Apparatus and method for wireless power transfer

Abstract

The present invention provides an apparatus for wireless power transfer including three or more coils, each coil defining a respective coil plane, and the coils being arranged in one or more power flow paths whereby each coil can be magnetically coupled to one or more of the other coils thereby to wirelessly transfer power along the one or more power flow paths. The present invention also provides a method for wirelessly transferring power, the method including: providing three or more coils, each coil defining a respective coil plane; and arranging the coils in one or more power flow paths whereby each coil can be magnetically coupled to one or more of the other coils thereby to wirelessly transfer power along the one or more power flow paths.

Claims

1. An apparatus for wireless power transfer, comprising: a source coil resonator directly connected to an AC power source; a load coil resonator directly connected to a load; and three or more intermediate coil resonators, each not directly connected to a power source and not directly connected to a load, arranged between the source coil resonator and the load coil resonator to guide power flow therebetween; each of the source coil resonator, the load coil resonator, and the intermediate coil resonators defining a respective coil plane; the intermediate coil resonators being arranged so as to form two curved power flow paths from the source coil resonator to the load coil resonator; the source coil resonator, the load coil resonator, and the intermediate coil resonators being magnetically coupled with each other only by magnetic resonance to wirelessly transfer power along the power flow path; wherein a ratio of a distance between any two of the coil planes to half the maximum dimension of any of said two coil planes is less than 3 such that magnetic coupling among the source coil resonator, the load coil resonator, and the intermediate coil resonators is non-radiative; and wherein the two curved power flow paths, when combined, are in a circular form.

2. The apparatus according to claim 1 wherein one or both of a resonant frequency and an impedance of the intermediate coil resonators is variable for affecting the power flow.

3. The apparatus according to claim 2 wherein the intermediate coil resonators each has one or both of a capacitance and an inductance, and the resonant frequency of one or more of the intermediate coil resonators can be varied by varying one or both of the capacitance and the inductance.

4. The apparatus according to claim 1 wherein a distance between one pair of the coil planes is not equal to a distance between another pair of the coil planes.

5. The apparatus according to claim 1 wherein the source coil resonator, the load coil resonator, and the intermediate coil resonators have an operating frequency of less than 100 MHz.

6. The apparatus according to claim 1 wherein the source coil resonator, the load coil resonator, and the intermediate coil resonators have an operating frequency of less than 10 MHz.

7. The apparatus according to claim 1 wherein the source coil resonator, the load coil resonator, and the intermediate coil resonators have an operating frequency of less than 5 MHz.

8. The apparatus according to claim 1 wherein the source coil resonator, the load coil resonator, and the intermediate coil resonators have an operating frequency of less than 1 MHz.

9. The apparatus according to claim 1 wherein the source coil resonator, the load coil resonator, and the intermediate coil resonators have an operating frequency of greater than 10 kHz.

10. The apparatus according to claim 1 wherein the intermediate coil resonators are made from superconductive material.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) Preferred embodiments in accordance with the best mode of the present invention will now be described, by way of example only, with reference to the accompanying figures, in which:

(2) FIG. 1 is a schematic diagram of a pair of loop resonators of the prior art;

(3) FIG. 2 is a graph showing the typical exponential decay of energy efficiency as a function of transmission distance for wireless power transfer;

(4) FIGS. 3a to 3c are schematic diagrams of a magneto-inductive waveguide of the prior art for signal transmission;

(5) FIG. 3d is a schematic diagram of PCB loop resonators used in the waveguide of FIGS. 3a to 3c;

(6) FIG. 4 shows schematic diagrams of a magneto-inductive 3-port signal power splitter of the prior art, together with a graph showing the performance of the signal power splitter;

(7) FIG. 5 is a schematic diagram of an apparatus of the prior art for wireless power transfer, which uses a pair of magnetically coupled coils;

(8) FIG. 6 is a schematic diagram of an apparatus for wireless power transfer in accordance with an embodiment of the present invention;

(9) FIG. 7a is a schematic diagram of an apparatus for wireless power transfer in accordance with another embodiment of the present invention, in which the coils are arranged in a straight power flow path;

(10) FIG. 7b is a schematic diagram of an apparatus for wireless power transfer in accordance with yet another embodiment of the present invention, in which the coils are arranged in a curved power flow path;

(11) FIG. 7c is a schematic diagram of an apparatus for wireless power transfer in accordance with yet another embodiment of the present invention, in which the coils are arranged in a power flow path that splits into two further power flow paths;

(12) FIG. 7d is a schematic diagram of an apparatus for wireless power transfer in accordance with a further embodiment of the present invention, in which the coils are arranged in two power flow paths that merge into one power flow path;

(13) FIGS. 8a to 8c are schematic diagrams of an apparatus for wireless power transfer in accordance with an embodiment of the present invention, in which one of the coils (shown bolded) is configured to deviate from being perpendicular to the power flow path in which it is arranged, thereby controlling the power being transferred;

(14) FIGS. 9a to 9c are schematic diagrams of an apparatus for wireless power transfer in accordance with another embodiment of the present invention, in which one or both of the resonant frequency and the impedance of two of the coils (shown dashed) is varied, thereby controlling the power being transferred;

(15) FIG. 10 shows schematic diagrams of an apparatus for wireless power transfer in accordance with yet another embodiment of the present invention, in which the coils form part of a flexible tubular structure;

(16) FIGS. 11 to 17 are schematic diagrams of experimental setups of various embodiments of the present invention;

(17) FIG. 18 is a schematic diagram of a circuit model of an apparatus for wireless power transfer in accordance with an embodiment of the present invention;

(18) FIG. 19 is a graph of the efficiency against different respective distances between the pairs of coils of the embodiment shown in FIG. 18; and

(19) FIG. 20 is a schematic diagram of an apparatus for wireless power transfer in accordance with a further embodiment of the present invention.

DETAILED DESCRIPTION OF THE BEST MODE OF THE INVENTION

(20) Following on from the discussion of the background of the present invention, the limitations of existing methods for wireless power or signal transfer can be identified as follows: (1) The use of only a pair of loop resonators has limitations either in terms of distance for the short-range method or in terms of energy efficiency for the mid-range method. (2) The use of high-frequency operation in excess of 100 MHz in the waveguide research discussed above could increase the AC resistance of the coupled coils, and therefore, reduces the energy efficiency if it is used for power transfer applications. (3) In designing waveguides for the purposes of wave propagation, the dimension of the loop resonator is inversely proportional to the operating frequency. Therefore, the operating frequency has to be very high, that is, well above 100 MHz, in order to reduce the size of the loop resonators. However, for power transfer via a coupled magnetic field, this use of very high frequency, that is, greater than 100 MHz, can be avoided. (4) In the 3 methods described above, there is no variable control of the power flow except for control from the power source. No mechanism has been proposed to vary the power flow along the power flow paths.

(21) Referring to FIGS. 6 to 20, preferred embodiments of the present invention provide an apparatus for wireless power transfer including three or more coils 1, each coil 1 defining a respective coil plane, and the coils being arranged in one or more power flow paths 2 whereby each coil can be magnetically coupled to one or more of the other coils thereby to wirelessly transfer power along the one or more power flow paths.

(22) The magnetic coupling between two or more of the coils is preferably resonant. In particular, the magnetic coupling is at a resonant frequency shared by the two or more coils. In one embodiment, all of the coils are magnetically coupled at a resonant frequency.

(23) It will be appreciated that the terms coil, loop, winding and other similar terms are interchangeable, as understood by those skilled in the art. Similarly, coils that can be operated at a resonant frequency can be termed resonators, coil resonators, loop resonators, winding resonators, or other similar terms, as understood by those skilled in the art. Further, it will be appreciated that coils arranged in a power flow path can also be termed a chain of coils, chain of loops, or chain of windings.

(24) The coils can be made of any conductive material. The coils can also be made from a superconductive material so that there are no conduction losses.

(25) Returning to the preferred embodiments of the present invention, the coils allow power to be wirelessly transferred along the one or more power flow paths via mutual induction between the coils.

(26) In particular, one or more of the coils are adapted to receive power from a power supply 3, the power being wirelessly transferable along one or more of the power flow paths via mutual induction between the coils. Also, one or more of the coils are adapted to provide power to a power consuming device. In one embodiment, each coil acts as an AC voltage source, and thereby, a power source.

(27) In some embodiments, such as that shown in FIG. 7c, one or more of the power flow paths splits into further power flow paths. In FIG. 7c specifically, one power flow path splits into two power flow paths. In other embodiments, such as that shown in FIG. 7d, two or more of the power flow paths merge into fewer power flow paths. In FIG. 7d specifically, two power flow paths merge into one power flow path.

(28) One or more of the power flow paths are straight (see, for example, FIG. 7a), curved (see, for example, FIG. 7b), circular, irregular-shaped, or any combination thereof.

(29) Thus, many different networks of power flow paths ranging from the simple to the more complex with multiple branches splitting into further branches and/or merging into fewer power flow paths, in which the power flow paths can also be of a variety of shapes, are possible in accordance with embodiments of the present invention.

(30) In a further embodiment, as depicted in FIG. 20, the coils are of different sizes and are arranged concentrically. In particular, the coils are circular, are of increasing diameter, and are arranged concentrically in a common plane. The power flow path in this embodiment is radial from the smallest diameter coil to the largest diameter coil on the outside.

(31) In one embodiment, one or more of the coils can be configured such that the respective coil plane deviates from being perpendicular to the power flow path in which it is arranged, thereby varying the mutual inductance between the one or more coil and an adjacent coil. This thereby controls the power flow, or the amount of power transferred wirelessly, along the one or more power flow paths.

(32) As shown in FIGS. 8a to 8c, the coils are arranged in one power flow path that splits into two power flow paths, that is, one main path that splits into two branch paths, an upper branch path and a lower branch path. The last coil (shown bolded in FIGS. 8a to 8c) in the main path before it splits into the two branch paths can be rotated about an axis that passes through the last coil and is perpendicular to the main and branch paths. Thus, the coil plane of the last coil deviates from being perpendicular to the power flow path in which it is arranged, thereby varying the mutual inductance between the one or more coil and an adjacent coil. More particularly, in FIG. 8b, the coil plane of the last coil is rotated towards the upper branch path (shown bolded in FIG. 8b), resulting in a larger power flow in the upper branch path relative to the lower branch path. In FIG. 8c, the coil plane of the last coil is rotated towards the lower branch path (shown bolded in FIG. 8c), resulting in a larger power flow in the lower branch path relative to the upper branch path.

(33) In another embodiment, one or both of the resonant frequency and the impedance of one or more of the coils can be varied. In one embodiment, one or more of the coils has a capacitance and the resonant frequency of the one or more coils can be varied by varying the capacitance. In another embodiment, one or more of the coils has an inductance and the resonant frequency of the one or more coils can be varied by varying the inductance. Again, this thereby controls the power flow, or the amount of power transferred wirelessly, along the one or more power flow paths.

(34) As shown in FIGS. 9a to 9c, the coils are arranged in one power flow path that splits into two power flow paths, that is, one main path that splits into two branch paths, an upper branch path and a lower branch path. Referring to FIG. 9b, one or both of the resonant frequency and the impedance of the first two coils (shown dashed in FIG. 9b) in the upper branch path are varied to de-tune or decouple the first two coils in the upper branch path. This subsequently results in a larger power flow in the lower branch path (shown bolded in FIG. 9b) relative to the upper branch path. Conversely, referring to FIG. 9c, one or both of the resonant frequency and the impedance of the first two coils (shown dashed in FIG. 9c) in the lower branch path are varied to de-tune or decouple the first two coils in the lower branch path. This subsequently results in a larger power flow in the upper branch path (shown bolded in FIG. 9c) relative to the lower branch path.

(35) Thus, the two foregoing embodiments represent two power flow control methods that can be utilized in embodiments of the present invention.

(36) In another embodiment shown in FIG. 10, the coils form part of a tubular structure 4. Preferably, the tubular structure is flexible. The flexible tubular structure can in this way form a new type of power cable having a hollow centre. Since no conductive material, such as copper, is required to fill the core of this new type of cable, much less conductive material is required. Also, the conductive material need not be continuous. Further, there is inherent electrical isolation between the two ends of this new type of cable.

(37) In preferred embodiments, the magnetic coupling between the coils is non-radiative. That is to say, near-field or short-range magnetic coupling is employed. In some embodiments, the ratio of the distance between any two of the coil planes and half the maximum dimension of any of said two coil planes is less than 3. The distance between any two of the coil planes is also termed the transmission distance between the two coils.

(38) In the embodiments depicted in FIGS. 6 to 9, the coils are circular, substantially identical, and are spaced a uniform distance apart from each other. Therefore, half the maximum dimension of any of the coil planes is the radius r. The transmission distance is labeled as din the figures.

(39) Although the embodiments depicted in FIGS. 6 to 9 show coils that are spaced a uniform distance apart from each other, this need not be the case. In other embodiments, the distance between a pair of the coil planes is unequal with the distance between another pair of the coil planes. In further embodiments, the respective distances between different pairs of the coil planes are selected to maximize the efficiency of the wireless power transfer. In one embodiment described in further detail below, the respective distances between different pairs of the coil planes are calculated, and thereby selected, to maximize the efficiency of the wireless power transfer. In fact, as will be described in further detail below, unequal respective distances between different pairs of the coil planes can maximize the efficiency of the wireless power transfer in certain applications.

(40) Thus, the distance between any pair of the coil planes can vary with respect to any other pair of the coil planes. To remove any doubt, one pair of the coil planes can include one coil plane that is the same coil plane that forms part of another pair of the coil planes, that is, two different pairs of the coil planes can share one common coil plane.

(41) The features above in respect of the relative distances between coils can of course be combined. In particular, in some embodiments, the ratio of the distance between any two of the coil planes and half the maximum dimension of any of said two coil planes is less than 3, and the distance between a pair of the coil planes is unequal with the distance between another pair of the coil planes. In other embodiments, the ratio of the distance between any two of the coil planes and half the maximum dimension of any of said two coil planes is less than 3, and the respective distances between different pairs of the coil planes are selected to maximize the efficiency of the wireless power transfer.

(42) In various embodiments, the coils have an operating frequency of less than 100 MHz, 10 MHz, 5 MHz, or 1 MHz. These ranges for operating frequencies advantageously result in low AC resistances in the coils, high quality factors, and low conduction losses, thereby improving the transmission energy efficiency. This is discussed further below. In embodiments where the magnetic coupling between two or more of the coils is resonant, the resonant frequency shared by the two or more coils can be within these ranges, resulting in the same advantages above. In other embodiments, the coils have an operating frequency of greater than 10 kHz. This advantageously results in frequencies above the audible range. In further embodiments, these frequency ranges can be combined, that is, the coils of further embodiments can have an operating frequency of between 10 kHz and one of 100 MHz, 10 MHz, 5 MHz, or 1 MHz.

(43) The present invention also provides a method for wirelessly transferring power. The method includes: providing three or more coils, each coil defining a respective coil plane; and arranging the coils in one or more power flow paths whereby each coil can be magnetically coupled to one or more of the other coils thereby to wirelessly transfer power along the one or more power flow paths.

(44) Preferred embodiments of the method include those that have already been described above. These include those that utilize the coils described above, and that arrange and configure the coils as described above.

(45) The following provides additional details, features, and advantages of the embodiments described above and further embodiments in respect of the present invention.

(46) In view of the above description, some embodiments of the present invention utilize a series of resonant magnetically coupled coils or loop resonators arranged in one or more power flow paths, thereby forming so-called domino chains or domino resonator chains. The coupled loop resonators are placed in the short-range regime where the energy efficiency is high. The short-range domino chain arrangement enables a longer overall transmission distance (for a given d/r ratio) between the power source resonator (i.e. the coil connected to a power supply) and the end receiver loop resonator (i.e. the last coil at an end of the power flow path away from the power source) where a load is connected, despite the use of more than two loop resonators.

(47) This advantage is illustrated by comparing the prior art apparatus shown in FIG. 5, which utilizes a pair of loop resonators, and the general embodiment of the present invention shown in FIG. 6, where three or more loop resonators are utilized.

(48) While the proposed domino resonator chain can be used at high frequency above the Mega-Hertz level, the use of a relatively large capacitor in each loop resonator can reduce the resonance frequency to the sub-Mega-Hertz region, if necessary, so as to reduce the AC resistance of the coils and increase the quality factor Q=L/R.sub.ac. A high Q value improves the transmission energy efficiency. This allows the minimization of R.sub.ac for power transfer, and thus, the i.sup.2R.sub.ac conduction loss.

(49) The use of the domino chain arrangement of the loop resonators enables the control of the power in a highly flexible manner. As described above, straight, curved, circular, even irregularly-shaped domino paths, or a combination thereof can easily be formed to direct the power flow to targeted locations. The resonant capacitor voltage of each resonator becomes an AC voltage source. Also as described above, a single power domino chain can be split into several chains. Several domino chains can also merge into one domino chain. See FIGS. 7c and 7d.

(50) Two power flow control methods were described above.

(51) An embodiment of the first method is control via the angle of the central axis of the loop plane. The angle of the central axis of the loop resonator can be altered in order to change the mutual inductance between adjacent coupled loop resonators as a means of power flow control. If the coupled loop planes are parallel with the axis of the power flow, this angle is zero. This method can be used within a single domino chain or at the junctions of domino chains, as shown in FIGS. 8a to 8c.

(52) An embodiment of the second method is control via the resonant frequency of the loop resonators, by controlling, for example, the impedance of the loop resonators. The impedance can in turn be controlled by controlling a capacitance and/or an inductance of the loop resonators. Since efficient power transfer is only feasible if the loop resonators have the same resonant frequency, by de-tuning or decoupling one or more loop resonators in a section of a power domino chain, the impedance can be altered to vary the power flow, as illustrated in FIGS. 9a to 9c. As out-of-tuned loop resonators have a high equivalent impedance, the control of the resonant frequency provides a simple means to control power flow. Means of altering the resonant frequency of a loop resonator include, but are not limited to, adding or reducing the capacitance of the loop resonators, or adding or reducing the inductance of the loop resonators.

(53) The use of a network of power domino resonators essentially provides a power network because the capacitor in each loop resonator provides an AC voltage source. It is analogous to the power sockets used in a domestic electrical system.

(54) As noted above, if a chain of coupled loop resonators is enclosed in a flexible tubular structure, it forms a power cable which can allow power transfer at a particular resonant frequency without a continuous conductive material such as copper. This is a new form of power cable that has inherent electrical isolation between the two ends of the cable. See FIG. 10. It requires much less conductive material, such as copper, and is suitable for power transfer at a particular resonant frequency of the cable.

(55) As an example, in one particular embodiment, such a power cable can be used in microsurgery, where the power cable can be used to treat tumors in a patient. This can be done by operating the coils at a resonant frequency that matches the resonant frequency of a tumor.

(56) As mentioned above, it is noted that while an equal-distance arrangement of the loop resonators, where the loop resonators are spaced a uniform distance apart (i.e. the respective distances between different pairs of the loop resonators are equal), is an easy and general approach, an optimized unequal-distance arrangement, where the distance between loop resonators varies (i.e. the distance between a pair of the loop resonators is unequal with the distance between another pair of the loop resonators), can in fact improve the overall energy efficiency in some specific applications.

(57) Referring to FIGS. 18 and 19, an embodiment using the unequal-distance arrangement referred to above will now be described.

(58) FIG. 18 shows the circuit model of an n-winding wireless power transfer (WPT) system according to an embodiment of the present invention, where each winding is represented by the subscript number from 1 to n. Z.sub.L (Z.sub.L=R.sub.L+jX.sub.L) represents the load impedance including the compensating capacitor for winding-n. In the following discussion, it is assumed that all the windings except winding-1 are resonant. Winding-1 resonance will not affect the efficiency of the system but will decrease the VA rating of the power supply. Therefore, in practice operation, winging-1 is also resonant.

(59) With the help of the circuit model in FIG. 18, the relationship among the currents in the windings can be expressed by the following equation:

(60) $\begin{array}{cc}\left[\begin{array}{cccccccc}j{M}_{12}& R_2& j{M}_{23}& j{M}_{24}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& j{M}_{2n}\\ j{M}_{13}& j{M}_{23}& R_3& j{M}_{34}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& j{M}_{3n}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& & \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ j{M}_{1\left(n-1\right)}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& j{M}_{\left(n-2\right)\left(n-1\right)}& R_{\left(n-1\right)}& j{M}_{\left(n-1\right)n}\\ j{M}_{1n}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& j{M}_{\left(n-2\right)n}& j{M}_{\left(n-1\right)n}& R_n+R_L\end{array}\right].Math.\left[\begin{array}{c}{I}_1\\ I_2\\ \mathrm{.Math.}\\ I_{n-1}\\ I_n\end{array}\right]=0& \left(U1\right)\end{array}$

(61) where M.sub.ij=k.sub.12{square root over (L.sub.iL.sub.j)}(i,j=1, 2, . . . , n; ij) is the mutual inductance between winding i and winding j and the RL is the load resistance which is connected to winding n.

(62) The following relationships can then be derived by solving this equation:

(63) $\begin{array}{cc}\frac{I_m}{I_n},m=1,2,\mathrm{.Math.},n-1.& \left(U2\right)\end{array}$

(64) Further, the efficiency of the n-winding system can be derived by substituting all the relationships of (U2) into the following equation:

(65) $\begin{array}{cc}=\frac{I_n^2{R}_L}{I_1^2{R}_1+I_2^2{R}_2+\mathrm{.Math.}+I_n^2\left(R_n+R_L\right)}=\frac{R_L}{{\left(\frac{I_1}{I_n}\right)}^2{R}_1+{\left(\frac{I_2}{I_n}\right)}^2{R}_2+\mathrm{.Math.}+{\left(\frac{I_{n-1}}{I_n}\right)}^2{R}_{n-1}+R_n+R_L}.& \left(U3\right)\end{array}$

(66) Based on equation (U3), the maximum efficiency and the optimum load can be calculated provided that the system is given. For embodiments where all the windings are placed in a straight line, the optimum distances between the windings can be calculated for a given total power transfer distance and a given number of windings.

(67) A simplified model will now be analyzed.

(68) In mid-range wireless power transfer applications, the mutual inductance between every two non-adjacent windings is actually small compared with the mutual inductance between two adjacent windings, and will barely affect the performance of the system. Therefore, a simplified model could be used to study the characteristics of the multi-winding WPT system.

(69) For a simplified model, equation (U1) can be rewritten as:

(70) $\begin{array}{cc}\left[\begin{array}{cccccccc}j{M}_{12}& R_2& j{M}_{23}& & & & & \\ & j{M}_{23}& R_3& j{M}_{34}& & & & \\ & & & & & & & \\ & & & & & j{M}_{\left(n-2\right)\left(n-1\right)}& R_{\left(n-1\right)}& j{M}_{\left(n-1\right)n}\\ & & & & & & j{M}_{\left(n-1\right)n}& R_n+R_L\end{array}\right].Math.\left[\begin{array}{c}{I}_1\\ I_2\\ \mathrm{.Math.}\\ I_{n-1}\\ I_n\end{array}\right]=0& \left(U4\right)\end{array}$

(71) The efficiency expression can be derived with the same steps described above.

(72) Then, by solving the equation:

(73) $\begin{array}{cc}\frac{}{R_L}=0,& \left(U5\right)\end{array}$

(74) we can derive the optimum load and the maximum efficiency, which can be expressed as follows:

(75) $\begin{array}{cc}{R}_{L\_\mathrm{OPT}}=R_n\sqrt{\frac{\underset{k=1}{\overset{n}{.Math.}}{A}_k^2{}_k}{\underset{k=1}{\overset{n-1}{.Math.}}{B}_k^2{}_k}},& \left(\mathrm{U6}\right)\\ {}_{\mathrm{ma}x}=\frac{{}_n}{2\sqrt{\left(\underset{k=1}{\overset{n}{.Math.}}{A}_k^2{}_k\right)\left(\underset{k=1}{\overset{n-1}{.Math.}}{B}_k^2{}_k\right)}+2\underset{k=1}{\overset{n-1}{.Math.}}{A}_k{B}_k{}_k+{}_n}\mathrm{where},A_k=\underset{E\left(k,n\right)}{.Math.}\underset{g=k+1}{\overset{n-1}{.Math.}}{}_{g\left(g+1\right)}^{e\left(g\right)},\mathrm{for}k=1,2,\mathrm{.Math.}n-2\mathrm{and}{A}_{n-1}=1,A_n=1;B_k=\underset{E\left(k,n-1\right)}{.Math.}\underset{g=k+1}{\overset{n-2}{.Math.}}{}_{g\left(g+1\right)}^{e\left(g\right)},\mathrm{for}k=1,2,\mathrm{.Math.}n-3\mathrm{and}{B}_{n-2}=1,B_{n-1}=1;{}_k=\underset{g=1}{\overset{k}{.Math.}}{}_{\left(g-1\right)g},\mathrm{for}k=1,2,\mathrm{.Math.}n;E\left(k,n\right)=\left\{\begin{array}{c}\left[\begin{array}{c}\begin{array}{c}e\left(k+1\right),\\ e\left(k+2\right),\mathrm{.Math.},\end{array}\\ e\left(n-1\right)\end{array}\right]|e\left(m-1\right)e\left(m\right)1,\\ m=k+1,\mathrm{.Math.},n-2\end{array}\right\},\mathrm{for}k=1,2,\mathrm{.Math.}n-2;e\left(k\right)\left\{0,1\right\},\mathrm{for}k=2,3,\mathrm{.Math.}n-1;{}_{k\left(k+1\right)}=k_{k\left(k+1\right)}^2{Q}_k{Q}_{k+1}=\frac{{}^2{M}_{k\left(k+1\right)}^2}{R_k{R}_{\left(k+1\right)}},\mathrm{for}k=1,2,\mathrm{.Math.}n-1\mathrm{and}{}_{01}=1.& \left(\mathrm{U7}\right)\end{array}$

(76) For identical coaxial circular windings, the analysis is as follows.

(77) Maxwell has derived an equation to calculate the mutual inductance between two coaxial circular filamentary currents:

(78) $\begin{array}{cc}M={}_0\frac{\sqrt{R_1{R}_2}}{f}\left[\left(2-f^2\right)K\left(f\right)-2E\left(f\right)\right]& \left(\mathrm{U8}\right)\end{array}$

(79) where K(f) and E(f) are complete elliptic integrals of the first and second kind, respectively, and:

(80) $f=\sqrt{\frac{4R_1{R}_2}{D^2+{\left(R_1+R_2\right)}^2}}$

(81) where R.sub.1, R.sub.2, and D are the radius of winding 1, winding 2 and the distance between them, respectively.

(82) For mid-range wireless power transfer, the mutual inductance of two coaxial circular windings can be calculated accurately by:

(83) $\begin{array}{cc}M=\underset{i=1}{\overset{n_1}{.Math.}}\underset{j=1}{\overset{n_2}{.Math.}}{M}_{\mathrm{ij}}& \left(\mathrm{U9}\right)\end{array}$

(84) Therefore, in the n-winding WPT system with identical coaxial circular windings, all the mutual inductances between every two adjacent windings can be calculated using (U9), and by substituting all the mutual inductances into (U7), we can derive the expression of efficiency as a function of the combination of distances in the system as follows:
.sub.max=f(D.sub.12,D.sub.23, . . . ,D.sub.(n-1)n)(U10)

(85) where D.sub.ij is the distance between winding i and winding j.

(86) With the help of equation (U10), the optimization of the distances of the windings can be determined provided that the total transfer distance is given.

(87) As an example, the calculations above were made for a 4-winding WPT system in accordance with an embodiment of the present invention, on the basis of a total transfer distance of 0.9 m. The results are shown in the graph of FIG. 19, in which D.sub.12 represents the distance between winding 1 and winding 2, and D.sub.23 represents the distance between winding 2 and winding 3. As can be seen, the unequal-distance arrangement (D.sub.12=0.285 m, D.sub.23=0.33 m, D.sub.34=0.285 m) has a higher efficiency than the equal-distance arrangement (D.sub.12=0.3 m, D.sub.23=0.3 m, D.sub.34=0.3 m).

(88) The measured efficiencies were as follows.

(89) 4-winding (total distance 0.9 m):

(90) 66.33% for the equal-distance arrangement; and

(91) 67.69% for the unequal-distance arrangement (0.282 m, 0.336 m, 0.282 m).

(92) As another example, the calculations above were made for a 8-winding WPT system in accordance with another embodiment of the present invention, on the basis of a total transfer distance of 2.1 m.

(93) The measured efficiencies were as follows. 8-winding (total distance 2.1 m): 45.81% for the equal-distance arrangement; and 47.53% for the unequal-distance arrangement (0.259, 0.314, 0.318, 0.318, 0.318, 0.314, 0.259)

(94) In summary, embodiments of the present invention are related to wireless power transfer methods and apparatuses based on non-radiative (near-field) magnetic coupling of conductive coupled loop resonators, whereby these coupled loop resonators are arranged along the path or paths of desired power flow, much like a series of dominoes. Such power flow can be split into or combined from a plurality of power flow channels.

(95) Means of controlling the power flow into split power flow channels can be achieved by altering the angle of the resonator coils and/or changing the resonant frequency of loop resonators in a section of a power flow path by, for example, changing the capacitance, and thus, the impedance of the power flow path.

(96) Existing waveguide technology typically operates at the radiative frequency range of hundreds of Mega-Hertz to tens of Giga-Hertz. Also, in existing waveguide technology, the loop resonator separation is determined by the wavelength of the propagating waves. By contrast, the domino resonators according to embodiments of the present invention can operate at low frequencies from a few tens of kilo-Hertz upwards with flexible resonator separation distances, thereby minimizing the AC resistance and maximizing the quality factor of the coupled coils for power transfer applications with great flexibility.

(97) A unique advantage of this invention is that the magnetically coupled resonators can be flexibly arranged in any form of domino chain arrangements. Further, if a series of magnetically coupled domino resonators are arranged within a flexible tubular enclosure, in accordance with one embodiment of the invention, they form an electrically isolated power cable, or powerguide cable, without a continuous solid conductive material through the cable structure. This new power cable has the unique property that it will not transmit power unless input power excitation is at the resonant frequency of the loop resonators which can be designed accurately.

(98) Practical experimentation has been undertaken to confirm the performance of various embodiments of the present invention. This is described below.

(99) Loop resonators were constructed, with each loop resonator formed by a coil connected in series with a capacitor. The radius of the coil was 15.5 cm. The number of turns of each coil was 8. Inductance L=90 H, capacitance C=1 nF, resonant frequency was about 520 kHz. The AC winding resistance at this frequency was R.sub.ac=0.98. The quality factor Q=290. One loop resonator was connected with a power supply 3. A compact fluorescent lamp (CFL) 5 was used as the electric load, that is, the power consuming device was in the form of the CFL 5. The following describes the results of utilizing different arrangements of resonators.

(100) (a) Straight Power Domino Resonator Arrangements with (i) Equal and (ii) Unequal Distance Approaches

(101) (i) Equal-Distance Arrangement

(102) As shown in FIG. 11, a domino chain comprising 8 resonators spaced apart with equal distances was set up. A 14 W CFL was connected across the capacitor of the last resonator in the chain. The last resonator was excited by a RF-power amplifier at 520 kHz.

(103) (ii) Unequal-Distance Arrangement

(104) The same experimental setup as above for (i) was repeated with the resonators spaced apart with unequal distances, as shown in FIG. 12. It was demonstrated that the unequal-distance approach is also practical.

(105) (b) L-Shape Power Domino Resonator Arrangement

(106) The domino chain method is highly flexible in directing power flow. This was demonstrated by arranging the resonators in an L-shape, in which the power flow path was bent by about 90, as shown in FIG. 13.

(107) (c) Circular Power-Domino Resonator Arrangement

(108) An interesting domino arrangement is to place the loop resonators in a circular form, which was also done during practical experimentation, as shown in FIG. 14. It was demonstrated that the CLF load can be connected across the capacitor in any loop resonator in the circular domino chain.

(109) (d) Irregular-Shaped (Y-Shape) Power Domino Resonator Arrangement Demonstrating Power Flow Control by Altering the Angle of the Loop Plane

(110) A feature of embodiments of the present invention is the ability of the domino approach to split the power flow and to vary the power flow. In practical experimentation, a curved power flow path was split into two branch paths to power two CFL loads with equal power, as shown in FIG. 15. As shown in FIG. 16, by turning the junction loop plane in an anti-clockwise direction slightly, more power was diverted to the branch path (the upper branch path in FIG. 16) towards which the junction loop plane was turned, so that the CFL on that branch path was brighter than that on the other branch path (the lower branch path in FIG. 16).

(111) Similarly, as shown in FIG. 17, by turning the junction loop plane slightly in a clockwise direction, more power was diverted to the branch path (the lower branch path in FIG. 17) towards which the junction loop plane was turned, and the CFL on that branch path was brighter than that on the other branch path (the upper branch path in FIG. 17).

(112) The advantages and disadvantages of embodiments of the present invention, as discussed in detail above, are summarized in Table 1 below, which compares major features between embodiments of the present invention and the prior art methods of short-range and mid-range wireless power transfer based on a pair of loop resonators, and the prior art magneto-inductive waveguide for signal transfer based on a chain of loop resonators.

(113) TABLE-US-00001 TABLE 1 Summary comparison between embodiments of the present invention and the prior art. Short-range Magneto- Embodiments of coupled resonator Mid-range coupled inductive the present pair resonator pair waveguide invention Structure A pair of coupled A pair of coupled A chain of loop Flexible domino loop resonators loop resonators resonators structure Application Power transfer Power transfer Signal transfer Power Transfer Typical ratio d/r <3 >3 <1 <3 Energy Relatively high Relatively low Radiative power Relatively high Efficiency for (~80%-95%) (~40%) (~80%-95%) non-radiative wireless power transfer Power flow One path One path Multi-paths Multi-paths possible possible Power flow No No No Yes control within the path Typical >10 kHz >5 MHz >100 MHz >10 kHz operating frequency Coil separation flexible flexible Governed by flexible distance wavelength of propagating waves

(114) Although the invention has been described with reference to specific examples, it will be appreciated by those skilled in the art that the invention can be embodied in many other forms. It will also be appreciated by those skilled in the art that the features of the various examples described can be combined in other combinations.