Patent Publication Number: US-10333353-B2

Title: Omnidirectional wireless power transfer system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority to U.S. Provisional Application No. 62/288,860, titled “Omnidirectional Wireless Power Transfer System,” filed Jan. 29, 2016, and claims the benefit of priority to U.S. Provisional Application No. 62/432,258, titled “Resonant Topologies with Coupling Load Independent Resonance for Wireless Power Transfer Applications,” filed Dec. 9, 2016, the entire contents of both of which applications are hereby incorporated herein by reference. 
    
    
     BACKGROUND 
     Wireless power or energy transfer is directed to the transmission of electrical energy from a power source to an electrical load without the use of conductors. Wireless power transfer can be achieved using a various power transmission technologies using time-varying electric, magnetic, or electromagnetic fields. Wireless power transfer can be particularly useful in situations where the use of conductors is inconvenient or dangerous, for example, to transfer power. 
     For near-field (i.e., non-radiative) wireless power transfer, inductive coupling is widely used and its applications include providing power to charge electric toothbrushes, radio-frequency identification (RFID) tags, smartcards, and implantable medical devices. Recently, more emphasis has been placed on the development of wireless power transfer systems for charging mobile and handheld computing devices. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily drawn to scale, with emphasis instead being placed upon clearly illustrating the principles of the disclosure. In the drawings, like reference numerals designate corresponding parts throughout the several views. 
         FIG. 1A  illustrates an example of a number of coils arranged in a bowl according to various examples described herein. 
         FIG. 1B  illustrates one of the coils shown in  FIG. 1A  according to various examples described herein. 
         FIG. 2A  illustrates an example wireless power transfer platform with three orthogonal, symmetric coils according to various examples described herein. 
         FIG. 2B  illustrates example excitation waveforms applied the orthogonal, symmetric coils X, Y, and Z shown in  FIG. 2A , respectively, according to various examples described herein. 
         FIG. 3  illustrates an example omnidirectional wireless power transfer system according to various aspects of the embodiments described herein. 
         FIGS. 4A-4C  illustrate perspective, side, and top-down views, respectively, of an arrangement of coils in the receptacle of the system shown in  FIG. 3  according to various aspects of the embodiments described herein. 
         FIG. 5  illustrates other components of the example omnidirectional wireless power transfer system shown in  FIG. 3  according to various aspects of the embodiments described herein. 
         FIG. 6  illustrates example magnetic field distributions provided by the receptacle of the system shown in  FIG. 3  at different time instants according to various aspects of the embodiments described herein. 
         FIG. 7  illustrates excitation currents used during an experiment according to various aspects of the embodiments described herein. 
         FIG. 8  illustrates measured magnetic field trajectory in an experiment according to various aspects of the embodiments described herein. 
         FIG. 9  illustrates four example resonant tank topologies according to various aspects of the embodiments described herein. 
         FIG. 10  illustrates an example series-series resonant converter topology according to various aspects of the embodiments described herein. 
         FIG. 11  illustrates an example equivalent circuit of the example series-series resonant converter shown in  FIG. 10  according to various aspects of the embodiments described herein. 
         FIGS. 12 and 13  illustrate voltage gain and phase of input impedance curves for different load resistances and resonant couplings according to various aspects of the embodiments described herein. 
         FIG. 14  illustrates gain characteristics of a resonant converter having a series resonant frequency between two parallel resonant frequencies according to various aspects of the embodiments described herein. 
         FIGS. 15A-15C  illustrate the general topology forms of resonant converters with coupling independent resonance and zero voltage switching according to various aspects of the embodiments described herein. 
         FIG. 16  illustrates a resonant converter having a series resonant frequency between two parallel resonant frequencies according to various aspects of the embodiments described herein. 
         FIG. 17  illustrates an example use of Norton&#39;s Theorem and Thevenin&#39;s Theorem to transform the resonant tank network shown in  FIG. 16  into a simple branch according to various aspects of the embodiments described herein. 
         FIG. 18  illustrates the simple branch developed using Norton&#39;s Theorem and Thevenin&#39;s Theorem from the relatively complicated resonant tank network shown in  FIG. 16  according to various aspects of the embodiments described herein. 
         FIGS. 19 and 20  illustrate voltage gain and phase of input impedance curves for different load resistances and resonant couplings of the resonant converter shown in  FIG. 16  according to various aspects of the embodiments described herein. 
         FIGS. 21-25  illustrate other example resonant converter topologies and gain curve characteristics according to various aspects of the embodiments described herein. 
     
    
    
     DETAILED DESCRIPTION 
     Near-field (i.e., non-radiative) wireless power transfer can be relied upon to transfer power in various applications or fields of use, such as in military, medical, consumer device, and automotive fields, among others. One challenge in the design of near-field wireless power transfer systems arises because the level of coupling between transmitter and receiver coils can vary. Particularly, the level of coupling can vary because there is no predefined physical connection or orientation between the transmitter and receiver coils. For example, in a wireless power transfer system where a user is expected to set or place a device upon a charging plate or base, the position and orientation of the receiver coil (with respect to the transmitter coil) is dependent on the user&#39;s placement of the device and will vary. Thus, the coupling coefficient between the transmitter and receiver coils is not fixed as in the conventional case where a transformer is used. Similarly, the load presented by the device can vary because the load presented by a battery can varies based on the different charging stages in the charging profile of the battery. 
     Many conventional non-radiative wireless power transfer platforms are designed to be directional, meaning that devices are charged efficiently only when placed in a predetermined orientation (or relatively narrow range of a few orientations). Small portable electronic devices can typically be placed near a wireless charging station in a number of different orientations, however, and some of those orientations may not be suitable for efficient wireless power transfer. Thus, a well-designed omnidirectional wireless power transfer system would be desirable for charging portable electronic devices. 
     To illustrate the types of problems that can be encountered with conventional wireless power transfer platforms, a bowl for wireless charging was recently demonstrated. The bowl includes four coils for the transmission of power wirelessly. A top-down view of the four coils arranged (e.g., embedded) in the bowl is shown in  FIG. 1A , and one of the coils is shown in  FIG. 1B . A bowl including the coils shown in  FIG. 1A  provides magnetic field in more than one direction, including a component of vertical field from the center of the bottom of the bowl (i.e., from the overlapping combination of coils at the center of the bottom of the bowl) and a number of components of relatively perpendicular field from the side surfaces of the bowl (i.e., a perpendicular component for each coil). However, the magnetic field distribution in the bowl is not omnidirectional even at the bottom of the bowl. 
     An example of another wireless power transfer platform with three orthogonal, symmetric coils, coil X, coil Y, and coil Z, is shown in  FIG. 2A . In one example case, the excitation waveforms applied to coil X, coil Y, and coil Z, respectively, are shown in  FIG. 2B  and in expressions (1)-(3) below. The amplitude of the excitation current of coil Y and coil Z is modulated by relatively low frequency sinusoidal waveforms. 
     
       
         
           
             
               
                 
                   
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     With these excitation currents, magnetic field induced at a center of the three symmetric coils can be expressed as: 
                         B   →     x     =         u   0       2   ⁢   R       ⁢     I   x     ⁢     x   →         ,         B   →     y     =         u   0       2   ⁢   R       ⁢     I   y     ⁢     y   →         ,       and   ⁢           ⁢       B   →     z       =         u   0       2   ⁢   R       ⁢     I   z     ⁢     z   →         ,   where           (   4   )               
u 0  is vacuum permeability, {right arrow over (x)}, {right arrow over (y)}, {right arrow over (z)} is the standard basis vector, and R is the radius of the coils.
 
     The total magnetic field induced at the center by three coils can be calculated as:
 
 {right arrow over (B)}   t   +{right arrow over (B)}   x   +{right arrow over (B)}   y   +{right arrow over (B)}   z .  (5)
 
     The total magnetic field at the center of the three symmetric coils is a time-varying vector, and the magnitude is constant according to expression (6) as: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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     As such, the field trajectory will be on the surface of a sphere. Thus, with a structure of three symmetric coils and modulated excitation current, omnidirectional field can be induced at the center and magnetic field will rotate in a three-dimensional manner over time. 
     Other than at the center point O, the magnetic field induced by each coil is not the same and the magnetic field trajectory is not on the surface of a sphere. For example, as for point A in  FIG. 2A , which is away from the center, the magnetic field induced by coil X and coil Y is very small and can be neglected compared with the magnetic field induced by coil Z. Therefore, there is no omnidirectional magnetic field at point A. For similar reasons, there is also no omnidirectional magnetic field at any other point other than the center point O. In practice, even with a spherical or semispherical container, devices will fall to the bottom and/or lay on side surfaces of the container, and there is no omnidirectional magnetic field in those areas with the coil structure shown in  FIG. 2A . 
     According to aspects of the embodiments, an omnidirectional wireless power transfer system includes high frequency power generator configured to generate a supply of high frequency oscillating power, a number of transmitter-side resonant tank circuits electrically coupled to the high frequency power generator, a receptacle including a number of coils arranged for omnidirectional power transfer to an electronic device placed in the receptacle, and a controller configured to activate individual ones of the transmitter-side resonant tank circuits to wirelessly transmit power to the electronic device through near-field resonant inductive coupling. In one example, the receptacle can be embodied as a bowl, and the controller can activate individual ones of the transmitter-side resonant tank circuits over time to generate an omnidirectional magnetic field distribution for wireless power transmission. In other aspects, various transmitter-side and receiver-side tank circuits for coupling independent resonance and zero voltage switching (ZVS) operation are described. 
     In the context of omnidirectional wireless power transfer according to the embodiments,  FIG. 3  illustrates an example omnidirectional wireless power transfer system  10 . The system  10  includes a receptacle  20  for wirelessly transmitting power to a number of electronic devices  30 - 33  placed in the receptacle  20 . The system  10  also includes a power transmission platform  50  configured to convert energy into radiant frequency power for wireless power transfer to the electronic devices  30 - 33  placed in the receptacle  20 . 
     The receptacle  20  can be formed in various shapes and sizes. Thus, the receptacle  20  is representative of one shape and size of a receptacle to hold devices for wireless power transfer but is not intended to be limiting as to other types which can be used. In that context, although the receptacle  20  is shown as a bowl in  FIG. 3 , receptacles of other shapes can be used. For example, the receptacle  20  can be formed as an open or closed spherical or semi-spherical, oval, ovoid, or semi-ovoid (having one or more axes of symmetry), conic or semi-ovoid, pyramid or semi-pyramid, square, rectangular, or other shape of receptacle. Further, the receptacle  20  can be any formed in suitable size. The receptacle  20  can be formed from any suitable material, such as wood, plastic, glass, ceramic, or other material or combination of materials. With regard to the type of material(s) used for the receptacle  20 , preference may be to use materials which do not interfere (or do not substantially interfere) with time-varying electric, magnetic, or electromagnetic fields, although such materials (e.g., metal materials, etc.) can be used to form the receptacle  20  (or portions of the receptacle  20 ) in certain cases. 
     Although not explicitly shown in  FIG. 3 , the receptacle  20  includes a number of coils for the transfer of power from the receptacle  20  to the electronic devices  30 - 33  through inductive coupling. As described in further detail below with reference to  FIGS. 4A-4C , the coils can be embedded or integrated in or on the receptacle  20  in a number of different arrangements. Similarly, the electronic devices  30 - 33  include coils for the transfer of power from the receptacle  20  to the electronic devices  30 - 33  through inductive coupling. For example,  FIG. 3  illustrates an example coil  40  of the electronic device  30 , and the other electronic devices  31 - 33  include similar coils for the transfer of power from the receptacle  20  to the electronic devices  30 - 33 . Using the coils in the receptacle  20  and in the electronic devices  30 - 33 , power can be transferred from the receptacle  20  to the electronic devices  30 - 33  through near-field resonant inductive coupling, electrodynamic induction, or inductive power transfer between magnetically coupled coils that are part of resonant circuits tuned to resonate at a common frequency. 
     The electronic devices  30 - 33  can include various types of devices, such as cellular phones, watches, gaming devices, fitness trackers, RFID-enabled keys and tags, wireless headphones, tablet computers, e-book readers, and other devices. In any case, the electronic devices  30 - 33  may include a number of relatively larger and smaller devices. As shown in  FIG. 3 , the electronic devices  30  and  31  (e.g., cellular phones) include two larger front and back surfaces and a number of relatively smaller (i.e., narrower) side surfaces. Thus, when placed in the receptacle  20 , the electronic devices  30  and  31  are more likely to rest on one of their larger front or back surfaces along a raised side of the receptacle  20 . At the same time, the relatively smaller electronic devices  32  and  33  (e.g., watches, keys, tags, etc.) may be more likely to settle on the bottom of the receptacle  20  than relatively larger devices. 
     The positions of the coils in the receptacle  20  can be known and constant based on its design. However, the positions and orientations of the coils in the electronic devices  30 - 33  cannot be known with certainty because the electronic devices  30 - 33  can settle in various ways (i.e., positions and orientations) when they are placed in the receptacle  20 . In practice, the number of ways that the relatively smaller electronic devices  32  and  33  are likely to settle in the receptacle  20  (e.g., front, back, right side, left side) could be greater than those that the relatively larger electronic devices  30  and  31  may settle (e.g., front or back) because of the physical characteristics of the electronic devices  30 - 31  and the shape and size of the receptacle  20 . In any case, the orientation of the electronic devices  30 - 33  and the coils in the electronic devices  30 - 33  can vary. 
     As described in further detail below, the power transmission platform  50  is configured to activate a number of resonant cell circuits (which include the coils in the receptacle  20 ) to provide a platform for omnidirectional wireless power transfer to the electronic devices  30 - 33 . Due to the omnidirectional nature of the wireless power transfer using the system  10 , the transfer of power to the electronic devices  30 - 33  (for charging or other purposes) can be increased as compared to other systems such as those shown in  FIGS. 1A, 1B, 2A, and 2B , among others. 
     Particularly, even though the orientation of the electronic devices  30 - 33  will vary from time to time when placed in the receptacle  20 , the omnidirectional nature of wireless power transfer using the system  10  offers greater power transfer than systems without such omnidirectional characteristics. In the context of the examples described below, the omnidirectional nature of the system  10  is related to the unique arrangement of the coils in the receptacle  20  and the ability for the power transmission platform  50  to activate those coils, individually or in combination with each other with modulation excitation current. The transfer of power during the activation of individual coils and combinations of coils is evaluated by the power transmission platform  50  to select certain coils which offer better transfer of power. Additionally, the power transmission platform  50  can also modulate the supply of radiant frequency power provided to individual resonant cell circuits in the system  10  to transfer highest power to the electronic devices  30 - 33 . 
     In other aspects, the system  10  can incorporate resonant converter gain characteristics in which one series resonance frequency is positioned or centered between two parallel resonant frequencies. Resonant converter topologies with such gain characteristics can achieve the advantages of coupling independent resonance and ZVS operation, which means this converter can always operate efficiently no matter how the electronic devices is positioned. Example resonant converter topologies exhibiting those gain characteristics are described in further detail below with reference to  FIGS. 9-24 . These resonant converter topologies are particularly suitable for applications with variable coupling and variable load, such as encountered during wireless power transfer. 
       FIGS. 4A-4C  illustrate perspective, side, and top-down views, respectively, of an arrangement of coils  60 - 64  in the receptacle  20  of the system  10  shown in  FIG. 3  according to various aspects of the embodiments described herein. Before describing them in further detail, it should be appreciated that the illustration of the coils  60 - 64  is representative in  FIGS. 4A-4B . In various embodiments, the coils  60 - 64  can be formed as a closed loop of any suitable number of turns of a single conductor or multiple conductors. The profile (e.g., cross-sectional shape) and gauge of the conductors used for the coils  60 - 64  can also vary among embodiments. One factor that can drive the selection of the type, length, and other electrical characteristics of the conductors used for the coils  60 - 64  is to create a suitable level of near-field resonant inductive coupling between the coils  60 - 64  in the receptacle  20  and the coils in the electronic devices  30 - 33  to achieve resonant circuits for power transfer. The coils  60 - 64  can be embedded or integrated in or on the receptacle  20  in any suitable way. In other cases, different arrangements of coils can be used in the receptacle  20 , including additional or fewer coils or pairs of coils. For example, additional coils or pair of coils can be uniformly (or non-uniformly) offset around the sides of the receptacle  20  as compared to the coils  60 - 63 . 
     In the arrangement shown in  FIGS. 4A-4C , the coils  60  and  61  are arranged in an opposing fashion along a first or “x” axis (although tilted), the coils  62  and  63  are arranged in an opposing fashion along a second or “y” axis (although tilted), and the coil  64  is arranged long a third or “z” axis. Collectively, the coils  60  and  61  are referenced as the coil-x. Similarly, the coils  62  and  63  are collectively referenced as the coil-y, and the coil  64  is referenced as the coil-z. The conductors of the coils  60 - 64  intersect at the bottom  70  of the receptacle  20  as shown in  FIGS. 4A and 4C . 
     One benefit of the arrangement of the coils  60 - 64  shown in  FIGS. 4A-4C  is that it permits the generation of magnetic fields in a number of different directions, particularly in the bottom  70  of the receptacle  20 . As described in greater detail below, the power transmission platform  50  can activate a combination of the coils  60 - 64  in various ways to generate a composite direction and magnitude of magnetic field using the coils  60 - 64 . The direction and magnitude of the magnetic field will depend, at least in part, upon which of the coils  60 - 64  is excited, and the magnitude and phase of the exciting current provided to the coils  60 - 64  respectively, as determined by the power transmission platform  50 . Thus, the power transmission platform  50  can activate or excite a number of the coils  60 - 64 —and at a particular, potentially modulated, magnitude and/or phase—depending upon where electronic devices, such as the electronic devices  30 - 33 , settle into the receptacle  20 . The generation of magnetic field at a particular, adjustable direction and magnitude is advantageous because the orientation of the coils in the electronic devices  30 - 33  can vary depending upon how the electronic devices  30 - 33  settle into the receptacle  20  as described above. 
       FIG. 5  illustrates other components of the example omnidirectional wireless power transfer system  10  shown in  FIG. 3 . Among other components, the power transmission platform  50  includes the power converter  100 , resonant power converter  110 , controller  120 , and resonant cells  130 - 134 .  FIG. 5  also illustrates a power supply  150  for the power transmission platform  50 . As described herein, the power transmission platform  50  can transfer power to the electronic device  30 , which includes the coil  40  and a power converter  160 . The resonant cells  130 - 134  are electrically coupled in a closed circuit with the coils  60 - 64 , respectively, and the coils  60 - 64  can be considered circuit elements in the resonant cells  130 - 134 . 
     The power supply  150  can be embodied as any suitable supply of power for the power transmission platform  50 . In that context, the supply of power can be provided from line or bulk power, one or more batteries or other charge stores, or other power supplies. In various cases, the supply of power can be provided in the form of alternating or direct current at suitable level of potential. 
     The power converter  100  is configured to convert the power provided by the power supply  150  to power suitable for the resonant power converter  110 . In that context, the power converter  100  can be embodied as any suitable topology of power converter, such as a switch mode converter including a buck or boost arrangement of switching power transistors, for example. In one case, the power converter  100  can be embodied as a buck converter to step down power provided by the power supply  150  at a first, higher DC voltage to power for the resonant power converter  110  at a second, lower DC voltage. In some cases, the controller  120  can provide one or more modulated control signals to the power converter  100  to control the duty cycle of its switching power devices and, thus, the supply of power to the resonant power converter  110 , although the power converter  100  can operate in other cases without any external control. In some cases, the function of power converter  100  can also be achieved by controlling the duty cycle of the resonant power converter  110 , and the power converter  100  can be eliminated. 
     As discussed in further detail below with reference to  FIG. 10 , the resonant power converter  110  forms, in part, a number of resonant circuits along with the resonant cells  130 - 134 , the coils  60 - 64 , the coil  40 , and the power converter  160 . The resonant power converter  110  can include a number of switching transistors in one or more switch banks. In that context, the resonant power converter  110  is configured to feed charge from the power converter  100  to a transmitter-side resonant tank in each of the resonant cells  130 - 134 . Various examples of transmitter-side resonant tank circuits that can be used for the resonant cells  130 - 134  are described below with reference to  FIGS. 9, 10, 11, 15, and 20-24 . From the resonant cells  130 - 134 , power is inductively coupled through one or more of the coils  60 - 64 , to the coil  40 , and to a receiver-side resonant tank in the power converter  160 . Examples of receiver-side resonant tank circuits for the power converter  160  are also described below with reference to  FIGS. 9, 10, 11, 15, and 20-24 . According to one aspect of the embodiments, the transmitter-side and receiver-side resonant tank circuits can be designed for coupling independent resonance with ZVS operation. 
     As noted above, the resonant power converter  110  includes circuitry to supply RF power (e.g., high frequency sinusoidal alternating current) to drive the resonant tank circuits in the resonant cells  130 - 134 . In one case, the resonant power converter  110  includes a switch bank of one or more switching transistors for each of the resonant cells  130 - 134 , and the resonant power converter  110  can supply RF power separately to each of the resonant cells  130 - 134 . In that case, the resonant power converter  110  is representative of a number of different resonant power converters for each of the resonant cells  130 - 134 , and modulated RF power can be provided respectively to each of the resonant cells  130 - 134 . The RF power can be respectively modulated in amplitude and/or phase through transistor switching control, modulation circuitry, or other circuitry directed by one or more control signals provided from the controller  120 . 
     In another case, the resonant power converter  110  includes a switch bank for one or more pairs of the resonant cells  130 - 134 , such as fort the X, Y, and Z coils. In that case, modulated RF power can be provided to the X 1  and X 2  resonant cells  130  and  131 , to the Y 1  and Y 2  resonant cells  132  and  133 , and to the Z resonant cell  134 . The RF power can be modulated respectively in amplitude and/or phase for the X, Y, and Z coils through transistor switching control, modulation circuitry, or other circuitry directed by one or more control signals provided from the controller  120 . 
     In other cases, the resonant power converter  110  can generate RF power for the resonant cells  130 - 134 , collectively, and include a one or more amplitude and/or phase modulation circuits to generate a number of amplitude and/or phase modulated versions of the RF power for the resonant cells  130 - 134 . In any case, the resonant power converter  110  includes circuitry to supply power that drives the resonant tank circuits in the resonant cells  130 - 134  for near-field resonant inductive coupling of power to the coil  40  of the electronic device  30 , among coils of other devices. 
     The controller  120  can be embodied as one or more processors and related circuitry to support the processors, such as one or more memory devices, crystal oscillators, linear regulators, analog-to-digital converters, digital-to-analog converters, local interfaces, etc. The local interface can include, for example, a data bus with an accompanying address/control bus between memory devices and processors. The processor can include a general- or specific-purpose processor, such as a microprocessor, microcontroller, digital signal processor, or other processing circuitry. The controller  120  can also be embodied, at least in part, as one or more discrete logic circuits, application specific integrated circuits (ASICs), programmable logic devices (e.g., field-programmable gate array (FPGAs), and complex programmable logic devices (CPLDs)). 
     In some cases, one or more processors of the controller  120  can execute computer-readable software or program instructions embodied in a non-transitory computer-readable medium (e.g., memory device). Through execution of the instructions, the controller  120  can be directed to perform one or more of the operations described herein. In other cases, the controller  120  can be designed to conduct or perform the operations described herein without the execution of software. 
     The controller  120  is configured to control the overall operation of the power transmission platform  50  and the transmission of power to devices. For example, the controller  120  is configured to control the resonant power converter  110  to activate (e.g., provide RF power to) one or more of the resonant cells  130 - 134 . In that way, the controller  120  can direct and control the wireless transmission of power to the electronic device  30 . For example, the controller  120  can generate one or more control signals to direct the resonant power converter  110  to generate RF power to induce resonant, inductive power transfer between magnetic-field-coupled coils in the resonant cell  130  and the coil  40  of the electronic device  30 . Similarly, the controller  120  can direct the resonant power converter  110  to induce power transfer between magnetic-field-coupled coils in any combination of one or more of the resonant cells  130 - 134  and the coil  40  of the electronic device  30 . 
     Further, the controller  120  can direct the resonant power converter  110  to generate RF power at a certain frequency, amplitude, and/or phase for the resonant cell  130  and the other resonant cells  131 - 134 , respectively. Thus, the controller  120  can control whether RF power is provided, as well as the frequency, amplitude, and phase of that RF power, to each of the resonant cells  130 - 134  individually. The manner in which the resonant cells  130 - 134  can be excited in the power transmission platform  50  is thus very flexible, as various combinations of the coils  60 - 64  can be selectively excited in various ways through the resonant cells  130 - 134  to induce a preferred magnitude and direction of the magnetic field in or around the receptacle  20 . In effect, the magnitude and direction of the magnetic field can be adjusted to account for different positions and orientations the coil  40  of the electronic device  30  and similar coils of other electronic devices in the receptacle  20 . 
     For example, if the electronic device  30  is placed in and rests along a side face of the receptacle  20  near the coil  60 , then the controller  120  can direct the resonant power converter  110  to generate RF power for the resonant cell  130  and the coil  60 . Because of the position and orientation of the electronic device  30  in proximity to the coil  60 , the excitation of the coil  60  is likely to lead to a relatively high power transfer through resonant inductive coupling, at least as compared to an excitation of the other coils  61 - 64 . 
     When the electronic device  30  is first placed into the receptacle  20 , however, the power transmission platform  50  may not know the position and orientation at which the electronic device  30  was placed or settled. Thus, the controller  120  is configured to sense a level of power transferred (or that can be transferred) to the electronic device  30  by exciting each of the resonant cells  130 - 134  (and, hence, the coils  60 - 64 ) individually over time. For example, the controller  120  can direct the resonant power converter  110  to provide RF power to each of the resonant cells  130 - 134 , individually, and to measure the amount of power transferred to the electronic device  30  by each one. The power transfer can be measured or sensed using any suitable techniques, such as through the identification of voltage drops or droops, the amount of current supplied, or other approaches. In that way, the controller  120  can identify a coefficient of power transfer or resonant inductive coupling between individual ones of the resonant cells  130 - 134  (and the coils  60 - 64 ) and the coil  40  of the electronic device  30 , respectively. 
     The controller  120  can also sense a level of power transferred to the electronic device  30  by the excitation of one or more combinations of the resonant cells  130 - 134  over time. In that case, the controller  120  can direct the resonant power converter  110  to provide RF power to various combinations of the resonant cells  130 - 134  over time and measure the amount of power transferred for each combination. Additionally, the RF power provided to respective ones of the resonant cells  130 - 134  can be modulated in amplitude and/or phase as compared to each other, and the controller  120  can measure the amount of power transferred for various combinations of that modulated power. 
     For the bottom  70  ( FIG. 4B ) of the receptacle  20 , combinations of the coils  60 - 64  can be excited simultaneously to induce rotating and, as averaged over time, omnidirectional magnetic field. For example, the coils  60  and  64  can be simultaneously excited by RF power offset in phase with respect to each other by 90 degrees. In that case, rotating magnetic field can be induced in the x/z plane over about half of the bottom  70 . In a similar way, rotating magnetic field in the x/y plane can be induced by simultaneously exciting the coils  60  and  62 , and still other combinations of the coils  60 - 64  can be excited. Thus, rotating magnetic field in different planes can be induced in the bottom  70  through the excitation of different combinations of the coils  60 - 64 . Also, by exciting one or more of the coils  60 - 64 , respectively, for different periods of time, using different amplitudes, and/or different phases of high frequency sinusoidal alternating current, omnidirectional magnetic field can be induced in the bottom  70  in an average sense. 
     Additionally, the coils  60 - 64  can be excited simultaneously to induce a three-dimensional rotating magnetic field in the bottom  70  of the receptacle  20 . One example of the excitation currents provided to the coils  60 - 64  is similar to that shown in  FIG. 2B . For that example case, the magnetic field distribution provided in the bottom  70  of the receptacle  20  at different time instants was simulated with finite element analysis (FEA) software, and the results are shown in  FIG. 6 . In  FIG. 6 , panes (a)-(d) correspond to magnetic field distributions at different time instants. As shown by the directional arrowheads in the bottom  70  of the receptacle  20 , the magnetic field distribution shifts over time between upward, downward, right, and left directions. 
     Thus, the controller  120  can achieve an omnidirectional magnetic field in the bottom  70  of the receptacle  20  through controlled excitation of the resonant cells  130 - 134  and the coils  60 - 64 . The excitation examples described herein are not exhaustive, however, and other ways are within the scope of the embodiments. With so many flexible ways of excitation, the proposed arrangement of the coils  60 - 64  in the receptacle  20  can achieve omnidirectional wireless power transfer. 
     In one experiment using a prototype receptacle similar to the receptacle  20 , resonant power converters were used to drive coils arranged similar to the coils  60 - 64  with high frequency (i.e., 6.78 MHz) sinusoidal alternating current. In the experiment, perpendicular magnetic field at a side face of a receptacle similar to the receptacle  20  and omnidirectional magnetic field in the bottom of the similar receptacle were induced. As part of the experiment, successful charging of a cellular telephone was demonstrated using a fabricated receiver coil to capture the energy transferred via the magnetic field. 
     In another experiment using a near-field probe and the prototype receptacle, the excitation currents shown in  FIG. 7  were used to excite the arrangement of coils similar to the coils  60 - 64 . In the experiment, the tip of a near-field probe was positioned with respect to the prototype receptacle at a position similar to the point “Q” shown in  FIG. 4B , and the probe was used to measure the magnetic field over time. 
     To visualize the direction of the magnetic field generated using the prototype, the trajectory of the magnetic field is plotted in  FIG. 8  based on the measured data. The ring shape magnetic field trajectory shown in pane (a) in  FIG. 8  corresponds to the time period T a  in  FIG. 7 , and the ring shape magnetic field trajectory shown in pane (b) in  FIG. 8  corresponds to the time period T b  in  FIG. 7 . Over the full excitation cycle shown in  FIG. 7 , the ring shaped magnetic field trajectories cover the whole surface of a sphere, as shown in pane (c) in  FIG. 8 . Thus, omnidirectional magnetic field distribution at a position on the prototype similar to the point “Q” was demonstrated. Similarly, magnetic field trajectories at other points over the bottom of the prototype are also on the surface of a sphere as shown in  FIG. 8 . Therefore, omnidirectional magnetic field distribution can be induced with the proposed wireless charging system. 
     Turing to other aspects of the embodiments, one challenge in the design of resonant converters is to design for ZVS operation of the switching devices. A recommended switching frequency of one wireless power transfer standard is 6.78 MHz. The use of such high switching frequencies can be detrimental to switching devices unless resonant converters are designed for ZVS operation. Without ZVS operation, switching losses can be relatively high and efficiency suffers. Additionally, electromagnetic compatibility of the system can also be a concern for designs that fail to account for ZVS operation. 
       FIG. 9  illustrates four example resonant tank topologies according to various aspects of the embodiments described herein. Particularly,  FIG. 9  illustrates a series-series resonant tank at pane (2), a parallel-series resonant tank at pane (b), a series-parallel resonant tank at pane (c), and a parallel-parallel resonant tank at pane (d). Among the four resonant tank topologies shown in  FIG. 9 , the series-series resonant converter is widely used. 
     In the example resonant tank topologies shown in  FIG. 9 , k is a coupling metric related to the level of inductive coupling between the transmitter coil and the receiver coil. In practice, the value of k may be based on the position and orientation of the receiver coils in the receiver-side resonant tanks as compared to the transmitter coils of the transmitter-side resonant tanks. In other words, as discussed above, in a wireless power transfer system where a user is expected to set or place an electronic device including a receiver coil into a charging receptacle, the position and orientation of the receiver coil (with respect to the transmitter coil) is dependent on the user&#39;s placement of the device and will vary. Thus, the value of k can vary dependent on the user&#39;s placement of the device into the charging receptacle. 
       FIG. 10  illustrates an example resonant converter  200  incorporating series-series resonant tank topology according to various aspects of the embodiments described herein. At the transmitter side of the resonant converter  200 , a power source  210  supplies charge to a switch bank  220 , which is configured to feed charge to a transmitter-side resonant tank  230 . The resonant converter  200  also includes a receiver-side resonant tank  240 , a rectifier bank  250 , a bulk charge store  260 , and a load  270 . The resonant converter  200  is representative and provided for context to describe certain features and advantages of the embodiments. Other circuit elements (and variations of the circuit elements shown) can be relied upon in various embodiments. 
     In  FIG. 10 , the power source  210  is representative of any suitable supply of power for the resonant converter  200 . The switch bank  220  includes an arrangement of switching transistors. Although designs using a single transistor are possible, half bridge and full bridge arrangements of transistors can be used to drive the transmitter-side resonant tank  230  more efficiently, and a half bridge is shown for the switch bank  220  in  FIG. 10 . The transmitter-side resonant tank  230  and the receiver-side resonant tank  240  include combinations of capacitive and inductive circuit elements that form a series-series resonant tank topology. The transmitter-side resonant tank  230  in  FIG. 10  includes a resonant capacitor C tx  and transmitter coil L tx , and the receiver-side resonant tank  240  includes the resonant capacitor C rx  and receiver coil L rx . The resonant capacitor C tx , transmitter coil L tx , resonant capacitor C rx , and receiver coil L rx  can be selected for use with a resonant operating frequency for near-field resonant inductive coupling. 
     Other combinations of capacitive and inductive circuit elements for other converter topologies, including any of those shown in  FIGS. 9, 10, 11, 15, and 20-24 , can be used. The rectifier bank  250  includes an arrangement of diodes to rectify the flow of power which is inductively coupled from the transmitter-side resonant tank  230  to the receiver-side resonant tank  240  for storage into the bulk charge store  260 . Any suitable arrangement of diodes (e.g., half bridge, full bridge, etc.) can be used in the rectifier bank  250 . 
     Here, it is noted that the power source  210  is representative of a supply of power, such as the supply of power provided by the power converter  100  shown in  FIG. 5 . Further, the resonant power converter  110  shown in  FIG. 5  can include a switch bank similar to the switch bank  220  for each of the resonant cells  130 - 133 , and the switching transistors can be controlled by control signals provided by the controller  120 . Each of the resonant cells  130 - 133  shown in  FIG. 5  can include a transmitter-side resonant tank similar to the transmitter-side resonant tank  230 . Similarly, each of the coils  60 - 64  shown in  FIG. 5  can include a transmitter coil similar to the transmitter coil L tx . The power converter  160  for the electronic device  30  shown in  FIG. 5  can include a receiver-side resonant tank similar to the receiver-side resonant tank  240 , and the coil  40  of the electronic device  30  can include a receiver coil similar to the receiver coil L rx . 
       FIG. 11  illustrates an example AC equivalent circuit of the series-series resonant converter shown in  FIG. 10  with a T model of the transformer. Based on the equivalent circuit, voltage gain and phase of input impedance curves are shown for different load resistances and resonant couplings in  FIGS. 12 and 13 . The k=0.4 case of coupling is shown in  FIG. 12 , and the k=0.2 case of coupling is shown in  FIG. 13 . 
     According to the voltage gain curves in  FIGS. 12 and 13 , there are three resonant frequencies in the series-series resonant converter topology, including two series resonant frequencies f s1 , f s2  and one parallel resonant frequency f p . The expressions for these three resonant frequency are: 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     = 
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 k 
                               
                               ) 
                             
                             ⁢ 
                             
                               L 
                               tx 
                             
                             ⁢ 
                             
                               C 
                               tx 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       f 
                       
                         s 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     = 
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 k 
                               
                               ) 
                             
                             ⁢ 
                             
                               L 
                               tx 
                             
                             ⁢ 
                             
                               C 
                               tx 
                             
                           
                         
                       
                     
                   
                   , 
                   and 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     f 
                     p 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                           
                             
                               L 
                               tx 
                             
                             ⁢ 
                             
                               C 
                               tx 
                             
                           
                         
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     According to the expressions, the two series resonant frequencies (SRFs) are coupling dependent and the parallel resonant frequency (PRF) is coupling independent. Therefore, the SRFs move and the PRF is fixed when the resonant coupling of the series-series resonant converter changes as shown in  FIGS. 12 and 13 . Further, for different load conditions, the voltage gain can change dramatically for the PRF. This variable voltage gain can be a challenge for system controllability in voltage output applications. For example, as discussed above, the load presented by electronic devices can vary as the load presented by a battery varies based on the different charging stages in the charging profile of the battery. However, the SRFs exhibit load-independent voltage gain, which is desirable from controllability point of view. 
     Compatible inductive input impedance is important for ZVS operation of switching devices in half bridges and related switching topologies. The phase of input impedance with different loads is also shown in  FIGS. 12 and 13 . As shown, the input impedance is resistive at the PRF, which is at the boundary between the ZVS and zero current switching (ZCS) regions. Therefore, ZVS operation can be lost around the PRF due to component tolerances. For the first SRF at f s1 , the input impedance is capacitive in most load ranges. Thus, ZVS operation is not available. On the contrary, ZVS operation can be achieved in most load SRF ranges at f s2 . 
     In summary, the resonant frequency characteristics of series-series resonant converters is that, for SRF f s1 : moving SRF with variable coupling, and no ZVS operation in most load ranges. For SRF f s2 : moving SRF with variable coupling, ZVS operation in most load ranges. For PRF f p : variable voltage gain with different loads, ZVS operation cannot be guaranteed. 
     Thus, there is no good operating region with variable coupling and load in series-series resonant converters. At the same time, parallel-series and parallel-parallel resonant converters are most suitable for current source input applications. In real applications, current source input applications are relatively difficult to implement, and those two topologies are not considered here. The series-parallel resonant converter has one moving SRF with variable coupling, which is similar to the series-series resonant converter. Thus, the four basic resonant topologies shown in  FIG. 9  are not ideal to solve the challenges of varying coupling and load conditions in wireless power transfer applications. 
     As described above, the gain characteristics of series-series resonant converters include two coupling dependent SRFs with load independent voltage gains and one coupling independent PRF with load dependent voltage gain, and the PRF is in the center of the SRFs. Therefore, the center resonance is coupling independent. Similarly, gain characteristics with one SRF in the center of two PRFs can achieve coupling and load independent resonance. One example of gain characteristics with one SRF in the center of two PRFs is shown in  FIG. 14 . With the type of gain characteristics shown in  FIG. 14 , coupling and load independent resonance can be achieved for near-field wireless power transfer at the center SRF. At the same time, at the left SRF, ZVS can be achieved due to the negative slope of the gain curve. Therefore, a resonant converter with this type of gain characteristics can be used to achieve coupling and load independent resonance with ZVS operation for near-field wireless power transfer. 
       FIG. 15A  illustrates the general topology form of a resonant converter with coupling independent resonance and zero voltage switching. The resonant converter shown in  FIG. 15  includes a parallel resonant cell  300 , a ZVS branch  310 , and a series resonant cell  320 . The parallel resonant cell  300  can be implemented in many ways.  FIG. 15B  illustrates example parallel resonant cells  300  implemented with two or three passive components. As shown in  FIG. 15 , one simple form of the ZVS branch  310  can be a capacitor, which can change the input impedance to inductive to make sure zero voltage switching occurs. However, other, more complicated forms of the ZVS branch  310  with more components can also be used to change the input impedance. The series resonant cell  320  can use the self-inductance of the receiver coil as part of resonant cell. Therefore, there is always an inductor in the left side of series resonant cell.  FIG. 15C  illustrates example series resonant cells  320  implemented with two or three passive components. 
     One example resonant converter topology, called a CLCL-LC resonant converter, is shown in  FIG. 16 . To find how the series resonance is formed in the CLCL-LC resonant converter, the use of Norton&#39;s Theorem and Thevenin&#39;s Theorem is shown in  FIG. 17  to transform the relatively complicated resonant tank network into a simple branch in series with a load resistor. Since the input source has no relationship with the resonant frequency of the resonant network, a simple branch with L rk  reflected into the primary (transmitter) side, as shown in  FIG. 17 , has the same SRF as the CLCL-LC resonant converter. 
     According to  FIG. 18 , if L r  and C r  are in resonance, power will go through L m , L rk , and C rx  due to the high impedance of the parallel resonance. Further, L m  and L rk  in series can be equivalent to the self-inductance of the receiver coil, which is coupling independent. If C rx  is designed to resonate with L rx  at the resonance frequency of L r  and C r , then the CLCL-LC resonant converter will have a coupling independent series resonant frequency given by: 
     
       
         
           
             
               
                 
                   
                     f 
                     s 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                           
                             
                               L 
                               r 
                             
                             ⁢ 
                             
                               C 
                               r 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         1 
                         
                           2 
                           ⁢ 
                           π 
                           ⁢ 
                           
                             
                               
                                 L 
                                 rx 
                               
                               ⁢ 
                               
                                 C 
                                 rx 
                               
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     As for the parallel frequency of the CLCL-LC resonant converter, L m  will join the resonance like LLC. The parallel resonance is formed by L r  and C r  in parallel, and will resonate with C tx , L rk , L m  in series. The expression for this calculation is given by: 
     
       
         
           
             
               
                 
                   
                     
                       
                         j 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             L 
                             r 
                           
                           · 
                           
                             1 
                             
                               j 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 C 
                                 r 
                               
                             
                           
                         
                       
                       
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             L 
                             r 
                           
                         
                         + 
                         
                           1 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               C 
                               r 
                             
                           
                         
                       
                     
                     + 
                     
                       j 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         L 
                         tk 
                       
                     
                     + 
                     
                       j 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         L 
                         m 
                       
                     
                     + 
                     
                       1 
                       
                         j 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           C 
                           tx 
                         
                       
                     
                   
                   = 
                   0. 
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     There are two solutions of expression (11), which means two PRFs exist in CLCL-LC resonant converter. The solutions of expression (11) are relatively complicated and, thus, not shown here. From the result of the solutions, however, one PRF is present on the left side of the SRF and another PRF is present on the right side of the SRF. Intuitively, in low frequency ranges, the series branch (L tk , L m , C tx ) is capacitive, which can be equivalent to a capacitor C eq . Therefore, the parallel frequency 
               f     p   ⁢           ⁢   1       =     1     2   ⁢   π   ⁢         L   r     ⁡     (       C   r     +     C   eq       )                   
is in the left side of f s . In high frequency ranges, the series branch (L tk , L m , C tx ) is inductive, which can be equivalent to an inductor L eq . So the parallel frequency
 
               f     p   ⁢           ⁢   2       =     1     2   ⁢   π   ⁢         (       L   r     //     L   eq       )     ⁢     C   r                   
is in the right side of f s .
 
     The voltage gain and phase of input impedance curves of the CLCL-LC resonant converter shown in  FIG. 16  with different loads and for different couplings are shown in  FIGS. 19 and 20 . The k=0.4 case of coupling is shown in  FIG. 19 , and the k=0.2 case of coupling is shown in  FIG. 20 . 
     As demonstrated by  FIGS. 19 and 20 , a coupling independent SRF with ZVS operation is achieved with the CLCL-LC resonant converter topology. The entire shaded region can be selected as the operation region. From the gain curve, there are two PRFs around the fixed SRF, with one PRF on the left side and the other PRF on the right side of the SRF. With this type gain characteristics, fixed SRF with ZVS operation can be achieved, which is an important concept in the design of coupling independent resonance frequency in variable coupling applications. 
     In extension to the CLCL-LC resonant converter topology shown in  FIG. 16 , other topologies of resonant converters with coupling independent resonance and ZVS operation can be found. Some example resonant converter topologies and gain curve characteristics of that type are shown in  FIGS. 21-25 .  FIG. 21  is the CLCL-LC resonant converter topology (similar to that shown in  FIG. 16 ), which is used as a reference for the other topologies. 
     The other resonant converter topologies shown in  FIGS. 22-25  have the same order as the CLCL-LC resonant converter topology in  FIG. 21 .  FIG. 22  is a LCCL-LC resonant converter topology,  FIG. 23  is a LC-LCCL resonant converter topology. Further, with the addition of more passive components, there are other resonant converter topologies with coupling independent resonance and ZVS operation. One such resonant converter topology having higher order than the CLCL-LC resonant converter topology is shown in  FIG. 24 .  FIG. 25  is a LCCL-LCL resonant converter topology. In all these resonant converter topologies, a fixed SRF is created in the center of two PRFs in gain characteristics. With this type of gain characteristics, coupling independent operation region with ZVS operation can be obtained. 
     The above-described examples of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications can be made without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.