A High-Efficiency Self-Synchronous RF–DC Rectifier Based on Time-Reversal Duality for Wireless Power Transfer Applications

Abstract

An RF–DC rectifier is an important part in a wireless power transfer system. Diode-based rectifiers are widely used in low-power harvesting scenarios, and for high power, a transistor based on the time-reversal duality was proposed. This paper presents a high-efficiency self-synchronous RF–DC rectifier based on a waveform-guided design method and an improved rectification model of a commercial GaN device. The main contributions of this paper are that (1) an improved transistor model with correct reverse bias is built for accurate rectifier simulation, and (2) a new design method of self-synchronous RF–DC rectifier is proposed: as soon as the operating mode of the rectifier, input power, and DC load are set, matching and coupling network can be calculated directly based on waveform-guided method, thus design and adjustment process of a conventional power amplifier (PA) due to the duality between a PA and a rectifier would no longer be required. A 5.8 GHz self-synchronous RF–DC rectifier is designed for validation, and the optimum RF–DC conversion efficiency is 68% with 12 W input power as well as 19.9 V output DC potential with 50 Ω load resistance. The proposed rectifier is suitable for high input power rectification applications of wireless power transfer.

1. Introduction

The RF–DC rectifier, which converts radio frequency (RF) power into direct current (DC) power, is the most distinguishing different component between the wireless power transfer (WPT) and wireless communication systems, which both transmit microwave power in one terminal and receive it in another side. A rectifier is not needed in wireless communication systems, but it is a very important part in the receiving end of the WPT link to convert microwave power into DC power for the application. Many remarkable pieces of research have been carried out in WPT rectifiers that operate for applications of energy harvesting and sensor wireless charging [1,2]. For some wireless sensors network applications that will benefit from the use of WPT techniques in power sensors [3], a study in [4] proposed sensor nodes in which the energy harvesting module is compatible with collecting energy directly from the WPT, and the WPT is recognized to be an attractive technology to supply power to IoT devices where battery replacement is difficult, or the maintenance cost is high [5].For these applications, the input power of the rectifier is very low, usually at mW, or even uW, level [6,7], and the diode is the proper device that can be used to perform RF to DC conversion; however, lower breakdown voltage of a diode is a restriction when input power increases, and at high input power, it is not the appropriate device anymore. Therefore, high input power rectification of WPT can cause a demand for a new type of device, which can be adaptable to endure high inverse voltage.

Based on time-reversal duality, the concept was introduced by David C. Hamill in 1990 [8]; with the reversed direction of power flow, any PA will function as a rectifier at microwave frequencies only by replacing the load resistor with RF input power at the drain and making the gate matching network open-terminated [9,10,11,12,13,14,15].

A few GaN HEMT devices can perform rectification behavior when the drain-source is biased reversely, but not all GaN HEMTs can be used as a diode; for example, those with reverse cut-off characteristics are not suited to rectify because the drain current and drain voltage in the third quadrant do not have the similar characteristics in comparison to a diode. Nowadays, designing microwave circuits mainly counts on the adequacy of the commercial software to simulate the performance of circuits accurately. However, transistor models used in PA are not appropriate for rectifier simulation because the operated region of the rectifier is the third quadrant region of DC characteristics, which means drain current and drain voltage are both negative. As the drain voltage must be above 0 volts for PA application, the device manufacturers had not measured and modeled the performance of the third quadrant by the time of modeling a transistor device. It has been proven that the I–V relation of the GaN device model embedded in commercial simulation software is symmetrical about the origin of coordinate, hence there is a quest for model refinement to achieve an accurate and reliable rectification model employed in simulation, and some discussions and research of correct device model for rectifying simulation have been carried out in recent years [16,17].

In addition, designing an RF–DC rectifier with a GaN HEMT device usually starts from a conventional PA design based on time-reversal duality, which means there is no special method for a rectifier design. In addition, for the purpose of synchronous rectification, an external phase shifter coupled from the RF input power port was brought in to compensate the drive power and adding a phase shifter would cause a complex adjustments process [18,19].

A high-efficiency self-synchronous RF–DC rectifier is presented in this paper. Firstly, the modeling and parameter-fitting process of a CGH40010F is first provided to obtain an accurate reverse bias model for rectifier simulation. Then, a waveform-guide design method is presented to validate the rectification model and designing method.

2. Rectification Model and Parameter Fitting

The Schottky diode is a common device adopted in microwave rectifiers because of DC characteristics in the first quadrant, and the transistor is composed of a Schottky barrier between gate and source, which is similar to the diode. Therefore, when the transistor is reversed bias, which means the voltage and current are both negative applied on a transistor, the transistor can be used as a rectifying device. However, the transistor model provided by the device manufacturer is mainly for the power amplifier, and the drain voltage must be above 0 volts to prevent reverse drain bias, so less attention has been focused on the I–V relation of the third quadrant. Taking Wolfspeed’s device model of CGH40010F for instance, the I–V relation is exactly symmetrical about the origin of coordinate in simulation software. It is so obvious this model is not appropriate for rectifying circuit design.

Therefore, it is necessary to build an accurate transistor rectification model based on existing commercial devices for rectifier design. A GaN device CGH40010F is used to design as it is so popular in PA and the design kit model provided by the manufacturer has been embedded in the advanced design system (ADS). As mentioned earlier, the vendor’s model does not include the behavior under reverse bias, which is the main operation region of a rectifier, so it is necessary to modify the original model to adapt to the correct rectification behavior. However, in software, the device model of CGH40010F is just a symbol and the internal structure and parameters are not open, considering that the manufacturer’s model is more reliable, so the characteristics of the positive drain-source voltage of our improved model are directly adopted by the manufacturer’s model by fitting characteristics of the manufacturer’s model and the EEsof scalable nonlinear HEMT (EEHEMT) model to extract the parameters in ADS. EEHEMT is an empirical analytic model that was developed by Keysight Technologies for the express purpose of fitting measured electrical behavior of HEMTs. The equivalent circuit of an EEMEMT model is shown in Figure 1. The reason for choosing the EEHEMT model is because it is integrated into ADS and can be easily obtained from Keysight’s product manual. In addition, it consists of parameters that are easily estimated from the measured data, which is suitable for rectifying simulation. Then, the nonlinear current source is extended to the reverse bias range to build the reverse bias model based on Callet formulae by actual negative-drain voltage data. Finally, a transistor rectification model in the form of symbolic defined devices (SDD) is accomplished in ADS.

2.1. Extract the Parameters

2.1.1. DC Characteristic Parameters

Two DC simulation circuits with identical schematics were created: one uses the manufacturer’s model and the other uses the EEHEMT model, and Id1 and Id2 are drain currents of circuits with the manufacturer’s model and EEHEMT model, respectively. With Id1 as the target, parameters in EEHEMT were fitted by making the difference between Id1 and Id2 as small as possible. The fitted EEHEMT model’s DC parameters are shown in

Table 1. Fitted DC parameters for CGH40010F’ EEHEMT model.

Parameter	Value	Units	Parameter	Value	Units	Parameter	Value	Units
Vto	−3.51	V	Gamma	3.63 × 10−4	1/V	Vgo	−2.38	V
Gmmax	0.72	S	Vsat	6.02	V	Kapa	1.21 × 10−7	S
Peff	89.32	W	Vtso	14.21	V	Is	1.3 × 10−10	A
Ris	6.31 × 10−7	Ohm	Rid	1.0 × 10−10	Ohm	Rd	0.77	Ohm
Rs	9.48 × 10−5	Ohm	Rg	8.37	Ohm	Vco	8.45	V
Vbc	5.66	V	Vba	4.0	V	Deltgm	−0.08	None

. A detailed description of the parameters can be found in ADS help documents.

2.1.2. Small Signal Characteristic Parameters

Harmonic balance simulations were carried out in the same way: two circuits were created, and the optimization target is the smallest difference of transconductance (gm) between simulation results of the manufacturer’s model circuit and EEHEMT model circuit. The fitted alternating current (AC) small signal characteristic parameters are given in

Table 2. Fitted AC small signal characteristic parameters.

Parameter	Value	Units	Parameter	Value	Units
Vtoac	−3.5	V	Gammaac	1.28 × 10−3	1/V
Gmmaxac	0.86	S	Kapaac	1.52 × 10−9	S
Peffac	89.53	W	Vtsoac	−3.61	V
Deltgmac	4.21	None

.

2.1.3. High-Frequency Characteristic Parameter and Parasitic Parameters

Note that CGH40010F is a packaged transistor, and the parasitic effect caused by the package has a great influence on its high-frequency performances that cannot be ignored. Therefore, parasitic capacitance and inductance should be extracted. The architecture of the package parameters is shown in Figure 2, and the dashed box represents the intrinsic parameters of the EEHEMT model. The optimization target was set to make the S-parameters difference between two circuits with different device models as small as possible.

Now that the parameter extraction has been accomplished, the fitted nonlinear charges and package parameters can be found in Table 1, Table 2 and

Table 3. Fitted high-frequency characteristic parameters and package parameters.

Parameter	Value	Units	Parameter	Value	Units	Parameter	Value	Units
Cdso	1.5 × 10−12	F	Cbs	3.0 × 10−11	F	C11o	1.59 × 10−12	F
C11th	2.43 × 10−16	F	Vinfl	1.4 × 10−4	V	Deltgs	1.2.27	V
Deltds	32.23	V	Lambda	0.033	1/V	C12sat	1.2 × 10−17	F
Cgdsat	6.38 × 10−16	F	Lpg	2.89 × 10−5	H	Cpg	2.0	F
Rpg	2.2 × 10−3	Ohm	Lpd	0.65	H	Cpd	0.54	F
Rpd	0.31	Ohm	Lps	0.04	H	ZTLpg	28.5	Ohm
θTLpg	11.6	deg	ZTLpd	15.4	Ohm	θTLpd	0.05	deg

. Finally, all the extracted parameters are integrated into the form of SDD in ADS. The advantage of this is that the intrinsic drain voltage and current can be measured, facilitating the design of a waveform-based RF–DC rectifier.

2.2. Verification of the Extracted Parameters

To verify the correctness of the extracted parameters, an identical wideband PA circuit with the improved model and the model provided by the manufacturer were simulated separately. When the simulation results of the two circuits are in good agreement, it can be demonstrated that the improved model and the manufacturer’s model have the same performance at the positive drain voltage. In other words, the extracted parameters can be demonstrated correctly. Figure 3 shows a comparison of the results for power added efficiency (PAE) and output power. It can be found that the simulation results of PAE and output power are in good agreement between the improved model and the manufacturer’s model, respectively. Therefore, the correctness of the extracted parameters was verified.

2.3. Reverse Bias Model

The parameter extraction of the reverse drain-source bias model is similar to the previous parameter extraction process; the only difference is the current formula. The current equations in [14] are also adopted to model the reverse bias states and, based on the Callet model and measured data of negative drain voltages, with the similar parameter extraction method, the fitted parameters are given in

Table 4. Fitted parameters at negative drain-source voltage.

Parameter	Value	Units	Parameter	Value	Units	Parameter	Value	Units
Idss	0.92	A	Vpo	4.48	V	p	0.008	None
Wneg	−0.13	None	Wpos	0.91	None	Aneg	0.015	None
Apos	0.3	None	Vknee	4.1	V	Sneg	32	S
gmvp	0.1	S	Ssatn	0.4	S	Vsatn	0.8	V
Ssat1p	0.66	S	Vsat1p	−2.1	V	Ssat2p	0.05	S
Vsat2p	2	V	atrval	−0.18	None	N	1.2	None
Vpdec	−0.2	V

, and the DC I–V waveform under negative drain bias is shown in Figure 4. It can be seen that DC characteristics in the third quadrant region are similar to characteristics of a diode.

Then, combining this reverse bias model with the fitted model above, and the improved model that contains the whole DC characteristics from negative to positive, the drain voltage is obtained. This accurate and complete transistor model is suitable for RF–DC rectifier simulation.

3. RF–DC Rectifier Design

3.1. Design Method

A brief diagram of the self-driving transistor rectifier including the device model and passive network is shown in Figure 5. The three-port passive network is used as matching, and gate-coupling circuits are used to match impendence, meanwhile coupled power from RF is input to the drive itself, and the device model has divided intrinsic parameters and package parameters: Z_G and Z_D are represented Z-parameters of gate package and drain package, respectively.

The intrinsic current source I_ds is determined by nonlinear function related to internal voltage V’_gs and V’_ds, and this function can be obtained by expanding the nonlinear I–V curve shown in Figure 4. Because waveform is defined at the intrinsic plane by waveform engineering, the first step of designing a self-synchronous RF–DC rectifier is determining the target waveforms, then calculating I_ds by V’_gs and V’_ds as variables to make an approximation to the target waveform. As soon as the target rectification waveform is determined by V’_gs and V’_ds, the next step is to calculate the Z-parameters Z_M of the matching and coupling network.

V’_ds, I’_ds could be related to the V_d, I_d at the actual device port with Z_D, and the relationship can be expressed as

$$\begin{array}{ll}{I}_d=& -\left\{V_{ds}^{\prime }+I_{ds}^{\prime }\frac{1}{jk\omega C_{dso}}\parallel \left[R_d+R_{pd}+jk\omega L_{pd}+\frac{1}{jk\omega C_{pd}}\parallel \left(-j{Z}_{pd}\cot k{\theta }_{pd}\right)\right]\right\}\\ & \times \left(\frac{j\sin k{\theta }_{pd}{Z}_A}{Z_{pd}}+\frac{\cos k{\theta }_{pd}}{Z_B}\right)\end{array}$$

(1)

where $Z_A=jk\omega C_{dso}\left(R_d+R_{pd}+jk\omega L_{pd}+\frac{1}{jk\omega C_{dso}}\right)$, $Z_B=\frac{1}{jk\omega (C_{dso}+C_{pd})-k^2{\omega }^2\left(R_d+R_{pd}+jk\omega L_{pd}\right)C_{pd}{C}_{dso}}$, and Z_pd and θ_pd are the characteristic impedance and electrical length of the transmission line TL_pd, respectively.

$$V_d=\frac{-I_{ds}^{\prime }}{j\sin k{\theta }_{pd}{Z}_A/Z_{pd}+\cos k{\theta }_{pd}/Z_B}-\frac{I_{ds}{Z}_{pd}(Z_C+Z_{pd}\tan k{\theta }_{pd})}{Z_{pd}+j{Z}_C\tan k{\theta }_{pd}}$$

(2)

where $Z_C=\frac{1}{jk\omega C_{pd}}\parallel \left(R_d+R_{pd}+jk\omega L_{pd}+\frac{1}{jk\omega C_{dso}}\right)$.

Likewise, I_g, V_g can be expressed as

$$I_g=\frac{V_{gs}^{\prime }+I_{gs}^{\prime }\frac{Z_{pg}\left(1-k\omega C_{pg}{Z}_{pg}\tan {\theta }_{pg}\right)}{jk\omega C_{pg}{Z}_{pg}+j\tan {\theta }_{pg}}}{-\cos {\theta }_{pg}{Z}_D+j{Z}_{pg}\sin {\theta }_{pg}{Z}_E}$$

(3)

where $Z_D=\frac{1}{jk\omega C_{pg}}\parallel \left(-j{Z}_{pg}\cot {\theta }_{pg}\right)$, $Z_E=\frac{1}{1+k\omega C_{pg}{Z}_{pg}\cot {\theta }_{pg}}$, and Z_pg and θ_pg are the characteristic impedance and electrical length of the transmission line TL_pg, respectively.

$$V_g=I_{gs}^{\prime }(\cos {\theta }_{pg}{Z}_D-j{Z}_{pg}\sin {\theta }_{pg}{Z}_E)-I_{gs}[R_g+R_{pg}+jk\omega L_{pg}+\frac{1}{jk\omega C_{pg}}\parallel (-j{Z}_{pg}\cot {\theta }_{pg})]$$

(4)

If the microwave input power injected into the rectifier is P_in, and the internal resistance of the power source is R_s, then the voltage and current of the RF power source are V_s and I_s.

Z-parameters of matching and coupling network Z_M can be calculated by

$$\left[\begin{array}{c}{V}_s\\ V_g\\ V_d\end{array}\right]=\left[Z_M\right]\left[\begin{array}{c}{I}_s\\ I_g\\ I_d\end{array}\right]$$

(5)

In the intrinsic part, I_gd and I_gs are ignored for the device works within safe operations. Therefore, from Kirchhoff’s current law, internal current I’_ds can be calculated as

$$I_{gs}^{\prime }=I_{gy}+I_{gc}$$

(6)

$$I_{ds}^{\prime }=I_{ds}-I_{gy}$$

(7)

I_gy, I_gc can be expressed as derivative of charge Q_gy and Q_gc that are calculated by V’_gs and V’_ds through a series of nonlinear equations; these equations can be found in the index of an EEHEMT model in ADS.

After the target waveform of the designed rectifier has been determined, according to the formula, V’_ds and V’_gs can be obtained, then Z_M can be calculated and obtained simultaneously, but Z-parameters are not popular for passive network synthesis, so the matching and coupling networks are carried out by converting the Z-parameters to their corresponding S-parameters and performing microwave synthesis.

3.2. Validation and Results

Based on the time-reversal duality, the inverse class F waveform of a classical PA was selected as target waveform to achieve high-efficiency rectifier design. The internal voltage V’_gs and V’_ds are designed to shape the target waveform according to the steps discussed in the previous section, and the input power and load of the rectifier were 10 W and 50 Ω, respectively. After optimization, the final values of V’_gs and V’_ds are listed in

Table 5. Voltages of gate and drain.

K=	1	2	3	4	5
V’gs, k Amplitude/Phase(rad)	2.4/−2.3	0.6/0.2	0.5/1.4	0.5/1.9	0.03/−2.96
V’ds, k Amplitude/Phase(rad)	32.3/0.9	17.1/1.8	4.6/2.8	0.04/2.67	0.2/1.8

. The calculated rectification waveform in a normalized period is shown in Figure 6. It can be found that the generated rectification waveforms are very close to the ideal target voltage and current waveforms of inverse class F, i.e., the voltage is half-sine, and the current is square.

Then, according to the target waveform characterized by the voltages list in Table 1, the matching and coupling network of Z_M can be calculated based on the formula. Converting Z_M to S_M for synthesizing the S_M by using practical microstrip lines, the circuit is built in Rogers 4350B with a thickness of 20 mils and dielectric constant of 3.66. The coupling network adopted a parallel microstrip line instead of a capacitor to avoid an inaccurate simulation model of capacitor in high frequency. The gap and microstrip line length can be optimized according to the performance of the rectifier. The circuit topology and dimension of the realized rectifier is shown in Figure 7.

The current and voltage waveforms shown in Figure 6 are calculated from the internal drain and gate voltages. Now, the rectifier is implemented as the circuit topology shown in Figure 7, and harmonic balance (HB) simulation was carried out in ADS. The results of comparing the waveforms achieved by HB simulation with the targets are shown in Figure 8. Very small waveform distance indicates that the proposed method is feasible.

The test setup of the rectifier is shown in Figure 9. The three ports of the rectifier are the RF power input, the gate negative voltage bias, and the DC output port, respectively. A 5.8 GHz microwave signal generated by the signal generator and amplified by the drive amplifier is fed into the RF input port of the rectifier through a coupler and an isolator. The coupling port of the coupler is connected to the power meter to measure the RF power fed into the rectifier, and the DC source provides −3.4 V bias for the gate. The DC output port is connected to the electronic load, which supplies 50 Ω load resistances, and the output voltage was read directly.

The measured results of the rectification efficiency, output power, and output voltage are shown in Figure 10.

The rectification efficiency of the rectifier is calculated as

$$E_{ff}=\frac{P_{out}}{P_{in}}=\frac{V_{out}^2/R_{load}}{P_{in}}$$

(8)

where P_out is the output DC power, V_out is the output voltage, R_load is the resistance value of the load, and P_in is the RF power fed into the rectifier.

The maximum rectification efficiency of 68% was obtained at 5.8 GHz with 12 W input power and 50 Ω load resistances.

The results reported in the literature are summarized in

Table 6. Comparison with other RF–DC rectifiers.

Reference	Frequency (GHz)	Input Power (W)	Efficiency (%)
2012 [9]	2.14	10	85
2015 [10]	5.36	1.3	66
2015 [11]	1.85	7.1	83.6
2016 [12]	0.91	10.15	85
2019 [13]	2.8	10	70.8
2019 [20]	5.78	13.2	44.8
2020 [14]	1.9	11.2	74.9
		6	80.7
2021 [15]	2.65–2.95	10	84.9
This work	5.8	12	68

. In terms of efficiency only, the rectification efficiency of 68% does not stand out among all results, but many other factors that affected the efficiency, such as frequency and input power, should be considered. It can be seen that the maximum rectification efficiency of 68% was pretty good at 5.8 GHz and 12 W input power.

4. Discussion

Based on the commercial transistor devices, a self-synchronous RF–DC rectifier at 5.8 GHz was designed, and it achieved an efficiency of 68% for a 12 W input power. The study found that the rectification efficiency is sensitive to the matching of the RF input port; a low reflection coefficient will reduce the reflection of input power so the power loss will also be reduced. In this work, a 50 Ω resistance needs to be satisfied in the rectifier operating region. However, the input port impedance of the rectifier will vary under different input power due to the transistor nonlinear characteristics and influence of intrinsic parameters. Therefore, input port impedance that can stay constant with a wide range of input power needs to be studied in further work.

The proposed rectifier can be utilized in the high input power rectification WPT applications, such as wireless charging of an electric bicycle at a parking spot, so it will be very convenient for users avoiding charging the battery actively. In addition, in a space WPT system, the transmitting microwave power can be increased to hundreds of watts, even the kilowatts range, because there will be no living creatures between the transmitting and receiving antennas. Therefore, the proposed rectifier is a possible candidate for future WPT applications in space.