Research on Self-Excited Inverter Rectification Method of Receiver in Wireless Power Transfer System

Abstract

To decrease the complexity and increase the efficiency of wireless power transfer (WPT) systems, this paper proposes a novel self-excited invert rectification method for the design of the invert rectifier of the receiver (Rx). The self-excited invert rectifier can perform the self-driving and soft-switching of the MOSFETs as well as the frequency-tracking function without a microcontroller. This allows us to greatly simplify the structure of the invert rectifier and increase the transfer efficiency (TE) of the WPT system. Firstly, a self-excited invert rectifier circuit is designed, and a self-excited invert rectification method is studied. Additionally, the power loss of the self-excited invert rectifier is analyzed. Finally, the self-excited invert rectifier of the WPT experimental system is designed. The self-excited invert rectification method is then verified. The key component parameters of the self-excited invert rectifier are provided and optimized. The TE of the WPT system that includes the self-excited invert rectifier is improved by more than 5% without a microcontroller. The self-excited invert rectifier of the Rx provides a practical solution for decreasing the complexity and increasing the TE of the WPT system.

1. Introduction

Tesla conducted a WPT experiment in the early 20th century [1]. WPT technology then made great progress [2,3]. In recent years, it has been widely used in many fields, including car mobile phones, electric vehicles, and mobile robots [4,5,6].

A WPT system typically contains AC power and a resonant system containing a transmitter (Tx), receiver (Rx), and rectifier [7]. The design of the rectifier is usually based on the full-bridge rectifier. The system has high efficiency. However, its structure is complex [8,9,10]. Ref. [11] introduced right-half-plane zeros into small-signal transfer functions to resolve the current source nature of the series–series compensation. They proposed adopting a different rectifier configuration for the system. A novel single-phase bidirectional ac–dc WPT topology is proposed in [12]. It allows the drawbacks of matrix-converter-based topologies to be overcome while retaining the advantages of single-stage topologies. A bidirectional WPT system, which can function in both forward and reverse modes, was proposed in [13]. Ref. [14] proposed the LCC-S type compensation topology because magnetically coupled WPT systems face a wide input voltage range and variable load in some specific application scenarios, resulting in variable output voltage. Ref. [7] proposed a novel full-bridge step density modulation for WPT systems based on the step density averaging principle, which can achieve full-range ZVS operation. Ref. [15] proposed a new six-switch topology based on the full-bridge converter, which achieves the self-adaptation of a dynamic change in system parameters. According to the above references, full-bridge inverters are used to convert DC to AC with a microcontroller on the Tx side. Additionally, four rectifier diodes are usually used for full-bridge rectification on the Rx side.

However, in the WPT research community, self-excited inverters are usually used on the Tx side. Ref. [16] used a self-excited inverter to construct the inversion stage of the WPT system without a PWM generator and a microcontroller, which greatly simplified the hardware structure. In addition, soft-switching (SS) and automatic frequency tracking (FT) can be performed without requiring additional control strategies, which also reduces the complexity. Ref. [17] proposed a self-excited inverter to obtain high-frequency AC power, which reduced the complexity of their WPT system. Additionally, the output voltage of the parallel–series WPT system with a self-excited inverter is resistant to load changes. An improved self-excited resonant circuit was also provided using a fully controlled low-power switch instead of a diode; the SS performance was improved, the temperature of the switch tube was reduced by about 7 °C, and the TE was also improved by about 4% [18]. The principle of a self-excited push–pull oscillation circuit was analyzed [19]. In a WPT system with a self-excited converter, the influence mechanism of magnetic shielding on the TE was analyzed; the optimal shielding distance was obtained [20]. These references indicate that self-excited inverters have a lot of excellent characteristics, such as SS, FT, the constant voltage output, etc. Thus, a method of the invert rectifier of the Rx is proposed by using the method and characteristics of the self-excited inverter on the Tx side, which is used to convert AC to DC without a microcontroller.

In view of the aforementioned studies, this paper proposes a novel self-excited invert rectification method to design the invert rectifier of the Rx, in order to reduce the complexity and increase the transfer efficiency (TE) of the WPT system. The self-excited invert rectifier can perform the self-driving (SD) and SS of the MOSFETs as well as the FT function without a microcontroller. This greatly simplifies the structure of the invert rectifier, and increases the TE of the WPT system. Firstly, a self-excited invert rectifier circuit is designed, and a self-excited invert rectification method is studied. Additionally, the power loss of the self-excited invert rectifier is analyzed. Finally, the self-excited invert rectifier of the WPT experimental system is then designed. The self-excited invert rectification method is then verified. The key component parameters of the self-excited invert rectifier are provided and optimized. The TE of the WPT system, which includes the self-excited invert rectifier, is improved by more than 5% without requiring a microcontroller. The self-excited invert rectifier of the Rx provides a practical solution for reducing the complexity and increasing the TE of the WPT system. In contrast to the existing works, the contributions of this article are as follows:

(1)

A self-excited invert rectification method is proposed and applied to design the invert rectifier of the Rx.

(2)

The key component parameters of the self-excited invert rectifier are provided and optimized to improve the TE.

The remainder of this paper is organized as follows. Section 2 describes the self-excited invert rectifier circuit, and provides a brief analysis of the working principle of the self-excited invert rectifier. Section 3 gives the analysis of the power loss of the self-excited invert rectifier. Section 4 presents the experiment results. Finally, conclusions are drawn in Section 5.

2. Design of the Self-Excited Invert Rectifier Circuit

The self-excited invert rectifier consists of a circuit with a symmetric structure, which can perform the SD and SS of the MOSFETs as well as the FT function without a microcontroller and without requiring additional control strategies.

A diagram of the WPT system with the self-excited invert rectifier, which includes a Tx and an Rx, is shown in Figure 1. Q₁–Q₄ are the MOSFETs used as switching transistors in a full-bridge inverter, V_dc is the input power, L₁ and L₂ are the coils, C₁ and C₂ are the capacitors, M is the mutual inductance of L₁ and L₂, D₁ and D₂ are the fly-wheeling diodes, R₁–R₄ are the voltage divide resistors, D₃ and D₄ are the rectifier diodes, D₅ and D₆ are the Zener diodes which provide a stable voltage to protect the Q₅ and Q₆ MOSFETs used as switching transistors in the self-excited invert rectifier, C₃ is the filter capacitor, R_L is the load resistor, u_a, u_b, u_c, and u_d are the voltages of points a, b, c, and d, respectively, and u_ab is the voltage between points a and b. The parameters of the circuit of the WPT system are shown in Table 1.

Figure 1. WPT system with self-excited invert rectifier.

Table 1. Parameters of the WPT system circuit with the self-excited invert rectifier.

Parameter	Value
Vdc	36 V
L1 and L2	15.0 μH
C1 and C2	294.6 nF
Q1–Q6	AGM035N10A is an N-channel MOSFET (drain-source on-state resistor: 3 mΩ)
R1 and R2	1 kΩ
R3 and R4	10 kΩ
D1 and D2	1N4148
D3 and D4	SB10100L (Vf: 670 mV@10 A)
D5 and D6	ZMM15
C2	100 V, 100 μF

According to Figure 1 and Table 1, the self-excited invert rectifier part only includes D₁–D₆, R₁–R₄, Q₅, and Q₆. The self-excited invert rectifier with a few components can perform the self-driving and soft-switching of the MOSFETs as well as the frequency-tracking function without a microcontroller. This allows us to greatly simplify the structure of the invert rectifier and increase the TE of the WPT system.

In the Rx, the self-excited invert rectifier consists of a circuit with a symmetric structure. The wireless power is transferred from the Tx to the Rx through magnetic coupling resonance. Under high-frequency sine voltage stimulation on the Rx side, because of the existence of R₁–R₄, Q₅ and Q₆ cannot simultaneously be in a blocked state nor in a conducting state. This indicates that at any moment, one MOSFET is on and the other one is off. A brief analysis of the working principle of the self-excited invert rectifier is then provided. According to this working principle, the self-excited invert rectifier is divided into four working modes. The obtained results are shown in Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6. Assuming that at the beginning, Q₅ is turned on while Q₆ is blocked, the four working modes with u_ab = −u_ba, where Uth is the gate threshold voltage, are given as follows:

Figure 2. Working mode 1 of the self-excited invert rectifier: Current flow is power and control loops; and 0 V is the same voltage level.

Figure 3. Working mode 2 of the self-excited invert rectifier: Current flow of red dotted lines is the first process section; and Current flow of green dotted lines is the second process section.

Figure 4. Working mode 3 of the self-excited invert rectifier: Current flow is power and control loops; and 0 V is the same voltage level.

Figure 5. Working mode 4 of the self-excited invert rectifier: Current flow of red dotted lines is the first process section; and Current flow of green dotted lines is the second process section.

Figure 6. Steady−state working waveform of the switching tubes in the self-excited invert rectifier.

(1) Mode 1: Based on Figure 2 and Figure 6, t₂ and t₃ are the on time of Q₅ (i.e., Q_5on time) and t₁–t₄ are the off time of Q₆ (i.e., Q_6off time). In other words, when u_ab increases from u_c = Uth to the peak and then decreases to u_c = Uth, Q₅ is turned on while Q₆ is blocked. The path of the current has two loops: power and control loops, (the red dotted lines in Figure 2). The power loop is from C₂, point a, D₄, and R_L to point o, while the control loop is from C₂, point a, R₁, point c, and R₃ to point o. Note that point o, Q₅, point b, and the bottom of L₂ have the same voltage level (0 V) (green dotted lines in Figure 2). In addition, R₁ and R₃ construct a voltage divider (VD) to provide bias voltage (BV) for Q₅. Similarly, R₂ and R₄ construct a VD to provide BV for Q₆. In this mode, Q₅ is turned on because u_ab > u_c > Uth. On the contrary, Q₆ is blocked because u_d = u_b = 0 v. Thus, the invert rectifier circuit performs positive half-cycle rectification.

(2) Mode 2: According to Figure 3 and Figure 6, when the high-frequency sine voltage u_ab decreases from u_c = Uth to zero, Q₅ enters the amplification region from the conductive one at t₃ and t₄. Q₅ is then blocked at time point t₄ and time regions t₄ and t₇. In addition, when Q₅ enters the amplification region and is blocked, the power is quickly released by a circuit loop of R₂ and D₂. This is the first process section (red dotted lines in Figure 3). On the other hand, the voltage is reversed at the next moment. When u_ba = −u_ab increases from zero to u_d = Uth, Q₆ enters the amplification region at the time regions t₄ and t₅. Q₆ then turns on at the time point t₅ and the time regions t₅ and t₆ when u_ba increases and u_d > Uth. In addition, R₂ and R₄ construct a VD to provide BV for Q₆, which remains turned on. This is the second process section (green dotted lines in Figure 3). Therefore, the invert rectifier circuit performs rapid switching of states.

(3) Mode 3: According to Figure 4 and Figure 6, t₄–t₇ are the off time of Q₅ (i.e., Q_5off time), and t₅ and t₆ are the on time of Q₆ (i.e., Q_6on time). In other words, when u_ba increases from u_d = Uth to the peak and then decreases to u_d = Uth, Q₆ turns on while Q₅ is blocked. The path of the current has two current loops: power and control loops (red dotted lines in Figure 4). The power loop is from L₂, point b, D₃, and R_L to point o, while the control loop is from L₂, point b, R₂, point d, and R₄ to point o. Note that point o, Q₆, point a, and the right side of C₂ have the same voltage (0 V) (green dotted lines in Figure 4). Moreover, R₁ and R₃ construct a VD to provide BV for Q₅. Similarly, R₂ and R₄ construct a VD to provide BV for Q₆. In this mode, Q₆ is turned on because u_ba > u_d > Uth. On the contrary, Q₅ is blocked because u_c = u_a = 0 v. Therefore, the invert rectifier circuit performs negative half-cycle rectification.

(4) Mode 4: According to Figure 5 and Figure 6, when the frequency sine voltage u_ba decreases from u_d = Uth to zero, Q₆ enters the amplification region from the conductive region in the time regions t₆ and t₇. It is then blocked at the time point t₇ and the time regions t₇ and t₁₀. In addition, when Q₆ enters the amplification region and is blocked, the power is quickly released by a circuit loop of R₁ and D₁. This is the first process section (red dotted lines in Figure 5). On the other hand, the voltage is reversed at the next moment. When u_ab increases from zero to u_c = Uth, Q₅ enters the amplification region in the time regions t₇ and t₈. It then turns on at the time point t₈ and the time regions t₈ and t₉ when u_ab increases and u_c > Uth. In addition, R₁ and R₃ construct a VD to provide BV for Q₅, which remains turned on. This is the second process section (green dotted lines in Figure 5). Therefore, the invert rectifier circuit also performs rapid switching of states.

It can be deduced from the aforementioned analysis that L₂ and C₂ comprise a series resonant tank, whose resonant frequency determines that of the sine voltage on the Rx side. Furthermore, the switching frequency of Q₅ and Q₆ and the rectification frequency of the rectifier diode are determined by the frequency of the sine voltage stimulation on the Rx side. More precisely, the function of automatic FT is performed, where R₁–R₄ play a crucial role. In addition, due to R₁–R₄, the self-excited invert rectifier performs the SD of MOSFETs during the inversion process without the need for the signal detector and microcontroller that are used in traditional rectifiers. This significantly reduces the complexity of the control and structure as well as the cost, and increases the TE of the WPT system. Furthermore, R₁ and R₃ construct a VD to provide BV for Q₅. Similarly, R₂ and R₄ construct a VD to provide BV for Q₆. Moreover, R₁ and D₁ construct a circuit loop and quickly release power when Q₆ is blocked. Note that R₂ and D₂ have the same function. The two circuit loops provide a quick energy release channel, which accelerates the mode switching and reduces the power loss of Q₅ and Q₆. In addition, the product of Q₅ and Q₆ is AGM035N10A, which obtains 3 mΩ from the drain-source on-state resistor. It can reduce the power loss during the functioning of Q₅ and Q₆. Finally, D₅ and D₆ perform voltage stabilization to protect Q₅ and Q₆.

3. Analysis of the Power Loss of the Self-Excited Invert Rectifier

The circuits of the self-excited invert rectifier can be equivalent according to Figure 7. The circuit model has two resonant circuits, linked magnetically by mutual inductance M. U_S is the input power of the Tx; R_S is the sum of the loss resistor and radiation resistor of the Tx; R_k is the sum of the loss resistor and radiation resistor of the Rx, which mainly includes the working resistors of Q₅, Q₆, D₃, and D₄; L₁ and L₂ are the inductors; C₁ and C₂ are the capacitors; R_L is the load resistor; U_L is the load voltage; and İ₁ and İ₂ are the currents of the Tx and Rx loops, respectively.

Figure 7. Equivalent circuit of the WPT system with self-excited invert rectifier.

According to Figure 7, Kirchhoff’s voltage law, and angular frequency ω, the WPT system with the self-excited invert rectifier can be expressed as

$$\left\{\begin{array}{l}{U}_S=Z_1{\stackrel{.}{I}}_1-j\omega M{\stackrel{.}{I}}_2\\ 0=Z_2{\stackrel{.}{I}}_2-j\omega M{\stackrel{.}{I}}_1\end{array}\right.$$

(1)

The self-impedance values Z₁ and Z₂ are given by

$$\left\{\begin{array}{l}{Z}_1=R_S+j\omega L_1+{\displaystyle \frac{1}{j\omega C_1}}\\ Z_2=R_k+R_L+j\omega L_2+{\displaystyle \frac{1}{j\omega C_2}}\end{array}\right.$$

(2)

The output power (OP) P_out can be given as [6]

$$P_{out}=|{\stackrel{.}{I}}_2{|}^2 R_L={\displaystyle \frac{\sigma \beta {\tau }^2(1+{\xi }^2)}{{\sigma }^2{(1+{\xi }^2+{\tau }^2)}^2+{\xi }^2{(1+{\xi }^2-\sigma {\tau }^2)}^2}}{\displaystyle \frac{{U_S}^2}{R}}$$

(3)

where σ = R_S/(R_k + R_L) and β = R_L/(R_k + R_L) are the resistor ratios, R = R_k + R_L is the resistor of the Rx side, τ = ωM/(R_S(R_k + R_L))^0.5 is the impedance-coupled factor, and ξ is the frequency-detuning factor.

The TE η can be written as [6]

$$\eta ={\displaystyle \frac{P_{out}}{P_{in}}}={\displaystyle \frac{|{\stackrel{.}{I}}_2{|}^2{R}_L}{|{\stackrel{.}{I}}_1{|}^2{R}_s+|{\stackrel{.}{I}}_2{|}^2(R_k+R_L)}}={\displaystyle \frac{\beta {\tau }^2}{1+{\xi }^2+{\tau }^2}}$$

(4)

According to Equation (3), σ = R_S/(R_k + R_L), β = R_L/(R_k + R_L), and R = R_k + R_L; when R_S and R_k decrease, the OP P_out increases. According to Equation (4), β = R_L/(R_k + R_L), and τ = ωM/(R_S(R_k + R_L))^0.5; when R_S and R_k decrease, and ξ = 0, the TE η increases.

In summary, when R_S and R_k decrease, the OP and TE improve. On the Rx side, the self-excited invert rectifier could reduce the value of R_k by decreasing the power losses of the MOSFETs (Q₅ and Q₆) and the forward voltage losses of the rectifier diodes (D₃ and D₄).

4. Experimental Results

Figure 8 shows an experimental block diagram of the WPT system that includes a self-excited invert rectifier, where R_S is the sum of the loss and radiation resistors of the Tx; R_k is the sum of the loss and radiation resistors of the Rx, which mainly includes the working resistors of Q₅, Q₆, D₃ and D₄; C₃ is the filter capacitor; U_L is the DC voltage of the load; and R_L is the load resistor. Table 2 presents the parameters of the self-excited invert rectifier experimental equipment.

Figure 8. Block diagram of the WPT system that includes a self-excited invert rectifier.

Table 2. Parameters of the self-excited invert rectifier experimental equipment.

Parameter	Tx	Rx
Natural frequency f0/kHz	81.3	81.3
Inductance L/μH	15.0	15.0
Capacitor C/nF	294.6	294.6
Inside diameter of the coil φ/mm	150	150
Outside diameter of the coil Φ/mm	180	180
Layers of the coil	1	1
Number of turns n	5	5
Coupling distance/mm	0–40
TE	<91.4%
Load RL/Ω	Lamp 20
Input voltage/V Vdc	36
Input power/W	200

Figure 9 shows a self-excited invert rectifier experimental equipment able to perform the SD and SS of the MOSFETs. It has a wireless power transfer capacity of 200 W. It mainly includes a TH2827A bridge analyzer (Tonghui, Changzhou, China), a TMi120S infrared thermal imaging instrument (UNI-T, Dongguan, China), a P6022 current probe (Tektronix, Beaverton, OR, USA), and a DS1054 digital oscilloscope (RIGOL, Suzhou, China).

Figure 9. A self-excited invert rectifier experimental equipment able to perform the SD and SS of the MOSFETs.

(1)

Experimental verification of the self-excited invert rectification method

Based on the aforementioned theory results, L₂ and C₂ comprise a series resonant tank, whose frequency determines that of the sine voltage at the Rx side. Furthermore, the switching frequency of Q₅ and Q₆ and the rectification frequency of the rectifier diode are determined by the frequency of the sine voltage stimulation on the Rx side. In Figure 10 and Figure 11, the working frequency of the self-excited invert rectifier is 75.7 kHz. Since the working frequency of the Tx is 75.7 kHz, the self-excited invert rectifier performs the FT. It can then be deduced that the self-excited invert rectifier can perform the SD and SS of the MOSFETs without a microcontroller, which greatly simplifies the structure of the invert rectifier.

Figure 10. Gate drive waveform (gate−source voltage) of the Q₅ and Q₆ switching tubes.

Figure 11. Working waveform (drain−source voltage) of the Q₅ and Q₆ switching tubes.

In Figure 10, the time delay of the gate drive waveform between the Q₅ and Q₆ switching tubes is 220 ns. In Figure 11, the time delay of the working waveform between Q₅ and Q₆ is also 220 ns. This indicates that they are alternately turned on, which ensures the safe and reliable rectification of the self-excited invert rectifier. More precisely, the function of the zero-voltage switch (ZVS) is achieved in the self-excited invert rectifier using D₁ and D₂, R₁ and R₃, and R₂ and R₄. Thus, the invert rectifier circuit performs rapid and reliable switching between Q₅ and Q₆.

In summary, the experimental results are consistent with those of the theoretical analysis of Section 2. They show that the self-excited inverter rectification method is effective.

(2)

Experiment for reducing the power loss of the self-excited invert rectifier

According to the aforementioned theory results, R₁–R₄ resistors, Q₅ and Q₆, and D₃ and D₄ are affected by the power loss of the self-excited invert rectifier. This also affects the TE. Thus, key component parameters of the self-excited invert rectifier are required to increase the performance of the self-excited invert rectifier. The key component parameters are shown in Table 3.

Table 3. Key component parameters of the self-excited invert rectifier.

Parameters	Values
R1–R4	R3 = R4 = 10 kΩ, R1 = R2 = 560 Ω, 1 kΩ, 2 kΩ
Q5 and Q6	AGM035N10A (drain-source on-state resistor: 3 mΩ, 112 A, 100 V), BSC0702LS (2.3 mΩ, 100 A, 60 V), APG011N04G (0.9 mΩ, 200 A, 40 V)
D3 and D4	Silicon carbide Schottky diode: FFSM0865B (Vf = 1.39 V@8 A, 650 V). Schottky barrier rectifiers: SB10100L (Vf: 670 mV@10 A, 100 V), SB1060L (Vf: 550 mV@10 A, 60 V), ST10100L (Vf: 590 mV@10 A, 100 V)

R₁ with R₃ and R₂ with R₄ first construct two VDs to provide BVs for Q₅ and Q₆, respectively. R₁ and R₂ should have a suitable value, which allows us to obtain a suitable current to drive Q₅ and Q₆ (e.g., 1 kΩ in Table 3). Thus, high R₁ and R₂ values do not have sufficient current to drive Q₅ and Q₆ (e.g., 2 kΩ in Table 3). On the other hand, lower R₁ and R₂ values lead to circuit damage due to the excessive carried current (e.g., 560 Ω in Table 3).

In addition, R₁ and D₁ construct a circuit loop and quickly release power when Q₆ is blocked. Note that R₂ and D₂ have the same function. The two circuit loops provide a quick energy release channel, which accelerates the mode switching and reduces the power loss of Q₅ and Q₆.

Moreover, a smaller drain-source on-state resistor of Q₅ and Q₆ results in a smaller power loss. In Table 3, the drain-source on-state resistor of APG011N04G is 0.9 mΩ, and its power loss is smaller than that of other components (e.g., AGM035N10A, BSC0702LS). However, the drain-source voltage should also be taken into consideration to be adapted to the WPT system. In this study, AGM035N10A was used to design the WPT experimental equipment.

Finally, a forward voltage of D₃ and D₄ results in a smaller power loss. In Table 3, the forward voltage of SB1060L is 550 mV, and its power loss is smaller than that of other components (e.g., FFSM0865B, SB10100L, and ST10100L). However, the forward voltage of FFSM0865B is 1.39 V, which is higher than that of other components. FFSM0865B was selected to design the WPT experimental equipment. When it functions, the temperature rapidly increases and the WPT experimental system is damaged. Additionally, the reverse voltage should also be taken into consideration in a WPT system. In this study, ST10100L was finally chosen due to its small forward voltage (590 mV) and higher reverse voltage (100 V).

In Figure 12a, D₃ and Q₅ are on the front of the circuit board. However, D₄ and Q₆ are on the back. Because these two sets of components are symmetrically arranged on the front and back of the circuit board, they should have the same thermal image. Figure 12b shows the thermal image of the front of the circuit board. Several conducted measurements show that the temperatures of D₃ and Q₅ are lower than 34.3 °C. This indicates that the self-excited invert rectifier has higher performance when adopting the aforementioned key component parameters.

Figure 12. (a) Circuit of the Rx and (b) temperature image of the self-excited invert rectifier.

In addition, the impact of temperature variation and load resistance needs to be considered in a WPT system. The power loss of the self-excited invert rectifier is low when the system works at an industrial-grade temperature. Moreover, appropriate load resistance is beneficial for improving TE.

In summary, the experimental results for reducing the power loss are consistent with the theoretical analysis of Section 3. It shows that the measures for reducing the power loss of the self-excited invert rectifier are effective.

(3)

Experiment for increasing the TE of the self-excited invert rectifier

According to the aforementioned optimizing results of the key component parameters, in Figure 13 and Figure 14, the OP P₁ and TE η₁ are obtained using the full-bridge inverter rectifier of the Rx. On the other hand, the OP P₂ and TE η₂ are obtained using the self-excited invert rectifier of the Rx. Due to the selection of suitable key component parameters for the self-excited invert rectifier, the OP of the WPT system with the self-excited invert rectifier is improved by more than 10 W. Similarly, the TE with the self-excited invert rectifier is increased by more than 5%. More precisely, it reaches 86.2%, while it is only 91.4% in the case of only optimizing the Rx side.

Figure 13. OP of the system as a function of the distance.

Figure 14. TE of the system as a function of the distance.

According to the aforementioned results of the key component parameters, the OP P₂ and TE η₂ are obtained at different frequencies, which are shown in Figure 15 and Figure 16. It can be seen that, for a transfer distance of 3 cm, the high and flat OP P₂ peaks are reached around 75.7 kHz. For a transfer distance of 1 cm, the peaks of the OP P₂ occur at 61 kHz and 91 kHz, respectively. Additionally, for a transfer distance of 2 cm, the peaks of the OP P₂ occur at 66 kHz and 86 kHz, respectively. Thus, the frequency splitting of the OP occurs at transfer distances of 1 cm and 2 cm [3,21]. However, the high and flat TE η₂ peaks are reached at around 75.7 kHz. The value of the TE η₂ is increased as the transfer distance decreases. According to the aforementioned analysis results, it can be concluded that the optimization of TE is needed to consider the impact of frequency splitting. Thus, in the self-excited invert rectifier experimental equipment, the working frequency of the Tx side is adaptively changed to obtain the maximum value of the TE when the transfer distance changes.

Figure 15. OP P₂ of the system as a function of the frequency.

Figure 16. TE η₂ of the system as a function of the frequency.

In summary, the experimental results are consistent with those of the theoretical analysis. They show that the self-excited inverter rectification method is effective. In addition, the self-excited invert rectifier can perform the SD and SS of the MOSFETs as well as the FT function without a microcontroller. This method provides a practical solution for reducing the complexity of the rectifier. It can be clearly seen that the TE is increased using the self-excited invert rectifier and the optimized key component parameters.

5. Conclusions

In this paper, a novel self-excited invert rectification method was proposed to design the invert rectifier of the Rx. This self-excited invert rectifier can perform the SD and SS of the MOSFETs as well as the FT function without a microcontroller. In addition, the TE of the WPT system with the self-excited invert rectifier and optimized key component parameters is increased by more than 5%. Finally, the self-excited invert rectifier of the Rx provides a practical solution for reducing the complexity of the WPT system.