A Novel High Controllable Voltage Gain Push-Pull Topology for Wireless Power Transfer System

Abstract

Wireless Power Transfer (WPT) is commonly used to transmit power from a transmitting coil to various movable power devices. In the WPT system, due to a resonant tank inherent characteristic, the system cannot achieve a high output voltage gain. This paper proposes a novel current-fed push–pull circuit to realize high output voltage gain by adding a bi-directional switch between the resonant network and inverter. To obtain a high voltage gain, this paper proposes energy storage and energy injection mode to realize an energy boost function. A duty cycle control method for mode switching is also proposed. The proposed method allows the converter to operate with a variable voltage gain over a wide range with high efficiency. Experimental validation shows that the system gain of a proposed circuit can achieve a variable gain from 2 to 7 of which the converter can be two times higher than the classical system with the same condition.

1. Introduction

The Wireless Power Transfer (WPT) system as a novel technology can realize power wireless transmission from power supply to electrical equipment with the aid of magnetic coupling. With its rapid development, more and more applications have appeared in electrical vehicles, biomedical implants and cell phone areas [1,2,3,4,5,6].

More and more applications in WPT technology require low DC voltage input and high voltage output. These applications include the Photovoltaic (PV) system, battery power supply system and Universal Serial Bus (USB) powered devices. However, it is not easy for the WPT system to obtain high voltage gain according to the following reasons—first, due to the WPT system being a weakly coupling system with very low coupling coefficient k (normally below 0.2) [7,8] and the coupling coefficient of transformer can almost reach 1. The second reason is the inherent characteristic of the resonant network. There are four fundamental resonant topologies SS, SP, PS, and PP (S and P denotes series and parallel topology, respectively). Series resonant network exhibits voltage source characteristics that cannot obtain a high voltage gain. The parallel resonant network exhibits current source characteristics that obtain high voltage gain on the light load condition. However, for heavy load conditions, it still cannot obtain high voltage gain. Furthermore, its reflecting impedance will bring relatively large frequency drift, which may cause a large reduction in output power [9,10]. For the same reason, composite resonant networks such as Inductor Capacitor Inductor (LCL), Inductor Capacitor Capacitor (LCC), and Capacitor Inductor Capacitor (CLC), which are combinations of the series and resonant topology, cannot reach high voltage gain. Reference [11] analyzes wireless charging circuit characteristics under hybrid compensation topology. The analysis results show that the output voltage gain is below three in hybrid compensation topology.

To achieve high output voltage gain, the classical method is implemented by placing an additional Boost converter at the primary or secondary side. However, the added Boost converter will increase the volume and weight of the whole system [12,13], and make the system complicated to control. There are few papers related with voltage gain improvement. Aiming at voltage gain optimization and control, Reference [14] proposes a uniform voltage gain control method. This method is implemented by control system operating frequency. However, the method only aims at improving the robustness against misalignment. Reference [15] proposes a detached magnetic core to improve the voltage gain method. The obtained voltage gain is 0.83. Reference [16] proposes an S/SP topology converter to obtain constant voltage gain. However, the voltage gain cannot be adjusted and will be very sensitive to frequency drift on the high gain condition.

In order to obtain a high and controllable output voltage gain WPT system, this paper proposes a novel current-fed push–pull converter at the primary side. A pair of Insulated Gate Bipolar Transistor (IGBT) switches, which act as a directional switch, is added in front of the resonant network to isolate the inverter and resonant network. An energy storage and injection switching mode is proposed to control the energy flowing into the resonant network. A switching duty cycle regulation method is also proposed to reach high voltage gain.

2. High Output Gain Push–Pull Circuit

The proposed high output gain push–pull circuit is shown in Figure 1. Compared with traditional push–pull circuits, the proposed circuit adds two additional switches S₃ and S₄ to form a bi-directional switch. At the primary side, a DC power supply is a series with an inductor to form a quasi-current source. A push–pull transformer including L₁ and L₂ is utilized to divide the DC current in half, so that the current flowing into the resonant tank is approximately a square waveform with half the magnitude of the input DC current. The primary side uses two main switches (S₁ and S₂) with a common ground and two auxiliary switches (S₃ and S₄) in series with a parallel-tuned resonant tank, which consists of a resonant capacitor C_P, a resonant inductor L_P and equivalent series resistance R_P. The secondary side comprises a parallel resonant tank, which consists of a resonant inductor L_S, equivalent series resistance R_S, and a resonant capacitor C_S. With the rectifier bridge (D₁–D₄) and Inductor Capacitor (LC) filter network, AC energy is transformed to DC output to the load R.

Aiming at voltage gain promotion, this paper proposes a resonant energy promotion method at the primary side. An energy storage mode is realized by shorting the DC inductor and phase-shifting transformer. An energy injection mode is realized by combining the storage energy and DC input energy together and outputting to the resonant tank. The switching between the energy storage and injection mode is implemented by auxiliary switch pair S₃ and S₄.

Figure 2 shows fundamental operation principles of the proposed method. The pulses and current waveforms of the proposed circuit switches are shown. V_GE1 to V_GE4 denotes the driving signals of switches S₁ to S₄, respectively. The current waveform of i_L2 is similar to the current waveform of i_L1, except for half-cycle delay. The function of anti-series switches (S₃ and S₄) is to control the connection between resonant tank and push–pull circuit. During one full switching cycle, the circuit operation can be divided into the following four modes and can be shown in Figure 3.

Mode I: t₀–t₁: In this mode, switches S₂ and S₄ are turned on; switches S₁ and S₃ are turned off. The operation of this mode is shown in Figure 3a. The energy stored in L₁ is transfer into the resonant circuit by switch S₄ and the reverse diode of S₃; switch S₂ is remaining conduction, so that the current flowing L₂ is rising slowly and L₂ is still working in the state of storage.

Mode II: t₁–t₂: In this mode, switches S₁ and S₂ are turned on and switches S₃ and S₄ are turned off. The operation of this mode is shown in Figure 3b. Switches S₃ and S₄ are turned off and the resonant circuit enters the state of free energy oscillation between L_P and C_P. Switches S₁ and S₂ are turned on and L₁ and L₂ are both working in the state of storage.

Mode III: t₂–t₃: In this mode, switches S₁ and S₃ are turned on; switches S₂ and S₄ are turned off. The operation of this mode is shown in Figure 3c. The energy stored in L₂ is transferred into the resonant circuit by switch S₃ and the reverse diode of S₄ and the current flowing through L₂ is decreasing; switch S₁ is remaining conduction, so that the current flowing L₁ is rising slowly and L₁ is still working in the state of storage.

Mode IV: t₃–t₄: This mode is similarly with Mode II, switches S₁ and S₂ are turned on and switches S₃ and S₄ are turned off. The operation of this mode is shown in Figure 3d. Switches S₃ and S₄ are turned off and the resonant circuit enters the state of free energy oscillation between L_P and C_P. Switches S₁ and S₂ are turned on and L₁ and L₂ are both working in the state of storage.

3. Voltage Gain Analysis

Assuming that the resonant cycle of the circuit is T, and the switching duty cycle of S₁ and S₂ is D; correspondingly, the duty cycle of S₃ and S₄ is (1 − D). According to the volt–second balance of inductors L₁ and L₂, the average voltage across L₁ and L₂ is equal to zero during one switching cycle period. During the steady state, the current flows through L₁ and L₂ is equal so that the energy stored in inductors L₁ and L₂ is equal as well. Next, the paper will calculate the output gain based on the fact that the energy stored and released in inductor L₁ is equal during one switching cycle.

In the steady state, the supply current is I_d, and the current flowing through L₁ or L₂ is I_d/2. Assuming the resonant network terminal voltage is U_AB, thus the volt-second balance equation can be obtained as

$$V_{in}\frac{I_d}{2}DT=(U_{AB}-V_{in})\frac{I_d}{2}(1-D)T.$$

(1)

Thus:

$$U_{AB}=\frac{V_{in}}{1-D}(0.5\le D<1).$$

(2)

Note that duty cycle of switches S₁ and S₂ is no less than 0.5. It is because when the duty cycle is less than 0.5, switches S₁ and S₂ will enter the state of turning off at the same time; correspondingly, switches S₃ and S₄ will enter the state of turning on. It will result that the current of L₁ and L₂ drops sharply to zero and the current will become discontinuities. On the assumption, system equivalent circuit can be shown as Figure 4.

At the secondary side, according to the energy balance equation, the equivalent resistance R_eq of DC part including rectifier, filter and load at the secondary side is

$$R_{eq}={\mathsf{\pi }}^{2}R/8.$$

(3)

The reflection impendence from the secondary to primary side can be expressed by

$$R_{ref}={\omega }^2{k}^2{L}_P{L}_S/Z_S,$$

(4)

where Z_S = (jωL_S + R_S) + R_eq/(jωC_SR_eq + 1) is the input impendence of secondary resonant network. Its resonant angular frequency is ω = 2πf.

The input impendence of the push–pull network can be expressed as

$$Z_P=\frac{j\omega L_P+R_P+R_{ref}}{j\omega C_P\left(j\omega L_P+R_P+R_{ref}\right)+1}.$$

(5)

The resonant current of the primary side I_P can be expressed as

$$I_P=U_{AB}/\sqrt{{\left(\omega L_P\right)}^2+{\left(R_P+R_{ref}\right)}^2}.$$

(6)

It is well known that the inductive voltage source of secondary side can be expressed as

$$V_S=\omega k{I}_P\sqrt{L_P{L}_S}.$$

(7)

On the resonant condition ω²L_SC_S = 1, the output voltage V_O the load can be obtained as

$$V_O=\frac{R_{eq}}{\left(j\omega C_S{R}_{eq}+1\right)}\frac{j\omega k{U}_{AB}\sqrt{L_P{L}_S}}{\left(j\omega L_P+R_P\right)Z_S+{\omega }^2{k}^2\left(L_P{L}_S\right)}.$$

(8)

Therefore, the voltage gain of the proposed circuit can be expressed as Equation (9)

$$\left|\frac{V_O}{V_{in}}\right|=\frac{\omega k\sqrt{L_P{L}_S}}{\sqrt{{\left(\omega L_P\right)}^2+{\left(R_P{Z}_S+{\omega }^2{k}^2{L}_P{L}_S\right)}^2}}\frac{R_{eq}}{\left(1-D\right)\sqrt{{\left(\omega C_S{R}_{eq}\right)}^2+1}}.$$

(9)

Equation (9) shows that the output voltage can be controlled by duty cycle D, coupling coefficient k, switching frequency f and the equivalent resistance R_eq. However, frequency f and the load R usually are constant in the proposed circuit, thus the output voltage can be regulated by the duty cycle D of the push–pull switches S₁ and S₂.

Compared with traditional full-bridge circuit, its equivalent AC input U_AB can be calculated by

$$U_{AB}=\frac{2\sqrt{2}{V}_{in}}{\mathsf{\pi }}.$$

(10)

In addition, the voltage gain of the full-bridge converter will be

$$\left|\frac{V_O}{V_{in}}\right|=\frac{\omega k\sqrt{L_P{L}_S}}{\sqrt{{\left(\omega L_P\right)}^2+{\left(R_P{Z}_S+{\omega }^2{k}^2{L}_P{L}_S\right)}^2}}\frac{2\sqrt{2}{R}_{eq}}{\mathsf{\pi }\sqrt{{\left(\omega C_S{R}_{eq}\right)}^2+\mathsf{\pi }}}.$$

(11)

As can be seen from Equations (9) and (11), we can draw a conclusion that the voltage gain of proposed topology can be at least two times than traditional full-bridge topology.

Compared with a traditional push–pull circuit, its equivalent AC input U_AB can be calculated by

$$U_{AB}=\frac{\mathsf{\pi }{V}_{in}}{\sqrt{2}}.$$

(12)

Furthermore, the voltage gain of the full-bridge converter will be

$$\left|\frac{V_O}{V_{in}}\right|=\frac{\omega k\sqrt{L_P{L}_S}}{\sqrt{{\left(\omega L_P\right)}^2+{\left(R_P{Z}_S+{\omega }^2{k}^2{L}_P{L}_S\right)}^2}}\frac{\pi R_{eq}}{\sqrt{2}\sqrt{{\left(\omega C_S{R}_{eq}\right)}^2+1}}$$

(13)

As can be seen from Equations (9) and (13), we can draw a conclusion that the voltage gain of proposed topology can achieve $\frac{\sqrt{2}}{\mathsf{\pi }\left(1-D\right)}\left(0.5\le D<1\right)$ times the traditional push–pull topology.

4. System Performance Analysis

In order to analyze the performance of the proposed method, several performance analyses are carried out including load variation, coupling coefficient and comparison with a traditional WPT system.

4.1. Influence of Load (R) Variation on Voltage Gain and Efficiency

According to Equation (9), Figure 5 shows the voltage gain against switching duty cycle D with different load R, and the efficiency against load R when k = 0.2. The analysis results show

(1)

With the increase of switch duty cycle D, the output gain enhancement increases obviously and the increasing rate of voltage gain increases gradually.

(2)

The voltage gain ratio is higher when the load R becomes larger at the same switching duty cycle D.

(3)

From Figure 5b, the system can keep efficiency above 85% in the whole duty cycle range.

4.2. Influence of Coupling Coefficient (k) Variation on the Gain Ratio and Efficiency

Because the WPT system is a loosely coupled system, the coupling coefficient will vary dynamically. It is necessary to analyze the influence of coupling coefficient variation.

Figure 6a shows curves of voltage gain against switching duty cycle D using Equation (9) at different coupling coefficients. It can be seen that the gain ratio increases as the switching duty cycle D increases. The gain ratio is higher when the coupling coefficient is larger.

Figure 6b shows the curves of system efficiency against different operating coupling coefficients. As the coupling coefficients k increases, the efficiency decreases while load R is larger. Overall, the system can keep running at efficiency above 75% on the condition of coupling coefficient and load variation.

4.3. Comparison of Traditional WPT System

In order to compare this topology performance with traditional WPT system, this chapter presents the voltage gain of four resonant networks (PP, PS, SP and SS) with the same resonant parameters. The voltage gain and efficiency of four compensation circuits are compared against load variation range from 0 to 100 Ω in Figure 7.

In Figure 7, for secondary series topology including PS and SS, this kind of topology cannot achieve high voltage gain due to its voltage source characteristic, and its efficiency is relatively low on the light load condition. Secondary parallel topology can achieve relatively high voltage gain (maximum gain equals 5.1) due to its current source characteristic, but voltage gain varies greatly with load variation. For heavy load conditions, its voltage gain is low.

Compared with the four basic compensation circuits, the proposed push–pull circuit can operate at an adjustable gain versus load R with high efficiency from the analyses A and B.

5. Experimental Verification

For the sake of verifying the performance of the proposed topology, a prototype system is built up. The system has been constructed according to the parameters provided in

Table 1. System parameters.

Parameters	Values
Resonant frequency f (KHz)	31.45
Primary resonant inductor LP ($\mathsf{\mu }\mathrm{H}$)	30.38
Primary inductor resistance RP ($\mathsf{\Omega }$)	0.025
Primary capacitor CP ($\mathsf{\mu }\mathrm{F}$)	0.66
Secondary resonant inductor LS ($\mathsf{\mu }\mathrm{H}$)	36.82
Secondary inductor resistance RS ($\mathsf{\Omega }$)	0.029
Secondary resonant capacitor CS ($\mathsf{\mu }\mathrm{F}$)	0.57
Coupling coefficient k	0.157
System load R ($\mathsf{\Omega }$)	50

and the device photo is shown in Figure 8.

Figure 9 shows the waveforms of the push–pull switches gate-driving signals and anti-series switching gate-driving signals. The resonant voltage V_CP and resonant current I_LP are shown in Figure 10 and the resonant voltage and current waveforms are sinusoidal waves, which indicate that the system can work under the state of resonance.

Figure 11 shows the waveforms of V_dS2, V_dS3 and V_CP from top to bottom. It can be seen that the synthesized waves of V_dS2 and V_dS3 are exactly half of the resonant wave V_CP on the condition of D = 0.6. The same result can be detected that the synthesized waves of V_dS1 and V_dS4 are exactly half of the resonant wave V_CP. When the duty cycle becomes D = 0.8, the waveforms of V_dS2, V_dS3 and V_CP are shown in Figure 12 and V_dS2 and V_dS3 are changing when the duty cycle D is changing. Figure 13 shows that V_O is controlled at 43 V for the condition of R = 50 Ω and D = 0.8, which achieves a gain of 4.3 times compared with the input voltage U_in = 10 V. It verifies that the system can realize a higher gain by regulating the duty cycle D.

Table 2. Experiment Results.

Input Voltage/Current (V/A)	Duty Cycle of S1 (D)	Output Voltage (V)	Output Power (W)	Gain	Efficiency
10/0.61	0.5	16.2	5.4	1.6	88%
10/1.09	0.6	21.7	9.5	2.17	87.4%
10/1.96	0.7	28.9	16.9	2.89	86%
10/2.80	0.75	34.5	23.8	3.45	85%
10/4.7	0.8	43.1	39.5	4.31	84.1%
10/8.08	0.85	53.8	67.5	5.38	83.6%
10/15.2	0.9	72.3	123	7.3	80.9%

presents the experimental data of the proposed topology. The controlled gain range is from 1.6 to 7.3. With higher gain, the system can get higher output power. Furthermore, system efficiency can remain above 80%. Figure 14 shows that the experimental results of voltage gain match with the theoretical results well, except that there is little difference at the maximum gain point. It is because power losses at the primary side will increase at the top gain point.

6. Discussion

In order to present a close loop control of the voltage gain, a Proportion Integration Differentiation (PID) control is applied to regulate the duty cycle D of the switches. The close loop control structure can be shown in Figure 15.

The information of output voltage V_O is measured and sent back to the primary side by an Radio Frequency (RF)-link. Furthermore, a PID controller is utilized to control the duty cycle of S₃ and S₄, according to the difference between V_O and V_ref.

A load switching test was carried out to evaluate the controller’s performance. In this test, load condition is set to switching between 10 Ω and 30 Ω. The DC input voltage is set at 5 V. The output reference voltage is set at 20 V. The experimental result can be shown in Figure 16.

As can be seen in Figure 16, there are two load switching events in the control process: one is from 20 Ω to 10 Ω (first switching) and the other is from 10 Ω to 20 Ω (second switching). In the control process, the output voltage is kept stable except for some switching disturbance. The experimental results verify the close loop control performance of the PID controller.

7. Conclusions

In order to achieve controllable high voltage gain output, this paper proposed a novel current-fed push–pull topology for the WPT system. This method utilizes a bi-directional switch that is added to isolate the inverter with resonant network and guide the power flow into the resonant tank. On the basis, an energy storage and injection switching mode is proposed to enhance voltage gain. A switching duty cycle is also proposed to implement gain control. This method can greatly improve the voltage gain in the WPT system and maintain a high system efficiency at the same time. This is important for low DC voltage input application including PV power supply and USB charger.