4438 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

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1 4438 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014 Self-Oscillating Contactless Resonant Converter With Phase Detection Contactless Current Transformer Kaiqin Yan, Qianhong Chen, Member, IEEE, Jai Hou, Xiaoyong Ren, Member, IEEE, and Xinbo Ruan, Senior Member, IEEE Abstract In this paper, a self-oscillating control strategy is proposed for a series series type contactless resonant converter (CRC). By detecting the secondary current phase of a CRC to control the inverter, better output controllability, dynamic response, and self-adaptability can be achieved. While the realization of selfoscillating control strategy depends on phase detection of secondary current. To provide a passive solution, a current transformer with shorted secondary, called phase detection contactless current transformer (PDCCT) is proposed. The proposed PDCCT can detect the current phase from the secondary side of a CRC and feedback to the primary side rapidly and accurately despite the changes in air gap. To guarantee the accuracy of self-oscillating control strategy, the time delay in control circuitry is studied and compensated. A 60-W self-oscillating CRC with PDCCT is then fabricated to demonstrate the validity of both PDCCT and selfoscillating control strategy. Besides, a testing circuit is designed to emulate the changes in converter parameters, and the dynamic performance shows that self-oscillating control strategy can respond to parameter changes in a switching period. Index Terms Contactless power transmission (CPT), phase detection contactless current transformer (PDCCT), self-oscillating, series series (SS) type contactless resonant converter (CRC). I. INTRODUCTION CONTACTLESS power transmission (CPT) is a new power supply method to achieve power transfer without mechanical contact. Since CPT is able to improve the flexibility of power supply, decrease maintenance cost and obtain high reliability, it has been applied in many applications such as battery charging systems, underwater devices and mining applications [1] [3]. The available power transfer capability of CPT systems can be several watts to tens of kilowatts. Low power applications include power supply to cellphones [4], [5] and artificial organs [6], [7]. Medium and high power applications focus on contactless charging of electric vehicles [8] [13] and material Manuscript received August 7, 2013; revised November 28, 2013; accepted January 2, Date of current version March 26, This work was supported in part by the National Natural Science Foundation of China under Grant , in part by the Natural Science Foundation of Jiangsu Province under Grant BK , and the Research Fund for the Doctoral Program of Higher Education of China under Grant Recommended for publication by Associate Editor R.-L. Lin. The authors are with the Aero-Power Sci-Tech Center, College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing , China ( yan_kaiqin@126.com; chenqh@nuaa.edu.cn; houjia@nuaa.edu.cn; renxy@nuaa.edu.cn; ruanxb@nuaa.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TPEL handling systems [14]. Besides, for the convenience of daily life, CPT systems also find application in kitchen appliances [15]. Though CPT systems have irreplaceable advantages in some specific applications, due to the loosely coupled transformer, the efficiency of a CPT system is relatively low compared to those conventional ones. Moreover, the parameters of the contactless transformer will change with changeable air gaps. This will in turn aggravate the complexity of the nonmonotonic output response and finally challenge the control of a CPT system. To date, numerous control strategies are proposed to adjust to variable parameters and obtain high efficiency. Variable frequency control strategy is a simple control strategy for resonant converter, and is also used in inchoate CPT systems [16]. Yet the efficiency is relatively low under light load due to the circulating loss. Pulse width modulation (PWM) + phase lock loop (PLL) control strategy is proposed in [6], PWM and PLL are dedicated to output voltage and zero-voltage switching (ZVS) realization. With this control strategy, constant output and high efficiency are both achieved. A recent research in KAIST shows a new method in output regulation [17], when the secondary of a series series (SS) type contactless resonant converter (CRC) is fully resonated, the secondary can be simplified as a constant voltage source according to Thevenin s theorem. However, the constant output characteristic will fail with changeable coupling coefficient of the contactless transformer. To improve the efficiency further, more detailed analysis is undertaken both in the selection of resonant components and the design of control strategy. In [18], the selection of resonant capacitors is discussed to make a balance between output voltage controllability and converter efficiency for an SS-type CRC. While in [19] an optimal efficiency control strategy is developed to obtain high efficiency and provide duty cycle information for latter stage boost converter. Consequently, an efficiency of over 90% is maintained on a 5-KW CPT system. The previously mentioned control strategies all concentrate on the achievement of constant output voltage and high efficiency, yet detailed analysis in dynamic property is lacking. While in some specific occasions, such as power supply to CPU and implantable devices [6], dynamic performance is also a considerable factor. Self-oscillating control is a control strategy which can achieve better dynamic performance and self-adaptability at various converter parameters, and has been adopted in many converters such as Jensen converter [20] and RCC converter. This paper focuses on the realization of self-oscillating control strategy for an SS-type CRC and is organized as follows. Taking winding resistances into account, the input impedance at IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See standards/publications/rights/index.html for more information.

2 YAN et al.: SELF-OSCILLATING CONTACTLESS RESONANT CONVERTER 4439 and v s1 stand for the fundamental component of v AB and v s, respectively. L p and L s are the self inductances of the primary and the secondary side, respectively, M is the mutual inductance, the coupling coefficient k of the contactless transformer satisfying k = M Lp L s. (1) Fig. 1. Fig. 2. Topology of an SS-type CRC. Fundamental equivalent circuit of an SS-type CRC. voltage gain intersections is analyzed in Section II, and the selfoscillating control strategy is proposed in this part. In Section III, the difficulty in secondary current phase detection is studied. To solve this problem, a current transformer with shorted secondary winding called phase detection contactless current transformer (PDCCT) is proposed. Section IV discusses the practical issues in the realization of a self-oscillating CRC (SOCRC), including the starting circuit and the time delay in control circuitry. In Section V, a 60-W prototype of SOCRC with PDCCT is fabricated, whose resonant capacitors are designed to obtain better output controllability. The validity of PDCCT and self-oscillating control strategy is verified by steady-state experimental results. In addition, a testing circuit is established to emulate the dynamic changes in air gap and the experimental results show the favorable dynamic performance of the proposed control strategy. II. DERIVATION OF SELF-OSCILLATING CONTROL STRATEGY A. Circuit Description The topology of an SS-type CRC with full-bridge inverter is shown in Fig. 1. The full-bridge inverter comprises four switches (Q 1 Q 4 ), which operate in complementary mode and convert a dc voltage V in into a high-frequency ac voltage v AB. Then resonant capacitor C p and the primary of the contactless transformer Tr are tuned by the high-frequency ac voltage, and alternating magnetic field is generated in the primary side. With magnetic coupling, a voltage is induced in the secondary side and powering the load R L through a serial capacitor C s. In the analysis of an SS-type CRC, fundamental model approximation is normally used since the fundamental component of the current in resonant tank is much larger than harmonics. Therefore, the rectifier and the load R L can be replaced by an equivalent load R E satisfying R E = (8/π 2 )R L [6], [18], [21]. Then the corresponding fundamental equivalent circuit of the converter can be got, as shown in Fig. 2, in which Tr is emulated with mutual inductance model. R p and R s stand for the winding resistances of the primary and the secondary respectively. v s represents the input voltage of the full-bridge rectifier, v AB1 B. Load-Independent Voltage Gain Characteristics Though the voltage gain analysis of the converter shown in Fig. 2 have been provided in [18], the derivation processes are still involved here briefly to ensure the integrity of this paper. Define Z p = jωl p R p Z s = jωl s R s. (2) jωc p jωc s The input-to-output voltage gain is G v (ω) = ωmr E Z p (Z s + R E )+ω 2 M 2 = jωm (3) Z p + Δ ω 2 C p C s R E + R p Z s +R s Z p R P R s R E ( ) where Δ=ω 4 C p C s M 2 L p L s +ω 2 (L p C p + L s C s ) 1. Considering the requirement of high efficiency, R p R E,R s R E, therefore (R p Z s +R s Z p R p R s )/R E is neglected: jωm G v (ω) Δ Z p +. (4) ω 2 C p C s R E When Δ=0, there are two frequencies at which the voltage gains are load-independent, and the two frequencies are ω2 p + ωs 2 (ωp 2 + ωs 2 ) 2 4(1 k 2 )ωp 2 ωs 2 ω L = 2(1 k 2 (5) ) ω2 p + ωs 2 + (ωp 2 + ωs 2 ) 2 4(1 k 2 )ωp 2 ωs 2 ω H = 2(1 k 2 (6) ) 1 where ω p = and ω s = 1 L p C p L. s C s The corresponding load-independent gains are G v (ω L )= jω L M Z p = n/ Z 1 1+ jnω L L M (7) G v (ω H )= jω H M Z p = n/ Z 1 1+ jnω H L M (8) where Z 1 = jωl l1 + 1/(jωC p )+R p,z 2 = jωl l2 + 1/(jωC s ) + R s. n is the turn ratio of the transformer, L l1 and L l2 are the leakage inductances for each side, L M stands for the magnetizing inductance. Obviously, the voltage gains at the intersections will be equal to turn ratio n if Z 1 = 0. Let us just set ω p = ω s, with the approximation L M kl p,n 2 L M kl s, (5), (6) can be simplified as

3 4440 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014 Fig. 3. Equivalent circuit of an SS-type CRC when Z 1 =Z 2 = 0. follows: ω L = ω H = ω p 1 (9) 1+k (Lp + L M )C p ω p 1. (10) 1 k Ll1 C p Substituting (9), (10) into (7), (8), respectively, the voltage gains at the two intersections are approximate to turn ratio n which means stable output response to parameter changes can be obtained if the operation frequency is set at the intersections. C. Transfer Impedance The aforementioned analysis discloses that the voltage gains at ω L and ω H are almost constant at different converter parameters. This constant voltage gain characteristic is more straight forward by adopting the leakage inductance model of the transformer, as shown in Fig. 3. For the specific case when Z 1 = Z 2 = 0, the input-to-output voltage gain will be load-independent and equal to turn ratio n. An interesting phenomenon is also found that the fundamental component of secondary current i s1 is in phase with v AB1 in this case. Enlightened by this finding, we want to know if this phenomenon is still valid for normal cases. Therefore, further analysis is done in the following to analyze the phase relationship between i s1 and v AB1 for normal cases with the mutual inductance model shown in Fig. 2. Define Z M = jωm. (11) According to KVL { ZpIp1 Z M Is1 = V AB1 Z M Ip1 +(Z s + R E ) I (12) s1 =0. To describe the phase relationship between i s1 and v AB1, transfer impedance is introduced, as shown in (13) at the bottom of the page. In which the definition of Δ is the same as in (3): Similar to the analysis in input-to-output voltage gain, the influence of the winding resistances is neglected, and (13) can be simplified as follows: ( ) ωl p 1 Δ ωc p R E j ω Z 21 = 2 C p C s. (14) ωm Z 21 = V AB1 I s1 = Z p(z s + R E ) ZM 2 j = Z M ( Substituting load-independent frequencies ω L and ω H into (14) respectively, it can be found that Re[Z 21 ] < 0 and Im[Z 21 ] = 0atω L, which means i s1 is 180 delay with v AB1 ; Re[Z 21 ] > 0 and Im[Z 21 ] = 0atω H, which means i s1 is in phase with v AB1. Obviously, i s1 is either in phase or 180 delay with v AB1 at the voltage gain intersections for an SS-type CRC. If the phase relationship of i s1 and v AB1 is ensured, will the converter be able to operate at the voltage gain intersections automatically? Assuming i s1 and v AB1 are in phase, according to (14), we have ( Δ ω 2 =0 ωl p 1 ) R E > 0. (15) C p C s ωc p Obviously, the load-independent frequency ω H in (5) is the solution of (15). That means the converter will operate at the voltage gain intersection automatically. When i s1 is 180 delay with v AB1, similar analysis and conclusion can be obtained. D. Self-Oscillating Control Diagram According to the transfer impedance analysis, i s1 is always in phase or 180 delay with v AB1 at the intersections under various air gaps and load conditions. Considering the ZVS realization, ω H is chosen as the operation frequency for self-oscillating control strategy. Since the secondary current i s is almost sinusoidal, the phase information of i s1 can be replaced by the zero-crossing points of i s. Meanwhile, v AB1 is the fundamental component of v AB. By using a comparator, when i s > 0, Q 1,Q 4 conduct setting v AB > 0, when i s < 0, Q 2,Q 3 conduct setting v AB < 0, the converter will, therefore, work at ω H. And the control diagram of self-oscillating control strategy can be drawn, as shown in Fig. 4. As shown in Fig. 4, the control circuitry comprises several blocks: current sensing block, zero-crossing comparator block, driver block and starting circuit. The operation of this control diagram is briefly explained as follows. With an enable signal, the starting circuit generates the initial driving signal to the inverter, thus exciting the secondary current i s of the CRC. Current sensing block detects the secondary current i s and transfers its phase information to the primary side. As shown in Fig. 4, the output ) ( ) ) Δ ω 2 C p C s + R p R s + R p R E +(R s + R E ) ωl p 1 ωc p + R p (ωl s 1 ωc s ωm (13)

4 YAN et al.: SELF-OSCILLATING CONTACTLESS RESONANT CONVERTER 4441 Fig. 6. Equivalent circuit of a current transformer with shorted secondary winding. Fig. 4. Self-oscillating control diagram for an SS-type CRC. Fig. 5. air gap. Equivalent circuit of a conventional current transformer with a large Fig. 7. Equivalent circuit of the proposed PDCCT. signal i s of the current sensing block is in phase with i s.after current phase detection, the signal i s can be converted into two complementary square waves by the zero-crossing comparator to drive the inverter through driver block and to continue the oscillation as well. Fig. 8. Equivalent circuit for PDCCT with lumped parasitic resistances. III. PROPOSED PDCCT A. Operation Principle of PDCCT It is obvious that current sensing block is a key part in the system which is also separated into two parts by the air gap, and should detect the phase of secondary current accurately. Active detection methods such as radio frequency and IR transmitters [22], [23] have been widely used in communication between the primary and the secondary. However, active detection methods require stable power supply in the secondary. So, passive current detection method is preferred. Current transformer is a basic passive current detection technique. Considering the effect of the air gap, the equivalent circuit of a conventional current transformer is drawn in Fig. 5. Where i 1 is the current to be detected, i 2 is the current of secondary winding, L 1 and L 2 stand for the leakage inductances of primary winding and secondary winding, respectively, L 3 is the magnetizing inductance, the turn ratio is represented by n 1. According to Fig. 5, the voltage of detection resistor R CS is V c = R CSI2 = 1 jωr CS L 3 n 1 jω(l 2 /n L 3)+R CS /n 2 I 1. (16) 1 It is readily known that the phase of v c is different from that of i 1, thus conventional current transformer cannot be used in this system. To overcome the difficulty in current phase detection, we propose a current transformer with shorted secondary winding. Its equivalent circuit is shown in Fig. 6. Hence, i 2 can be derived as follows: I 2 = 1 jωl 3 n 1 jωl 3 + jωl 2 /n 2 1 I 1 = 1 L 3 n 1 L 3 + L 2 /n 2 I 1. (17) 1 As can be seen from (17), i 2 and i 1 are always in phase regardless of the changes in air gap. To transfer the current signal to a voltage one, another cascaded current transformer is adopted, as shown in Fig. 7. The two cascaded current transformer 1 and current transformer 2 constitute a PDCCT. B. Phase Detection Accuracy Analysis Though through current transformer 1, accurate phase information of i 1 can be obtained, some nonideal factors may bring error in current phase detection, such as the impedance introduced by current transformer 2 and the parasitic resistances in the circuit. To analyze the detection error caused by these two parts, an equivalent circuit is shown in Fig. 8, in which the parasitic resistances are supposed to be lumped. The expression of i 2 and v c can be derived as follows: I 2 = jωm 1 R 2 + jω(l s 1 + L p 2 )+ V c = jωm 2 I2 R CS I1 (18) ω 2 M 2 2 jωl s 2 +R 3 +R CS jωl s 2 + R 3 + R CS. (19) Here L p 1,L s 1,L p 2, and L s 2 are the self inductances of PDCCT, M 1 and M 2 are the mutual inductances, the parasitic resistances are represented by R 1,R 2, and R 3.

5 4442 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014 Fig. 10. Starting circuit of SOCRC. Fig. 9. Vector diagram of a PDCCT with lumped parasitic resistances. For a conventional current transformer, R CS R 3, ωl s 2 R CS, therefore (18) can be simplified as follows: I 2 jωm 1 R 2 + jω(l s 1 + L p 2 ) jωm2 2/L I 1. (20) s 2 And the phase detection error θ can be got as shown in (21) at the bottom of the page. In (21), θ 1 is the phase angle between i 1 and i 2, θ 2 is the phase angle between i 2 and v c. According to Taylor formula, the phase detection error in (21) can be simplified as in (22) at the bottom of the page. It is readily known that the phase detection error is related to not only the parameters of PDCCT but also the operation frequency. To visualize the phase detection error, a vector diagram is drawn in Fig. 9. Where v Ls 1,v Ls 2,v Lp 2,v R2, and v R3 are the voltage across L s 1,L s 2,L p 2,v R2, and v R3, respectively. It vividly tells that v c leads i 1, and the phase detection error is generated due to R 2,R 3, and R CS. Besides the detection error, magnetic field coupling from the main contactless transformer also affects the phase detection accuracy of PDCCT. To solve this problem, magnetic shielding materials such as aluminum foil and copper foil can be applied. IV. PRACTICAL ISSUES AND SOLUTIONS FOR SOCRC In the realization of SOCRC, other practical issues such as circuit starting and the time delay in control circuitry should also be considered. A. Starting Circuit Before the operation of an SOCRC, the amplitude of secondary current is zero, and no signal can be employed to start the oscillating. Thus, a starting circuit should be adopted to provide initial driving signals. The starting circuit used here is an analog one [24], [25], which comprises a resistor R st, a diode D st, a capacitor C st, and a bidirectional trigger diode DIAC, as shown in Fig. 10. Before the oscillation, the voltage of C st is zero. When V in is supplied, C st is charged by V in through R st. As soon as the voltage of C st reaches the breakdown voltage of DIAC, DIAC is on, therefore, the gate of Q 3 is charged by C st, and Q 3 is consequently on. Then C st is discharged through Q 3 and D st, as a result, DIAC and Q 3 are off, which accomplishes the starting process. B. Time Delay Analysis and Its Compensation In SOCRC, the time delay in control circuitry will bring deviation in operation frequency, and may lead to distinct changes in output voltage. Hence, it is necessary to analyze the time delay in each control block. 1) Time Delay in Control Circuitry: As can be seen from Fig. 4, time delay may come from current sensing block, zerocrossing comparator block and driver block. According to the analysis in Section III, we know that PDCCT will introduce a time leading. In practical application, the time leading is about tens of nanoseconds, which is less than 1% of the switching period, therefore can be ignored. The zero-crossing comparator block and driver block are realized by integrated circuits lm311 and IR2110, respectively. And the time delay generated by these two blocks is almost fixed and around the order of hundreds of nanoseconds. 2) Compensator: Since the time delay in control circuitry is mainly caused by the driver and zero-crossing comparator, and is almost a fixed one around the order of hundreds of nanoseconds, a compensator is needed to provide a nearly constant leadingtime compensation. Therefore, the control diagram is redrawn in Fig. 11. Since the operation frequency of the converter is changing automatically, the main difficulty in the design of a compensator is to achieve nearly constant leading-time compensation within a range of frequencies. Fig. 12 shows a normally used RC leading-time compensator. Obviously, the compensation time is changing under different operation frequencies. An improved R 2 θ = θ 1 + θ 2 arctan ωl s 1 + ωl p 2 ωm2 2/L + arctan R 3 + R CS s 2 ωl s 2 (21) R 2 θ ωl s 1 + ωl p 2 ωm2 2/L + R 3 + R CS 1 ( ) 3 R 2 s 2 ωl s 2 3 ωl s 1 + ωl p 2 ωm2 2/L 1 ( ) 3 R3 + R CS s 2 3 ωl s 2 (22)

6 YAN et al.: SELF-OSCILLATING CONTACTLESS RESONANT CONVERTER 4443 TABLE I SPECIFICATIONS OF AN SS-TYPE CRC Fig. 11. Self-oscillating control diagram for an SS-type CRC. ing frequency so as to provide a nearly constant leading-time compensation. The precise compensation time t c at different operation frequencies can be obtained as shown in (24) at the bottom of the page. It can be seen from (24) that by neglecting the high-order terms, leading-compensation time t c is nearly irrelevant to operation frequency ω: V. SIMULATION AND EXPERIMENTAL RESULTS Fig. 12. Fig. 13. Fig. 14. Conventional time-leading RC compensator. Proposed time-leading compensator used in SOCRC. Bode diagram of the compensator. leading-time compensator is proposed with another resistor introduced, as shown in Fig. 13. It comprises two resistors R 1,R 2 and a capacitor C. Its transfer function is shown as follows: G(s) = = (1 + sr 1 C)R 2 R 1 + R 2 + SR 1 R 2 C R 2 sr 1 C +1 R 1 + R 2 sr 1 R 2 C/(R 1 + R 2 )+1. (23) According to (23), the bode diagram of the compensator can be easily got, as shown in Fig. 14. In the operation area as shown in Fig. 14, the leading phase angle increases with the increas- A. Specifications and Design Procedures of an SS-Type SOCRC To make an experimental verification, a 60-W SS-type SOCRC with an air gap of mm is fabricated, referred to the specifications required by a CRC powering an artificial heart [6], [21]. Detailed specifications are shown in Table I. The design of a CRC mainly lies in the selection of the resonant components. It can be divided into several steps as follows. 1) Determination of Turn Ratio n of the Contactless Transformer: As has been proved in Section II, the voltage gain is approximate to turn ratio n when the converter operates at the voltage gain intersections. Thus, n can be obtained n = V o = 24 =0.8. (25) V in 30 Due to the effect of winding resistances, a design margin should be considered, choosing n = 17:19 = ) Determination of Quality Factor Q: The quality factor Q is an important parameter which not only affects the efficiency of the converter, but also affects the voltage rating of resonant capacitors. Low Q will result in high circulating loss and low efficiency, high Q will lead to high voltage rating of resonant capacitors. Here, Q max < 10 is desired for low voltage rating of resonant capacitors. Q min = 1.5 is chosen, hence P o max Q max = Q min = =7.5. (26) P o min 12 3) Determination of Resonant Frequency: Considering the efficiency, the resonant frequency is selected 1 f 0 = 2π 1 = L l1 C p 2π = 200 khz. (27) L l2 C s 4) Fabrication and Measurement of the Contactless Transformer: Fig. 15 shows the fabricated contactless transformer, t c = π 180ω { = π 180 [ arctan(ωr 1 C) arctan R 2 1C R 1 + R R3 1C 3 1 ( )] ωr1 R 2 C R 1 + R 2 [ ( ) [ 3 ( R2 1] ω 2 1 ) } 5 R 1 + R 2 5 R5 1C1 5 R2 1] ω 4 + R 1 + R 2 πr 2 1C 180(R 1 + R 2 ) (24)

7 4444 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014 Fig. 15. side. Fabricated contactless transformer. (a) Primary side. (b) Secondary TABLE II PARAMETERS OF THE RESONANT COMPONENTS OF AN SS-TYPE CRC Fig. 16. Practical realization of the control circuitry. TABLE IV POWER COMPONENTSUSED INCRC TABLE III VALUES OF ξ UNDER DIFFERENT DESIGN OCCASIONS in which Litz wire is used to decrease ac resistances of the windings. And the measured parameters are shown in Table II. 5) Selection of Resonant Capacitors: The resonant capacitors can be selected according to (24). However, the leakage inductances at different air gaps are changeable. It should be determined whether to design the capacitors at the smallest air gap or the biggest one. Considering the winding resistances, the load-independent voltage gain will deviate from the intersection under different load conditions. Consequently, the capacitors can be designed to minimize the deviation to achieve better output stability. And (3) is derived as follows: jωm G v (ω) = Z p + Δ ω 2 C P C S R E + ξ+r P R S R E (28) where ξ = R p (jωl s +1/(jωC s ))+R s (jωl p +1/(jωC p )). As R p and R s are fixed in a certain transformer, the difference in output voltage at full load range will be smaller if ξ is minimized. When the capacitors are designed at different air gaps, the values of ξ are shown in Table III. As shown, when designed at 10-mm air gap, ξ is smaller at both 10 and 20 mm air gap. Consequently, the capacitors are chosen to satisfy (27) at 10-mm air gap. Fig. 16 shows the practical circuit of the control circuitry, in which v c represents the output voltage of PDCCT. As shown in Fig. 16, a voltage follower realized by amplifier Tl074 is adopted TABLE V PARAMETERS OF THE CURRENT TRANSFORMER 1 to isolate the impedance affection between PDCCT and the later circuits. The compensator, zero-crossing comparators and driver are cascaded, which generate the driving signals for the inverter. Other detailed information of CRC and current transformer 1 is shown in Tables IV and V, respectively. The position of PDCCT and the main contactless transformer is illustrated in Fig. 17, and they share the same air gap. B. Simulation Results Figs. 18 and 19 show the calculated input-to-output voltage gain and transfer impedance phase angle using software MATH- CAD, respectively. As seen, when winding resistances are taken into consideration, the voltage gain and transfer impedance are similar to those with zero R p and R s. The existing of winding

8 YAN et al.: SELF-OSCILLATING CONTACTLESS RESONANT CONVERTER 4445 Fig. 17. Placement of PDCCT and the main contactless transformer. Fig. 18. Calculated frequency response of input-to-output voltage gain of an SS-type CRC. (a) With zero R p and R s and (b) with actual R p and R s. resistances only slightly decreases the voltage gain. Therefore, the approximations in Section II are reasonable. C. Experimental Evaluations of PDCCT and Time Delay Compensation Table VI shows the detailed parameters of the PDCCT measured by Chroma automatic component analyzer 3302 at 10 and Fig. 19. Calculated transfer impedance phase angle of an SS-type CRC. (a) At 10-mm air gap with zero R p and R s, (b) at 20-mm air gap with zero R p and R s, (c) at 10-mm air gap with actual R p and R s, and (d) at 20-mm air gap with actual R p and R s.

9 4446 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014 TABLE VI PARAMETERS OF PDCCT WITH LUMPED RESISTANCES Fig. 20. Operation waveforms of PDCCT when a 2-Ω resistor is added into the R 2 branch. Fig. 22. Operation waveforms of the compensator. (a) At 10-mm air gap. (b) At 20-mm air gap. Fig. 21. air gap. Operation waveforms of PDCCT. (a) At 10-mm air gap. (b) At 20-mm TABLE VII TIME DELAY IN CONTROL BLOCKS 20 mm air gap. As can be seen, the parasitic resistors are very small as well as the resultant leading-time which can be calculated by (21). To verify the validity of (21), a 2-Ω resistor is added in series with R 2. The phase detection error calculated by (21) is about 31.5, approximate to 430 ns, which agrees with the measured result shown in Fig. 20 very well. The operation waveforms of the proposed PDCCT at different air gaps are tested as shown in Fig. 21. In the waveforms, i 1,i 2, and v c are almost in phase. By calculation, v c ranges from 2.3 to 2.8, 30 to 45 ns leading to i 1 within simulated frequency range. For the follower shown in Fig. 16, the time delay is about 30 ns which can be compensated by the PDCCT. Measured time delay of zero-crossing comparator block and driver block are nearly constant, which are shown in Table VII. As seen, the time delay in control circuitry mainly comes from these two blocks. Thus, the compensator should provide nearly 600 ns leadingtime compensation. The components in the compensator are chosen as R 1 = 4.9 kω, R 2 = 1.4 kω, and C = 0.31 nf. Substi- Fig. 23. Measured frequency response of input-to-output voltage gain of an SS-type CRC. tuting the parameters into (24), the leading-time compensation ranges from 550 to 630 ns during the simulated frequency range. The calculated time variation is ±8.3% of 600 ns and ±1% of the switching period. Obviously, nearly constant time compensation is achieved. Fig. 22 shows the corresponding waveforms of the compensator, where v c and v c stand for the input and the output of the compensator, respectively. As can be seen from Fig. 22, v c is nearly 600 ns leading v c at different air gaps. D. Steady-State Experimental Results of SOCRC Fig. 23 shows the frequency response of input-to-output voltage gain without the control circuitry in Fig. 4. f H kmin (168 khz) and f H kmax (194 khz) are the load-independent frequencies under 20 and 10 mm air gap, respectively, and are quite close to those in Fig. 18. Fig. 24 shows the self-oscillating controlled waveforms under these two air gaps, and the operation frequencies are also close to f H kmin and f H kmax.

10 YAN et al.: SELF-OSCILLATING CONTACTLESS RESONANT CONVERTER 4447 Fig. 26. Testing circuit for dynamic response of SOCRC. Fig. 27. Dynamic response of SOCRC. (a) Switch out L l. (b) Switch in L l. Fig. 24. Operation waveforms of an SS-type SOCRC. (a) P o = 55 W at 10-mm air gap. (b) P o = 30 W at 10-mm air gap. (c) P o = 13 W at 10-mm air gap. (d) P o = 60 W at 20-mm air gap. (e) P o = 30 W at 20-mm air gap. (f) P o = 13 W at 20-mm air gap. Fig. 28. Load regulation of SOCRC. Fig. 25. Starting waveforms of primary current and output voltage. E. Dynamic Performance of SOCRC Fig. 25 shows the starting waveform of the converter, in which v o represents the output voltage of the converter. To verify the rapid response of SOCRC, a testing circuit is established to emulate the parameter changes. As shown in Fig. 26, L l (10 μh) and the two switches (IRF530 N) are added to emulate the parameter changes. Fig. 27 shows the dynamic performance of the SOCRC, and it should be noted that the dc input is only 10 V to ensure the safety of the two switches S 1 and S 2. As shown in Fig. 27, when L l is switched in or out of the circuit, the operation frequency can suit to the new self-oscillating operation frequency in a switching period. Fig. 29. Measured efficiency from dc input to dc output of the SOCRC. F. Load Regulation and Converter Efficiency Fig. 28 shows the load regulation curves under different air gaps, and the output voltage is almost load-independent. It should be noted that the curve with the coupling coefficient k min has a distinct change when the load gets lighter, this is because of the distortion of i s. At this circumstance, the zerocrossing points of i s can no longer substitute for the fundamental component i s1. Fig. 29 shows the measured efficiency from dc

11 4448 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014 input to dc output of the converter, and relative high efficiency has been achieved, 89.2% for 10-mm gap, 84% for 20-mm gap. VI. CONCLUSION In this paper, a self-oscillating control strategy which based on secondary current phase feedback is proposed for SS-type CRC. During the operation of SOCRC, nearly constant voltage gain is achieved since the voltage gain is only related to the turn ratio of the contactless transformer. Therefore, better selfadaptability is also obtained under different air gaps and load conditions. Due to the difficulty in contactless current phase detection, a current transformer with shorted secondary winding called PDCCT is proposed. In addition, practical issues in the realization of SOCRC such as starting circuit and the time delay in control circuitry are studied. The final experimental results on a 60-W prototype verify the validity of both self-oscillating control strategy and PDCCT, the rapid response of SOCRC is also illustrated by dynamic experimental results. When operating at 10-mm air gap, an efficiency of 89.2% can be achieved. REFERENCES [1] K. W. Klontz, D. M. Divan, D. W. Novotny, and R. D. Lorenz, Contactless power delivery system for mining applications, IEEE Trans. Ind. Appl., vol. 31, no. 1, pp , Jan [2] T. Kojiya, F. Sato, H. Matsuki, and T. Sato, Construction of noncontacting power feeding system to underwater vehicle utilizing electromagnetic induction, Oceans, vol. 1, pp , [3] J. T. Boys, G. A. Covic, and A. W. Green, Stability and control of inductively coupled power transfer system, IEE Proc., vol. 147, no. 1, pp , Jun [4] S. Y. R. Hui and W. C. Ho, A new generation of universal contactless battery charging platform for portable consumer electronic equipment, IEEE Trans. Power Electron., vol. 20, no. 3, pp , May [5] X. 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Bronson, A high efficiency 5 KW inductive charger for EVs using dual side control, IEEE Trans. Ind. Informat., vol. 8, no. 3, pp , Aug [20] J. L. Jensen, An improved square-wave oscillator circuit, IRE Trans. Circuit Theory, vol. 4, no. 3, pp , Sep [21] G. B. Joung and B. H. Cho, An energy transmission system for an artificial heart using leakage inductance compensation of transcutaneous transformer, IEEE Trans. Power Electron., vol.13,no.6, pp , Nov [22] P. Si, A. P. Hu, J. W. Hsu, M. Chiang, Y. Wang, S. Malpas, and D. Budgerr, Wireless power supply for implantable biomedical device based on primary input voltage regulation, in Proc. IEEE Conf. Ind. Electron. Appl., Harbin, China, 2007, pp [23] S. Chopra, V. Prasanth, B. E. Mansouri, and P. Bauer, A contactless power transfer-supercapacitor based system for EV application, in Proc. IEEE 38th Annu. Conf. Ind. Electron. Soc., Montreal, Canada, 2012, pp [24] R.-L. Lin, Y.-F. Chen, and Y.-Y. Chen, Analysis and design of selfoscillating full-bridge electronic ballast for metal halide lamp at MHz operating frequency, IEEE Trans. Power Electron., vol. 27, no. 3, pp , Mar [25] F. Chen, T.-J. Liang, R.-L. Lin, and J.-F. Chen, A novel self-oscillating, boost-derived DC DC converter with load regulation, IEEE Trans. Power Electron., vol. 20, no. 1, pp , Jan Kaiqin Yan was born in Jiangsu Province, China, in She received the B.S. degrees in electrical engineering and automation from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2011, where she is currently working toward the M.S. degree in electrical engineering. Her current research interests include contactless resonant converters and wireless power transfer system. Qianhong Chen (M 06) was born in Hubei Province, China, in She received the B.S., M.S., and Ph.D. degrees in electrical engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 1995, 1998, and 2001, respectively. In 2001, she joined the Teaching and Research Division of the Faculty of Electrical Engineering at NUAA, Nanjing, China, and is currently a Professor with the Aero-Power Sci-Tech Center in the College of Automation Engineering. From April 2007 to January 2008, she was a Research Associate in the Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong, China. Her research interests include application of integrated-magnetics, inductive power transfer converters, soft-switching dc-dc converters, power factor correction, and converter modeling. She has published more than 40 papers in international journals and conferences, and is the holder of seven patents.

12 YAN et al.: SELF-OSCILLATING CONTACTLESS RESONANT CONVERTER 4449 Jia Hou was born in Jiangsu Province, China, in She received the B.S. degrees in electrical engineering and automation from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2011, where she is currently working toward the Ph.D. degree in electrical engineering. Her current research interests include contactless resonant converters and wireless power transfer system. Xiaoyong Ren (S 04 M 11) was born in Jiangsu Province, China, in He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2002, 2005, and 2008, respectively. From 2009 to 2011, he was a Postdoctoral Research with the Center for Power Electronics systems, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA. He is currently with the College of Automation Engineering, NUAA. He has authored and coauthored more than ten technical papers published in international journals and conference proceedings. His current research interests include dc-dc conversion, converter control techniques, GaN device application, and renewable power systems. Xinbo Ruan (M 97 SM 02) was born in Hubei Province, China, in He received the B.S. and Ph.D. degrees in electrical engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 1991 and 1996, respectively. In 1996, he joined the Faculty of Electrical Engineering Teaching and Research Division, NUAA, where he became a Professor in the College of Automation Engineering in 2002 and has been engaged in teaching and research in the field of power electronics. From August to October 2007, he was a Research Fellow in the Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong, China. Since March 2008, he has been also with the College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, China. He is a Guest Professor with Beijing Jiaotong University, Beijing, China, Hefei University of Technology, Hefei, China, and Wuhan University, Wuhan, China. He is the author or coauthor of four books and more than 100 technical papers published in journals and conferences. His main research interests include soft-switching dc-dc converters, soft-switching inverters, power factor correction converters, modeling the converters, power electronics system integration and renewable energy generation system. Dr. Ruan was a recipient of the Delta Scholarship by the Delta Environment and Education Fund in 2003 and was a recipient of the Special Appointed Professor of the Chang Jiang Scholars Program by the Ministry of Education, China, in From 2005 to 2013, he has been serving as Vice President of the China Power Supply Society, and since 2008, he has been a member of the Technical Committee on Renewable Energy Systems within the IEEE Industrial Electronics Society. He has been an Associate Editor for the IEEE TRANSAC- TIONS ON INDUSTRIAL ELECTRONICS and the IEEE JOURNAL OF EMERGING AND SELECTED TOPICS ON POWER ELECTRONICS since 2011 and 2013, respectively. He is a Senior Member of the IEEE Power Electronics Society and the IEEE Industrial Electronics Society.

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