energy in the environment. The rectifier should operate in three or more frequency bands [22,23] to increase the energy gained. However, the nonlinearity of the diode causes its input impedance to vary significantly with frequency. In order to maintain a high PCE, it is usually necessary to design a complex network for multi-band impedance matching and harmonic suppression, which leads to a large circuit size. In [24], the authors proposed a tri-band rectifier circuit. The structure is designed with a separate rectifier unit for impedance matching for each frequency separately. The rectifier structure proposed in References [25,26] uses only a single diode. Since it focuses only on IMNs, it is not possible to guarantee high efficiency while achieving a compact size. The structure proposed in Reference [27] is suitable for low-input-power environments. The operating frequencies are GSM900, GSM1800 and UMTS2100. A three-band differential rectifier is proposed in Reference [28]. In Reference [29], a triple-frequency rectifier is obtained by an impedance transformer and inductive circuit design. In References [30,31], tri-band rectification is achieved by adding Transmission Lines (TLINs), thereby increasing the operating frequency. Reference [32] presents a high-band triple-frequency rectifier circuit structure operating at 24, 28 and 38 GHz. However, existing rectifiers use multiple diodes, resulting in high losses, large size, or low efficiency at low input power.

This paper proposes a rectifier design method based on the combination of a multi-impedance matching network with a single diode and a three-band second harmonic suppression. This method reduces circuit costs during processing by reducing the number of TLINs and the complexity of the structure. Three TLINs are used to provide very high impedance for second harmonic concurrence. The Harmonic Suppression Network (HSN) proposed in this structure is independent of other parts and reduces the sensitivity of the rectifier. This approach makes the space between the TLINs more compact. The HSN proposed in this paper reduces the number of TLINs as compared to Reference [24]. Furthermore, the IMN proposed in this paper can be used for arbitrary impedance matching in wavelet transform applications. The impedance matching network matches complex impedances to the source of 50Ω using an open stub, a short stub, and a microstrip transmission line. This IMN uses only three TLINs, which reduces the insertion loss and simplifies the derivation process compared to References [30,33]. Broadband rectifiers [34,35] can be realised without an impedance matching network, but the operating frequency is limited. For verification, a tri-band rectifier operating at 2.45, 3.5, and 5.8 GHz is designed. At three bands, the input return loss (|S₁₁|) is of less than −10 dB. At a load of 200 Ω, the maximum PCE is 75.4%, 71.2%, and 80.9%. Tri-band rectifiers can be widely used in IoT, Internet of Vehicle (IoV) and wearable devices.

2. Design and Analysis of Tri-Band Rectifier

The proposed structure is shown in Figure 2. The structure consists of three parts: an impedance matching network, a harmonic suppression network, and a DC pass filter. The input impedance is converted by the IMN of three TLINs. The HSN achieves second harmonic suppression in three bands. The TLINs are labelled as TL₁–TL₆. Each TL_i is determined by ${\theta }_i$ and $z_i\left(i=1-6\right)$, which represent the electrical length and the characteristic impedance. $y_i$ is the normalised admittance. $y_L$ is the normalised admittance of the input impedance. $y_{in}$, $y_{in1}$, and $y_{in2}$ denote the normalised admittance of the impedance matching network at different nodes, respectively. L is the inductance. C is the capacitance. $R_L$ is the load.

2.1. Design of Tri-Band Impedance Matching Network

The rectifier is a non-linear element; so, excellent impedance matching in each band is required to increase the PCE. A novel tri-band impedance matching network is proposed in this paper. Firstly, the admittance of the load is calculated in three bands. The normalized impedance and admittance are shown by lowercase variables.

The normalised input admittances of the open stub and the short stub are as shown in (1) and (2), respectively:

$$y_i={\displaystyle \frac{1}{j{z}_i\tan {\theta }_i}}, i=6$$

(1)

$$y_i=-{{\displaystyle \frac{1}{j{z}_i\cot \theta }}}_i, i=4.$$

(2)

Step 1 is as shown in Figure 3a; following the short stub, the normalised input admittance $y_{in1}$ can be expressed as in (3):

$$y_{in1}\left(f_i\right)=y_6+y_L={\displaystyle \frac{1}{j{z}_6\tan {\theta }_6}}+y_L,$$

(3)

Assuming $y={\displaystyle \frac{1}{z}}=g+jb$, since $z=r-jx$, $g$ and $b$ can be derived as $g={\displaystyle \frac{r}{r^2+x^2}}$ and $b={\displaystyle \frac{x}{r^2+x^2}}$.

Since $y_{in1}=g_{in1}+j{b}_{in1}$, $y_L=g_L+j{b}_L$, (4) and (5) can be obtained as follows:

$$g_{in1}=g_L$$

(4)

$$b_{in1}=-{\displaystyle \frac{1}{z_6\tan {\theta }_6}}+b_L,$$

(5)

$g_L$ represents the normalised conductance making up $y_L$ and $b_L$ represents the normalised susceptance of $y_L$. Step 2 is as shown in Figure 3a; $y_{in1}$ is converted to $y_{in2}$ by a transmission line (TL₅). The expression for $y_{in2}$ is as in (6):

$$y_{in2}\left(f_i\right)={\displaystyle \frac{1}{z_5}}{\displaystyle \frac{g_{in1}+j\left(b_{in1}+\frac{1}{z_5\tan {\theta }_5}\right)}{\left(\frac{1}{z_5}-b_{in1}\tan {\theta }_5\right)+j{g}_{in1}\tan {\theta }_5}},$$

(6)

Rewriting (6) with knowing that the real part of $y_{in2}$ is 1 results in (7):

$$g_{in1}^2{\tan }^2{\theta }_5-{\displaystyle \frac{g_{in1}\left(1+{\tan }^2{\theta }_5\right)}{{z_5}^2}}+{\left({\displaystyle \frac{1}{z_5}}-b_{in1}\tan {\theta }_5\right)}^2=0.$$

(7)

Since $g_{in1}=g_L$, the value of $b_{in1}$ at three frequencies can be derived. This is necessary to determine the parameters of TL₅. The imaginary part of $y_{in2}$ can be obtained by inserting $b_{in1}$ into (6) and the value of $b_{in2}$ can be found at different frequencies. The equation can be solved by substituting $b_{in1}$ into (5) to obtain the parameters of TL₆. Step 3 is shown in in Figure 3a; the imaginary part of $y_{in2}$ is eliminated using the open stub (TL₄) in order to bring $y_{in}$ to 1. The input admittance $y_{in}$ can be expressed as in (8):

$$y_{in}\left(f_i\right)={\displaystyle \frac{1}{z_4}}+y_{in2},$$

(8)

Since $z_4$ is conjugate at $f_1$ and $f_2$, the conjugacy relation is satisfied when ${\theta }_4$ satisfies (9):

$$y_{in}\left(f_i\right)=-{\displaystyle \frac{1}{j{z}_4\cot {\theta }_4}}+j{b}_{in2}+1.$$

(9)

Equation (10) can be derived since the imaginary part of $y_{in}$ is 0:

$${\displaystyle \frac{1}{z_4\cot {\theta }_4}}+b_{in2}=0,$$

(10)

$b_{in2}$ has been calculated and the parameters of TL₄ are found by substituting $f_i\left(i=1,2,3\right)$ into (10). As shown in Figure 3b, $y_{in}$ is located in the centre of the Smith Chart, indicating good impedance matching at three bands.

2.2. Design of Harmonic Suppression Network

By designing a harmonic suppression network, the proposed rectifier accurately suppresses the second harmonic in order to maximise the PCE. As shown in Figure 2, the suppression of $2f_1$ is realised at the anode of the diode by a short stub. The suppression of $2f_2$ and $2f_3$ is realised at the cathode of the diode by the open stub as in (11); $Z_T$ denotes the anode of the diode impedance, and $Z_H$ denotes the cathode of the diode impedance:

$$Z_T^{2f_1}=\infty , Z_H^{2f_2,2f_3}=0.$$

(11)

The short stub that is connected to the anode of the diode is used to determine $Z_T^{2f_1}$ as in (12).

$$Z_T^{2f_1}={\displaystyle \frac{j\tan {\theta }_1^{2f_1}}{Y_{01}}}.$$

(12)

Based on the fact that $2f_1$ is at $Z_T=\infty$, Equation (13) is derived.

$${\theta }_1^{2f_1}=\lambda /4.$$

(13)

The diode cathode realises the second harmonic suppression of $f_2$ and $f_3$ through TL₂ and TL₃. The electrical lengths of TL₂ and TL₃ are defined as in (14) and (15):

$${\theta }_2^{2f_3}=\lambda /4$$

(14)

$${\theta }_3^{2f_2}=\lambda /4.$$

(15)

The HSN is independent of the other parts. The structure is simple, with low sensitivity, and easy to process when compared to Reference [36].

2.3. 2.45/3.5/5.8 GHz Tri-Band Rectifier Parameter Settings

To demonstrate, the three bands of the rectifier are set to 2.45, 3.5 and 5.8 GHz. The design parameters of the proposed structure are obtained from the derivation. To facilitate rectifier processing, the actual physical lengths and widths are given in

Table 1. Design parameters for the tri-band rectifier.

TLIN	Length (mm)	Width (mm)
TL1	2.85	1.92
TL2	14.99	7.20
TL3	10.80	6.23
TL4	18.66	9.06
TL5	3.15	14.74
TL6	12.84	1.21

.

3. Results and Discussion

To validate the theoretical analysis, the proposed rectifier is simulated and measured. The structure is fabricated using an ROG4003C substrate (${\epsilon }_r=3.55$, $\tan \delta =0.0027$) with a thickness of 1.508 mm. The diode selected is HSMS-2860 (Avago, California, USA). The DC pass filter consists of a shunt capacitor of 24 pF (MuRata GRM1555C1H240JA01, MuRata, Kyoto, Japan), and a series inductor with a value of 10 nH (MuRata LQW18AN10NG00, MuRata, Kyoto, Japan). The DC-Block consists of a 24 pF capacitor (MuRata GRM1555C1H240JA01, MuRata, Kyoto, Japan). The structure achieves compact dimensions of 38 × 33 mm. The proposed rectifier was simulated in the Advanced Design System (ADS, Agilent, CA, USA). ADS is a commercially available software for circuit design. The version used for our paper is ADS2020. Measurement devices for the rectifier circuit include an RF signal source (N5171B, Agilent, Santa Clara, CA, USA), a power metre (E4418B, Agilent, Santa Clara, CA, USA), and a digital display multimetre (34401A, Agilent, Santa Clara, CA, USA). The RF signal source provides RF energy to the rectifier circuit, the power metre is used to measure input power to the structure, and the digital display multimetre is used to measure output voltage. Figure 4 shows the fabricated rectifier.

Figure 5 shows the peak PCE distribution at different loads. The performance of the rectifier is improved under different loads. Load values in the range of 180 Ω–260 Ω ensure that the rectifier achieves a high PCE at different input powers. The load value of 200 Ω should be determined during fabrication.

As shown in Figure 6a, at 20 dBm, the simulated |S₁₁| is −16.5 dB, −13.3 dB, and −17.6 dB when the frequencies are 2.45, 3.5, and 5.8 GHz. The measured |S₁₁| is −13.4 dB, −11.5 dB, and −14.2 dB, respectively. The simulated and measured |S₁₁| are essentially the same. There is an error between the simulation and the experiment due to losses in the device during processing. The proposed rectifier achieves good input impedance matching over the specified frequency range. The PCE versus frequency at an input power of 20 dBm is shown in Figure 6b. The measured and simulated results are in good agreement, and the simulated PCEs are 82.2%, 59.4% and 86.4% at 2.45, 3.5 and 5.8 GHz, respectively. The measured PCEs are 75.4%, 62.5% and 75.8%, respectively.

The PCE is calculated as follows:

$${\eta }_{PCE}={\displaystyle \frac{P_{out}}{P_{in}}}=V_{out}^2\left({\displaystyle \frac{1}{R_L\times P_{in}}}\right)$$

(16)

where ${\eta }_{PCE}$ represents the PCE of the rectifier, $P_{in}$ is the equivalent input power of the source, $P_{out}$ is the output DC power, $V_{out}$ is the voltage across the load, and $R_L$ is the load value. The simulation and measurement results of the PCE with the input power are shown in Figure 7a. When the PCE exceeds than 50%, the measured results show an input power of 8 to 24 dBm at 2.45 GHz, 10 to 20 dBm at 3.5 GHz, and 2 to 23 dBm at 5.8 GHz. The measured maximum efficiencies at 2.45, 3.5, and 5.8 GHz are 75.4% at 20 dBm, 71.2% at 19 dBm, and 80.9% at 19 dBm, respectively. Subsequently the PCE decreases as the input power increases. This is a result of impedance mismatch due to the nonlinearity of the rectifier. As shown in Figure 7b, the output voltages are divided into 3.0 V, 3.2 V, and 3.3 V when the three bands reach the maximum PCE. The results of the rectifier are essentially the same for simulation and fabrication. The reasons for the differences can be analysed: Firstly, these are caused by dimensional differences in the TLINs during fabrication. Secondly, there are losses in the components.

The proposed rectifier is compared with existing studies, as shown in

Table 2. Performance comparison with the state-of-the-art tri-band rectifiers.

Reference	Freq. (GHz)	Size (mm2)	Diode	No. of Diodes	${\mathit{\eta }}_{\mathbf{PCE}\_\mathbf{peak}}$ (%)
[24]	0.915	29.5 × 21.3	MA4E1317	3	72.6
	2.45				71.8
	5.8				73.5
[31]	0.9	54 × 42	HSMS2852	3	52
	1.8				50
	2.45				46
[33]	1.95	36 × 22	HSMS2860	1	65.5
	2.7				62
	5.8				57.1
[37]	1.78	N/A	BAT15-03W	3	60.1
	2.35				71.4
	4.97				54.0
[26]	1.85	44 × 81	MA4E1317	1	48.0
	2.15				52.0
	2.48				45.0
[38]	1.85	32 × 32	SMS7630	4	64.0
	2.15				70.0
	2.45				60.0
[39]	0.895	34 × 44	BAT15-03W	1	80.0
	2.37				74.6
	5.57				73.6
This work	2.45	38 × 33	HSMS2860	1	75.4
	3.5				71.2
	5.8				80.9

. The goal of this paper is to reduce structural complexity by reducing the number of TLINs and to maintain a high PCE. Multiple diodes are used in References [24,31,37], which increases the complexity of the structure and leads to a decrease in efficiency. The structure proposed in Reference [26] is larger in size and has low rectification efficiency. The frequency ratio of the structure proposed in Reference [38] is too low for practical applications. The proposed rectifier is competitive in terms of efficiency and size compared to other studies. The proposed novel impedance matching network is generalisable.

4. Conclusions

In this paper, a new method for the design of arbitrary three-band rectifiers is proposed, with the following main contributions:

• Based on the theoretical analysis of closed-form equations, a new multiband IMN consisting of three TLINs is proposed, reducing the structural complexity by reducing the number of microstrip lines.
• This method achieves second harmonic suppression in all three frequency bands using only three TLINs. The HSNs are independent of the other parts, which reduces the interaction between the TLINs and simplifies the derivation process.
• The use of a single diode to achieve a three-band rectifier reduces the insertion loss of the structure.
• This design method achieves a high rectification efficiency while ensuring a compact structure.
• It enriches the design methodology of three-band rectifiers.

For verification, a tri-band rectifier with operating frequencies of 2.45, 3.5 and 5.8 GHz was designed. The performance parameters of the structure are good, which verifies the effectiveness of the method we propose:

• At three frequencies, the input return loss of (|S₁₁|) is less than −10 dB. The impedance matching performance of the structure is verified.
• At 200 Ω, the maximum PCE is 75.4%, 71.2%, and 80.9%, respectively.
• At three frequencies, a high PCE can be maintained over a wide input power range.
• The output voltage at the three frequencies is 3 V, which can effectively realize the power supply of small sensors.
• The measured structure size is 38 × 33, which is both efficient and compact compared with other studies. There is good agreement between the simulated and measured results.

In low-input-power environments, micro-watt rectifier circuits are more sensitive to the operating temperature, which has an impact on the rectification efficiency. In order to verify the advantages of the proposed method more accurately, the operating temperature when the rectifier diode performance is optimal should be selected for testing in subsequent studies. This research has great potential for powering low-power devices and wireless power transmission. And it is suitable for commercial production due to its simple structure and low processing cost. Subsequent research will be conducted on the integration of energy harvesting and rectification, and the application of information and energy co-transmission for small devices. This will further drive the development of low-power devices in the energy internet.

Table 3. Correspondence between abbreviation and full name.

Full Name	Abbreviation
Advanced Design System	ADS
Harmonic Suppression Network	HSN
Impedance Matching Network	IMN
Internet of Things	IoT
Internet of Vehicle	IoV
Industrial, Scientific and Medical	ISM
Power Conversion Efficiency	PCE
pseudomorphic High-Electron-Mobility Transistor	pHEMT
Radio Frequency Energy Harvesting	RFEH
Transmission Line	TLIN
Wireless Power Transfer	WPT

shows the correspondence between abbreviations and their full names as they appear in this paper.