1. Introduction

Currently, the reduction of weight and size for the portable wireless charging devices have become increasingly important, as many consumers prefer easy-to-carry and compact-size devices ⁽¹⁾. Meanwhile, such the WPT systems have a structure in which a transmitter-side (Tx) and a receiver-side (Rx) are physically separated. Especially, in Rx of a WPT system, the rectifier stage and the battery control converter are generally used to ensure stable output for the battery with many number of components causing low power density ^(2-7).

Fig. 1 (a) shows the conventional typical structure for the WPT system. As seen in Fig. 1 (a), the WPT system is configured with two parts: transmitter-side (Tx) and receiver-side (Rx). The role of Tx is to deliver energy to the Rx by inverting DC input to AC. On the other hand, the Rx is composed of two power stages such as the rectifier stage and battery control converter. Here, the rectifier stage converts the energy transferred as AC from the Tx to DC. And the battery control converter serves to provide a stable output voltage $V_{o}$ to the battery, the final output. Fig. 1 (b) shows the circuit diagram of the conventional WPT system including the general full-wave rectifier stage and battery control converter using Synchronous Rectifier (SR) buck converter with easy implementation. However, since the two power stages have a large number of components on the conduction path, it degrades the overall efficiency and power density of the WPT system. Besides, in the WPT system, since the unstable communication control between Tx and Rx have to be used due to its physical contactless structure as shown in Fig. 1 (b).

Especially, due to slow and unstable communication feedback (Ex.1data/50ms) as described in Fig. 1 (b), the Tx still cannot effectively control the Rx rectifier output $V_{rect}$ in case of misalignment conditions. Therefore, the rectifier output voltage $V_{rect}$ differs from the originally designed voltage level. To relieve these drawbacks, a new receiver-side post regulator (RSPR) is proposed with high power density and a simple control method for the WPT system. Since the proposed structure takes integrating a single-switch into the full-wave rectifier as shown in Fig. 2, it is possible to achieve high power density compared to the conventional WPT systems.

Fig. 1. Conventional Wireless Power Transfer (WPT) System (a) Circuit Diagram (b) Each Power Stage Structure with Easy Implementation

Fig. 2. Derivation Process of the Proposed Converter (a) A Integrated Single-switch $S_{3}$ into the Full-wave Rectifier (b) Proposed Receiver-side Regulator (RSPR) Structure by Applying Transformer Modeling Method

Here, the integrated single-switch $S_{3}$ replaces the role of a conventional battery control converter, providing stable output to the battery. Moreover, to control integrated single-switch $S_{3}$, simple phase detection and control method are utilized without conventional unstable communication feedback control. By utilizing the proposed simple phase detection and control, the conventional unstable communication control method can be removed.

Fig. 3. Operational Mode of the Proposed RSPR Structure(a) Mode 1(t0~t1), (b) Mode 2(t1~t2), (c) Mode 3(t2~t0’)

Moreover, the proposed control method enables soft-switching operation such as zero current switching (ZCS) turn-on with lower switching losses than the conventional one.

2. Analysis of the Proposed Converter

2.2 Control Method of the Proposed Converter

In this section, the control method of the proposed RSPR structure is going to be explained in detail.

Fig. 4. The Control of the Proposed Converter (a) Key Waveforms and Control Concepts of the Proposed Converter (b) Control Circuit Diagram

As shown in Fig. 4 (a), in order to acquire phase-shift operation for the Rx switch $S_{3}$ based on phase information of the Tx switch $S_{1}$, the simple additional winding $N_{A}$ is required as shown in the Fig. 4 (b). Through the $N_{A}$, the phase information of the Tx switch $S_{1}$ can be easily obtained as $V_{NA}$. The $V_{NA}$ is the (+) terminal input of the internal comparator inside the digital MCU, and an arbitrary DAC value is input to the (-) terminal and finally ‘comp.out’ signal is generated as shown in Fig. 4 (a). At the rising edge of this ‘comp.out’ signal, the synchronized ‘event.sync’ signal is created.

Fig. 5. Equivalent circuit of the Proposed Converter (a) Equivalent lumped circuit model (b) Simplified model

With the ‘event.sync’ signal, phase-shift operation of the Rx switch $S_{3}$ is adjusted according to the load variation. Meanwhile, the gain curve characteristic of the proposed RSPR structure is expressed as shown in Fig. 6. To perform a voltage gain analysis of the proposed circuit, the proposed WPT system can be equivalently modeled as shown in Fig. 5 (a). This equivalent circuit is composed of a coupling coefficient k, two inductances $L_{p}$ and $L_{s}$, and two capacitances $C_{p}$ and $C_{s}$. Furthermore, the proposed converter can be simplified to an equivalent circuit model for the fundamental component, as shown in Fig. 5 (b). Here, the input voltage source $v_{pri_1}$ represents the fundamental component of the voltage $v_{pri}$ generated by the inverter. $Z_{p}$ represents the impedance of the transmitter resonant tank, which is composed of $L_{p}$ and $C_{p}$, while $Z_{s}$ represents the impedance of the receiver resonant tank, which is composed of $L_{s}$ and $C_{s}$. $Z_{M}$ represents the impedance due to the magnetizing inductance. In addition, the currents flowing through the transmitter and receiver side in the equivalent circuit of Fig. 5 (b) can be expressed by the current division law as follows: $i_{p}$ and $i_{S}$ as expressed in equations (1) and (2).

(1)

$$ i_p=\frac{v_i}{Z_M \| n^2 \cdot\left(Z_s+Z_L\right)} $$

(2)

$$ i_s=\frac{v_i}{Z_M \| n^2 \cdot\left(Z_s+Z_L\right)} \cdot \frac{Z_M}{Z_M+n^2 \cdot\left(Z_s+Z_L\right)} $$

$$ \text { effective duty ratio, } n=\sqrt{\frac{L_P}{L_S}} $$

Here, n is the effective turns ratio of the wireless charging coil, and the n² is applied during the process of equivalently reflecting the impedance of the Rx side to the Tx side.

Fig. 6. The Gain Characteristics of the Proposed Converter Under the rated conditions and normalized frequency ($w_{N}$=$f_{s}$/$f_{r}$)

Table 1. Design Parameters of Conventional and Proposed one.

Also, the load impedance $Z_{Leq}$ is expressed as a variable resistor that varies with phase like equation (3).

(3)

$$ Z_{L e q}=\frac{v_{s_{-} 1}}{i_{s_{-} 1}}=\frac{4}{\pi} \cdot R_L \cdot \frac{(1+\cos \phi)}{\sin \left(\frac{\pi-\phi}{2}\right)} \cdot e^{j\left(\frac{\phi}{2}\right)} $$

Based on this approach, the transfer function M of the resonant tank is obtained as a function of the normalized frequency $w_{N}$(=$f_{s}$/$f_{r}$), the phase angle Φ, and the load condition $R_{L}$ as decribed in equation (4).

(4)

$$ \begin{aligned} & M\left(f, \phi, R_L\right)=\left|\frac{v_o}{v_{p r i}}\right| \\ & =\left|\frac{v_i}{Z_M \| n^2 \cdot\left(Z_s+Z_{L e q}\right)} \cdot \frac{n^2 \cdot Z_{L e q} \cdot Z_M}{Z_M+n^2 \cdot\left(Z_s+Z_{L e q}\right)}\right| \end{aligned} $$

Assuming a constant load condition, the voltage gain curve of the system is shown in Fig. 6. The voltage gain curves for different values of $w_{N}$ are plotted, and the effect of Φ on the voltage gain curves can be observed. As described above, it can be seen that the larger phase-shift occurs, the lower the converter gain acquires due to the chopping effect of powering current iS as shown in Fig. 4 (b).

Table 2. Design Parameters of Tx coil and Rx coil

Fig. 7. Experimental Configurations (a) Tx Coil Prototypes [*$C_{P}$: 7.5nF] (b) Rx Coil Prototypes with Additional Winding, $N_{A}$ [*CS: 500nF] (c) Test Configurations for the Experimental Verification

3. Experimental Results

Based on the former analysis, the feasibility of the proposed converter has been verified by experimental results with a prototype under the 380$V_{DC}$ input and 250W/25V output. The experimental results compare the proposed RSPR structure and the conventional WPT system including general full-wave rectifier and SR buck converter.

The switching frequency of both inverter stages is 85kHz in consideration of the resonant frequency of the two coils and resonant capacitors in both structures. Also, the switching frequency for switches $S_{1}$ and $S_{2}$ of the Tx has been determined in order to ensure stable ZVS soft-switching operation and proper gain characteristics. Besides, the switching frequency used for the SR buck converter in the conventional structure is designed for 200kHz in consideration of power density and efficiency. The operating frequency of the proposed RSPR structure is 85kHz, which is the same as the frequency of the Tx inverter stage.

Fig. 8. Verification waveform of phase information Vsync

Fig. 9. Experimental waveforms of component voltage stress (a) Under 50% load condition (b) Under 100% load condition

The detailed parameters regarding main components and experimental test configurations are listed in Table I, and Fig. 7. The experimental configurations are composed of Tx board, Tx coil, Rx coil, and Rx board as shown in Fig. 7 (c). Especially, Table II shows the design parameters of suitable turns and self-inductances for the Tx coil $N_{P}$ and Rx coil $N_{S}$. Also, these parameters have to take into account the effective turns ratio like equation (3), and voltage stress on the resonant tank. Also, the vertical separation distance between Tx and Rx coils is 20mm as shown in Fig. 7 (c). The proposed converter obtains the phase information of the Tx switch $S_{1}$ by using an additional winding, $N_{A}$. Although the same coil as the Rx coil $N_{S}$ was used in this experiment for the sake of convenience, a much thinner coil can be used for the sensing purposes of the additional winding $N_{A}$. As depicted in the waveform of Fig. 8, the proposed simple phase detection method allows for the clean acquisition of the phase information of the Tx switch $S_{1}$ without any interference to the Rx coil $N_{S}$.

Fig. 10. Measured efficiency and calculated loss distribution chart according to the load variation (a) Measured Efficiency, (b) Loss distribution chart

Fig. 11. Comparison with the Two Fabricated Prototypes (a) The Prototype of the Conventional Structure (b) The Prototype of the Proposed Structure

Fig. 9 shows the steady-state waveforms of the proposed RSPR structure from light load to heavy load conditions. As shown in Fig. 9 (a), when the converter is under the light load condition, the gain of the converter can be increased. To compensate for these characteristics, the proposed converter gradually shifts the turn-on time of $S_{3}$ compared to the turn-on time of the switch $S_{1}$.

On the other hand, when the converter is under heavy load, the gain of the converter can be decreased. To compensate for decreased gain, the proposed converter turns-on switch $S_{3}$ as close as possible to the near point at which switch $S_{1}$ turns-on time as shown in Fig. 9 (b).

Fig. 10 (a) shows the measured efficiency with Yokogawa WT1600 power analyzer under the rated output conditions. In the 50% or less light load conditions, the proposed structure shows remarkably higher efficiency than the conventional one. This tendency is due to the large difference in switching loss with ZCS turn-on characteristics as shown in Fig. 9.

Fig. 11 shows the fabricated prototypes of the conventional RX structure and the proposed RSPR structure. Comparing the power density numerically, it can be seen that the power density of the proposed RSPR structure is improved by about 12% compared to the conventional one. Therefore, high power density can be secured through the proposed converter.

4. Conclusions

In this paper, a new receiver-side post regulator (RSPR) for high power density and a simple control method is proposed.

Through the integrated single-switch $S_{3}$ into the full-wave rectifier on the Rx, the proposed RSPR structure can have reduced number of components compared to the conventional Rx structure resulting in higher power density and reduced switching loss with ZCS turn-on. In addition, the proposed simple control method with additional winding can reduce conventional unstable communication control.