FIELD

The present invention relates to wireless power transfer. In particular, the present invention relates to wireless power transfer from an array of inductively-coupled electrical resonators to a receiver.

BACKGROUND

It would be convenient to be able to provide power to electronic devices without the need for a wired connection to a fixed power supply. The rapid growth of autonomous devices, such as mobile phones, tablets, laptops, household robots means that such technology is more relevant than ever. Most such autonomous devices are presently battery powered and charging is often inconvenient. There are significant implications with large batteries, which impact cost and device weight and increase device size. A more convenient way of providing electrical power to devices would mitigate the need for large batteries, by improving the ease with which a device can be kept topped-up with charge.

Furthermore, wired connections are potentially clumsy and require manipulation of a connector fitted to the cable in order to electrically connect a device to a power supply.

Power and connectors are furthermore notorious points of failure for electronic devices, either simply as a result of repeated cycles of connection and disconnection, or as a result of a trip or similar accident imposing a mechanical load on the connector via the cable.

A significant amount of research and development has been undertaken in wireless power transfer. A number of standards exist for wireless power supply, including AirFuel and Qi. Both systems employ a powered coil in a power transmission unit, and a further receiver coil in the device to be wirelessly powered. Qi systems have a relatively short range, and require relatively close proximity (e.g. 5mm) inductive coupling between the powered coil and receiver coil. In AirFuel systems, a resonant inductive coupling between the powered coil and receiver coil is used to transfer power to the target device. The resonant coupling between the powered coil and receiver coil means that power can be transmitted over a greater distance.

Arrays of inductive-coupled electrical resonators for wireless power transfer have been disclosed in several publications.

WO 2011/070352 A1 discloses a common communications device comprising an array of near-field coupled resonant elements, the elements each comprising a coupling portion comprising a loop portion with free ends, the device being provided in combination with a data transmission unit and a data reception unit, each unit having a coupling portion, the units being arranged to communicate with one another by means of the coupling portion of each unit and the common communications device, the coupling portion of the data transmission unit comprising a resonant element comprising a loop portion arranged to be near-field coupled to the loop portion of a first resonant element of the device, the coupling portion of the data reception unit comprising a resonant element comprising a loop portion arranged to be near-field coupled to the loop portion of a second resonant element of the device not being the first resonant element.

WO 2012/172371 A1 discloses a magneto -inductive waveguide comprising a plurality of resonant elements, the plurality of resonant elements including a first resonant element comprising a conductive loop broken by at least one capacitive gap, and a second resonant element comprising a conductive loop broken by at least one capacitive gap, the second resonant element for magneto-inductively coupling with the first resonant element; wherein the first resonant element and second resonant element are conductively coupled.

WO 2015/033168 A1 discloses a waveguide for carrying waves by inductive coupling comprises a plurality of resonant elements, the plurality of resonant elements including a first resonant element; a second resonant element; and a coupling section capacitively coupling the first and second resonant elements, wherein the coupling between the first and second elements produces a first pass-band and a second-pass band, different from the first pass-band, the first pass-band being associated with the resonance of the resonant elements and the second pass-band being associated with resonance of the coupling section.

WO 2017/158374 A1 discloses a re -configurable magnetoinductive waveguide, comprising a plurality of resonator cells, wherein each resonator cell comprises a primary resonator that is inductively coupled to a primary resonator of at least one other resonator cell, and wherein at least one of the plurality of resonator cells is a controllable cell which further comprises a control element, the control element having an active control component that is operable to adjust the impedance of the primary resonator of the controllable cell in response to a control signal; wherein: the control element comprises a secondary resonator, the secondary resonator is inductively coupled to the primary resonator, and the active control component is arranged to vary the electrical properties of the secondary resonator in response to the control signal.

WO 2018/229494 A1 discloses a method of configuring a metamaterial structure comprising a plurality of electrical resonators that support magnetoinductive waves. The method comprises: powering at least one of the electrical resonators with an alternating current at an excitation frequency, the at least one powered electrical resonator providing a source of magnetoinductive waves in the structure; adjusting parameters of the metamaterial structure to create constructive interference of one- two- or three-dimensional magnetoinductive waves at one or more target resonators of the electrical resonators, to improve power transfer from the at least one powered electrical resonator to the one or more target resonators.

EP 2,617,120 discloses wireless energy transfer systems in which repeater resonators are used to transfer power from a source resonator to a target area. At least one of the repeater resonators is detuned according to a routing algorithm.

In some circumstances it may be challenging to locate a target device relative to an array of resonators arranged to support magnetoinductive waves. It may also be challenging to configure an array of resonators to optimise power transfer to the target device. These problems are increased when there is more than one target device. A solution to these problems is desirable. SUMMARY

According to a first aspect of the present disclosure, there is provided an apparatus for inductive wireless power transfer, comprising an array of resonators. At least adjacent resonators in the array are mutually electromagnetically coupled. For each resonator in the array, a resonance frequency of the resonator is configured in dependence on the number of neighbouring resonators that are coupled to the resonator and/or the strength of coupling with each neighbouring resonator. In certain embodiments, for each resonator in the array, the self-impedance of the resonator may be configured in dependence on the number of neighbouring resonators that are coupled to the resonator and/or the strength of coupling with each neighbouring resonator. The resonance frequency of each resonator may be configured in dependence on the number of first-order nearest neighbours. The resonance frequency of each resonator may be configured in dependence on the number of any higher order nearest neighbours. The resonance frequency of each resonator may be tuned using the formula: where / ₀ is the resonance frequency of the resonator, G is the number of nearest neighbours of the resonator, k _t is the coupling coefficient which is defined as the ratio of mutual inductance between the neighbouring resonator to the self-inductance of the resonator, and f _d is a design frequency (which may be a resonance frequency of a receiving coil).

Where a change in resonance frequency is affected by changing the capacitance of the LCR circuit of the resonator, the intrinsic impedance (assuming low loss so that the damped resonance frequency is substantially equal to the undamped resonance frequency) can be related to the resonance frequency by: where w ₀ = 2p/ ₀ , R is the (real) resistance, L the inductance and w the angular frequency. The resonance frequency may be configured in dependence on a classification of the resonator that is dependent on: a position of the resonator within the array; and/or a number of neighbouring resonators that are coupled to the resonator.

When the resonators are assembled in a rectangular- or square-lattice array, each resonator may be classified as one of: a corner element, an edge element, a main-body element and an annex element. In some embodiments, the corner elements may be configured to have a resonance frequency in a first frequency band, the edge elements may be configured to have a resonance frequency in a second frequency band, and the main-body elements may be configured to have a resonance frequency in a third frequency band and the annex elements may be configured to have a resonance frequency in a fourth frequency band. The first, second, third and fourth frequency bands may be different from one another. There may be overlap or at least partial overlap of one or more of the frequency bands. In some embodiments, the first frequency band may be a first resonance frequency, the second frequency band may be a second resonance frequency, the third frequency band may be a third resonance frequency, the fourth resonance frequency band may be a fourth resonance frequency. The first, second and third resonance frequencies may be different from one another.

In some embodiments, the corner-element class may comprise a plurality of first subclasses and/or the edge-element class may comprise a plurality of second subclasses and/or the main-body-element class may comprise a plurality of third subclasses, and/or the annex-element class may comprise a plurality of fourth subclasses.

The number of neighbouring resonators may comprise a number of l ^st -order-nearest- neighbour resonators and/or a number of 2 ^nd -order-nearest-neighbour resonators and/or a number of n ^th -order-nearest-neighbour resonators, where n is an integer greater than or equal to 3.

The resonators of the same classification may be configured to have substantially the same resonance frequency. The resonators that are of different classifications may be configured to have substantially different resonance frequencies. In some embodiments, the array of resonators may comprise resonators of at least two different classifications. The resonators of one classification may be configured to have a resonance frequency in a first frequency band. The resonators of another classification may be configured to have a resonance frequency in a second frequency band. The first and second frequency bands may be distinct from one another.

The resonance frequency of each resonator may be selected so that the self-impedance of each resonator is approximately: where Z _t is the self-impedance of the resonator, Z ₀ is the intrinsic impedance

Iw of a resonator, e.g. Z ₀ = R + ja> _d L + — — ² , where w ₀ = 2nf ₀ is the self-resonance frequency of the resonator, R is the (real) effective resistance, L is the inductance., max is the highest order coupling taken into account, is the number of neighbours of y ^th order of the i ^th classification of resonator, is the mutual impedance of the resonator in the i ^th classification and the / ^h order neighbour.

Each resonator may comprise a variable capacitance. The variable capacitance may comprise a capacitive network or a variable capacitor such as a varactor. Alternatively or additionally, each resonator may comprise a variable inductance. The variable inductance may comprise an inductive network comprising a series of lumped inductors (comprising one or more inductors that contribute to the self-inductance, without substantially contributing to the mutual inductance with a neighbouring resonator).

In some embodiments, the apparatus may be configured such that a power-transfer efficiency of wireless power transfer from the array of resonators to a receiver is substantially uniform across at least a majority of the area of the array.

In some embodiments, the apparatus may be configured such that the magnetic field induced by the array of resonators is substantially uniform across at least a majority of the area of the array. The apparatus may be configured to be employed in a magnetic sensing application or an MRI application, for example. The apparatus may be further configured to detect a receiver positioned proximate the array of resonators. For each resonator in the array, the resonance frequency of the resonator may be configured in dependence on the one or more of the other resonators of the array upon detection of two or more receivers coupled to the array.

In some embodiments, the apparatus may have a first mode and a second mode. In the first mode, the apparatus may be configured to provide a one dimensional waveguide for inter-element excitation waves, including magnetoinductive waves, to propagate from one or more powered resonators of the array to one or more target resonators of the array and/or the apparatus may be configured to provide constructive interference of the inter-element excitation waves, including magnetoinductive waves, at the one or more target resonators of the array. In the second mode, for each resonator in the array, the resonance frequency of the resonator may be configured in dependence on the number of neighbouring resonators that are coupled to the resonator and/or the strength of coupling with each neighbouring resonator. In the first mode, a power- transfer efficiency of wireless power transfer from the array of resonators to one or more receivers may be substantially maximal at the one or more target resonators. In the second mode, a power-transfer efficiency of wireless power transfer from the array of resonators to one or more receivers may be substantially uniform across at least a majority of the area of the array.

The apparatus may comprise a receiver. An electronic device configured to receive wireless power from the array of resonators may comprise the receiver. The receiver may receive power by wireless power transfer from the array of resonators at a frequency equal to f _d, where f _d is the design frequency.

According to a second aspect, there is provided a method of configuring a wireless power transfer apparatus. The wireless power transfer apparatus comprises an array of resonators and at least adjacent resonators in the array are mutually electromagnetically coupled. The method comprises configuring, for each resonator in the array, a resonance frequency of the resonator in dependence on the number of neighbouring resonators that are coupled to the resonator and/or the strength of coupling with each neighbouring resonator. Configuring the resonance frequency of the resonator in dependence on the number of neighbouring resonators that are coupled to the resonator and/or the strength of coupling with each neighbouring resonator may comprise: classifying each resonator in the array into a plurality of groups of resonators, wherein the classifying is dependent on a position of the resonator within the array and/or the number of neighbouring resonators that are coupled to the resonator and/or the strength of coupling with each neighbouring resonator; and configuring resonators in the same group to have substantially the same resonance frequency which is different to each resonance frequency that resonators in each other group are configured to have.

Classifying each resonator in the array into a plurality of groups of resonators may comprise: classifying each resonator as one of the following four elements: a corner element, an edge element, a main-body element, and an annex element.

The method may further comprise: detecting the number and/or the position of any receivers that are coupled to the array; and configuring the apparatus in a first mode if only one receiver is detected; and configuring the apparatus in a second mode if a plurality of receivers is detected or if no receivers are detected.

Configuring the apparatus in the first mode may comprise: i) configuring the apparatus to provide a one dimensional waveguide for inter-element excitation waves, including magnetoinductive waves, to propagate from one or more powered resonators of the array to one or more target resonators of the array; and/or ii) configuring the apparatus to provide constructive interference of inter-element excitation waves, including magnetoinductive waves, at the one or more target resonators of the array.

Configuring the apparatus in the second mode may comprise, for each resonator in the array, configuring the resonance frequency of the resonator in dependence on the number of neighbouring resonators that are coupled to the resonator and/or the strength of coupling with each neighbouring resonator.

The method may further comprise reconfiguring the apparatus between the first and second modes upon detection of a change in the number and/or the position of the receivers that are coupled to the array of resonators.

The method may further comprise configuring the apparatus such that an efficiency of wireless power transfer from the array of resonators to a receiver is substantially uniform across at least a majority of the area of the array.

Configuring the resonance frequency of the resonator may comprise varying the capacitance and/or the inductance of the resonator to vary the self-impedance and/or the resonance frequency of the resonator. The varying of the capacitance and/or inductance may be achieved by adding or removing a tuning capacitor and/or inductor, or by tuning a variable capacitor and/or inductor.

Features described with reference to the first aspect may be applicable to the second aspect. Features described with reference to the second aspect may be applicable first aspect.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in further detail below by way of example and with reference to the accompanying drawings, in which:

Figure 1 is an apparatus for wireless power transmission comprising a ID array of power transfer elements, in which current is directly injected at the input element;

Figure 2 is a system similar to that of Figure 1, but in which current is provided wirelessly to the input element;

Figure 3 is a system for wireless power transfer, applied to a coffee table;

Figure 4 is an equivalent circuit for an input element at which current is directly injected; Figure 5 is an equivalent circuit for an input element at which current is excited by inductive coupling with a further resonator; Figure 6 is an apparatus for wireless power transfer, applied to the underside of a table, for providing power to target device on top of the table;

Figure 7 is a generalised equivalent circuit for a controllable element, comprising a primary resonator and a secondary resonator;

Figure 8 shows the impedance of a single controllable cell as shown in Figure 7;

Figure 9 is an array of resonators in which each of the resonators is controllable; Figure 10a illustrates the power-transfer efficiency profile of an array of resonator elements comprising a 3x3 planar square array of inductively-coupled coils and having a uniform wireless-power-transfer efficiency profile according to an embodiment of the present invention; Figure 10b illustrates, for comparison, the power-transfer efficiency profile of the same array, but where the inductive elements/coils are all tuned to same frequency;

Figure 11a illustrates an embodiment of an array of resonators comprising 35 electrical resonator elements arranged in a 5x7 lattice, for which only first-order coupling between the elements is considered, and for which the elements are classified into three different types of elements;

Figure l ib illustrates an embodiment of an array of resonators comprising 35 electrical resonator elements arranged in a 5x7 lattice, for which up to fifth-order coupling between the elements is considered, and for which the elements are classified into six different types of elements;

Figure l ie illustrates an embodiment of an array of resonators comprising 35 electrical resonator elements arranged in a 5x7 lattice, for which up to fifth-order coupling between the elements is considered, and for which the elements are classified into three different types of elements;

Figure 12 illustrates another embodiment of an array of resonators comprising 37 electrical resonator elements arranged in a 5x7 lattice, with an additional element positioned adjacent to a corner element of the 5x7 lattice, and with an additional element positioned adjacent to an edge element of the 5x7 lattice;

Figures 13a and 13b show simulated and measured power transfer efficiencies between a receiver device and a wireless power transfer array configured in accordance with an embodiment;

Figure 14a and 14b show the magnitude and phase of the transmission parameter S _2i for the array of Figure 13a and 13b; and

Figure 15 shows a map of wireless power transfer efficiency for a 3x5 array that has been optimised for uniform power transmission in accordance with an embodiment.

DETAILED DESCRIPTION

Referring to Figure 1, an apparatus 1000 for wireless power transmission is shown, comprising an array of elements 100. Each element 100 comprises an electrical resonator 110 comprising a series combination of an inductor 120 (in the form of a conducting loop) and capacitor 130. Each element in the example of Figure 1 is disposed on a separate substrate or tile, and the tiles are configured such that, when they are placed side-by-side, there is sufficient coupling between the adjacent substrates/tiles to form a medium (or metamaterial) capable of propagating magnetoinductive waves.

In other embodiments the resonators may be defined on a common substrate. In some embodiments there may be capacitive coupling between adjacent resonators, as described, for example in W02015/033168. In some embodiments there may be conductive coupling between adjacent resonators, for example as described in WO2012/172371. The coupling between adjacent resonators may therefore result from any combination of conductive coupling, inductive coupling and capacitive coupling. In some embodiments, the coupling between adjacent elements is only inductive - this may simplify the construction of the apparatus.

In order to achieve inductive coupling between adjacent elements, the magnitude of the coupling coefficient (defined as the ratio of mutual inductance between adjacent electrical resonators 110 and the geometric mean of the self-inductance of each of the adjacent electrical resonators 110) between adjacent electrical resonators 110 may be at least 0.025. Each resonator 110 may be designed with a resonance frequency that is nominally equal to a system design resonance frequency. A high coupling coefficient between adjacent electrical resonators may be achieved by arranging the conducting loop of each inductor 120 close to the conducting loop of the inductor 120 of an adjacent resonator, for example, within less than 2 mm separation. This may be achieved by placing the inductors side-by-side, by at least partially overlaying inductors on top of each other, and/or by providing different layers of resonators to enhance coupling (e.g. a brick-wall type configuration, with a second layer overlaying a first layer and offset by a half pitch of the resonators).

A sufficiently high degree of coupling may allow the resonators 110 to form a medium capable of propagating magnetoinductive waves so as to transmit power to each of the elements 100, thereby enabling any of the elements to provide wireless power to a proximate target device 300.

Each of the resonators 110 may have an inductor that is matched with the inductor of each of the other resonators (e.g. of the same layout). Each of the resonators 110 may also have a matched capacitance, thereby producing a nominally identical resonance frequency. In other embodiments the array may comprise dissimilar resonators.

Each of the resonators may be designed with a relatively high Q, for example at least 50, at least 100, or at least 200. The Q of a resonator relates to the losses of an oscillating current in the resonator - a greater resistance in the resonator results in higher losses and lower Q. In practice it may be difficult to reduce the effective resistance of the inductor loop. Practical trade-offs between competing design parameters may limit the Q to a few hundred for a practical device. Power is provided to one of the resonators 100 from an external power supply 350. A resonator that is configured to receive power from the external power supply 350 may be termed a powered resonator 150. The powered resonator 150 may comprise a connector for receiving AC or DC power from an external power supply (in a wired connection), as schematically illustrated in Figure 1. Figure 2 illustrates an alternative arrangement in which the external power supply 350 provides wireless (inductively coupled) power to the powered resonator 150.

Intermediate resonators 200 provide a medium for magnetoinductive waves (and hence power) to be transmitted from the powered resonator 150 to an output resonator 250. More generally, in embodiments with conductive and or capacitive coupling, the resonators may provide a medium for the transmission of electromagnetic waves (which term encompasses magnetoinductive waves).

The output resonator 250 is in proximity with a target device 300, which is itself configured to derive power inductively from the oscillating magnetic field of the output resonator 250. The output resonator 250 may be of the same design as the intermediate resonators 200 - the term output resonator is merely used to denote a resonator 110 that is providing power to a target device 300. The output resonator 250 may also be termed the target resonator.

Each resonator may have nominally identical design (i.e. matched inductance and capacitance, and therefore matched resonance frequency), but this is not essential (non-identical and non-periodic arrays of resonators are also envisaged). In the example of Figures 1 and 2, a one-dimensional array of resonators is illustrated, with the ellipses denoting ‘n’ further tiles. At the other end of the array, an object or target device 300 is placed in proximity to the output resonator 250. The object 300 in this example may be a mobile phone, but could equally be a laptop, monitor, loudspeaker, lamp, etc. The object 300 receives power by electromagnetic induction from the output resonator 250.

An advantage of a system comprising tiles or elements that couple sufficiently strongly to form a medium supporting inter-element excitation waves, including magnetoinductive waves, when placed in a 2D array is that such a system can be used to produce a relatively large area surface that can deliver electrical power to compatible wireless devices that are placed more or less anywhere on the surface. This is illustrated in Figures 1 and 2, in which tiles comprising the resonators are placed on the underside of a surface 400 (e.g. of a table or desk), such that any devices 30 placed on the surface 400 can receive wireless power from the resonator 250 nearest to the device 300.

Figure 3 more clearly illustrates the concept of a table 410 (e.g. coffee table) that is configured as a large area wireless power providing surface using an array of resonators (e.g. tiled resonators). At least some of the resonators in the array would be powered resonators, for example at the edge of the table 410, by which the remaining resonators in the array are energised, such that devices placed on the table surface receive power wirelessly by propagation of inter-element excitation waves, including magnetoinductive waves, through the array of resonators.

Although an example has been described in which tiles with single resonators are used, this is not essential, and embodiments in which the plurality of resonators are provided on a common substrate are also envisaged.

Figure 4 illustrates an example circuit diagram 150a for a resonator 110 in which current is directly injected. The resonator 110 comprises an inductor 120, capacitor 130, resistance 170 and current injection nodes 160.

For the sake of simplicity in this disclosure, capacitance, resistance and inductance may be depicted as lumped elements, but it will be appreciated that in a real system at least some of these may be distributed (at least to some extent). For instance, a conductor loop may have distributed self-inductance and resistance, and some distributed capacitance with any adjacent conductors (or ground plane).

A powered resonator 150 configured to receive directly injected current may further comprise drive electronics (not shown), which may include an impedance matching network between an AC supply (voltage or current) and the resonator. The powered resonator 150 may further comprise a controller (e.g. processor or microcontroller), and may include control functionality (e.g. software/firmware) for configuring and optimally driving the array of elements coupled (magnetoinductively) thereto. More than one input element may be provided to feed the array with power. This may be appropriate for relatively large arrays (e.g. comprising more than 4, 5, 6, or 10 elements in extent).

Figure 5 illustrates an alternative circuit diagram 150b for a powered resonator, in which power is provided to the resonator by inductive coupling M with a further resonator (which may be patterned within the resonator, or on the opposite side of the tile to the resonator). The further resonator comprises an inductor 420, capacitor 430, resistance 470 and current injection nodes 460 for injecting current from drive electronics (which may also be provided on the input element 150). An advantage of this indirect drive is that the further resonator may be less constrained in design than the resonator (which should have high Q for efficient power transfer), and the further resonator may be more straightforwardly matched to a drive circuit.

The powered resonator 150 may be powered by electromagnetic induction from a power supply 350 (as shown in Figure 2). The adjacent resonators may be operable to communicate electrical power from a power supply 350 comprising an Qi or Airfuel compliant charging pad to a Qi or Airfuel compliant receiver (at the target device 300). This is merely an illustrative example, and the invention does not rely on compliance with a particular standard.

Referring to Figure 6, an apparatus is shown comprising a two dimensional array of elements 100, each element 100 comprising a resonator. Each element may be provided on a separate tile (or all the elements may be provided on a common substrate). The elements may be placed on the underside of a table (or integrated in a housing). The element in the top left of the array comprises a powered resonator 150, which receives power from an external power supply 350, and which feeds the array with a magnetoinductive wave, which propagates through the intermediate resonators 200 to the output resonators 250. The output resonators 250 are those with high inductive coupling with the target devices 300 placed on the table top surface. Each of the output resonators 250 may provide electrical power to a respective target device 300 on top of the table. In this example, there are three target devices 300.

Some embodiments include resonators that are controllable. A controllable resonator may comprise means for changing the electrical properties of the resonator, so as to change the effective impedance of the resonator at the frequency at which current is injected into the array (which may alter the degree to which the controllable resonator participates as an element of the medium supporting waves of inter-element excitation, including magnetoinductive waves). Under some circumstances, more optimal distribution of power through the array may be achieved by effectively disabling some elements of the array (e.g. by giving that resonator a high impedance or low Q at the resonance frequency).

An example of a controllable resonator 1000 is illustrated in Figure 7. The controllable resonator 1000 comprises a primary resonator 1100 and a control device 1200. The primary resonator 1100 comprises a capacitor 112, inductor 113 and a resistor 111. The control device 1200 comprises a secondary resonator that includes a capacitor 122, resistor 121 and inductor 123. The secondary resonator is inductively coupled to the primary resonator 1100 by the mutual inductance Me between the inductors 113, 123. The resistor 121 of the secondary resonator is a variable resistor, and the capacitor 122 is a variable capacitor (both responsive to control signals, that are not shown).

Using an inductively coupled control device 1200 avoids the need to interfere with the design of the primary resonator 1100. Adding tuning elements into the primary resonator 1100 may degrade the Q factor thereof, or reduce the mutual coupling between adjacent primary resonators of the waveguide.

Since the secondary resonator 1200 is inductively coupled to the primary resonator 1100, it contributes to the impedance thereof. Varying the resistance and capacitance of the control device 1200 therefore affects the impedance of the primary resonator 1100.

The impedance contribution Z _e from the secondary resonator 1200 is given by:

Where Z _m = R _m + j L _m — , and the impedance of the primary resonator Z _p is given by: Several possibilities for the control device 1200 can be considered. Where R _m is very large, the contribution Z _e of the secondary resonator 1200 to the impedance Z _p of the primary resonator 1100 will be very small. Where R _m is small, and L _m C _m =LC (i.e. the resonance frequencies of the primary and secondary resonators 1100, 1200 are matched), the effect of the secondary resonator will be to cause an anti-resonance (high impedance) in the impedance of the primary resonator 1100 at the resonance frequency m _c of the un-coupled primary resonator 1100 (m _c = 1 /VåC). The coupled system of the primary and secondary resonator 1100, 1200 will have two resonant modes: a first mode in which the currents in the inductors 113, 123 of the primary and secondary resonator are in-phase, and a second in which these currents are out-of- phase. Tuning R _m allows the effect of the secondary resonator to be changed. For instance, the effect of a secondary resonator 1200 with matched frequency and a larger R _m would be to reduce the Q factor of the resonance of the primary resonator 1100.

Where R _m is small, and L _m C _m ¹LC (i.e. the resonance frequencies of the primary and secondary resonators 1100, 1200 are not matched), the effect of the secondary resonator 1200 will be to cause two coupled modes of current oscillation with different frequencies.

Figure 8 shows the impedance of a single controllable cell 1000, as shown in Figure 7, in a first state 201 in which the secondary resonator 1200 has a high resistance, and in a second state 202 in which the secondary resonator 1200 has a low resistance. In the first state 201, the primary resonator 1100 has a low impedance of 0.8ohms at the design frequency 2pw _a , which in this case is 57.2MHz. In the second state 202, the primary resonator 1100 has a high impedance of 66 Ohms at the design frequency. The Q factor in the first state is 80. The change in impedance at the design frequency may be at least a factor of 10 (in this case, a factor on the order of 100 is achieved).

The primary and secondary resonator may be nested square printed copper coils with surface mount capacitors and transistors.

Some or all of the resonators in an array may be controllable elements. A system in which each resonator is controllable provides a maximum degree of flexibility in configuring the array. However, a sufficient degree of control over the propagation of inter-element excitation waves, including magnetoinductivec waves, through the system may be achieved when only a subset of the elements are controllable.

Figure 9 illustrates an example similar to that of Figure 6, in which each of the resonators is controllable. A target device 300 is placed at the top right of the array, and a further target device 300 is placed at the bottom edge of the array, four resonators across (and five resonators down) from the powered resonator 150. In order to more efficiently transfer power to the target devices 300, only some resonators 200 of the array (shown in solid lines) may be placed in a high Q state, with low impedance at the system frequency (i.e. the frequency at which the input element injects inter-element excitation waves, including magnetoinductive waves, into the medium formed by the elements). The remaining resonators (shown in broken lines) may be placed into a high impedance state at the system frequency, so that they do not form part of the medium.

At least some resonators may comprise a transmitter and/or receiver. For example, a controllable resonator may comprise a receiver for receiving control instructions, instructing the controllable resonator to vary the impedance of the resonator 11 (e.g. so as to switch the element into and out of coupling with the medium). The transmitter and/or receiver may use wireless signals, or wired connections. Any existing wireless technology may be used to provide wireless communication between tiles, for example ZigBee, Wifi, or Bluetooth.

When a power receiving device (Rx) (such as a mobile phone) moves in an x-y plane at a height z above a wireless power transmitting array (Tx) comprising coupled - resonator-elements, it may receive power with a power transfer efficiency, defined as the ratio of power dissipated in the load of the Rx and the power supplied to the Tx (for example, by an external power source). In accordance with the present invention, it may be possible to achieve a uniform or quasi-uniform efficiency profile for the Rx (comprising the load), at specific Rx-Tx distance (z axis). The quasi-uniform efficiency profile may be defined as the efficiency profile with minimised difference between the maximal and minimal efficiency available to the Rx in the x-y plane above the Tx array, while with the minimum efficiency available to the Rx above the Tx maximised. Locating the position of a target device (such as a mobile phone) may be difficult. This may be particularly so where there is more than one device to receive power on the array. Locating a device and controlling the propagation of power through the array (e.g. my forming a ID waveguide to the device, or using constructive interference to maximise power transfer) may be complex, and require significant computing resources to optimise, which may not be cost effective. This disclosure provides an approach in which the impedance/resonance frequency of the elements of the array are tuned to maximise uniformity of power transfer to a target device (or devices) regardless of where there are positioned with respect to the array. Elements of the array may comprise a tuneable primary resonator, in which the effective impedance at the power injection frequency is adjustable, so that the array can be configured in accordance with this disclosure on demand (e.g. by adjustment of a tuneable capacitance/switched capacitor network associated with the primary resonator). In other embodiments, the elements may not be controllable, and may simply be pre-configured at manufacturing in accordance with this disclosure, to provide relatively uniform power transfer to a target device placed anywhere on the array. Figure 10a illustrates the power-transfer efficiency profile of a power transmitting array comprising a 3 x 3 planar square array of inductively-coupled coils and configured to have a uniform wireless-power-transfer efficiency profile. The centre resonator element is powered. The efficiency of wireless power transfer is relatively high over the whole of the array. This is achieved in accordance with embodiments described herein in which the frequency/self-impedance of each coil is selected/tuned dependent on the number of nearest neighbours to each coil. By way of comparison, Figure 10b illustrates the power-transfer efficiency profile of the same power transmitting array, but where the resonator elements are all tuned to same frequency. Identical receivers and a 10 Ohm load are used in both cases. It can be seen that where the elements are all tuned to the same frequency, the uniformity of power transfer is poor, with high efficiency near the powered resonator, but poor efficiency at the edges and corners.

In embodiments, the elements (inductive coils or electrical resonators) of a power transmitting array are tuned to specific resonance frequencies depending on their position in the power transmitting array. The tuning may additionally or alternative comprise tuning to specific self-impedances. More specifically, individual elements in the power transmitting array can be classified as being one of several types depending on the number of other elements of the array they are coupled to.

Figure 12a illustrates a Tx array 2000 comprising 35 electrical resonators arranged in a 5 x 7 lattice. Under the approximation that only nearest neighbours are coupled (i.e. first-order coupling only), there are effectively three different types of elements in the array 2000. The first type, 2001 is a corner element which has two nearest neighbours. The second type 2002 is an edge element which has three nearest neighbours and the third type 2003 is an internal element which has four nearest neighbours.

Figure l ib illustrates a power transmitting array 3000 comprising 35 electrical resonators arranged in a 5 x 7 lattice. In this example, higher order coupling between elements is considered. Specifically, the characterization of elements in the array takes account of fifth-order coupling between elements leading to six different types of elements in the array. The dashed black lines show which elements are coupled using the example of the top left element.

According to the present disclosure, it has been appreciated that a high and uniform power transfer efficiency may achieved over most of the power transmitting array by tuning the elements of the array to different frequencies, based on the number of other elements to which each element is coupled, and the strength of that coupling.

In the nearest-neighbour (or first order neighbour) approximation, coupling with only adjacent elements is considered. Under this approximation, assuming all elements are identical and assuming the receiver is coupled to only one element of the array in any position, the inventors have derived theoretically and demonstrated experimentally, that the elements of a 3 x 3 array should have the self-impedance of Z _t = R — where i = 1,2,3 is the element type, is the number of nearest neighbours depending on the element type; R is the real part of the array element’s self impedance (total resistance of the tuned coil at its resonance frequency) and is the imaginary value equal to the mutual impedance between the adjacent elements of the array. In the case of higher-order coupling, the self-impedances of the elements of the power transmitting array are defined as Z _t = where OC is the highest order of coupling taken into account, is the number of neighbours of j-th order of the i- th type of element; is the mutual impedance of the i-th element and its j-th order neighbour . For the case shown in Fig. 2 (right):

The distance at which power receiving device should be placed above the power transmitting array is defined by the inter-element coupling strength between the power transmitting array. The optimal distance between the power receiving device (Rx) and the power transmitting array (Tx) will have the most uniform power-transfer efficiency profile. This optimal distance can be defined via numerical optimisation. For example, at such a distance, the mutual inductance between the Rx and the Tx element, assuming the coils are axially aligned, is equal to M ^(Rx) =p*M ⁽¹⁾ , where p is a coefficient. The values of p can be in the range of -0.1 to -2.9 (but are not restricted to this range).

An element’s self-impedance is preferably adjusted by varying the resonance frequency that the element is tuned to Assuming that the Rx in a power-receiving mode is tuned to resonate at f ₀ , and that the power is transferred to the power transmitting array at the same frequency, then, taking into account only the nearest- neighbour coupling in the array, the corner, edge and main-body elements (Zi, Z ₂ , Z ₃ , respectively) should be tuned to a frequency of approximately _^ Jl — G * k _t * f ₀ , where G is the number of nearest neighbours (for example, 2, 3, and 4 for the corner, edge and main-body elements respectively) and ki is the coupling coefficient between the nearest neighbours which is defined as the ratio of mutual- and self-inductances.

In the case of higher-order coupling (for example, a case taking into account fifth- order coupling between elements), it may be possible to achieve the uniform-field effect by tuning only three different types of elements to three distinct frequencies. Figure 12c illustrates a Tx array 4000 comprising 35 electrical resonators arranged in a 5 x 7 lattice, for which fifth-order coupling is considered, and for which the resonator elements of the array are categorised into three groups of elements (corner, edge, and main-body elements).

The frequency values may be determined via numerical optimisation. The numerical optimisation may comprise a parametric search for the values of self-impedances of the elements of each type that: (i) maximise the minimal wireless power transfer efficiency; and (ii) minimise the difference between the maximum and minimum efficiency available for the Rx moving above the elements of the Tx. In some embodiments, only a ‘useful area’ (up to the centres of the outermost elements of the power transmitting array) is taken into account during the numerical optimisation.

In some embodiments, the array is a square array. In the square array, the typical values of G may be as follows: 1.5-2.8 for the corner elements; 2.9-4.5 for the edge elements; and 3.9 - 5.5 for the main-body elements. Further numerical optimisation may be used to account for cases in which Rx is coupled to more than one element of the power transmitting array.

In some embodiments, the coupling between the Tx elements may be anisotropic, i.e. not the same along the x and y axes. In such a case, it may be desirable to tune the top-bottom edge elements differently from the right-left elements, for example.

The strength of coupling between the corner elements and their nearest neighbours may be different from the strength of coupling between other adjacent elements in the array (for example, between an edge element and a main-body element, or between two edge elements, or between two main-body elements). The value of the strength of coupling may be optimised to achieve a quasi-uniform efficiency profile of power transfer from the Tx to the Rx.

The imaginary part resulting from capacitance and/or inductance) of the self impedance of all the elements in the power transmitting array may be optimised to achieve a quasi-uniform efficiency profile of power transmission efficiency to a receiving device, regardless of position of the receiving device with respect to the power transmitting array.

Figure 12 illustrates another embodiment power transmitting array 5000 in which two additional resonator elements 5100, 5200 are coupled to a 7x5 rectangular array of resonator elements (for example, as shown in Figures 12a-c). Resonator elements 5100, 5200 may be termed “annex” elements of the array. Such annex elements may be positioned proximate to, or coupled to any of the corner or edge elements of, a square or rectangular (or other shaped) array, and are not necessarily limited to the embodiment shown in Figure 12. Annex elements may be added to the array to provide a bespoke shaped array (for example, to provide a uniquely-shaped surface of a table with the ability to provide wireless charging to a receiver, such as a mobile phone). In Tx array 5000, element 5100 has one first-order neighbour (a corner element of the 7x5 array, and element 5200 also has one first-order neighbour (an edge element of the 7x5 array). The elements of the 7x5 Tx array 5000 may be configured to provide a quasi-uniform efficiency profile of power transfer from the Tx array to the Rx as discussed in relation to any of the other embodiments (for example, by configuring the self-impedance or the resonance frequency of each resonator element according to the class of the resonator element). The values of the self-impedance/resonance frequency of resonator element 5100 and/or 5200 may then be optimised to provide a quasi uniform efficiency profile of power transfer across the whole of the Tx array 5000.

Figure 13a and 13b respectively show simulated and measured power transfer efficiencies between a receiver device and a wireless power transfer array comprising a 3x3 array of resonator elements, with the central resonator powered. The range of the plot corresponds with the a useable area of the array: the area delimited by the centres of the outermost resonators of the array. The measured efficiency has a minimum, maximum and mean values h _min = 0.52, r} _max = 0.61 and rj _mean = 0.58, which is in excellent agreement with the simulated values of h _m;n = 0.51, h^ _c = 0.61 and Jmean 0.57.

Figure 14a and 14b show the magnitude and phase of the transmission parameter S _2i , measured using a small loop probe scanning above the array, where the array comprises a 3x3 array of resonators with self-impedances optimised in accordance with this disclosure to achieve a quasi-uniform power efficiency profile. The magnitude of the transmission parameter S _2i is proportional to the magnitude of the magnetic flux above the array, and the phase of the transmission parameter S _2i is proportional to the phase of the magnetic flux above the array. The magnitude of the magnetic field clearly varies very little over the useable area of the array, and the phase is similarly almost constant (varying by less than 20 degrees over this region).

Figure 15 shows an example plot of wireless power transfer efficiency for a 3x5 array that has been optimised in accordance with an embodiment. In this example, elements were tuned with different resonance frequencies based on the number of nearest neighbours, as described with reference to Figure l ib. The efficiency values give are illustrative, and different (e.g. higher or lower) values can be obtained, for example with different receiver coil geometries.

In the example of Figure 15, the coils in the array have the values shown below (with frequencies normalised with respect to the operating/power injection frequency). There are 6 classes of element, comprising: i) corner (tuned to 0.81); ii) edge between corners (tuned to 0.69); iii) edge neighbouring corner (tuned to 0.67); iv) edge centre (tuned to 0.72); v) main body (tuned to 0.63) and vi) main body centre (tuned to 0.52). 0.81 0.67 0.72 0.67 0.81

0.69 0.63 0.52 0.63 0.69

0.81 0.67 0.72 0.67 0.81

Very similar efficiency profiles may also be obtained with the following tuning arrangement:

0.81 0.69 0.69 0.69 0.81

0.69 0.59 0.59 0.59 0.69

0.81 0.69 0.69 0.69 0.81

There are 3 classes of element, comprising: i) corner (tuned to 0.81); ii) edge (tuned to 0.69); and iii) main body (tuned to 0.59).

Although specific examples have been discussed, it will appreciated that variations are possible within the scope of the invention, which should be determined with reference to the accompanying claims. Variations are intentionally within the scope of the claims.