IN RECENT years, resonant wireless power transfer (WPT)

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 64, NO. 6, JUNE 2017 615 A Self-Resonant Two-Coil Wireless Power Transfer System Using Open Bifilar Coils Caio M. de Miranda and Sérgio F. Pichorim Abstract Usually, self-resonant coils are restricted to use on the intermediary circuits of multiple-coil wireless power transfer (WPT) systems. This is because a source sees a parallel resonance when connected to a typical coil at self-resonance, and parallel associations in the primary and secondary sides of a twocoil system are not as practical as the respective series associations. However, many applications require two-coil systems due to their reduced size and simplicity. In this work, a self-resonant two-coil WPT system is proposed. The presented system uses open bifilar coils that lead to a series resonance at the resonant frequency. In this way, no capacitor is used in the whole system and it behaves as a series association of coil self-capacitance and inductance at the resonant frequency. Thus, the proposed system has a reduced size and also avoids capacitor damage due to high individual voltages caused by resonance effects. Practical measurements and theoretical results of the system efficiency and relative power transfer show good agreement and validate the proposed scheme as a promising solution for a two-coil self-resonant WPT system. Index Terms Open bifilar coils, self-resonance, two-coil systems, wireless power transfer (WPT). I. INTRODUCTION IN RECENT years, resonant wireless power transfer (WPT) systems have been gaining attention due to their ability to deliver relatively large power transfer at mid-range distances. This characteristic makes these circuits suitable for many industrial and biomedical applications [1] [7]. A common trend in the field of WPT is the use of more than two coils, or multiple coils, in the system [8], [9]. The advantage of using more than two coils is mainly to increase the link distance. However, the maximum power transfer is lower than in two-coil systems due to inherent losses in the intermediary circuits [9], [10]. A common problem in WPT systems is the fact that, in resonance conditions, the voltage or current over the inductors and capacitors is Q times greater than the voltage (v) or current (i) applied by an external source (in series or parallel connections), where Q is the quality factor of the system. In this way, the involved capacitors can be damaged [11] or even change their nominal values and detune the circuit after some time Manuscript received June 3, 2016; revised July 15, 2016; accepted July 24, 2016. Date of publication July 27, 2016; date of current version May 26, 2017. This work was supported in part by the Brazilian Council for Scientific and Technological Development (CNPq) under Grant 307509/2015-0 and by the Brazilian Council for the Improvement of Higher Education (CAPES) under Postgraduate Research Grant CPF: 066.339.13931. This brief was recommended by Associate Editor S. C. Wong. The authors are with the Graduate School of Electrical Engineering and Computer Science (CPGEI), Federal University of Technology Paraná (UTFPR), Curitiba 80230-901, Brazil (e-mail: caio.demiranda@gmail.com; pichorim@utfpr.edu.br). Digital Object Identifier 10.1109/TCSII.2016.2595402 Fig. 1. Lumped inductor model, where R S and C S represent the stray resistance and capacitance, respectively, and L is the self-inductance. of operation due to dielectric damages. A promising solution is to use self-resonant coils, i.e., coils that resonate with their intrinsic or stray capacitance [12] and self-inductance, avoiding the use of discrete capacitors. However, a typical lumped inductor model (shown in Fig. 1) leads to a parallel resonance with high impedance at the resonant frequency. Thus, a source connected with this coil actually sees a high impedance. Therefore, the current and consequently the magnetic field created by the coil can be very weak so that power transfer is low. An alternative is to use a current source to drive the system in a parallel resonance. However, it is known that, when a parallel connection is used in the secondary circuit, the reactive part of the impedance reflected by the secondary is not zero. Thus, if the primary circuit also has parallel connection, then the cancellation of the reflected reactance depends on the mutual inductance M and on the load value, complicating the use of parallel parallel connections as showed in [7] and [13]. On the other hand, in a series association, no reactive component is reflected at resonant frequency so that the system operation is simpler [7]. In this way, the most suitable option is to use aserieslc association in primary and secondary circuits. Therefore, due to the aforecited limitations and the fact that a source directly connected with a self-resonant coil (Fig. 1) sees a parallel resonance, as far as it is known, self-resonant coils have not been used in two-coil WPT systems. In fact, they have been used as intermediary or repeater circuits in multiple-coil systems (note that the voltage externally induced in the circuit of Fig. 1 is in series with this circuit) [9], [14], [15]. In the famous work of [15], self-resonant coils are used in the intermediary circuits (circuits 2 and 3) of a four-coil WPT system, while circuits 1 and 4 (source and load circuits, respectively) consist of not-tuned loop coils. These loop coils are only used to transmit and receive the signal at the selfresonant frequency of the intermediary coils (thus, no capacitor is used in this system). In this way, the link distance can be increased with respect to a two-coil WPT system. However, due to inherent losses on intermediary circuits, the maximum power transfer of a multiple-coil system is lower than in a 1549-7747 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

616 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 64, NO. 6, JUNE 2017 Fig. 2. Two-coil series WPT system. A voltage source (v) excites the system at its resonance. R 1 represents the losses of circuit 1, whereas R 2 represents the combination of the load resistance and the losses of circuit 2. two-coil WPT system [9], [10]. Moreover, due to their reduced number of coils and implementation facility, two-coil WPT systems have great practical importance in many industrial and biomedical applications, such as electric vehicle charging [1], [2] and artificial organ powering [6], [16], for example. However, as mentioned, self-resonant WPT systems composed of two coils have been scarcely explored in literature. In this work, an alternative strategy for the use of selfresonant coils in two-coil systems is proposed. The proposed scheme uses open bifilar coils in order to obtain series resonance with minimum impedance at the self-resonant frequency of the coils. II. DEVELOPMENT A. Two-Coil WPT Systems A typical two-coil series resonant WPT system is shown in Fig. 2. The system resonance is given by ( L 1 C 1 ) 1 = ( L 2 C 2 ) 1. Writing the system equations, the power transferred to the load R 2 (P 2 ) and the power dissipated at R 1 (P 1 ) can be found as R 1 R2 2 P 1 = v2 (R 1 R 2 + ω0 2M (1) R 2 ω0 2 P 2 = M 12 2 v2 (R 1 R 2 + ω0 2M. (2) A maximum power transfer condition can be found by doing dp 2 /dm 12 =0, which gives ω0 2 M 12 2 = R 1R 2 (3) or, in terms of the coupling coefficient k 12 = M 12 L1 L 2,it can also be written as R1 R 2 k c = (4) ωl 1 ωl 2 where k c denotes a critical coupling coefficient, i.e., the coupling coefficient that causes the maximum power transfer to the load. The overall system s efficiency can be found as the relation [10] η = P 2 ω 2 2 0 M 12 = P 1 + P 2 R 1 R 2 + ω 02 M 2. (5) 12 Fig. 3. Bifilar coil composed of conductors a b and c d, with terminals c and d opened. In this way, substituting (3) in (5) results show that maximum power transfer occurs when the overall efficiency is 50%. Also, substituting (3) in (2) gives that the maximum power transfer is P MAX = v 2 /4R 1, as shown in the maximum power transfer theorem [9], [10]. A relative power transfer (P REL ) can be found as the relation P 2 /P MAX, i.e., [10] P REL = 4R 1R 2 ω0 2M 12 2 (R 1 R 2 + ω0 2M. (6) B. WPT With Self-Resonant Open Bifilar Coils As mentioned before, the classical inductor model of Fig. 1 leads to a parallel resonance with maximum impedance at the resonant frequency. This characteristic reduces the current in the primary and the power transmission for other tuned circuits is low (when a voltage source is used). Also, when parallel association is used in the primary, the resonant frequency is dependent on mutual inductances and load resistance. This physical characteristic causes the use of typical self-resonant coils in two-coil systems to be not practical. To avoid these limitations, the use of an open bifilar coil (a coil consisting of two conductors wound in parallel) is proposed. Bifilar coils were first used in the 19th century [17] and have been used in transformers, relay windings, wirewound resistors, and others. An open bifilar coil is shown in Fig. 3. The bifilar coil is composed of conductors a b and c d. Since in the open bifilar coil terminals c and b are kept open, at low frequencies (below the resonance) the impedance seen at terminals a and d of the coil is capacitive. At the selfresonant frequency, the impedance is minimum and purely resistive, whereas for higher frequencies (above resonance) the impedance is inductive, i.e., a typical series resonance. The equivalent lumped model of an open bifilar coil is shown in Fig. 4. The capacitance between conductors a b and c d is represented by C S, whereas the combination of the individual resistances of these conductors and the losses in the dielectric (wire insulation) is represented by R S and the self-inductance of the coil is denoted by L (see Fig. 5). The equivalent capacitance between conductors a b and c d is represented by C S, and the equivalent resistance of the coil is represented by R S. The equivalent inductance of an open bifilar coil connected to a generator can be found from the high-frequency equivalent circuit shown in Fig. 5.

DE MIRANDA AND PICHORIM: SELF-RESONANT TWO-COIL WPT SYSTEM USING OPEN BIFILAR COILS 617 Fig. 4. Equivalent lumped electric model of an open bifilar coil, seen from terminals a and d. Fig. 6. Proposed WPT scheme using open bifilar coils L 1 and L 2. The losses of circuit 1 are represented by R 1, whereas the losses of circuit 2 combined with the load resistance are represented by R 2. Fig. 5. Equivalent high-frequency model of an open bifilar coil connected to a voltage source. The mutual inductance between conductors a b and c d is represented by M ab. Since the coils are wound together (Fig. 3), both share the same magnetic flux so that the coupling coefficient can be considered as k ab 1 and M ab = L a = L b. Considering these characteristics and the fact that, as the coils are equal, then i a = i b, the circuit equations can be written and the equivalent inductance of the circuit can be found as L eq = L a + L b +2M 4 = L + M 2 where L = L a = L b and M = M ab = M ba. In this case, since M = L, the equivalent inductance is (7) L eq = L a = L b (8) i.e., the equivalent inductance is equal to the inductance of one of the conductors isolated. This result is also commented in [18]. The proposed WPT scheme is shown in Fig. 6. A voltage source (v) tuned at the self-resonant frequency of the bifilar coils (L 1 and L 2 ) excites the system. The losses in the primary coil and the impedance of the generator are combined and represented by R 1, and the losses in the secondary coil combined with the load impedance are represented as R 2. The equivalent circuit of the scheme is that of Fig. 2, where C 1 and C 2 in this case represent the series capacitance of the bifilar coils (see Fig. 4) [19]. III. RESULTS Two bifilar coils with a 15-cm diameter, 22 turns of singlelayer enameled-copper wire with 19 AWG, tightly wound, were constructed. Since the coil is open, the inductance of the open bifilar coil cannot be measured at low frequencies. Fig. 7. Practical impedance curves (magnitude and phase) for the developed open bifilar coil and the point of resonance (f o). These curves show that the open bifilar coil behaves as an RLC series circuit. Hence, the inductance was measured from the resonance curve characteristics, from the approximation [20] L = R oq (9) 2πf 0 where R o is the series resistance at the resonant frequency f o and Q is the quality factor. The impedance magnitude and phase of one isolated bifilar coil (without the other coil, or secondary, coupled), measured with an Agilent 4294A vector impedance analyzer, are shown in Fig. 7. The series resistance of 4.57 Ω is found at the minimum impedance point at the resonant frequency of 802 khz, whereas a Q of 33 is determined by the ratio of the resonant frequency and the bandwidth (width between the frequencies where the phase angle is 45 ). Through (9), an inductance of 30 μh is yielded, whereas the calculated inductance of one isolated conductor from classical inductance formulas [21] is about 32 μh (a coil with the same dimensions and 11 turns). From the inductance and resonant frequency values, a capacitance of 1.32 nf is obtained. Although the theoretical calculation of the capacitance is out the scope of the present work, some works have presented satisfactory methods for this issue [12]. Also, two conventional coils with the same dimensions were

618 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II: EXPRESS BRIEFS, VOL. 64, NO. 6, JUNE 2017 Fig. 8. Theoretical coupling coefficient (k) between the open bifilar coils, from the distance of 2 20 cm. constructed for comparison purposes. The self-inductances and series resistances are approximately 128 μh (a similar inductance is found from classical formulas [21]) and 3.3 Ω in the range of 100 900 khz, respectively. Of course, since the number of turns of the conventional coil (22 turns) is two times greater than that of the equivalent open bifilar coil (11 turns), the inductance is approximately four times higher. For the theoretical calculation of efficiency and relative power transfer using (5) and (6), the coupling coefficient k in the function of the distances between two coaxially aligned coils was numerically calculated using the classical Neumann equation [22]. Of course, as mentioned, for the open bifilar coils the number of turns considered should be that of one isolated conductor (the equivalent inductance), in this case 11 turns. The theoretical coupling coefficient for the open bifilar coils is shown in Fig. 8. The efficiency and relative power transfer were measured as the distance between the bifilar coils was varied. In order to measure the currents in the primary and secondary circuits, i 1 and i 2, respectively, a shunt resistor (R 0 ) of 10 Ω was used in a series with coil 1, and a 10-Ω resistor was used as partial load (R l ) (the resistors presented measured stray inductances of about 40 nh at 802 khz). A signal generator (Tektronix AFG 3101) was used as voltage source so that its internal impedance (R G =50Ω)should be considered since it is in series with coil 1. Thus, the total resistance of the circuit is R 1 = R 0 + R S + R G =64.57 Ω. On the other hand, the resistance of circuit 2 is R 2 = R l + R S =14.57 Ω. For simplicity, R 2 and not R l is considered to be the load of the system. A voltage signal (v) of 7.8 V RMS in the system-resonant frequency of 802 khz was applied on coil 1. The voltages on R 0 and R l were measured using an oscilloscope (Agilent MSO6034), in the range of 2 20 cm between the coils (the distance considered is between the last turn of coil 1 and the first turn of coil 2) in steps of 0.5 cm so that the currents i 1 and i 2 are founded in each step. Finally, the dissipated powers are P 1 = R 1 i 2 1 and P 2 = R 2 i 2 2. Thus, η = P 2/(P 1 + P 2 ) and P rel. = P 2 /P MAX, where P MAX = v 2 /4R 1. The theoretical values are calculated through (5) and (6) using the theoretical coupling coefficient from the Neumann equation. The results are shown in Fig. 9, with the measurements represented by dots (full dot for P rel. and hollowed circle for η) and the calculated curves by solid lines. Fig. 9. Measured efficiency (hollowed circles) and relative power transfer (full dot); theoretical values are represented by the solid lines. Fig. 10. Measured efficiency (hollowed circles) and relative power transfer (full dot) for a conventional coil of the same dimensions tuned with real capacitors. Theoretical values are represented by the solid lines. The correlation coefficients between the measured and calculated data for efficiency and relative power transfer are both greater than 0.99. It can be seen that the relative power transfer of 100% occurs when efficiency is 50%, as predicted in theory. Of course, in a practical system, impedance compensation techniques can be used for other load values. For the conventional coil, the same series resonant frequency of 802 khz was tuned by using an association of three variable capacitors or trimmers (the self-resonant frequency of the conventional coil is 6 MHz). The total R S including the losses in capacitors is 4.6 Ω. The coupling coefficient is also calculated from the Neumann equation and, using the same methodology, the practical and calculated efficiency and relative power transfer are shown in Fig. 10. It can be seen that, since the inductance is greater for a conventional coil with the same dimensions, from (4), the maximum power transfer occurs at a smaller critical coupling coefficient or larger distances. Also, for comparison, the conventional coils were used at their self-resonant frequency of 6 MHz. The coils have an unloaded Q of 47 and resistance of 220 kω at the resonant frequency (in this case, it is parallel resonance with maximum impedance at f o ). Using the same WPT scheme, the power transfer is practically null, yielding a relative power transfer less than 1%.

DE MIRANDA AND PICHORIM: SELF-RESONANT TWO-COIL WPT SYSTEM USING OPEN BIFILAR COILS 619 It is also important to notice that the self-resonant frequency of a bifilar coil is smaller than that of the corresponding conventional coil (802 khz versus 6 MHz). This can be expected since, for the same voltage applied on both coils, a greater voltage between the adjacent turns is achieved in the bifilar coils, in such a way that the equivalent capacitance of this coil is greater. However, the calculation of the capacitance is out of the scope of the present work. IV. CONCLUSION The proposed self-resonant scheme for two-coil WPT systems, which uses open bifilar coils, has been shown to be suitable for practical applications. The main advantage of the proposal is that no capacitor is used in the system. Thus, it is suitable for medium- and high-power applications such as EV contactless charging, avoiding capacitor damage. Of course, in a practical system, the breakdown voltage on the wire specification should be observed and, depending on the application, wires with thicker isolation should be used. It should be also observed that, as mentioned before, at series resonance the voltage over the individual components, L and C, isq times the source voltage v. However, as seen in a two-coil system, the quality factor only affects the critical coupling coefficient or the optimum distance so that maximum power transfer can always be achievable for any Q value. The proposed system is also suitable for any application in which dimension restrictions are critical, such as in powering biomedical implants. The main disadvantage of the proposed scheme is that the equivalent inductance of the open bifilar coil is smaller than that of a conventional coil with the same dimensions. However, this disadvantage can be compensated by using more turns in the bifilar coil and impedance transformation techniques. 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