Frequency Adaptive Topology to Realize Constant Output and Soft Switching for the WPT System

The main emphasis of research for battery wireless charger should be on four parts, including load-independent output to satisfy the charging requirement, zero voltage switching of power devices to increase transmission efficiency, minimum component counts to reduce cost and simple control strategy. However, the existing studies have not taken these all into account, which greatly limits the application of battery wireless charger. This paper proposes a WPT system based on the simplest S/S compensation network. By replacing the secondary compensation capacitor with an $L$ - $C$ branch, the same circuit structure can realize the load-independent constant current (CC) and voltage (CV) output with zero voltage switching at two different switching frequency. A current amplitude detection circuit is added in the primary side to determine the switching point of CC mode and CV mode. Compared with existing research, the component numbers in proposed circuit are less, the control strategy is easier to implement and avoids the communication between the primary and secondary sides. Finally, a wireless battery charger for 60V/3.6A is built to verify the feasibility of proposed system. And the experimental results perform well on realizing a load-independent output with ZVS operation.


I. INTRODUCTION
Nowadays, the traditional connecting way by wires makes the life more and more tedious with the developing of electrical devices. By comparison, wireless power transfer (WPT) technology has attracted more and more attention due to its flexibility, convenience and safety. And it has huge application value and potential in various fields, such as biomedical implants [1], [2], daily electrical consumption [3] and electrical vehicle [4]- [6]. Among them, the battery serves as a very important part of energy storage system, a lot of researches on the battery wireless charger have been done. The typical charging curve for lithium battery is shown in Fig.1 [7]. From Fig. 1, the wireless power charger should work at constant current (CC) mode first and then the constant voltage (CV) mode. The large charging current at the CC mode can reduce the charging time. The constant charging voltage at the CV mode will ensure the battery is full charged. Besides, the equivalent battery impedance (EBI) is increasing with the charging process going on. Therefore, according The associate editor coordinating the review of this manuscript and approving it for publication was Chi-Seng Lam .
to the charging curve, load-independent current and voltage output are the focus of research. Various control strategies have been investigated to realize CC or CV output in the past few years [8], [9]. The operating frequency adjustment strategy is adopted to realize a CC and CV output for the LLC resonant converter [10], however, if the load varies seriously, the frequency needs to be adjusted over a wide range and the system stability will be killed due to the frequency bifurcation phenomenon. Two dc/dc converters are normally controlled cooperatively for the requirements of output regulation and maximum efficiency tracking [11], however, system size and cost will increase due to the existing of additional converter. Meanwhile, the system transmission efficiency will be affected by the power loss of extra components. In [12], the phase shift angle tracking strategy can compensate the effect of variations to output current until the output current equals the desired output, however, the control strategy requires a communication between the primary side and secondary side. Besides, the ZVS condition is hard to maintain if the phase shift angle is too large. The load-independent constant output can be realized without additional components component counts according to the proper design of the compensation network [13], however, the existing compensation network needs too many passive components, which to some degree reduces its practicality.
When it comes to the switching method from CC mode to CV mode, changing the circuit compensation network structure by adding additional AC switches is proposed in [14] and [15], The charging current and charging voltage are nearly constant during the transient switching interval. However, the additional AC switches will increase the system cost and the corresponding driving circuits will also make the whole circuit bulky. An integrated IPT system design employing variable inductor control is proposed to achieve a target constant current (CC) and constant voltage (CV) battery charging profile with misalignment tolerance [16], however, the realization of variable inductor needs an addition of BUCK converter, which increases the complexity of control process. By comparison, the realization of the CC and CV charging modes at two fixed operation frequencies is more acceptable.
Based on the above analysis, this paper presents a twocoil structure WPT system based on the improved S/S compensation network. The improvement of S/S compensation network makes it possible to realize the CV and CC charging modes with the ZVS condition at two different operation frequencies, respectively. The switching point of two charging mode can be obtained according to a current detection circuit, which avoids the communication between the primary and secondary sides. And the adjustment of operation frequency can be executed in the DSP, which avoids the addition of redundant segments.
The paper is organized as follows. Section II analyzes the load-independent output characteristics of the simple compensation network, and then proposes a simplest and desired compensation network structure. In Section III, the parameters design, verification of load-independent output characteristics, test of robustness performance and comparison with other counterparts are given. Then follows the experimental part in Section IV. Finally, the Section V is the conclusion content.

II. LOAD-INDEPENDENT CC AND CV OUTPUTS WITH ZVS OPERATION A. DERIVATION OF SIMPLEST COMPENSATION NETWORK TO REALIZE LOAD-INDEPENDENT CC OUTPUT
As shown in Fig. 2, the S/S compensation network is widely used in wireless power transfer system. The V s and i T represent the input AC voltage and current, respectively. Similarly, the V o and i R are the output AC voltage and current, respectively. The L p is the self-inductance of transferring coil and L s is that of receiving coil. M is determined by the transmission distance of coupling coils and reflect the coupling ability. R L is an ac load. The R p is the series internal resistor of L p -C p branch and R s is the series internal resistor of L s -C s branch. The C p and C s are the corresponding compensation capacitors in the primary and secondary side, respectively. And the value of them are chosen to meeting the circuit requirements. According to the mutual inductance theory, the circuit in Fig. 2 can be equivalent to the circuit in Fig. 3. And then based on the Kirchhoff voltage Law (KVL), the mathematical expression of the circuit can be given as where the ω 1 means the resonant angle frequency in loadindependent CC mode. When the following conditions are given The relationship between the output current and input voltage is derived as From (4), i R is related to the load R L due to the existence of R p . However, the R p is quite small, the difference caused by the R p and R s can be ignorable during the CC charging mode. Finally, the output current can be simplified as In addition, the input impedance of given circuit is expressed without the consideration of R p and R s Moreover, under the conditions (2) and (3), Z inc is given by Therefore, the input impedance Z inc is inductive no matter how R L changes. Further, the power devices of high frequency inverter can realize the ZVS turn-on to improve transmission efficiency in the whole CC mode.

B. DERIVATION OF SIMPLEST COMPENSATION NETWORK TO REALIZE LOAD-INDEPENDENT CV OUTPUT
The similar analysis process can be used in the loadindependent CV output mode. The KVL equation can be changed into (8), which is shown as follows where the ω 2 is the resonant angle frequency in loadindependent CV mode. Then the relationship between the output AC voltage and input AC voltage is given as In (9), if the R p and R s are overlooked, with the following condition The output voltage is load-independent, and the expression of output voltage yields as Furthermore, according to (10), the input impedance of given circuit Z inv is expressed as Obviously, with the follow condition The input impedance Z inv is inductive and the ZVS turnon is realized during the CV mode too. Besides, to satisfy the (10) and (13) simultaneously, the C s in the secondary side should be an inductor L 1 , and its value is independent on the ω 2.

C. DERIVATION OF SIMPLEST COMPENSATION NETWORK TO REALIZE LOAD-INDEPENDENT CV/CC OUTPUT
Based on the analysis result in Section A and B. The same compensation network structure can realize the loadindependent output voltage and current at two different operation angle frequency ω 1 and ω 2 . However, the loadindependent ZVS condition cannot be achieved in CC and CV modes simultaneously. To solve this problem, an adaptive branch L r -C r is used to replace the capacitor C s . And the equivalent impedance of this branch will change with the variation of operation frequency. The function of adaptive branch is equivalent as a capacitor C s in operation frequency f 1 and an inductor L 1 in operation frequency f 2 . The equivalent impedance of this branch against the operation frequency is drawn as shown in Fig. 4. The branch inductance L r and capacitor C r will be determined once the capacitor C s in operation frequency f 1 and the inductor L 1 in operation frequency f 2 are given. The relationship among them can be expressed as Then the value of inductance L r and capacitor C r are obtained as The compensation network to realize the load-independent CC output with ZVS condition and CV output with ZVS condition at two different operation frequencies is drawn in Fig. 5. When the operation frequency is f 1 , the whole circuit works at CC mode and the L r -C r branch is equivalent to a capacitor, the ZVS of power devices of high frequency inverter is realized. To obtain a CV output with ZVS condition, the operation frequency is changed to f 2 . At present, the L r -C r branch can be seen as an inductor. In short, the ZVS condition can be satisfied during the whole charging process.

III. EVALUATIONS
Based on the analysis result in Section II, the topology to realize the load-independent current and voltage output with ZVS condition under two different operation frequencies is given in Fig. 6.

A. PARAMETER DESIGN
The output and input characteristics are determined by the circuit parameters. Therefore, a detailed flowchart to describe the design procedure of the system parameters is presented in Fig.7. And the detailed introduction is given below. Firstly, the load-independent CC operation frequency f cc is set. Then based on the battery datasheet, the charging voltage and current are given. And the relationship between the input and the output of rectifier can be derived with the following equations [17] The output voltage V p of the H-bridge inverter can be controlled by adopting the phase shift angle adjustment and the dc voltage V dc . The fundamental component magnitude V p of inverter output voltage with zero phase shift can be expressed as Reasonable coil design will promote the improvement of system transmission efficiency and output power, simultaneously, the size, weight and cost of the coils will be reduced as well [18]. The spiral coil structure is chosen due to the stronger coupling coefficient under the same working condition. The Litz wire is used to weaken the skin effect and further abate the ac resistance value. The transmitting coil and receiving coil adopt the same structure and design parameters, which can reduce the production cost and ensure the consistency of parameters for resonance. The coil model is analyzed by Ansoft Maxwell to estimate its self-inductance. Simultaneously, Fig 8 shows Fig. 8 would be a reference to determine the transmission distance for required output. Based on the analysis in Section II, from (2), the compensation capacitor C p in the primary side can be derived. The value of C s has an important influence on the circuit performance of proposed system, therefore, the C s should be set as large as possible under the condition (3).
The transmission of working mode is implemented by changing the working frequency of HFI. The resonant frequency f cc at the CC mode has been already set. The relationship between the circuit parameters and operation frequency f cv at CV mode is obtained in equation (10), then the operation frequency f cv can be deduced as where the L eq is represented as The adaptive branch parameters are related with the two operation frequency f cc and f cv . And the expression is already given in equation (15). The circuit parameters of the designed WPT system obtained based on the aforementioned design flow are provided in Table 1. During the parameter design process, the mutual inductance M is fixed. The variation of M due to the coils misalignment will affect the loadindependent voltage output characteristic. It will be given full consideration in future work.

B. THE VERIFICATION OF LOAD-INDEPENDENT OUTPUT AND INPUT IMPEDANCE CHARACTERISTICS
It is crucial to verify the rationality of the parameters design method for the proposed two-coil WPT system.   Table 1 are adopted to verify the output and input characteristics. The curves of the voltage transfer ratio G vv and the phase angle a of the Z inv versus frequency at different load conditions are shown in Fig. 9. As shown in Fig. 9(a), there are two switching frequency points (93 kHz and 115 kHz), where the output voltage is both loadindependent. However, according to Fig. 9(b), the phase angle at the first frequency point (93 kHz) is negative, which means the ZVS condition of the HFI is not satisfied. Therefore, the frequency 93 kHz will be abandoned. On the contrary, the ZVS is achieved at the frequency point (115 kHz) due to the positive phase angle value. Therefore, the frequency point (115 kHz) is selected as the operation frequency at CV mode. And the G vv in the frequency point (115 kHz) is 1.199, which agrees well with the theoretical analysis result. The graphs of the current transfer ratio G cv and the phase angle of the corresponding input impedance Z inc under different loads are illustrated in Fig. 10. It can be seen that the load-independent current output and ZVS condition are both satisfied at the set resonant frequency 100 kHz. And the current transfer ration G cv in 100 kHz is 0.0883, which is the ratio of output current to input voltage. As a conclusion of the figures in Fig. 9 and Fig. 10, the design procedure in Fig. 7 can enable the proposed topology to obtain the desired load-independent CC and CV output characteristics as well as the associated ZVS conditions at two fixed switching frequency points, respectively.

C. THE ROBUSTNESS ANALYSIS COMES FROM THE ESRS OF THE CAPACITORS AND INDUCTANCES
In the practical application, the equivalent series resistances (ESRs) of the inductors and capacitors are inevitable. The influence comes from them should be taken into consideration. The ESR values of adopted passive components are given in Table 2. The output and input characteristics without ESRs are analyzed by simulation due to the absence of ideal passive components in practical. The normalized output voltage and input impedance angle curves in CV mode are drawn in Fig. 11(a) and Fig. 11(b), respectively. According to the comparison result in Fig. 11(a), the output voltage will be affected by the ESRs. Normally, the output voltage will 148888 VOLUME 9, 2021 FIGURE 11. The normalized output voltage and input impedance angle curves in CV mode.
decrease due to the existing of ESRs. And the maximum difference happens when the load value is minimum. The reason is that the ESRs will lead a voltage drop during the whole transmission process. However, the difference is so small that it is acceptable in practical occasion. Similarly, the input impedance angle will be affected by the ESRs. Yet the input impedance angle is still positive, therefore, the ZVS of HFI will maintain in practical application. The Fig. 12 shows the normalized current output and input impedance angle curve against the load when the ESRs is considered or not. From Fig. 12(a), when the ESRs are added in the simulation system, the output current will decrease. Moreover, the difference value will increase with the increasing of load and the maximum error ratio is 1.75% at the crossing point of two charging mode. Similar with the input characteristic at CV mode, the ESRs will affect the input impedance angle but not change the positive or negative characteristics. In other words, the ZVS condition will not be affected by the ESRs. In short, the ESRs of passive components will cause some influence to the output and input characteristics but they are acceptable in practical.

D. THE COMPARISON WITH THE OTHER COUNTERPARTS
A lot of papers have been done on the research of the battery wireless charger. Normally, when the system is adopted, the system size and cost are focus of concern. The composition of the compensation network part in serval counterparts [14], [17]- [20] are making a comparison in Table 3. The application of multi-coil to realize a CC or CV output can increase the coupling ability, however, it takes up a lot of space and increases the system cost. Among the twocoil system, the proposed converter only uses one inductor, hence, the power density of whole system can be very high.  Simultaneously, it also has the least amount of capacitor. As a result, the cost in proposed converter can be cut down greatly. In addition, there is no additional switches used in proposed topology. In [20], the switch connected with a passive component may have potential danger when the switch turns off with residual energy. The parasitic parameters of the switches will also have an important influence on the system performance. In sum, the proposed converter performs better in the comprehensive performance of the system when the load-independent CC and CV output with ZVS condition is required for wireless battery charger.

E. CONTROL STRATEGY
Based on the parameters design procedure, the proposed topology can realize load-independent CC output and CV output with ZVS condition at two different operation frequencies, respectively. During the battery charging process, the whole system works at CC mode firstly and then the CV mode. The transparent signal of the switching point from CC mode to CV mode is that the output voltage reaches the preset charging voltage in CV mode, or the equivalent battery internal resistance rises to R set , the equivalent battery internal VOLUME 9, 2021 resistance can be evaluated by detecting the input current i p . The control diagram for the proposed WPT system is provided in Fig. 13, where I p and I set are the input current magnitude and reference current corresponding to the R set , respectively. A current detective circuit is introduced to measure the magnitude of input current i p . The resonant tank current in the primary side is converted into ac voltage signal by a Hall current sensor HBC-ES3.3, then an RMS calculator AD637 is employed to obtain the effective value V _odc of ac voltage signal. Then the V _odc is sent into the digital-signal processor TMS320F28335. When the input current magnitude I p is smaller than the reference charging current I set , the operation frequency is chosen as f cc to work at CC mode. When input current magnitude I p reaches the reference charging current I set during the charging process, the operation frequency is adjusted to f cv . The charging mode will be changed to CV mode by changing the operation frequency to f cv . The proposed WPT system can operate in CC mode or CV mode by changing the operation frequency of HFI, and both two operation modes can achieve ZVS. The performance comparison on the control strategy is presented in Table 4. Compared with [17], [20] and [21], there is no communication between the primary side and secondary side in the proposed WPT system, which can not only save the cost but also avoid the error caused by the instability of wireless communication. Meanwhile, the input current magnitude I p is the only variable required to be measured. The detection execution in the proposed system will become simpler than the detection circuits in [22]- [26]. In general, the control strategy is easy, simple and economical to implement in practical application for battery charger.

IV. EXPERIMENTAL RESULTS
To verify the feasibility of the theoretical analysis, an experimental platform with 60V charging voltage and 3.6A charging current output based on the proposed circuit structure is built in Fig. 14. The component parameters in Table 1 are used. It is need to say that the experimental setup is constructed to confirm the practicability of proposed circuit topology and control strategy. The whole experimental prototype can be adjusted properly when it is adopted to different applications.

A. EXPERIMENTAL PLATFORM
In the experimental platform, in the primary HFI part, the Infineon IRFP4227 is adopted due to its low conduction resistance in high frequency occasions. the gate driving chip SI8233BD is chosen to drive the MOSFETs. The full bridge rectifier in the secondary side is constructed by the Schottky diode PSM20U200GS. The polypropylene film capacitor is adopted as the compensation capacitor due to its stability in high frequency condition. Simultaneously, multiple nominal capacitors are connected in parallel, as a result, the equivalent B. Cheng, L. He: Frequency Adaptive Topology to Realize Constant Output   series resistance in practical application is reduced, and the capacitor value error between the designed and measured resonant capacitor value can be diminished to near zero. As for the resonant inductor L r , the magnetic core material is preferably ferrite material with lower loss and the Litz wire is extremely suited due to its lower skin effect loss and smaller equivalent series resistance in high frequency occasion. The electronic load is used to imitate the changing equivalent battery internal resistor during the charging process.

B. EXPERIMENTAL RESULTS
When the charging process starts, the system works at the CC mode firstly. The waveforms of input current i p , input voltage V p , output current i B and output voltage V B in 7.5 and 15 are shown in Fig. 15(a) and Fig. 15(b), respectively. As shown in Fig 15(a) and Fig. 15(b), the resonant frequency is 100 kHz and the output current maintains 3.6A. Besides, the waveforms of S 2 are shown in Fig. 17(a), the input current lags input voltage by tens of degrees, therefore, the reverse parallel body diode of S 2 is turned on, and the voltage V ds2 is choked as the forward conduction voltage drop of the parallel body diode. Hence, the crossing area of V ds2 and i p is close to zero, which means the ZVS for S 2 has been realized. The other switches have the same working principle with S 2 . The transient waveforms of load changing from 7.5 to 15 at the CC mode are shown in Fig. 15(c). It is obvious that the charging current remains almost constant after a small overshoot. The slight output current error happens due to the unideal devices in practical experimental setup. And the difference is so small that it can be negligible.
The output voltage changes proportionally with the load at the CC mode. The whole system enters into CV mode when the output voltage reaches 60V. The switching point is determined by the measurement of input current amplitude. The transient waveforms of mode switching from CC mode to CV mode are given in Fig. 17(c). From Fig. 17(c), the response is fast and the charging voltage and current will return to normal after a small drop happens. In addition, since there is difference between the equivalent circuits in CC and CV mode, the amplitude of input current in two modes are different. Moreover, there is no voltage and current spike during the switching process, compared with the other switching way by controlling additional switches, Good stability and safety makes it more practical in battery charging application.
The whole system works at CV mode until the end of charging process. The waveforms of input current i p , input voltage V p , output current i B and output voltage V B in 17 and 34 are shown in Fig. 16(a) and Fig. 16(b), respectively. The resonant frequency is around 115 kHz and the output voltage is hold at ∼ 60V. Once again, the waveforms of S 2 at CV mode are shown in Fig. 17(b), the V ds2 has been dropped to zero before the V gs2 is given, the ZVS is realized for all switches due to the inductive input impedance. Besides, the V ds raise from zero when S 2 is turned off due to the existing of C oss . As a result, the quasi ZVS turn-off is also thought to be realized. Similarly, to test the response performance of the proposed system at the moment of load changes, the corresponding waveforms of load changing from 17 to 34 are shown in Fig. 16(c). Obviously, the output voltage has almost no change and the output current slowly drops by half. There is no voltage or current spike during the switching process, meaning a good stability. The measured output voltage and current curves are put in Fig. 18(a). From the Fig. 18(a), the output current has a slight downward trend with the increasing of battery internal resistor in CC mode. When the circuit enters into CV mode, the output voltage increases slowly with the charging process going on. Nevertheless, the highest output voltage at the end point of charging process is 62.4V, which is 4% of rated output voltage. According to the parameter ''Float charging Voltage'' in the datasheet of Lead-Acid battery, the variation voltage value is proper. The transmission efficiency (from the DC source to the battery load) curve versus Log(R B ) is drawn in Fig. 18(b). The transmission efficiency rises up at the CC mode with the increasing of output power, and then it decreases at the CV mode with the decreasing of charging power. The peak efficiency in CC mode and CV mode are up to 91.6% and 91.66%, respectively. Besides, the peak efficiency happens in the crossing point of CC mode and CV mode. Additionally, the charging process comes to an end when the output current reaches one in ten constant charging current in CC mode and the lowest efficiency is 71.37% at this time, which is mainly because that the WPT system works in light-load conditions.

V. CONCLUSION
To increase the system power density and reduce the system cost, the detailed analysis of the simplest S/S compensation network on load-independent output with ZVS is given. Then the WPT system with an adaptive L r -C r branch is proposed. The CC mode and CV mode are realized at two different resonant frequencies, respectively. In addition, the influence comes from the ESR of passive component are taken full consideration, which proves the strong robustness of proposed wireless charger. an input current detection circuit is added in the primary side to seek the switching point of two working mode, which avoids the communication between the transfer side and receiver side. Moreover, the good sinusoidal performance of input current waveform makes the error of estimation very small. Finally, the peak transmission efficiency reaches 91.66% and the average transmission efficiency is at a high level due to the ZVS realization during the full charging process. The experimental results are consistent with the theoretical analysis and verify the expected circuit performance. In sum, the proposed WPT system has the advantages of high power density, low system cost and higher transmission efficiency.