A Switched Capacitor-Based Single Switch Circuit with Load-Independent Output for Wireless Power Transfer

Abstract

Double-sided Inductor–Capacitor–Capacitor (LCC) or hybrid compensation network is often used in the traditional methods to realize load-independent output in wireless power transfer; however, these methods require the changes of operating frequency or compensation network, and the adoption of more switches and components, resulting in the reduction in the reliability of the system. In this article, a single switch topology using a switched capacitor was proposed, which can realize load-independent output characteristics by only switching the branch once, characterized by the strength of fewer components, simple control, and high reliability. The analysis of this topology and the accurate parameter design method were given, and the sensitivity analysis was also carried out. Finally, a 180 W wireless charging prototype with 60 V/3 A was built using the proposed topology, which confirmed the accuracy of model analysis and the practical feasibility of the proposed strategies.

1. Introduction

Wireless power transfer (WPT) is a method used for transferring power by coupling the magnetic fields of the transmitting and receiving coils. It is characterized by multiple inherent strengths, e.g., security, convenience, reliability, electrical isolation, low cost, no need for bulky wires and heavy connectors, and the ability to be applied in extreme environments and special applications. These merits make WPT increasingly widely recognized and studied. According to different principles, WPT can be classified into three forms, i.e., magnetic field coupling power transfer, electric field coupling power transfer, and microwave wireless power transfer. Nowadays, magnetic field coupling power transfer is popular in electrical vehicle (EV) wireless charging, aerospace and ocean exploration, household appliances, and so on [1,2].

Currently, in the medium to high power applications of WPT, full-bridge inverter topology is generally adopted [3]. The scheme of the full-bridge inverter circuit is mature; however, the inverter consists of four switches, which leads to the disadvantages of large volume and heavy weight, complex control, poor reliability, and difficulty to realize zero voltage switching (ZVS) [4,5]. Single switch circuit, e.g., Class E circuit, is widely adopted in the field of low-power WPT because of its merits of fewer components, simple control, and zero voltage switching, but the conventional Class E topology can be utilized only in low-power situations due to high voltage stress [6,7,8]. In [9], the author reveals a reconfigurable Class E topology-based wireless power transmitter of 6.78 MHz. This proposed topology in [9] enjoys the benefits of charging different types of multi-components while remaining very high efficiency; however, the transmission power of 39 W greatly limits the application of the Class E circuit.

In this paper, a hybrid topology of the Class E circuit, which can realize bidirectional excitation, is proposed. The proposed topology can transmit energy to the load no matter whether the switch is on or off, which improves the utilization of the power source. In addition, the power transmission level is increased from several hundreds of watts to thousands of watts, thus greatly improving the power transmission capacity of the circuit. Moreover, this novel topology achieves load-independent output characteristics by switching the branch only once. It is of significance to realize load-independent output to extend the life span of batteries in wireless battery-charging applications [10]. Nowadays, load-independent output in a WPT system is usually achieved by the addition of a double-sided Inductor–Capacitor–Capacitor (LCC) compensation network to a full-bridge inverter topology [11,12,13]. In [14], the authors recommend a double-sided LCC compensation network for the WPT system, as well as a tuning approach for it. The resonant frequency of the circuit in [14] is unaffected by both the coupling coefficient between coils and the load conditions. In low to mid-power applications, however, it necessitates more passive components, resulting in bigger system sizes, more resonant loops, and worse efficiency. Furthermore, as the switching frequency of the circuit must be altered when the system is switched between constant current (CC) and constant voltage (CV) modes, its stability has reduced. Authors presented two hybrid circuits for electric vehicle charge in [15], employing either SS (Series–Series) and PS (Parallel–Series) compensation or SP (Series–Parallel) and PP (Parallel–Parallel) compensation. Although this method is available to convert between CC and CV modes without modifying the operating frequency, the circuit topology is complicated since there are three switching switches. In addition, the new resonant loop modified the previous compensation circuit; therefore, it is important to find a simple topology structure to realize CC and CV output at a fixed switching frequency. In [16], a full-bridge circuit and a primary reconfiguration of the compensation network are used, and the CC and CV modes can be implemented by switching only once, but more passive devices are used, which is not suitable for applications with small transmitter reflection impedance.

This novel Class E topology presented in this paper has a Series/Capacitor–Inductor–Capacitor (S/CLC) structure, which reduces the number of passive components. In addition, to transition between CC and CV mode, only one switch is required, with no changes to the compensation network. Compared with full-bridge topology, this presented Class E topology has the strength of high stability, small volume, and light weight, simple structure, and control. In addition, it is simple to achieve ZVS and there are no issues with shoot-through [17,18]. Moreover, this output power is no longer limited to a few watts; instead, it can reach hundreds of watts, thereby expanding its range of application in medium power.

2. Analysis of a Novel Class-E Topology

2.1. Topology of Main Circuit

To solve the above problems, a novel Class E topology and S/CLC compensation network are presented, as shown in Figure 1. The transmitter circuit is a basic Class E topology; the receiver circuit adopts a CLC compensation network and a bridge rectifier topology, which requires no change of operating frequency and compensation network, and only needs to switch the branch once to achieve load-independent output. In addition, it enables ZVS to meet the need for mid-power and small power applications.

This proposed topology consists of an inverter unit, a magnetically coupled structure, and a high-frequency rectifier. Among them, the Class E unit is composed of L₁, Q, C₁, which transforms the input DC power into high-frequency AC power. The magnetically coupled structure is composed of L_p, C_p, L_s, C_s1, C_s2, C_s3, S, and L₂, which transmits power from the transmitting circuit to the receiving circuit through a magnetic field. In the case that the switch S is closed, the receiving side capacitors are C_s1, C_s2; the system works in CC mode; when the switch S is on, the receiving side capacitors are a combination of C_s1 and C_s3 in parallel, and the system works in CV mode. The switch S is not a high-frequency switch, so it only needs to be switched once in the process of charging the battery. The high-frequency rectifier is a full-bridge rectifier, composed of four diodes, that can transform the high-frequency AC power to DC power and supply the load.

Figure 2 shows the working process waveform of the Class E inverter using Saber simulation. Here u_gs, refers to voltage through the gate source of the switch Q; u_ds stands for voltage across the drain source of the switch Q; i_Lp and i_Ls represent the current in the transmitting and receiving coil, respectively, u_Cs1 and u_Cs2 are the voltage waveform on capacitor C₁ and C₂; u_L1 and i_L1 denote the voltage and current waveforms on inductor L₁, respectively.

From Figure 2, it can be seen that when u_ds goes to zero, therefore, the switch S exhibits the zero-voltage switching characteristic.

2.2. Constant Current Output Mode

As shown in Figure 3, a T-type equivalent network is used to analyze the magnetically coupled structure of the Class E topology.

As can be seen from Figure 3, the primary inductor L_p is decomposed into L_p1 and L_p2, respectively. Cp compensates for the partial inductance of the transmitting coil Lp1, so that the T1 network can achieve the voltage source to the voltage source (V–V) transformation [19]. Cs refers to the secondary compensation capacitor and its value is subject to the state of the switch S. On the other hand, u_in is expressed as a sine wave input voltage, the load is approximated as a pure resistance R_eq, the output voltage before rectification is U_o, and the output current is I_o. Due to the fact that capacitor C₁ is in parallel with the voltage u_in, it does not affect CC and CV of the compensation network. Capacitor C₁ only affects the ZVS characteristics of the system.

It is assumed that the system realizes CC output only at the frequency f. Moreover, in cases where the transmitting coil compensation capacitor C_p and inductor L_p1 are resonant at this frequency, the total impedance of C_p and L_p1 becomes zero. According to Thévenin’s and Norton’s theorem, the T1 network shown in Figure 3 could be equivalent to an inductor, given in Figure 4a. In case the equivalent inductor L_s − M²/L_p2, C_s1 and L₂ resonate at f, the structure shown in Figure 4b can be obtained.

It is shown in Figure 4b that the magnetically coupled structure is equivalent to a constant current source in series with capacitor C_s2 and equivalent resistance R_eq. In other words, the CC output mode is achieved. According to the previous analysis, the circuit needs to meet the following requirements to realize constant current output:

$$\left\{\begin{array}{l}\omega L_{\mathrm{p}1}=\frac{1}{\omega C_{\mathrm{p}}}\\ \omega \left(L_{\mathrm{s}}-\frac{M^2}{L_{\mathrm{p}2}}\right)-\frac{1}{\omega C\mathrm{s}1}=-\omega L_2\end{array}\right.$$

(1)

where ω = 2πf. Through the aforementioned analysis, at the switching frequency of f, the calculation of the compensation network output current can be expressed:

$${\stackrel{·}{I}}_{\mathrm{o}}=\frac{j\omega C_{\mathrm{s}1}{\stackrel{·}{U}}_{\mathrm{in}}M}{L_{\mathrm{p}2}-{\omega }^2{C}_{\mathrm{s}1}\left(L_{\mathrm{s}}{L}_{\mathrm{p}2}-M^2\right)}$$

(2)

From (2), it can be seen that the compensation network output current of the CC mode is subject to the voltage U_in, inductor M, L_s, L_p2, and capacitor C_s1. Where L_p2 can be separated from the inductor L_p; therefore, this design approach significantly enhances the design freedom of the system.

2.3. Constant Voltage Output Mode

At the CV output mode, the secondary compensation capacitor C_s is the combination of C_s1 and C_s3 in parallel, i.e., the switch S is turned on. As seen in Figure 4a, If the inductor L_s − M²/L_p2, L₂ and C_s1 are combined in parallel to resonate with C_s2 at switching frequency f, an equivalent circuit can be given as shown in Figure 5.

Figure 5 shows that the magnetically coupled structure is equivalent to a constant voltage in series with equivalent resistance R_eq; therefore, the voltage across R_eq is dependent on the value of resistance, which achieved constant current output. According to the previous analysis, the circuit needs to meet the following requirements to realize constant voltage output:

$$\left\{\begin{array}{l}{C}_{\mathrm{s}}=C_{\mathrm{s}1}+C_{\mathrm{s}3}\\ \left(\mathrm{j}\omega L_0+\frac{1}{\mathrm{j}\omega C_{\mathrm{s}}}\right)//\mathrm{j}\omega L_2+\frac{1}{\mathrm{j}\omega C_{\mathrm{s}2}}=0\\ L_0=L_{\mathrm{s}}-M^2/L_{\mathrm{p}2}\end{array}\right.$$

(3)

where ω = 2πf. Through the aforementioned analysis, at the switching frequency of f, the calculation of the compensation network output voltage can be expressed:

$${\stackrel{·}{U}}_{\mathrm{o}}=\frac{{\stackrel{·}{U}}_{\mathrm{in}}M{\omega }^2{L}_2{C}_{\mathrm{s}}}{{\omega }^2{C}_{\mathrm{s}}{L}_{\mathrm{p}2}\left(L_0+L_2\right)-L_{\mathrm{p}2}}$$

(4)

From (3), the expression of the compensation capacitor C_s2 can be reformulated as:

$$C_{\mathrm{s}2}=\frac{1-{\omega }^2{C}_{\mathrm{s}}\left(L_0+L_2\right)}{{\omega }^2{L}_2\left(1-{\omega }^2{L}_0{C}_{\mathrm{s}}\right)}$$

(5)

3. Parameter Analysis

The AC output current and voltage are rectified using a full-bridge diode rectifier; the current I_b and voltage U_b can be obtained as follows:

$$\left\{\begin{array}{l}{I}_{\mathrm{b}}=\frac{2}{\pi }{I}_{\mathrm{o}}\\ U_{\mathrm{b}}=\frac{\pi }{4}{U}_{\mathrm{o}}\end{array}\right.$$

(6)

To simplify the calculation, the variables α, β, and k are introduced, which can be expressed as:

$$\left\{\begin{array}{l}{L}_{\mathrm{p}2}=\alpha L_{\mathrm{p}}\\ k=\frac{M}{\sqrt{L_{\mathrm{p}}{L}_{\mathrm{s}}}}\\ C_{\mathrm{s}1}=\beta C_{\mathrm{s}}\end{array}\right.$$

(7)

Substituting (2), (4), and (7) into (6), expressing ω with α, β, and k can be obtained as:

$$\omega =\frac{2U_{\mathrm{b}}{I}_{\mathrm{b}}{L}_{\mathrm{p}}{\alpha }^2\left(1-\beta \right)}{U_{\mathrm{in}}{}^2{k}^2{C}_{\mathrm{s}}{L}_{\mathrm{s}}\beta }$$

(8)

For the application of 48 V, 20 AH battery, the proposed Class E topology is designed with the parameters of 100 V input voltage and 60 V/3 A output voltage and current, and the parameters of the whole system may be calculated according to the above analysis. Given a set of transmitting coil and receiving coil, for example, L_p = 20 μH, L_s = 30 μH. From Figure 6, the switching frequency f versus the coupling coefficient k for different α and β can be derived.

From Figure 6, it may be observed that for a certain switching frequency, the required value of α becomes larger, and the value of β becomes smaller with the increase in the coupling coefficient; however, the maximum value of α is 1; therefore, the system parameters are limited by f and k. The higher the f, the smaller the feasible range of k. At given f and k, the coefficients α and β can be determined from Figure 6.

To show the relationship between parameters α, β, and frequency f, a three-dimensional image was created, as shown in Figure 7.

All parameters of the topology can be calculated by analyzing the above figures and formulas; therefore, the parameters of the novel Class E topology and its compensation network are calculated as illustrated in

Table 1. Class E topology parameter.

Parameter	Description	Value
f	frequency	100 kHz
Udc	Input DC voltage	100 V
Ub	Output voltage	60 V
Ib	Output current	3 A
LP	Transmitting coil inductance	20 μH
LS	Receiving coil inductance	30 μH
M	Mutual inductance	6.12 μH
α	Scale factor	0.61
β	Scale factor	0.5
Cp	Primary compensation capacitor	324.7 nF
Cs	Compensation capacitor in CV mode	98 nF
Cs1	Compensation capacitor in CC mode	49 nF
Cs2	Secondary compensation capacitor	768 n
L1	Primary side inductance	16 μH
L2	Secondary side inductance	24.5 μH

.

Sensitivity analysis of the topology was performed in order to verify the sensitivity of the system at this parameter. The variation of CV-mode normalized output voltage and CC-mode normalized output current with C_s, α and L₂ normalization parameter is shown in Figure 8. It is obvious that the change of C_s is sensitive to the output current. At the same time, the value of L₂ is not sensitive to the variation of constant voltage output.

4. Experiment Results

To verify the correctness of the above analysis and the feasibility of the proposed topology, a 180 W wireless charging prototype with 60 V/3 A was built using the proposed topology, as shown in Figure 9. The prototype is composed of an inverter unit, a transmitting coil, a receiving coil, and a rectifier marked as 1–4 in turn. Figure 10a,b present the u_ds and u_gs in both CC mode and CV mode.

As seen in Figure 10, both modes achieved ZVS, and the blocking voltage of the switch in CC mode is smaller than that of CV mode by 25 V. Figure 11a,b show the waveform of output voltage and current as the power turns from full-power to half-power and then back to full-power in two modes, respectively.

As shown in Figure 11, with the change of the load, i_L in CC mode remains at 3 A, and u_L in CV mode is kept at 60 V. The CC and CV output characteristic is well achieved.

Figure 12 shows the dynamic performance of the system at the load of 20 Ω. The output voltage and current change relatively swiftly when the system switches from CC mode to CV mode, and the dynamic response is fast.

The measured and theoretical output voltage and current at different loads are shown in Figure 13.

Finally, the curve of efficiency from the DC power source to the resistive load processed can be seen in Figure 14. It can be seen from the results that the max efficiency of CC mode is 89.5% and that of CV mode is 90.3%. Efficiency increases when the mode switches, which is because the output power will increase when it changes from CC mode to CV mode.

The operating performances of this paper were compared with the WPT system using Class E topology, which is shown in

Table 2. Comparison of WPT system using Class E topology.

Topology	Frequency	Output Power	Efficiency	CC/CV
Proposed	100 kHz	180 W	90.3%	Yes
[6]	6.78 MHz	30 W	80%	Yes
[9]	6.78 MHz	39.7 W	81.4%	No
[20]	1 MHz	3 W	79.6%	No
[21]	1 MHz	27.8 W	74.7%	No
[22]	13.56 MHz	25.6 W	73.4%	No

.

It is clear from Table 2 that Class E topology is mainly applied in MHz-frequency and low-power applications of WPT. The work detailed in this paper expands its application range and achieves higher output power and efficiency. In addition, compared with [4], a simpler method is adopted to achieve CC and CV output.

5. Conclusions

In this paper, a novel hybrid Class E topology with load-independent output was proposed. Compared to the traditional Class E topology, this hybrid topology presented in this paper can transmit higher power and realize the load-independent output characteristics only by switching the branch once, characterized by the strength of fewer components, simple control, and high reliability. The topology parameters were designed in detail. To improve the design freedom, the compensation method of manually separating the transmitting coils is used, which can also be applied to other WPT systems. Moreover, the relationship between the system parameters and the sensitivity of the topology was analyzed. Finally, a 180 W wireless charging prototype with 60 V/3 A was built using the proposed topology; the experimental results showed perfect agreement with the theoretical analysis and confirmed the feasibility of our novel approach.