An Optimizable Circuit Structure for High-Efficiency ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 1, JANUARY 2013

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An Optimizable Circuit Structure for High-Efficiency Wireless Power Transfer Linhui Chen, Shuo Liu, Yong Chun Zhou, and Tie Jun Cui, Senior Member, IEEE

Abstract—Since the magnetically resonant coupling was suggested for wireless power transfer (WPT), the theoretical analysis and experimental verifications of several resonant coupling structures have been investigated by several groups. Series-resonant and shunt-resonant structures are two common circuit models which are widely used in WPT. Here, a simple circuit topological structure, the series-shunt mixed-resonant coupling, is presented with better performance in the transfer distance and efficiency. In the experimental verification, a pair of resonant coils with 10-cm diameter was used. The experimental results show that high efficiency of 85% was achieved at a distance of 10 cm (one relative distance) and 45% efficiency at 20 cm (two relative distances). The proposed structure has another advantage that circuit parameters can be easily optimized for high transfer efficiency under different distances. Index Terms—Mixed-resonant coupling, relative distance, transfer efficiency, wireless power transfer (WPT).

I. I NTRODUCTION

I

N RECENT YEARS, there has been an increasing interest in the research and development of wireless power transfer (WPT) across large air gaps, which may finally eliminate the cable from mobile devices such as cell phones and cameras. In the early time, several circuit structures with the inductive coupling technique [1]–[5] have been proposed for WPT which attempt to transfer a few watts within several centimeters [6], [7] or around one coil diameter [8], [9]. Then, circuit structures like SS, SP, PS, and PP, in which compensated capacitors are only in serious or only in shunt with the primary side and secondary side [10]–[14], were adopted in WPT. Recently, a nonradiative magnetically coupling approach [10], [15]–[20] has been investigated, which has shown great potential to deliver power more efficiently than the traditional lower frequency inductive systems. There have been several reports on the theoretical analysis and experimental verifications using the coupled mode theory [15] and circuit theory [17],

Manuscript received February 19, 2011; revised July 31, 2011 and September 22, 2011; accepted November 15, 2011. Date of publication December 9, 2011; date of current version September 6, 2012. This work was supported in part by the National Science Foundation of China under Grants 60990320, 60990324, 60871016, 60496317, and 60901011 and in part by the 111 Project under Grant 111-2-05. The authors are with the State Key Laboratory of Millimeter Waves, Department of Radio Engineering, School of Information Science and Engineering, Southeast University, Nanjing 210096, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2011.2179275

[21]–[23]. Both simulations and experiments show that better transfer efficiency has been achieved because higher frequency was adopted. However, in addition to the four-loop structure [17], [20], [22], the circuit topologies are still the same with traditional ones. Hence, the shortcomings of the PS and PP structures are derived directly. Until now, the effective transfer range is still basically restricted to one coil diameter unless relay resonators are adopted [24]. In this paper, an optimizable circuit structure [25], the serious-shunt mixed-resonant circuits, was used for WPT. From the circuit analysis and numerical simulations, advantages of the series-shunt mixed-resonant coupling are demonstrated through comparisons with the traditional resonant-coupling schemes. A new scaling factor, the relative distance, is proposed to evaluate the WPT performance, which is defined as the ratio of transfer distance to the resonant-coil diameter. Experiments have been conducted to validate the higher efficiency of the new circuit model using the relative distance. It is found that the transfer efficiency is not high in long distance when we tune the circuit of the series-resonant coupling or shunt-resonant coupling for the fixed load and coupling coefficient, which implies that they are not suitable for long-distance WPT. However, the efficiency becomes much higher when the series-shunt mixedresonant structure is used with the optimized capacitors. This is particularly useful if the coupling coefficient is very small, allowing a longer transfer distance or smaller receiver coil in real applications. II. M IXED -R ESONANT C OUPLING M ODEL In previous research works [20]–[22], a physical distance was used to evaluate the performance of the power transfer system, while the size of the resonant coil was not taken into account. It was very easy to get a transfer efficiency of 80% at a distance of 20 cm when the resonant coil diameter is 50 cm. However, the transfer efficiency will become a big challenge if the coil diameter is reduced to 5 cm, which is suitable to be embedded into small mobile devices such as cellphones and cameras. Here, we propose a new concept of relative distance, which is defined as the ratio of distance to the resonant-coil diameter. In the following discussions, we will pay more attention on the high efficiency achieved in how many times of the coil diameter rather than in how many centimeters. The circuit model of the proposed mixed-resonant coupling is shown in Fig. 1(a), whose three degenerated forms are the series-resonant circuit model, the shunt-resonant circuit model, and the uncompensated inductive circuit model, as shown in Fig. 1(b)–(d), respectively. In the proposed model, the

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Fig. 1. (a) Mixed-resonant coupling circuit model for WPT and (b)–(d) its three degenerated forms. (a) Mixed-resonant circuit model. (b) Series-resonant circuit model. (c) Shunt-resonant circuit model. (d) Uncompensated inductive circuit model.

capacitors C1 and C4 are in series and C2 and C3 are in shunt connected to the coils L1 and L2 , which behave like an LC circuit to make the system resonant at a certain frequency so that the resonant coupling can be achieved. This new circuit reduces to the series-resonant coupling shown in Fig. 1(b) when C2 and C3 tend to zero and reduces to the shunt-resonant coupling when C1 and C4 tend to infinity, as shown in Fig. 1(c). Let C2 and C3 be zero and C1 and C4 be infinity; we get the simplest model of the uncompensated inductive circuit model, as shown in Fig. 1(d). To simulate and analyze the transfer characteristics of the new circuit model, we extract the transfer function using the Thevenin’s theorem. Since the WPT system can be viewed as a two-port network with one port being input fed by the source and the other being output fed by the load, the transfer efficiency will be represented in terms of the linear magnitude of the scattering S parameter |S21 |. Since S-parameters can be measured using a vector network analyzer (VNA), it can offer us an intuition of the variation trend to the transfer efficiency. In fact, the scattering parameter is an effective way to evaluate the transfer efficiency although it may be not always an accurate method to calculate the whole efficiency. This will be pointed out in the later simulations and experiments. Based on the scattering parameter, the function of power transfer efficiency is defined as η = |S21 |2 when the network

ZLs

is matching at both ports, in which |S21 | is given by |S21 | = 2 ·

VL · VS



RS RL

 12

 = 2 · zLL zSS zLS ·

RS RL

 12 (1)

in which ZLs is given in (2) shown at the bottom of the page, and k is the coupling coefficient between the two coils. Let C2 and C3 be zero in (2); we get the substitution of the transfer function for the series-resonant coupling circuit model as given in (3) shown at the bottom of the next page. Similarly, when C1 and C4 tend to infinity in (2), we get the substitution for the shunt-resonant coupling circuit model as given in (4) shown at the bottom of the next page. Since the S-parameters of the proposed circuit model are complicated and difficult for the analytical analysis, we use numerical simulations to find out the key factors which affect the transfer efficiency. Before considering the mixed-resonant coupling model, the two degenerated forms, the series- and shunt-resonant coupling models, are first studied. This will provide a deeper understanding to the advantages of the new model. According to [22], there is a distance parameter called as the critical coupling point, beyond which the system can no longer drive a given load at the maximum efficiency. Assume that kcritical is the critical coupling coefficient and S21critical is the

  √ 1+jωC4 RL jωk L1 L2 Rp2 + jωC4 +jωC 2C C R −ω 3 3 4 L   = 1+jωC1 Rs 1+jωC4 RL jωL1 + Rp1 + jωC1 +jωC2 −ω2 C1 C2 Rs jωL2 + Rp2 + jωC4 +jωC + ω 2 k 2 L1 L2 2 3 −ω C3 C4 RL jωC4 RL 1 + jωC4 RL + (jωC4 + jωC3 − ω 2 C3 C4 RL )Rp2 c1 = c1 + c2 + jωC1 C2 Rs

ZLL = zss

(2)

CHEN et al.: OPTIMIZABLE CIRCUIT STRUCTURE FOR HIGH-EFFICIENCY WIRELESS POWER TRANSFER

magnitude of S21 at the critical coupling point. Then, kcritical reveals the effective distance that power can be transferred, and S21critical reveals the maximum transfer efficiency. A perfect WPT system will own the high efficiency and long transfer distance simultaneously. However, the two merits generally contradict each other; hence, the designer will expect to obtain the highest efficiency at a fixed distance or the longest transfer range within an acceptable efficiency. Based on the aforementioned discussion, we first analyze the series- and shunt-resonant coupling models. To simulate and measure the system more easily, we consider a symmetrical circuit whose source resistance RS and load resistance RL are of the same value, i.e., 50 Ω. The experimental results in Section III will reveal that the mixed-resonant circuit is also suitable for the design of unsymmetrical circuit or non-50-Ω system. For the series-resonant model, we define the resonant radian frequency as 1 1 =√ . ω = ω0 = √ L1 C1 L2 C4

(5)

Then, the magnitude of S21 is a function of k   √   2 · ωk L1 L2 RL . f (k) = |S21 (k)| =  2 2 (Rp1 + Rs )(RL + Rp2 ) + ω k L1 L2  (6) By solving the derivative of the function f (k), we obtain  (Rp1 + Rs )(RL + Rp2 ) √ kcritical = . (7) ω L1 L2 For a symmetrical system, we have kcritical =

R + Rp 1 R + Rp =  = . ωL Qs L/C

ZLL =

(8)

341

Fig. 2. Group of S21 magnitudes versus the coupling coefficient k for the series-resonant coupling with the increase of L at the same resonant frequency f0 = 4 MHz.

Substituting (8) into (6) yields S21critical = 

RL . (Rp1 + Rs )(RL + Rp2 )

(9)

For the symmetric system S21critical =

RL . RL + Rp

(10)

The aforementioned equations show that kcritical is greatly constricted by ωL and the load resistance. This is why the series system cannot transfer power at long distance. The author in [26] has already realized that smaller load resistance was more suitable for the series-resonant structure to get longer distance and the bigger load was more suitable to get higher efficiency. Substituting (3) into (1), the system transfer function for the series-resonant coupling is plotted in Fig. 2, showing a group of S21 magnitudes versus the coupling coefficient k with increasing L at the same resonant frequency f0 = 4 MHz. It

jωC4 RL 1 + jωC4 RL + jωC4 Rp2

zss = 1 ZLS

  √ 4 RL jωk L1 L2 Rp2 + 1+jωC jωC4   = 1 Rs 4 RL jωL1 + Rp1 + 1+jωC jωL2 + Rp2 + 1+jωC + ω 2 k 2 L1 L2 jωC1 jωC4

ZLL = zss =

ZLS

(3)

RL RL (1 + jωC3 RL )Rp2 1 1 + jωC2 Rs

  √ Rl jωk L1 L2 Rp2 + 1+jωC 3 RL   = RS RL jωL1 + Rp1 + 1+jωC2 Rs jωL2 + Rp2 + 1+jωC + ω 2 k 2 L1 L2 3 RL

(4)

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is obvious that a larger L will result in a smaller kcritical , as predicted in (7), and S21critical is kept constant while RL and Rp are fixed. This is also consistent with (10). To reach a higher S21critical , we should increase the load resistance, but this will lead to a bigger kcritical too. The only solution is to increase ωL, which, however, may bring a large Rp . All these restrictions limit the applications of the seriesresonant structure. Similarly, we analyze the shunt-resonant model and obtain (11) shown at the bottom of the page. For a symmetric system, we have f (k) = |S21 (k)|     2 · ωkLR   = 2 2 2 2 2 (jωL + Rp + jωCRRP ) + ω k L (1 + jωCR)     2 · ωkLR    (12) = √ A2 + B 2  in which

 A = Rp2 − (ωL − ωCRRp )2 + ω 2 k 2 L2 1 − (ωCR)2

B = 2Rp (ωL − ωCRRp ) + 2ω 2 k 2 L2 ωCR. Letting the derivative of the function f (k) be zero, we obtain

(CRRp )2 + L2 + Rp2 LC − 2LCRRp √ kcritical = . (13) L2 + LCR2 For the shunt-resonant coupling, we have  1 jωC · R imag = −ωL. 1 jωC + R

(14)

Then, we get R2  Furthermore



kcritical =  ≈  =

L . C

2 LC − 2LCRR (CRRP )2 + L2 + RP P √ L2 + LCR2

(CRRP )2 + L2 − 2LCRRP √ LCR2 (CRRP − L)2 RP →0 1 √ −−−→

2 C LCR 2 RR

and R →0

P Scritical −− −→ 1.

  f (k)=|S21 (k)|=

(15)

Fig. 3. Group of S21 magnitudes versus the coupling coefficient k for the shunt-resonant coupling with the increase of L under the same resonant frequency f0 = 4 MHz.

The aforementioned equations show that the shunt-resonant system has opposite characteristics to the series-resonant system, which is shown in Fig. 3. Different from the case of series-resonant coupling, Fig. 3 implies that the coupling coefficient k decreases surprisingly as L turns small to keep the S21 magnitude as a constant. That is to say, the smaller L is, the longer effective transfer distance will be achieved. More simulations of this feature have been conducted, all of which demonstrate very good performance to the power transfer efficiency under long distance when the parasitic resistance is ignored. However, there is a sharp contrast of the sensitivity to the parasitic resistance between the series-resonant and the shuntresonant couplings. For the shunt-resonant case, a small Rp will cause dramatically a drop to the performance. However, the shunt-resonant structure was preferred by a few papers since Rp is less sensitive and ωL is relatively small (ωL = R) at low frequencies [10], [11], [27]. The self-resonant frequency of the uncompensated inductive circuit model is too high to be adopted in real applications because the parasitic capacitance is very small. Since it has little relationship with the nonradiative magnetic resonant coupling system, there is no need to analyze its characteristics here. From the aforementioned numerical simulations and qualitative analysis, we conclude that both series- and shuntresonant couplings have their own advantages and limitations. The series-resonant coupling is featured by its high maximum transfer efficiency due to the low sensitivity to the parasitic resistance. However, the increase of inductance for longer effective transfer distance will lead to large-sized coils, which will, in turn, bring a larger parasitic resistance that will increase the system loss and decrease the efficiency. The shunt-resonant coupling can overcome the shortcomings of the series-resonant coupling because its transfer efficiency is inversely proportional

 √  jωk L1 L2 RL  [(jωL1 + Rp1 + jωC2 Rs Rp1 )(jωL2 + Rp2 + jωC3 RL Rp2 ) + ω 2 k 2 L1 L2 (1 + jωC2 Rs )(1 + jωC3 RL )]  (11)

CHEN et al.: OPTIMIZABLE CIRCUIT STRUCTURE FOR HIGH-EFFICIENCY WIRELESS POWER TRANSFER

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Fig. 4. Three-dimensional distributions of S21 magnitudes versus the coupling coefficient k and frequency: (a) the mixed-resonant coupling, (c) the seriesresonant coupling, and (e) the shunt-resonant coupling. Two-dimensional distributions of S21 magnitudes versus the coupling coefficient k: (b) the mixed-resonant coupling, (d) the series-resonant coupling, and (f) the shunt-resonant coupling.

to the ratio L/C. Theoretically, the increase of the capacitance or decrease of the inductance can improve the transfer efficiency dramatically, both of which are applicable. However, due to the fact that the shunt-resonant coupling is subject to the restriction of parasitic resistance, the transfer efficiency is seriously affected, and this sensitivity will be aggravated with the increase of the ratio L/C. Hence, there should be a possibility to use the advantages of both series-resonant and shunt-resonant circuit models and eliminate their limitations. Now, we consider the new mixedresonant circuit model shown in Fig. 1(a). To demonstrate the superiority of the mixed-resonant coupling, a straightforward comparison among the three circuit models is conducted by 3-D distributions of S21 magnitudes versus the coupling coefficient and frequency and 2-D distributions of S21 magnitudes versus the coupling coefficient k, as shown in Fig. 4. Note that the frequency splitting is clearly visible, where the frequency

corresponding to the maximum transfer efficiency has a shift to the intrinsic resonant frequency. This can be interpreted that the transfer efficiency is kept stable when the coupling coefficient k is larger than the critical point kcritical but begins to fall down precipitously with the increase of the distance once the coil leaves the effective region. From the aforementioned analysis, it is obvious that the mixed-resonant coupling has a much better performance than the series- and shunt-resonant couplings. Comparing Fig. 4(b) with Fig. 4(d), we observe that the kcritical value of the mixedresonant coupling is ten times smaller than that of the seriesresonant coupling, implying that the mixed-resonant coupling has inherited a longer effective transfer distance. Comparing Fig. 4(b) with Fig. 4(f), we observe that the mixedresonant coupling achieves much higher transfer efficiency than the shunt-resonant coupling because it inherits the lowsensitive feature from the series-resonant coupling. For the

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Fig. 5. Relationships between the ratio of Cs/C and the transfer efficiency under different coupling coefficients k.

mixed-resonant coupling, it is also noticed that a little sacrifice in the transfer efficiency will bring a longer effective transfer distance. This is because the mixed-resonant coupling is a mixture of the series- and shunt-resonant couplings. A sweep simulation is conducted to show the relationship between the ratio Cs /C and S21 with different coupling coefficients k, as shown in Fig. 5. Here, every single k correlates to different ratios of Cs /C to get the highest transfer efficiency. Clearly, the smaller the coupling coefficient is, the smaller the ratio Cs /C is needed to get a bigger ratio of Cp /L, in which Cp represents the shunt capacitance. This makes the system perform more like the shunt-resonant coupling, which can get higher transfer efficiency in a longer relative distance. In other words, the mixed-resonant coupling inherits the advantage of long effective transfer distance of shunt-resonant coupling. However, the transfer efficiency begins to fall down with the decrease of L/Cp as shown in Fig. 3, since the shunt-resonant coupling is more sensitive to the parasitic resistance when the ratio L/Cp is small. Hence, we conclude that the ratio Cs /C is a key factor that determines to which direction (series or shunt) that the mixed-resonant coupling should change for different distances. In real applications, when the electronic device (receiving coil) is near to the transmitting coil, a higher ratio of Cs /C is appropriate for less power wasted on the transfer network, while a lower ratio of Cs /C will increase the transfer distance although it is not efficient enough, enabling the users to use the wireless electronic devices more conveniently. The design of a practical WPT system is similar to that of S-parameters as mentioned earlier, i.e., we have to try our best to improve S21 as large as possible at a rather long distance. In fact, the problem that we need to focus on is how to improve the transfer efficiency with a small k (i.e., at a long distance), in which case the reflected impedance from the receiving end to the transmitting end is very small. Thus, the mixed-resonant coupling structure can be used to transform the load impedance to a smaller one so that the reflected impedance will be large enough to receive powers from the transmitting end. For practical applications, the parasitic resistor puts a limit on the maximum transfer efficiency, particularly when the ratio L/C is low. The skin effect and the proximity effect are two factors that affect the parasitic resistors, which should be considered to improve the overall performance of WPT.

Fig. 6. Relationship between the coupling coefficient lg(k) and the relative distance (calculated and measured).

Increasing the diameter of copper wires is one way to reduce the parasitic resistance and provides a big improvement in the maximum transfer efficiency. Using litz wire is another way to reduce the parasitic resistance, but the parasitic capacitance will be very large if the wire is a large number strand and the frequency is high. Another issue is that ferrite can be used to shape and guide the field; hence, the coupling will be stronger, and the leakage can be avoided [12]. Here, we focus on how to improve the transfer efficiency using the novel circuit with certain parameters, particularly when k is very small. Any improvement in parasitic resistance and coupling coefficient will also help improve the transfer efficiency. III. M ODEL VALIDATION AND E XPERIMENTAL R ESULTS The relation between the relative distance and the coupling coefficient k should be first figured out because the distance rather than the coupling coefficient k will be commonly used in the design of WPT in real applications. Using numerical simulations, the curves of lg(k) versus the relative distance of three different-diameter coils are shown in Fig. 6, in which the function of k is described as

π 2 b · 02 √2 sin θ −1 2 M 1−(b sin θ)   8r  = (16) k=√ ln a − 2 L1 L2 where



b=

 4r1 r2 4r2 r1 =r2 ( − − − →) (r1 + r2 )2 + d2 4r2 + d2

(17)

π

2

√

M = μN1 N2 r1 r2 · b · 0

2 sin θ2 − 1 r1 =r2 ,N1 =N2  −−−−−−−−−→ 1 − (b sin θ)2

π

2 μN · r · b · 2

0

2 sin θ2 − 1  . 1 − (b sin θ)2

(18)

CHEN et al.: OPTIMIZABLE CIRCUIT STRUCTURE FOR HIGH-EFFICIENCY WIRELESS POWER TRANSFER

Fig. 7.

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Experimental setup of the mixed-resonant coupling model.

The measured values of lg(k) versus the relative distance using a pair of coils (10 cm in diameter) are also plotted in Fig. 6. From the figure, we notice that the measured lg(k) coincides very well to the calculated data from the formula, so that we can directly use the measured k to design the circuit. It should be noted that the measured result is a little bit bigger than the calculated value, because the self-inductance of a real coil is comparatively smaller due to its loose winding. The experimental setup used to validate the theoretical model is shown in Fig. 7. There are two identical resonant coils winded by five turns tightly on the cylindrical Plexiglas, which are the transmitter (left) and the receiver (right). Both resonant coils have a diameter of 10 cm and are connected to several fixedvalue capacitors and a tunable capacitor, helping to tune the system to resonant at the desired frequency. An SMA connector is placed on the printed circuit board to link with the VNA. Based on the first-round simulations and experiments, copper wires with 2.5-mm diameter are chosen to get small parasitic resistances. Both resonant coils are supported by the Plexiglas armatures. It is very crucial to tune the circuit to the designed resonant frequency as exact as possible since a small mismatch will cause the system to be detuned, which further results in a drop of transfer efficiency. To guarantee the parameters extracted from the real model, we fabricated, to be accurate enough, a high-frequency Q meter which is used to measure the inductance and parasitic resistance. For accurate measurements of the transfer efficiency under different distances and frequencies, we use VNA to get the scattering parameter S21 in the decibel form. The detailed circuit parameters for the simulation model and the measurement are as follows: L1 = 4.30 μH, L2 = 4.30 μH, f0 = 4 MHz, Rp1 = 0.36 Ω, Rp2 = 0.38 Ω, and RL = 20, 50, or 100 Ω. According to the previous references, four kinds of circuits are studied for a more comprehensive analysis of other groups’ contributions, including the series-compensated primary and secondary (SS), series-compensated primary and parallel-compensated secondary (SP), parallel-compensated primary and secondary (PP), and parallel-compensated primary and series-compensated secondary (PS) [13], [28]. Good

Fig. 8. S21 magnitudes versus distances for the SS, SP, PS, and PP circuit structures.

Fig. 9. S21 magnitudes versus distances for the mixed-resonant model with different capacitance ratios.

agreements have been achieved between the simulation and experimental results. The S-parameters versus distances of the SS, SP, PS, and PP circuits and the mixed-resonant coupling model with different capacitance ratios are measured and demonstrated in Figs. 8 and 9, respectively. From Fig. 8, we find that S21 of all four circuit structures decreases dramatically with the increase of distances. It should be pointed out that the SS mode is better when (ω 2 M 2 /RL ) < (M 2 RL /L22 ) and the PP mode is better when (ω 2 M 2 /RL ) > (M 2 RL /L22 ) [14]. Thus, the SS structure is better than the PP structure with the chosen parameters, which can also be clearly seen in Fig. 8. However, none of these circuits have shown good performance at long distance. In Fig. 9, however, we find that S21 of the mixed-resonant circuits with certain capacitance ratios will achieve different peaks at rather long distances, such as half relative distance, one relative distance, one and a half relative distances, and two

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Fig. 10. (a) Mixed-resonant coupling circuit model in ADS. (b) Waveforms of the voltage and current at the source terminal and the load.

relative distances, which are much higher than those in the SS, SP, PP, and PS circuits. The lower S21 at short distances is for the reason that the reflection at the transmitting terminal is very strong, which will affect the output power of the source (e.g., a voltage source). However, the efficiency is still very high. Before measuring the efficiency of different structures, we must confirm that the circuits in our experiments are carefully tuned to the resonant frequency of 4 MHz, so that the reflected impedance at the transmitting terminal will be purely resistance. As a result, the whole impedance will be a pure resistance when we look into the circuit from the source, and the whole impedance will still be a pure resistance. Then, the power will be totally divided by the resistors. Considering such reasons, we need to adjust the tunable capacitor carefully to make the two coils resonant at the same frequency. To validate the aforementioned conclusions, an equivalentcircuit model is set up using the commercial software, the Agilent Advanced Design System (ADS), as shown in Fig. 10(a). Here, circuit parameters are set the same with the value in the former experiment (including the parasitic resistance of both coils). We simulate the time-domain waveforms of a WPT system at two relative distances with a load of 100 Ω. The results in Fig. 10(b) show that the voltage and current are strictly in phase. Hence, the input power can be obtained by the product of input voltage and current, and the output power can be obtained by the product of output voltage and current. Hence, we get the total transfer efficiency. A voltage source is used to provide the power for the transmitting terminal in the measurement for convenience. We use an oscilloscope to measure the voltage waveforms at the source terminal and the load. As shown in Fig. 11(a), the green line

Fig. 11. (a) Voltage waveforms at the source terminal and the load. (b) Voltage waveforms of both ends of a resistor in series of the circuit.

is the voltage on the load, and the brown line is the output voltage of the source. Since we know that the voltage source has a resistor of 50 Ω, the impedance of the circuit seen from the source can be obtained from the no-load output voltage and operating output voltage of the source, so that we can obtain the input power. Similarly, the output power can be achieved from the load resistance and the voltage waveform on the load. Since we have carefully tuned the circuits to the frequency f0 , the impedance is a pure resistor when we look into the circuit from the source. To prove that, an additional resistor is added between the source and the circuits, and then, we observe the voltage waveform from both ends of the resistor, as shown in Fig. 11(b). Clearly, we can see that the two voltage waveforms are in phase. Hence, we conclude that the impedance of the whole circuit is purely a resistance. The efficiencies measured for the series-resonant coupling and the mixed-resonant coupling are shown in Fig. 12(a)–(c) for different loads of 20, 50, and 100 Ω, respectively. It is noticed that the mixed-resonant coupling circuit is much better than the series-resonant coupling in long-distance WPT. For instance, the efficiency of the mixed-resonant coupling is about 40% higher than that of the series-resonant coupling at the distance of 20 cm. Moreover, it is obvious that the transfer efficiency of the mixed-resonant coupling circuit is kept stable when the load impedance varies in a large range if we optimize the capacitance properly. Another phenomenon is that, for different loads, C1 and C2 are always the same for a certain distance, but

CHEN et al.: OPTIMIZABLE CIRCUIT STRUCTURE FOR HIGH-EFFICIENCY WIRELESS POWER TRANSFER

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Fig. 13. Practical WPT system driven by a class-E PA, in which the receiving coil can be placed arbitrarily around the transmitting coil.

impedance to a proper value for the source. In addition, we also observe that the series-resonant coupling is more efficient for small loads at long distance. Since the performance of shuntresonant coupling is similar to that of series-resonant coupling, the detailed results are not given here because of limited space. A practical WPT prototype system driven by a class-E power amplifier (PA) has been fabricated according to the designed coil parameters and the coupling coefficient, as shown in Fig. 13, in which the receiving coil can be arbitrarily oriented and placed around the transmitting coil. A dc source is used as a power supply for PA so that we can calculate the total power going into PA from the source. From the figures, we observe that the light bulb at the receiving coil works very well for any orientations and locations around the transmitting coil. The output power of the dc source in this experiment is 3 W, while the power lighting the bulb is 2 W. Hence, the efficiency of the whole system is above 50% for all locations and orientations shown in Fig. 13, which is an obvious advantage for WPT to be used in real applications. Fig. 12. Measured efficiencies versus distances for different circuit structures: (a) for the load of 20 Ω, (b) for the load of 50 Ω, and (c) for the load of 100 Ω.

C3 and C4 are different. This is because C3 and C4 need to transform different loads to a proper value, which is decided by the transfer distance, while C1 and C2 transform the reflected

IV. C ONCLUSION The proposed mixed-resonant coupling model has showed an excellent performance in WPT, making a further step for the magnetically coupled resonant structures toward practical applications. We have achieved 85% transfer efficiency within

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one relative distance and 50% within two relative distances with a pair of resonant coils coaxially aligned. The other advantage of the model is the option between the effective transfer range and the maximum transfer efficiency, which allows WPT to be more adaptable in real applications. The previous approaches such as the series- and shunt-resonant coupling models do not have such abilities. We have provided a set of unique benefits of the mixedresonant coupling model, which have shown great superiority in both transfer efficiency and transfer distance than the traditional series- and shunt-resonant coupling structures. The numerical simulations reveal that a tradeoff between the maximum transfer efficiency and the effective transfer distance can be simply realized by changing the ratio of Cs/C, offering a convenient method to maximize the transfer efficiency at different distances. Experimental results have shown very good agreements to the theoretical analysis. How to establish the analytical model of a resonant coil and how to analyze the transfer efficiency in a more clear and essential way are our future work. We are also considering the use of ferrite to shape the magnetic field to meet the ICNIRP regulations [29], [30] when working toward the target of longer effective transfer distance and smaller coil size, so that the proposed model can be used in practical applications in daily life. R EFERENCES [1] S. A. A. M. Ilyas, RFID Handbook: Applications, Technology, Security, and Privacy. Boca Raton, FL: CRC, 2008. [2] J. Murakami, F. Sato, T. Watanabe, H. Matsuki, S. Kikuchi, K. Harakawa, and T. Satoh, “Consideration on cordless power station—Contactless power transmission system,” IEEE Trans. Magn., vol. 32, no. 5, pp. 5037– 5039, Sep. 1996. [3] K. Hatanaka, F. Sato, H. Matsuki, S. Kikuchi, J. Murakami, M. Kawase, and T. Satoh, “Power transmission of a desk with a cord-free power supply,” IEEE Trans. Magn., vol. 38, no. 5, pp. 3329–3331, Sep. 2002. [4] C. S. Wang, O. H. Stielau, and G. A. Covic, “Design considerations for a contactless electric vehicle battery charger,” IEEE Trans. Ind. Electron., vol. 52, no. 5, pp. 1308–1314, Oct. 2005. [5] G. A. Covic, J. T. Boys, M. L. G. Kissin, and H. G. Lu, “A three-phase inductive power transfer system for roadway-powered vehicles,” IEEE Trans. Ind. Electron., vol. 54, no. 6, pp. 3370–3378, Dec. 2007. [6] N. A. Keeling, J. T. Boys, and G. A. Covic, “Unity power factor inductive power transfer pick-up for high power applications,” in Proc. 34th IEEE IECON, 2008, vol. 1–5, pp. 1039–1044. [7] Y. T. Jang and M. M. Jovanovic, “A contactless electrical energy transmission system for portable-telephone battery chargers,” IEEE Trans. Ind. Electron., vol. 50, no. 3, pp. 520–527, Jun. 2003. [8] M. Budhia, G. Covic, and J. Boys, “A new IPT magnetic coupler for electric vehicle charging systems,” in Proc. 36t IEEE IECON, 2010, pp. 2487–2492. [9] M. Budhia, G. A. Covic, and J. T. Boys, “Design and optimisation of magnetic structures for lumped inductive power transfer systems,” in Proc. IEEE ECCE, 2009, pp. 2081–2088. [10] Z. N. Low, R. A. Chinga, R. Tseng, and J. Lin, “Design and test of a high-power high-efficiency loosely coupled planar wireless power transfer system,” IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1801–1812, May 2009. [11] Z. N. Low, J. J. Casanova, P. H. Maier, J. A. Taylor, R. A. Chinga, and J. Lin, “Method of load/fault detection for loosely coupled planar wireless power transfer system with power delivery tracking,” IEEE Trans. Ind. Electron., vol. 57, no. 4, pp. 1478–1486, Apr. 2010. [12] A. J. Moradewicz and M. P. Kazmierkowski, “Contactless energy transfer system with FPGA-controlled resonant converter,” IEEE Trans. Ind. Electron., vol. 57, no. 9, pp. 3181–3190, Sep. 2010. [13] C. S. Wang, G. A. Covic, and O. H. Stielau, “Power transfer capability and bifurcation phenomena of loosely coupled inductive power trans-

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Linhui Chen was born in China in 1988. He received the B.E. degree in electronic engineering from Wuhan University, Wuhan, China, in 2010. He is currently working toward the Ph.D. degree at the State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing, China. His current research interests are wireless power transfer and millimeter-wave circuit design.

CHEN et al.: OPTIMIZABLE CIRCUIT STRUCTURE FOR HIGH-EFFICIENCY WIRELESS POWER TRANSFER

Shuo Liu was born in China in 1988. He received the B.E. degree in information engineering from Southeast University, Nanjing, China, in 2010. He is currently working toward the Ph.D. degree at the State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing. His current research interest is wireless power transfer.

Yong Chun Zhou was born in China in 1987. He received the B.S. degree in physics from Nanjing University, Nanjing, China, in 2009. He is currently working toward the M.E. degree at the State Key Laboratory of Millimeter Waves, Department of Radio Engineering, Southeast University, Nanjing. His current research interest is wireless power transfer (WPT) technology, and he is now developing industrial products on WPT with Power-One SED China JV, Shenzhen, China.

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Tie Jun Cui (M’98–SM’00) received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from Xidian University, Xi’an, China, in 1987, 1990, and 1993, respectively. In March 1993, he joined the Department of Electromagnetic Engineering, Xidian University, and was promoted to an Associate Professor in November 1993. From 1995 to 1997, he was a Research Fellow with the Institut fur Hochstfrequenztechnik und Elektronik, University of Karlsruhe, Karlsruhe, Germany. In July 1997, he joined the Center for Computational Electromagnetics and Electromagnetics Laboratory, Department of Electrical and Computer Engineering, University of Illinois, Urbana, first as a Postdoctoral Research Associate and then a Research Scientist. He has been with the Southeast University, Nanjing, China, where he was a Cheung Kong Professor with the Department of Radio Engineering in September 2001 and is currently the Associate Dean with the School of Information Science and Engineering and the Associate Director of the State Key Laboratory of Millimeter Waves. He is a Coeditor of the book Metamaterials—Theory, Design, and Applications (Springer, 2009) and the author of six book chapters. He has published over 200 peer-reviewed journal papers in Science, Nature Communications, Physical Review Letters, IEEE T RANSACTIONS, etc. He is in the editorial boards of Progress in Electromagnetic Research (PIER) and Journal of Electromagnetic Waves and Applications. He is currently a Principal Investigator of more than 20 national projects. His research interests include metamaterials, computational electromagnetic, wireless power transfer, and millimeter-wave technologies. Dr. Cui was a recipient of a Research Fellowship from the Alexander von Humboldt Foundation, Bonn, Germany, in 1995; a Young Scientist Award from the International Union of Radio Science (URSI) in 1999; a Cheung Kong Professorship under the Cheung Kong Scholar Program by the Ministry of Education, China, in 2001; the Distinguished Young Scholars Award by the National Science Foundation of China in 2002; the Special Government Allowance Award by the Department of State, China, in 2008; the Award of Science and Technology Progress from Shaanxi Province Government in 2009; and a May 1st Labour Medal by Jiangsu Province Government in 2010. He is a member of URSI Commission B and a Fellow of Electromagnetics Academy, Massachusetts Institute of Technology (MIT), Cambridge. He was an Associate Editor in IEEE T RANSACTIONS ON G EOSCIENCE AND R EMOTE S ENSING. He serves as an Editorial Staff in IEEE A NTENNAS AND P ROPAGATION M AGAZINE. He served as a General Cochair of the International Workshop on Metamaterials (2009), the Asia-Pacific Microwave Conference (2005), and the PIER Symposium (2004). His research on “invisibility cloak” and “electromagnetic black hole” was selected as one of the “10 Breakthroughs of Chinese Science in 2010” and has been widely reported by Nature News, Scientific American, New Scientist,Nano Times, MIT Technology Review, Discovery, Discover News, Physics World, etc. His research works have also been selected as one of the “Best of 2010” in New Journal of Physics, research highlights in Europhysics News, Journal of Physics D: Applied Physics, and Nature China.