Open AccessArticle

A Family of Hybrid Topologies for Efficient Constant-Current and Constant-Voltage Output of Magnetically Coupled Wireless Power Transfer Systems

Yingyao Zheng

Ronghuan Xie

Tao Lin

Xiaoying Chen

Xingkui Mao

^* and

Yiming Zhang

Fujian Engineering Research Center of High Energy Batteries and New Energy Equipment & Systems, College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108, China

Authors to whom correspondence should be addressed.

World Electr. Veh. J. 2024, 15(12), 578; https://doi.org/10.3390/wevj15120578

Submission received: 20 November 2024 / Revised: 12 December 2024 / Accepted: 13 December 2024 / Published: 15 December 2024

(This article belongs to the Special Issue Wireless Power Transfer Technology for Electric Vehicles)

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Browse Figures

Figure 1
Schematic diagram of wireless charging for EVs. "> Figure 2
Schematic diagram of the lithium battery charging process. "> Figure 3
Proposed reconfigurable topologies. (a) Half–Half bridge topology. (b) Full–Full bridge topology. (c) Full–Half bridge topology. "> Figure 4
Equivalent circuit. (a) CC mode. (b) CV mode. "> Figure 5
Half–Half bridge topology operating modes. (a) Switches Q1 and Q2 are open. (b) Switches Q1 and Q2 are closed. "> Figure 6
Full–Full bridge topology operating modes. (a) Switches Q1 and Q2 are open. (b) Switches Q1 and Q2 are closed. "> Figure 7
Full–Half bridge topology operating modes. (a) Switches Q1 and Q2 are open. (b) Switches Q1 and Q2 are closed. "> Figure 8
Photo of the experimental prototype. "> Figure 9
Calculated and experimental results for the Full–Full bridge topology. (a) DC charging current and voltage. (b) DC efficiency and output power. "> Figure 10
Calculated and experimental results for the Full–Half bridge topology. (a) DC charging current and voltage. (b) DC efficiency and output power. "> Figure 11
Calculated and experimental results for the Half–Half bridge topology. (a) DC charging current and voltage. (b) DC efficiency and output power. ">

Versions Notes

Abstract

In the field of wireless charging technology for electric vehicles, the charging process of lithium-ion batteries is typically divided into two stages: constant-current (CC) charging and constant-voltage (CV) charging. This two-stage charging method helps protect the battery and extend its service life. This paper proposes a family of circuit topology design schemes that achieve a smooth transition from CC to CV charging stages by using two relays. Additionally, the paper derives the corresponding system efficiency formulas and provides constraints on device parameters to ensure that the charging efficiency remains high during different charging stages. The proposed family of circuit topologies adopt unified device parameters and relay control logic, simplifying the design and operation process, and making these topologies more suitable for large-scale applications. To verify the practical performance of these topologies, the paper constructs experimental prototypes and conducts tests. The experimental results show that the proposed family of topologies can stably achieve CC and CV output, with smooth transitions between the two charging modes, and the efficiency can be maintained above 89% before and after mode switching over a wide load range. Furthermore, the mode switching points of the proposed family of topologies are multiples of two.

Keywords:

constant current; constant voltage; efficiency optimization; wireless power transfer

1. Introduction

Under the impetus of global environmental protection and sustainable development, the rapid growth of electric vehicles (EVs) has become a significant trend in the automotive industry. This shift not only reduces dependence on traditional fossil fuels but also has a positive impact on reducing greenhouse gas emissions and improving air quality. Concurrently, the proliferation of EVs has generated an urgent demand for efficient charging infrastructures. The integrity of the charging network plays a decisive role in enhancing the practicality of EVs and attracting users. The main advantages of the efficient charging system encompass increasing charging convenience, extending the range of EVs, and promoting the development of the EV industry, as well as fostering environmental sustainability from various aspects.

Wireless power transfer (WPT) technology, characterized by its convenience, safety, and contactless connection, has shown significant potential in the field of EV charging [1,2,3]. In recent years, wireless charging technology for EVs based on inductive power transfer (IPT) has attracted widespread attention from academia and industry [4,5]. This technology utilizes electromagnetic fields to transfer energy between primary and secondary coils, thereby achieving the wireless charging of EVs [6,7,8], as shown in Figure 1. Lithium-ion batteries are widely used in EVs due to their high power and energy density. The charging process of lithium-ion batteries typically includes two main stages: a constant-current (CC) charging phase and a constant-voltage (CV) charging phase. The CC charging phase refers to the battery being charged in a CC mode until the battery voltage reaches a preset voltage threshold. Subsequently, the CV charging phase begins, during which the battery voltage is maintained constant and the charging current gradually decreases until the charging is completed [9,10,11], as shown in Figure 2. To accommodate these two charging stages, the WPT system needs to be capable of outputting both a CC and a CV. This means that the WPT system must be able to adjust its output according to the battery’s charging status, ensuring that the battery can be charged safely and efficiently.

The current methods to achieve CC output and CV output can be divided into three main types. The first method is through the use of controllers, which can be divided into transmitter-side control [12,13] and receiver-side control [14]. If transmitter-side control is adopted, communication between the transmitter and receiver is required to implement closed-loop control by collecting the output voltage or current from the receiver. Some researchers use parameter identification methods to predict the values on the secondary side, thereby eliminating the communication process [13]. If receiver-side control is adopted, the communication process can be directly eliminated. The method that uses controllers requires a high precision for both sampling and control. The second method involves the specific design of the compensation network, using dual frequencies to achieve the CC mode and CV mode. However, under zero phase angle conditions, it is not possible to simultaneously achieve CC and CV outputs with basic topologies [15]. To address this problem and achieve both CC and CV outputs, LCC-LCC topologies or other forms of higher-order compensation networks are primarily employed [16], but they may introduce significant reactive power. The third method achieves the transition between CC mode and CV mode via topological switching. At a fixed resonant frequency, SS and LCC-LCC topologies provide CC output, while LCC-S and S-LCC deliver CV output [17,18]. Based on this characteristic, refs. [19,20] introduced multiple relays for CC and CV outputs to form a hybrid topology, but did not fully account for the changes in the system efficiency curve before and after switching between the CC and CV modes.

This paper proposes a family of hybrid topologies based on the principle of the third method, aiming to achieve the transition between CC and CV modes without complex control methods, using as few relay switches as possible while ensuring high efficiency before and after the transition. To ensure the ease of use of this family of topologies, the device parameters for each topology are consistent. The paper first provides an overview of the proposed family of topological structures. Secondly, it analyzes the CC mode and CV mode of each topology in sequence and provides the switching points for both modes. Then, a theoretical analysis of the efficiency of the proposed topological structures is conducted, and corresponding constraints are proposed. Finally, the feasibility of the proposed topological structures is verified by constructing experimental prototypes and comparing them with other CC and CV schemes.

2. Principles of Operation

The proposed series of reconfigurable topologies is shown in Figure 3. The three topologies shown in Figure 3 share a common compensation network. Switching tubes S₁, S₂, S₃, and S₄ form a full-bridge inverter, with L_P represents the primary coil and C_P is the resonant capacitor for L_P. L_S is the secondary coil, and L_F is the compensation inductor. Diodes D₁, D₂, D₃, and D₄ can be configured as a full-bridge rectifier, and through switching, they can operate as a half-bridge rectifier. R_P, R_S, and R_F are the parasitic resistances of the primary coil, secondary coil, and compensation inductor, respectively.

The primary side compensation networks of the three topologies are all configured in series, and a full-bridge inverter is employed, which is identical on the primary side. The distinctive features of the three topologies lie in the compensation networks and rectifier structures on the secondary side.

The commonality in the secondary compensation networks of these three topologies is that, when Q₁ and Q₂ both are open-circuited, capacitors C_S and C_F are connected in series to compensate for the secondary coil L_S, which corresponds to the CC output mode; when Q₁ and Q₂ are both closed, capacitors C_S and C_F resonate with the secondary coil L_S, and at the same time, the compensation inductor L_F resonates with the compensation capacitor C_F to compensate for the secondary side coil, which corresponds to the CV output mode. The differences lie in the operating modes of the rectifier bridge before and after the switching of Q₁ and Q₂.

Figure 3a is a Half–Half bridge topology, where the rectifier is a half-bridge structure before and after the switching of switches Q₁ and Q₂; Figure 3b is a Full–Full bridge topology, where the rectifier is a full-bridge structure before and after the switching of switches Q₁ and Q₂; Figure 3c is a Full–Half bridge topology, where the rectifier is a full-bridge structure before the switching of switches Q₁ and Q₂, and a half-bridge structure after the switching of switches Q₁ and Q₂. The differences in the rectifier bridge can result in different smooth switching points for the modes. Under these conditions, relay switches Q1 and Q2 have only two states: either both are open or both are closed simultaneously.

2.1. CC and CV Design

Figure 4 shows the AC-simplified equivalent circuit for the CC and CV outputs before and after the switching of Q₁ and Q₂.

In this scenario, the system is designed to resonate at the operating angular frequency ω. When Q₁ and Q₂ are open, the compensation network of the WPT system is an S-S structure, achieving a CC output; when Q₁ and Q₂ are closed, the compensation network of the WPT system is an S-LCC structure, achieving a CV output.

ω = \frac{1}{\sqrt{L_{P} C_{P}}} = \frac{1}{\sqrt{L_{S} \frac{C_{S} C_{F}}{C_{S} + C_{F}}}} = \frac{1}{\sqrt{L_{F} C_{F}}}

(1)

When calculating the output without considering the effects of inductance and coil parasitic resistance, the corresponding output values for the CC and CV modes are:

I_{CC} = - \frac{U_{IN}}{j ω M}

(2)

U_{CV} = \frac{L_{F} U_{IN}}{M}

(3)

The voltage conversion under the full-bridge inverter is given as:

U_{IN} = \frac{2 \sqrt{2}}{π} V_{IN}

(4)

When the rectifier operates in different modes, the system’s DC output voltage and DC output current will change, and the system’s equivalent AC impedance also varies. Figure 5 shows the working states of switches Q₁ and Q₂ before and after switching in the Half–Half bridge topology. When switches Q₁ and Q₂ are in the open state, diodes D₃ and D₄ are not operating, while diodes D₁ and D₂ form a half-bridge rectifier that operates. The system is in CC mode, and the constant DC output current I_HH is defined as:

I_{HH} = \frac{\sqrt{2}}{π} I_{CC}

(5)

Substituting Equations (2) and (4) into Equation (5) yields:

I_{HH} = \frac{4 V_{IN}}{π^{2} ω M}

(6)

When switches Q₁ and Q₂ are closed, diodes D₁ and D₂ do not operate, while diodes D₃ and D₄ form a half-bridge rectifier that operates. The system is in CV mode, and the constant DC output voltage V_HH is defined as:

V_{HH} = \frac{π}{\sqrt{2}} U_{CV}

(7)

Substituting Equations (3) and (4) into Equation (7) yields:

V_{HH} = \frac{2 L_{F} V_{IN}}{M}

(8)

Figure 6 illustrates the working modes of switches Q₁ and Q₂ before and after switching in the Full–Full bridge topology. When switches Q₁ and Q₂ are open, diodes D₅ and D₆ are not operating, while diodes D₁, D₂, D₃, and D₄ form a full-bridge rectifier that operates.

The system is in CC mode, and the constant DC output current I_FF is defined as:

I_{FF} = \frac{2 \sqrt{2}}{π} I_{CC}

(9)

Substituting Equations (2) and (4) into Equation (9) yields:

I_{FF} = \frac{8 V_{IN}}{π^{2} ω M}

(10)

When switches Q₁ and Q₂ are closed, diodes D₁ and D₂ do not operate, while diodes D₃, D₄, D₅, and D₆ form a full-bridge rectifier that operates. The system is in CV mode, and the constant DC output voltage V_FF is defined as:

V_{FF} = \frac{π}{2 \sqrt{2}} U_{CV}

(11)

Substituting Equations (3) and (4) into Equation (11) yields:

V_{FF} = \frac{L_{F} V_{IN}}{M}

(12)

Figure 7 illustrates the working modes of switches Q₁ and Q₂ before and after switching in the Full–Half bridge topology. When switches Q₁ and Q₂ are open, diodes D₁, D₂, D₃, and D₄ operate as a full-bridge rectifier. The system is in CC mode, and the constant DC output current I_FH is defined as:

I_{FH} = \frac{2 \sqrt{2}}{π} I_{CC}

(13)

Substituting Equations (2) and (4) into Equation (13) yields:

I_{FH} = \frac{8 V_{IN}}{π^{2} ω M}

(14)

When switches Q₁ and Q₂ are closed, diodes D₁ and D₂ form a half-bridge rectifier, and diodes D₃ and D₄ also form a half-bridge rectifier that operates in parallel with the half-bridge rectifier composed of D₁ and D₂. The system is in CV mode, and the constant DC output voltage V_FH is defined as:

V_{FH} = \frac{2 L_{F} V_{IN}}{M}

(15)

The rectifier in the three topologies is either a half-bridge rectifier or a full-bridge rectifier. We define R_LeqF and R_LeqH as the equivalent AC loads in full-bridge mode and half-bridge mode, respectively. The relationship between R_LeqF and R_L, as well as the relationship between R_LeqH and R_L, can be expressed as:

R_{LeqF} = \frac{8}{π^{2}} R_{L}

(16)

R_{LeqH} = \frac{2}{π^{2}} R_{L}

(17)

During the switching process of switches Q₁ and Q₂, it is easy to cause fluctuations in output voltage and output current, leading to system oscillations. To avoid oscillations in output voltage and current, it is necessary to operate the switches at the right moments. In the charging process of EVs, the load will gradually increase, and when the load changes to a suitable value, a transition from CC to CV mode is achieved. The AC-equivalent resistance value of this suitable value is:

R_{LeqQ} = \frac{U_{CV}}{I_{CC}} = ω L_{F}

(18)

The corresponding transition load switch points for the three topologies are:

R_{LQFF} = \frac{π^{2} ω L_{F}}{8}

(19)

R_{LQHH} = \frac{π^{2} ω L_{F}}{2}

(20)

R_{LQFH} = \frac{π^{2} ω L_{F}}{4}

(21)

In summary, it is known that, when the equivalent impedance is less than the load switch point, the system operates in CC mode; when the equivalent impedance is greater than the load switch point, the system operates in CV mode. From Equations (19)–(21), it can be seen that the switch points of the three proposed topologies are different, allowing them to be used in different EVs. The relationship between the switch points of the three topologies is:

R_{LQHH} = 2 R_{LQFH} = 4 R_{LQFF}

(22)

2.2. Efficiency Optimization Design

When implementing CC and CV output modes, the issue of efficiency optimization must also be considered. For each topology, there will be a peak in efficiency as the load changes. To avoid situations where efficiency may be low before and after topology switching, this paper proposes corresponding constraints on system parameters.

According to Kirchhoff’s voltage law, the S-S topology and S-LCC topology can be described as:

[\begin{matrix} U_{IN} \\ 0 \end{matrix}] = [\begin{matrix} R_{P} \\ - j ω M \end{matrix} \begin{matrix} - j ω M \\ R_{S} + R_{Leq} \end{matrix}] \cdot [\begin{array}{l} I_{P} \\ I_{S} \end{array}]

(23)

[\begin{matrix} U_{IN} \\ 0 \\ 0 \end{matrix}] = [\begin{matrix} R_{P} & - j ω M & 0 \\ - j ω M & R_{S} & - 1 / j ω C_{F} \\ 0 & - 1 / j ω C_{F} & R_{Leq} + R_{F} \end{matrix}] \cdot [\begin{matrix} I_{P} \\ I_{S} \\ I_{F} \end{matrix}]

(24)

The structural parameters of each compensation network are identical, and the efficiency of the S-S topology and the S-LCC topology can be expressed as:

η_{SS} = \frac{k I_{S} I_{S}^{*} R_{Leq}}{I_{P} I_{P}^{*} R_{P} + I_{S} I_{S}^{*} (R_{Leq} + R_{S})}

(25)

η_{SLCC} = \frac{k I_{F} I_{F}^{*} R_{Leq}}{I_{P} I_{P}^{*} R_{P} + I_{S} I_{S}^{*} R_{S} + I_{F} I_{F}^{*} R_{Leq} (R_{Leq} + R_{F})}

(26)

where k = 0.975 is the loss coefficient from AC efficiency to DC efficiency.

The values obtained in Equations (23) and (24) can be substituted into Equations (25) and (26), respectively.

η_{SS} = \frac{k ω^{2} R_{Leq} M^{2}}{(R_{S} + R_{Leq}) (ω^{2} M^{2} + R_{P} R_{S} + R_{P} R_{Leq})}

(27)

η_{SLCC} = \frac{k ω^{4} C_{F}^{2} R_{Leq} M^{2}}{(A ω^{2} R_{S} + 1) (A ω^{4} M^{2} + A ω^{2} R_{P} R_{S} + R_{P})}

(28)

where A = R_FC_F² + R_LeqC_F².

The load points corresponding to the maximum efficiency are R_LeqSSopt and R_LeqSLCCopt, respectively.

R_{LeqSSopt} = \frac{\sqrt{ω^{2} R_{P} R_{S} M^{2} + R_{P}^{2} R_{S}^{2}}}{R_{P}}

(29)

R_{LeqSLCCopt} = \sqrt{\frac{(B + 1) (ω^{4} C_{F}^{2} R_{F} M^{2} + B R_{P} + R_{P})}{ω^{4} C_{F}^{4} R_{S} (ω^{2} M^{2} + R_{P} R_{S})}}

(30)

where B = ω²C_F²R_SR_F.

To maintain a high efficiency before and after switching between CC and CV modes, the parameters must meet the condition:

R_{LeqSSopt} < R_{LeqQ} < R_{LeqSLCCopt}

(31)

3. Experimental Verification

With the constraints of the previous section satisfied, the corresponding experimental platform was built as shown in Figure 8. The parameters are shown in Table 1. The proposed method is primarily applicable to wireless charging for residential EVs, as in this scenario, the battery charging current is relatively low, and heat issues are not the main concern. However, to minimize the impact of thermal effects, the system can take the following measures during the experimental process: on one hand, heat sinks can be been installed on the inverter and rectifier bridge to reduce temperature; on the other hand, fans can be used to dissipate heat from the load and circuitry.

This paper conducted experimental tests on three topological structures and compared the experimental data with theoretical calculation results. The experimental results and theoretical predictions are intuitively presented in Figure 9, Figure 10 and Figure 11. Specifically, Figure 9a, Figure 10a, and Figure 11a, respectively, demonstrate the output characteristics of the three topological structures during the charging process, transitioning from the CC stage to the CV stage. These figures show the output values of CC and CV before and after the topology switching.

The experimental results indicate that the measured CC and CV output values are close to the theoretically calculated values, which validates the effectiveness of the theoretical model in predicting charging behavior. Although there are some minor discrepancies, these are likely due to inaccuracies in device parameters and minor deviations in the resonant state. However, these differences do not affect the overall charging effect, and a smooth transition from CC to CV was successfully achieved in the experiment.

Further analysis of Figure 9a, Figure 10a and Figure 11a reveals that the critical resistance load R_LQ values for the three topological structures are approximately 19.8 Ω, 39.7 Ω, and 79.5 Ω, respectively. These dispersed switch points indicate that these topological structures can accommodate the charging requirements of lithium-ion batteries with different load characteristics, providing flexibility for battery charging.

Additionally, Figure 9b, Figure 10b and Figure 11b display the DC efficiency and corresponding power consumption under different load conditions in both CC and CV modes. It is evident from these charts that after transitioning from the CC stage to the CV stage, the DC efficiency shifts from a declining trend to an increasing trend, indicating an optimization of charging efficiency. This enhancement in efficiency is crucial for increasing the battery charging speed and conserving energy.

The comparison with other work is shown in Table 2. The advantages of the work proposed in this paper are as follows:

(1) The proposed family of topologies achieve CC and CV through topology switching, eliminating the need for communication between the primary and secondary sides, as well as the corresponding closed-loop control process, which reduces the complexity of the system.

(2) The proposed family of topologies operate at a single working frequency, optimizing efficiency while achieving CC and CV, resulting in a wider range of high efficiency before and after switching, and thus a higher overall system efficiency.

(3) The proposed family of topologies share a set of parameters, which can be selected based on actual application scenarios, making them more operable.

4. Conclusions

This paper has addressed wireless charging for EVs by proposing a family of circuit topologies that have achieved smooth transitions between CC mode and CV mode through the use of two relay switches, thereby facilitating the charging of lithium batteries in EVs. The paper has calculated and derived the switching points for these topologies, which share the same device parameters and similar overall configurations. The distribution of smooth switching points has been determined to be a multiple of two, enabling the selection of appropriate topologies for different battery loads with varying characteristics. Additionally, the paper has proposed constraints on the device parameters of the proposed topologies to maintain a high charging efficiency before and after mode switching. In the experimental prototypes constructed in this paper, as the load varied from 5 Ω to 110 Ω, the Full–Full bridge topology had a smooth switching point at 19.8 Ω, the Full-Half bridge topology at 39.7 Ω, and the Half–Half bridge topology at 79.5 Ω. The output values of the three proposed topologies in both CC and CV modes were close to theoretical values and remained stable. The efficiency of the three proposed topologies was maintained above 89% over a wide load range before and after the transition between CC and CV modes.

Author Contributions

Study conception and design: Y.Z. (Yiming Zhang) and Y.Z. (Yingyao Zheng); data collection: Y.Z. (Yingyao Zheng); analysis and interpretation of results: Y.Z. (Yiming Zhang) and Y.Z. (Yingyao Zheng); draft manuscript preparation: Y.Z. (Yingyao Zheng), R.X., T.L., X.C., and X.M. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported in part by the National Natural Science Foundation of China (52407197, 52107183) and in part by the Natural Science Foundation of Fujian Province (2022J06011).

Data Availability Statement

The data presented in this study are available upon request from the corresponding author. Due to the privacy of the data, the data are not shared here.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Schematic diagram of wireless charging for EVs.

Figure 2. Schematic diagram of the lithium battery charging process.

Figure 3. Proposed reconfigurable topologies. (a) Half–Half bridge topology. (b) Full–Full bridge topology. (c) Full–Half bridge topology.

Figure 4. Equivalent circuit. (a) CC mode. (b) CV mode.

Figure 5. Half–Half bridge topology operating modes. (a) Switches Q₁ and Q₂ are open. (b) Switches Q₁ and Q₂ are closed.

Figure 6. Full–Full bridge topology operating modes. (a) Switches Q₁ and Q₂ are open. (b) Switches Q₁ and Q₂ are closed.

Figure 7. Full–Half bridge topology operating modes. (a) Switches Q₁ and Q₂ are open. (b) Switches Q₁ and Q₂ are closed.

Figure 8. Photo of the experimental prototype.

Figure 9. Calculated and experimental results for the Full–Full bridge topology. (a) DC charging current and voltage. (b) DC efficiency and output power.

Figure 10. Calculated and experimental results for the Full–Half bridge topology. (a) DC charging current and voltage. (b) DC efficiency and output power.

Figure 11. Calculated and experimental results for the Half–Half bridge topology. (a) DC charging current and voltage. (b) DC efficiency and output power.

Table 1. The proposed system’s experimental parameters.

Parameter	Value	Parameter	Value	Parameter	Value
f (kHz)	85.00	M (μH)	20.45	R_L (Ω)	5–110
L_P (μH)	78.19	L_S (μH)	77.33	L_F (μH)	30.15
R_P (mΩ)	208.8	R_S (mΩ)	206.5	R_F (mΩ)	161.0
C_P (nF)	44.96	C_S (nF)	75.40	C_F (nF)	115.40

Table 2. Comparison with other CC/CV methods.

Comparisons	CC and CV Method	Peak Efficiency	Power Rating	Communication Requirements	Efficiency Optimization	Degree of Complexity
[12]	SPWM control strategy	92.50%	9 W	Yes	N/A	High
[13]	Load estimation and double closed-loop control strategy	91.16%	1.95 kW	No	N/A	High
[21]	LCCC/S compensation and dual resonant frequencies	93.98%	144 W	Yes	N/A	High
[22]	Switching transitions and PFC	90.06%	370 W	No	No	Mid
[20]	Hybrid topologies and switching transitions	91.80%	1 kW	No	No	Mid
This paper	Switching transitions and efficiency optimization	94.32%	1.78 kW	No	Yes	Low

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Zheng, Y.; Xie, R.; Lin, T.; Chen, X.; Mao, X.; Zhang, Y. A Family of Hybrid Topologies for Efficient Constant-Current and Constant-Voltage Output of Magnetically Coupled Wireless Power Transfer Systems. World Electr. Veh. J. 2024, 15, 578. https://doi.org/10.3390/wevj15120578

AMA Style

Zheng Y, Xie R, Lin T, Chen X, Mao X, Zhang Y. A Family of Hybrid Topologies for Efficient Constant-Current and Constant-Voltage Output of Magnetically Coupled Wireless Power Transfer Systems. World Electric Vehicle Journal. 2024; 15(12):578. https://doi.org/10.3390/wevj15120578

Chicago/Turabian Style

Zheng, Yingyao, Ronghuan Xie, Tao Lin, Xiaoying Chen, Xingkui Mao, and Yiming Zhang. 2024. "A Family of Hybrid Topologies for Efficient Constant-Current and Constant-Voltage Output of Magnetically Coupled Wireless Power Transfer Systems" World Electric Vehicle Journal 15, no. 12: 578. https://doi.org/10.3390/wevj15120578

APA Style

Zheng, Y., Xie, R., Lin, T., Chen, X., Mao, X., & Zhang, Y. (2024). A Family of Hybrid Topologies for Efficient Constant-Current and Constant-Voltage Output of Magnetically Coupled Wireless Power Transfer Systems. World Electric Vehicle Journal, 15(12), 578. https://doi.org/10.3390/wevj15120578

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