Abstract:
A wireless power transmission device for transmitting power from a power source to a load includes a three-dimensional source conductive element that is electrically coupled to the power source and that induces an alternating current therein. A first three-dimensional resonating conductive element surrounds the source conductive element, but is physically decoupled therefrom and resonates in response to the alternating current induced in the source conductive element. A second three-dimensional resonating conductive element is physically spaced apart from the first three-dimensional resonating conductive element and resonates in response to an oscillating field generated by the first three-dimensional resonating conductive element. A three-dimensional load conductive element is within the second three-dimensional resonating conductive element, but is physically decoupled therefrom. The three-dimensional load conductive element applies power to the load in response to resonation in the second three-dimensional resonating conductive element.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    This application claims the benefit of U.S. Provisional Patent Application Ser. No. 61/658,596, filed Jun. 12, 2012, the entirety of which is hereby incorporated herein by reference. This application also claims the benefit of U.S. Provisional Patent Application Ser. No. 61/658,636, filed Jun. 12, 2012, the entirety of which is hereby incorporated herein by reference. This application also claims the benefit of U.S. Provisional Patent Application Ser. No. 61/662,674, filed Jun. 12, 2012, the entirety of which is hereby incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to power transfer devices and, more specifically, to a wireless power transfer device. 
         [0004]    2. Description of the Related Art 
         [0005]    Wireless power transfer devices can be used to transfer power from a source to a load without requiring a wired connection between the two. They can also be used to transfer data wirelessly as well. Such devices are commonly used in situations where it is either impractical to use wired connections or potentially unsafe to do so. For example, many electric tooth brush systems use wireless power transfer to recharge the batteries in the tooth brush. Since the elements of the system are covered in non-conductive plastic, there is little chance of electric shock with such systems. 
         [0006]    Modern digital devices, such as smart phones, tablets and the like, require frequent recharging. However, most such systems require the digital device to be plugged into a recharger. Because doing so is somewhat inconvenient, users often forget to recharge their devices. 
         [0007]    Numerous wireless power transfer methods have been proposed and studied in the past for various applications. Specifically, wireless power transfer has been achieved using near-field coupling in several applications such as, RFID tags, telemetry and implanted medical devices. In addition, certain inductive coupling techniques have been reported to exhibit high power transfer efficiencies (on the order of 90%) for very short distances (1-3 cm). However, the efficiency of such techniques drops drastically for longer distances. 
         [0008]    One type of wireless power transfer system employs a strongly coupled magnetic resonance (SCMR) method. A typical SCMR system employs an inductive transmitter loop and a spaced apart inductive receiver loop. Each loop resonates as substantially the same frequency. An alternating current source is used to excite the transmitter loop, which when resonating causes the receiver loop to resonate. The receiver loop is inductively coupled to a load and transfers power to the load as a result of its resonating. 
         [0009]    Loop misalignment can result is a substantial decrease in efficiency. Conventional SCMR systems tend to be highly sensitive to the alignment between transmitter loop and receiver loop. The loops can be angularly misaligned, in which the loops exist on non-parallel planes. A greater angular difference in the planes results in lower power transfer efficiency. The loops may also be laterally misaligned, in which the loops may be parallel to each other but are on laterally spaced apart axes. Again, a greater distance between the axes results in a lower power transfer efficiency. 
         [0010]    One approach to correcting SCMR&#39;s angular misalignment sensitivity employs tuning circuits. This method is generally not able to maintain high efficiency above 60° of misalignment. Also, tuning circuits add to the complexity of SCMR systems and they cannot compensate for large angular and radial misalignments as they cannot recover the lost flux density between transmitter and receiver. However, tuning circuits can be useful for compensating the effects of variable axial distance between the transmitter and the receiver. 
         [0011]    Many digital devices require frequent data updating. One convenient time to update a digital device is during periods of non-use, such as when the device is being recharged. 
         [0012]    Therefore, there is a need for a convenient wireless power transfer system that is efficient at longer distances. 
         [0013]    Therefore, there is a need for a convenient wireless power transfer system that is efficient when the transmitter and the receiver are misaligned. 
         [0014]    Therefore, there is a need for a convenient wireless power transfer system that facilitates both power transfer and data transfer simultaneously. 
       SUMMARY OF THE INVENTION 
       [0015]    The disadvantages of the prior art are overcome by the present invention which, in one aspect, is a wireless power transmission device for transmitting power from a power source to a load that includes a three-dimensional source conductive element that is electrically coupled to the power source and that is configured to induce an alternating current therein that has been received from the power source. A first three-dimensional resonating conductive element surrounds the source conductive element, but is physically decoupled therefrom and is configured to resonate in response to the alternating current induced in the source conductive element. A second three-dimensional resonating conductive element is physically spaced apart from the first three-dimensional resonating conductive element and is configured to resonate in response to an oscillating field generated by the first three-dimensional resonating conductive element. A three-dimensional load conductive element is disposed within the second three-dimensional resonating conductive element, but is physically decoupled therefrom. The three-dimensional load conductive element is configured to apply power to the load in response to resonation in the second three-dimensional resonating conductive element. 
         [0016]    In another aspect, the invention is a wireless power transmission system for transmitting power from a power source to a load that includes a source unit and a load unit. The source unit includes a source conductive element and a first resonating conductive element. The source conductive element is electrically coupled to the power source and includes a first source loop portion, a second source loop portion and a third source loop portion, wherein each source loop portion is orthogonal to each other source loop portion. The first resonating conductive element is electrically decoupled from the source conductive element. The first resonating conductive element includes a first resonating loop portion, a second loop resonating portion and a third loop resonating portion, wherein each loop resonating portion is orthogonal to each other loop resonating portion. The first resonating conductive element defines an outer region and the source conductive element is disposed inside of the outer region. The first resonating conductive element has a resonant frequency and a maximum quality factor at the resonant frequency. The load unit is spaced apart from the source unit and includes a second resonating conductive element and a load conductive element. The second resonating conductive element is spaced apart from the first resonating conductive element and includes a first resonating loop portion, a second loop resonating portion and a third resonating loop portion, wherein each resonating loop portion is orthogonal to each other resonating loop portion. The second resonating conductive element has a resonant frequency that is substantially the same as the resonant frequency of the first resonating conductive element and has a maximum quality factor at the resonant frequency. The first resonating conductive element defines an outer region. The load conductive element is disposed within the outer region of the second resonating conductive element and is electrically coupled to the load. The load conductive element includes a first load loop portion, a second load loop portion and a third load loop portion, wherein each load loop portion is orthogonal to each other load loop portion. 
         [0017]    In yet another aspect, the invention is a method of transmitting power from a source to a load, in which an alternating current is generated at the source and the alternating current is caused to flow through a three-dimensional source conductive element. A periodic electromagnetic field resulting from the alternating current flowing through the three-dimensional source conductive element is inductively coupled to a first three-dimensional resonating conductive element that surrounds the three-dimensional source conductive element. The first three-dimensional resonating conductive element is inductively coupled to a second three-dimensional resonating conductive element. The second three-dimensional resonating conductive element and the first three-dimensional resonating conductive element have a substantially same resonant frequency. A three-dimensional load conductive element is inductively coupled to the second three-dimensional resonating conductive element, thereby inducing a current in the three-dimensional load conductive element. The current induced in the three-dimensional load conductive element is applied to the load. 
         [0018]    These and other aspects of the invention will become apparent from the following description of the preferred embodiments taken in conjunction with the following drawings. As would be obvious to one skilled in the art, many variations and modifications of the invention may be effected without departing from the spirit and scope of the novel concepts of the disclosure. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES OF THE DRAWINGS 
         [0019]      FIG. 1  is a schematic diagram of one embodiment of a wireless power transfer system. 
           [0020]      FIG. 2A  is a schematic diagram of a model SCMR power transfer system in air. 
           [0021]      FIG. 2B  is a graph demonstrating the relationship between Q max  and the electrical length of the helix. 
           [0022]      FIG. 2C  is a graph demonstrating the efficiency of SCMR systems with different r/r, ratios. 
           [0023]      FIG. 3  is a schematic diagram of an embodiment of a wireless power transfer system employing spiral resonant elements. 
           [0024]      FIG. 4  is a schematic diagram of an embodiment of a wireless power transfer system employing bifilar spiral resonant elements. 
           [0025]      FIG. 5  is a schematic diagram of an embodiment of a wireless power transfer system employing three-dimensional elements. 
           [0026]      FIGS. 6A-6C  are schematic diagrams showing an embodiment of a wireless power transfer system employing three-dimensional elements formed by folding a flat sheet on which conductors are printed. 
           [0027]      FIGS. 7A-7B  are schematic drawings of an embodiment in which each element employs three orthogonal loops. 
           [0028]      FIG. 8A  is a schematic diagram of a wireless power transfer system employing multiple resonator elements. 
           [0029]      FIG. 8B  is a graph relating efficiency to frequency in the embodiment shown in  FIG. 7A . 
           [0030]      FIG. 9A  is a schematic diagram of a wireless power transfer system employing multiple resonator elements and multiple source/load elements. 
           [0031]      FIG. 9B  is a graph relating efficiency to frequency in the embodiment shown in  FIG. 8A . 
           [0032]      FIGS. 10A-10C  are photographs of one experimental embodiment. 
           [0033]      FIG. 11  is a photograph of a second experimental embodiment. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0034]    A preferred embodiment of the invention is now described in detail. Referring to the drawings, like numbers indicate like parts throughout the views. Unless otherwise specifically indicated in the disclosure that follows, the drawings are not necessarily drawn to scale. As used in the description herein and throughout the claims, the following terms take the meanings explicitly associated herein, unless the context clearly dictates otherwise: the meaning of “a,” “an,” and “the” includes plural reference, the meaning of “in” includes “in” and “on.” Also, as used herein “Q factor” means the quality factor associated with a resonant circuit. 
         [0035]    As shown in  FIG. 1 , one embodiment of a wireless power transmission system  100  includes a source unit  110  (transmitter unit, or TX) and a load unit  120  (receiver unit, or RX). The source unit  110  includes a planar source conductor  112  that generates a first periodically fluctuating electromagnetic near field in response to an alternating current received from the power source  114 . A planar resonant source element  116  that is coplanar with the planar source conductor  112 . The planar resonant source element  116  has a Q factor that is at a maximum at its resonant frequency. In one embodiment, the planar resonant source element  116  includes an inductive loop having a first end and a different second end with a capacitor  118  that couples the first end to the second end. The planar resonant source element  116  resonates with a first oscillating current at the first resonant frequency in response to excitation from the periodically fluctuating electromagnetic near field generated by the planar source conductor  112 . The load unit  120  includes a planar resonant load element  126  that is spaced apart from the planar resonant source element  116  and that is preferably aligned therewith. The planar resonant load element  126  is configured to resonate at the first resonant frequency with a second oscillating current in response to excitation from the planar resonant source element  116 . The planar resonant load element  126  generates a second periodically fluctuating electromagnetic near field when resonating with the second oscillating current. In one embodiment, the planar resonant load element  126  includes an inductive loop having a first end and a different second end and a capacitor  128  that couples the first end to the second end. A planar load conductor  122  is electromagnetically coupled to and coplanar with the planar resonant load element  126  and generates a current in response to the second periodically fluctuating electromagnetic near field, which is applied to a load  124 . The elements are typically made from conductive wires (such as copper) or conductive ink. 
         [0036]    In one embodiment, the invention employs a wireless powering system based on a strongly coupled magnetic resonance (SCMR) method, which is discussed theoretically in  FIGS. 2A-2C . The SCMR method is a non-radiative wireless mid-range power transfer method, which in one embodiment is effective for transferring power across a distance of between 10 cm to 300 cm. SCMR can provide wireless power transfer efficiencies that are significantly higher than the efficiencies of conventional inductive coupling methods. To achieve high efficiency, the transmitting and receiving elements (typically loops or coils) are designed so that they resonate at the desired operational frequency that coincides with the frequency of where the elements exhibit maximum Q-factor. 
         [0037]    SCMR systems use resonant transmitters and receivers that are strongly coupled. Strongly coupled systems are able to transfer energy efficiently, because resonant objects exchange energy efficiently versus non-resonant objects that only interact weakly. A standard SCMR system consists of four elements (typically four loops or two loops and two coils) as shown in  FIG. 2A . 
         [0038]    The source element is connected to the power source, and it is inductively coupled to the TX element. The TX element exhibits a resonant frequency that coincides with the frequency, where its Q-factor is naturally at a maximum. Similarly, the RX exhibits a resonant frequency that coincides with the frequency where its Q-factor is naturally at a maximum. Furthermore, the load element is terminated to a load. The analysis that follows assumes that the entire system operates in air. Also, SCMR requires that the TX and RX elements are resonant at the same frequency in order to achieve efficient wireless power transfer. 
         [0039]    The analysis that follows employs TX and RX elements that have an arbitrary number of helical loops. However, in the simple embodiment shown above, only a single loop is used. The TX and RX elements can be equivalently represented by a series RLC circuit. Helices are often preferred as TX and RX SCMR elements because they exhibit both distributed inductance and capacitance and therefore, they can be designed to self-tune to a desired resonant frequency, f r , without the need of external capacitors. Also, external capacitors have losses, which in practice can reduce the Q-factor of the TX and RX elements and in turn decrease the efficiency of SCMR systems. Based on the equivalent RLC circuit of an SCMR system, its resonant frequency, f r , can be calculated, by following equation: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     r 
                   
                   = 
                   
                     1 
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                        
                       
                         LC 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The resonant frequency, f r  is also the operational frequency for the SCMR wireless powering system. The Q-factor of a resonant RLC circuit is given by: 
         [0000]    
       
         
           
             
               
                 
                   Q 
                   = 
                   
                     
                       
                         
                           ω 
                           r 
                         
                          
                         L 
                       
                       R 
                     
                     = 
                     
                       
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                             
                         
                          
                         
                           f 
                           r 
                         
                          
                         L 
                       
                       R 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Therefore, the Q-factor of a resonant helix (i.e., self resonant) can be written as: 
         [0000]    
       
         
           
             
               
                 
                   Q 
                   = 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                        
                       
                           
                       
                        
                       
                         f 
                         r 
                       
                        
                       
                         L 
                         helix 
                       
                     
                     
                       
                         R 
                         ohm 
                       
                       + 
                       
                         R 
                         rad 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where L, R rad , and R ohm  are the self-inductance, radiation resistance and ohmic resistance of the helix, which is for a short helix or solenoid (2r&gt;h) are given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     helix 
                   
                   = 
                   
                     
                       μ 
                       o 
                     
                      
                     
                       
                         rN 
                         2 
                       
                        
                       
                         [ 
                         
                           
                             ln 
                              
                             
                               ( 
                               
                                 
                                   8 
                                    
                                   r 
                                 
                                 
                                   r 
                                   c 
                                 
                               
                               ) 
                             
                           
                           - 
                           2 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     rad 
                   
                   = 
                   
                     
                       ( 
                       
                         π 
                         / 
                         6 
                       
                       ) 
                     
                      
                     
                       η 
                       o 
                     
                      
                     
                       
                         
                           N 
                           2 
                         
                          
                         
                           ( 
                           
                             2 
                              
                             π 
                              
                             
                                 
                             
                              
                             
                               f 
                               r 
                             
                              
                             
                               r 
                               / 
                               c 
                             
                           
                           ) 
                         
                       
                       4 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     
                       ohm 
                        
                       
                         ( 
                         helix 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             μ 
                             o 
                           
                            
                           ρ 
                            
                           
                               
                           
                            
                           π 
                            
                           
                               
                           
                            
                           
                             f 
                             r 
                           
                         
                       
                       ) 
                     
                      
                     
                       Nr 
                       / 
                       
                         r 
                         c 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0040]    where μ is the permeability of free space, ρ is the helix&#39;s material resistivity, r is the radius of the helix, r c  is the cross sectional wire radius, N is the number of turns (the simple single turn embodiment above uses N=1), f is the frequency, η o  is the impedance of free space and c is the speed of light, h is the height of the helix. It should also be noted that equations (3)-(6) are valid only when r&lt;λ/6π. 
         [0041]    SCMR requires that both RX and TX helices also exhibit maximum Q-factor at their resonant frequency f r , in order to achieve maximum wireless power efficiency. This can also be seen by the equation for describing the efficiency of an SCMR system derived in at it operation frequency f r  as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     η 
                      
                     
                       ( 
                       
                         f 
                         r 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           k 
                           
                             ( 
                             TX_RX 
                             ) 
                           
                           2 
                         
                          
                         
                           ( 
                           
                             f 
                             r 
                           
                           ) 
                         
                       
                        
                       
                         
                           Q 
                           TX 
                         
                          
                         
                           ( 
                           
                             f 
                             r 
                           
                           ) 
                         
                       
                        
                       
                         
                           Q 
                           RX 
                         
                          
                         
                           ( 
                           
                             f 
                             r 
                           
                           ) 
                         
                       
                     
                     
                       1 
                       + 
                       
                         
                           
                             k 
                             
                               ( 
                               TX_RX 
                               ) 
                             
                             2 
                           
                            
                           
                             ( 
                             
                               f 
                               r 
                             
                             ) 
                           
                         
                          
                         
                           
                             Q 
                             TX 
                           
                            
                           
                             ( 
                             
                               f 
                               r 
                             
                             ) 
                           
                         
                          
                         
                           
                             Q 
                             RX 
                           
                            
                           
                             ( 
                             
                               f 
                               r 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where K TX     —     RX  is the mutual coupling between the RX and TX helices and where Q TX  and Q RX  are the Q-factors of the RX and TX helices, respectively. If the TX and RX helices are identical, then their Q-factors are equal i.e., Q TX =Q RX =Q; therefore equation (7) can be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     η 
                      
                     
                       ( 
                       
                         f 
                         r 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           k 
                           
                             ( 
                             TX_RX 
                             ) 
                           
                           2 
                         
                          
                         
                           ( 
                           f 
                           ) 
                         
                       
                        
                       
                         
                           Q 
                           TX 
                           2 
                         
                          
                         
                           ( 
                           
                             f 
                             r 
                           
                           ) 
                         
                       
                     
                     
                       1 
                       + 
                       
                         
                           
                             k 
                             
                               ( 
                               TX_RX 
                               ) 
                             
                             2 
                           
                            
                           
                             ( 
                             
                               f 
                               r 
                             
                             ) 
                           
                         
                          
                         
                           
                             Q 
                             TX 
                             2 
                           
                            
                           
                             ( 
                             
                               f 
                               r 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0042]    Equation (8) shows that in order to maximize the efficiency of an SMCR system, the operation frequency f r  must be equal to the frequency f max , where the Q-factor is maximum. In what follows, the maximum Q-factor of a resonant helix is derived. The Q-factor of a resonant helix can be expressed in terms of its geometrical parameters using (3)-(6) as: 
         [0000]    
       
         
           
             
               
                 
                   
                     Q 
                      
                     
                       ( 
                       
                         
                           f 
                           r 
                         
                         , 
                         r 
                         , 
                         
                           r 
                           c 
                         
                         , 
                         N 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         f 
                         r 
                       
                        
                       
                         μ 
                         0 
                       
                        
                       r 
                        
                       
                           
                       
                        
                       
                         
                           N 
                           2 
                         
                          
                         
                           [ 
                           
                             
                               ln 
                                
                               
                                 ( 
                                 
                                   
                                     8 
                                      
                                     r 
                                   
                                   
                                     r 
                                     c 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             2 
                           
                           ] 
                         
                       
                     
                     
                       
                         
                           ( 
                           
                             
                               
                                 μ 
                                 0 
                               
                                
                               ρ 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 f 
                                 r 
                               
                                
                               
                                 r 
                                 2 
                               
                                
                               N 
                             
                             
                               r 
                               c 
                               2 
                             
                           
                           ) 
                         
                         
                           1 
                           2 
                         
                       
                       + 
                       
                         20 
                          
                         
                             
                         
                          
                         
                           π 
                           2 
                         
                          
                         
                           
                             
                               N 
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   
                                     f 
                                     r 
                                   
                                    
                                   r 
                                 
                                 c 
                               
                               ) 
                             
                           
                           4 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0043]    The maximum Q-factor, Q max , and the frequency, f max , where Q max  occurs, can be derived from (9) using calculus as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       f 
                       max 
                     
                      
                     
                       ( 
                       
                         r 
                         , 
                         
                           r 
                           c 
                         
                         , 
                         N 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         c 
                         
                           8 
                           / 
                           7 
                         
                       
                        
                       
                         μ 
                         
                           1 
                           / 
                           7 
                         
                       
                        
                       
                         ρ 
                         
                           1 
                           / 
                           7 
                         
                       
                     
                     
                       
                         4 
                         · 
                         
                           15 
                           
                             2 
                             / 
                             7 
                           
                         
                       
                        
                       
                         N 
                         
                           2 
                           / 
                           7 
                         
                       
                        
                       
                         r 
                         c 
                         
                           2 
                           / 
                           7 
                         
                       
                        
                       
                         π 
                         
                           11 
                           / 
                           7 
                         
                       
                        
                       
                         r 
                         
                           6 
                           / 
                           7 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       Q 
                       max 
                     
                      
                     
                       ( 
                       
                         r 
                         , 
                         
                           r 
                           c 
                         
                         , 
                         N 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                        
                       
                           
                       
                        
                       
                         f 
                         max 
                       
                        
                       
                         μ 
                         0 
                       
                        
                       r 
                        
                       
                           
                       
                        
                       
                         
                           N 
                           2 
                         
                          
                         
                           [ 
                           
                             
                               ln 
                                
                               
                                 ( 
                                 
                                   
                                     8 
                                      
                                     r 
                                   
                                   
                                     r 
                                     c 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             2 
                           
                           ] 
                         
                       
                     
                     
                       
                         
                           ( 
                           
                             
                               
                                 μ 
                                 0 
                               
                                
                               ρ 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                   
                               
                                
                               
                                 r 
                                 2 
                               
                                
                               
                                 f 
                                 max 
                               
                                
                               N 
                             
                             
                               r 
                               c 
                               2 
                             
                           
                           ) 
                         
                         
                           1 
                           2 
                         
                       
                       + 
                       
                         20 
                          
                         
                             
                         
                          
                         
                           π 
                           2 
                         
                          
                         
                           
                             
                               N 
                               2 
                             
                              
                             
                               ( 
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   
                                     f 
                                     max 
                                   
                                    
                                   r 
                                 
                                 c 
                               
                               ) 
                             
                           
                           4 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Based on the above discussion, an SCMR system requires that 
         [0000]        f   r   =f   max   (12)
 
         [0000]    which can be written based on (10) as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       f 
                       r 
                     
                      
                     
                       ( 
                       
                         r 
                         , 
                         
                           r 
                           c 
                         
                         , 
                         N 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         c 
                         
                           8 
                           / 
                           7 
                         
                       
                        
                       
                         μ 
                         
                           1 
                           / 
                           7 
                         
                       
                        
                       
                         ρ 
                         
                           1 
                           / 
                           7 
                         
                       
                     
                     
                       
                         4 
                         · 
                         
                           15 
                           
                             2 
                             / 
                             7 
                           
                         
                       
                        
                       
                         N 
                         
                           2 
                           / 
                           7 
                         
                       
                        
                       
                         r 
                         c 
                         
                           2 
                           / 
                           7 
                         
                       
                        
                       
                         π 
                         
                           11 
                           / 
                           7 
                         
                       
                        
                       
                         r 
                         
                           6 
                           / 
                           7 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Therefore, (13) shows that the geometrical parameters of a helix can be appropriately chosen so that the helix has maximum Q-factor at a chosen frequency, f r . For example, if the parameters f r , r c , N and ρ are specified by a designer, (13) can be solved for the radius of the maximum Q-factor, r max , as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                     max 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             c 
                             
                               8 
                               / 
                               7 
                             
                           
                            
                           
                             μ 
                             
                               1 
                               / 
                               7 
                             
                           
                            
                           
                             ρ 
                             
                               1 
                               / 
                               7 
                             
                           
                         
                         
                           
                             4 
                             · 
                             
                               15 
                               
                                 2 
                                 / 
                                 7 
                               
                             
                           
                            
                           
                             r 
                             c 
                             
                               2 
                               / 
                               7 
                             
                           
                            
                           
                             N 
                             
                               2 
                               / 
                               7 
                             
                           
                            
                           
                             π 
                             
                               11 
                               / 
                               7 
                             
                           
                            
                           
                             f 
                             r 
                           
                         
                       
                       ] 
                     
                     
                       7 
                       / 
                       6 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0044]    Next, the helices are analyzed using (10), (11) and (14) to study the behavior of the maximum Q-factor, Q max , versus the electrical length of the helix (C dev /λ Q     max   ) at f max , which can be written as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       C 
                       dev 
                     
                     
                       λ 
                       max 
                     
                   
                   = 
                   
                     
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         
                           r 
                           max 
                         
                       
                       
                         λ 
                         max 
                       
                     
                     = 
                     
                       
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                             
                         
                          
                         
                           r 
                           max 
                         
                          
                         
                           f 
                           max 
                         
                       
                       c 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where L dev  is the length of the helix (device), λ max  is the wavelength corresponding to f max  given by (10). Specifically, optimum SCMR loops with N=1 are designed in the frequency range 100 KHz≦f≦5 GHz for four values of the cross-sectional radius, r c =0.01, 0.1, 1.0 and 10 mm. The material of the helices is assumed copper and for each pair of f max  and r c , the optimum r is calculated by (14). Then Q max  from (11) is plotted in  FIG. 2B  versus the electrical length of the helices (C dev /λ Q     max   ), which is calculated by (15). Specifically,  FIG. 2B  illustrates that for each pair of f max  and r c  there is an r max  that provides the global maximum for the Q-factor, Q Gmax . 
         [0045]    In what follows the global maximum Q-factor of the helix, Q Gmax , is formulated. First, the local maximum Q-factor, Q Lmax , is derived by substituting (10) into (11): 
         [0000]    
       
         
           
             
               
                 
                   
                     Q 
                     Lmax 
                   
                   = 
                   
                     
                       
                         2 
                         · 
                         
                           3 
                           
                             6 
                             / 
                             7 
                           
                         
                       
                        
                       
                         r 
                         c 
                         
                           6 
                           / 
                           7 
                         
                       
                        
                       
                         c 
                         
                           8 
                           / 
                           7 
                         
                       
                        
                       
                         μ 
                         
                           8 
                           / 
                           7 
                         
                       
                        
                       
                         N 
                         
                           6 
                           / 
                           7 
                         
                       
                        
                       
                         
                           ρ 
                           
                             1 
                             / 
                             7 
                           
                         
                          
                         
                           [ 
                           
                             
                               ln 
                                
                               
                                 ( 
                                 
                                   
                                     8 
                                      
                                     r 
                                   
                                   
                                     r 
                                     c 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             2 
                           
                           ] 
                         
                       
                     
                     
                       
                         5 
                         
                           1 
                           / 
                           7 
                         
                       
                        
                       
                         π 
                         
                           2 
                           / 
                           7 
                         
                       
                        
                       
                         
                           r 
                           
                             3 
                             / 
                             7 
                           
                         
                         [ 
                         
                           
                             
                               c 
                               
                                 4 
                                 / 
                                 7 
                               
                             
                              
                             
                               μ 
                               
                                 4 
                                 / 
                                 7 
                               
                             
                              
                             
                               ρ 
                               
                                 4 
                                 / 
                                 7 
                               
                             
                           
                           + 
                           
                             6 
                              
                             
                               r 
                               c 
                               
                                 1 
                                 / 
                                 7 
                               
                             
                              
                             
                               N 
                               
                                 1 
                                 / 
                                 7 
                               
                             
                              
                             
                               r 
                               
                                 3 
                                 / 
                                 7 
                               
                             
                              
                             
                               
                                 
                                   
                                     c 
                                     
                                       8 
                                       / 
                                       7 
                                     
                                   
                                    
                                   
                                     μ 
                                     
                                       8 
                                       / 
                                       7 
                                     
                                   
                                    
                                   
                                     ρ 
                                     
                                       8 
                                       / 
                                       7 
                                     
                                   
                                 
                                 
                                   
                                     r 
                                     c 
                                     
                                       2 
                                       / 
                                       7 
                                     
                                   
                                    
                                   
                                     N 
                                     
                                       2 
                                       / 
                                       7 
                                     
                                   
                                    
                                   
                                     r 
                                     
                                       6 
                                       / 
                                       7 
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using again calculus, we can find out that the global maximum for the Q-factor occurs when: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       r 
                       
                         ( 
                         Gmax 
                         ) 
                       
                     
                     
                       r 
                       c 
                     
                   
                   = 
                   
                     
                       
                          
                         
                           13 
                           / 
                           3 
                         
                       
                       8 
                     
                     ≈ 
                     9.52 
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
         [0000]    This result shows that the ratio between the helix radius, r, and the cross-sectional radius, r c , must be approximately 9.52 in order to achieve the maximum Q-factor. This ratio is also independent of frequency and material. 
         [0046]    Also, by substituting (17) into (16) we can write the global maximum for the Q-factor as: 
         [0000]    
       
         
           
             
               
                 
                   
                     Q 
                     Gmax 
                   
                   = 
                   
                     
                       
                         28 
                         · 
                         
                           2 
                           
                             2 
                             / 
                             7 
                           
                         
                       
                        
                       
                         r 
                         c 
                         
                           3 
                           / 
                           7 
                         
                       
                        
                       
                         c 
                         
                           8 
                           / 
                           7 
                         
                       
                        
                       
                         μ 
                         
                           8 
                           / 
                           7 
                         
                       
                        
                       
                         N 
                         
                           6 
                           / 
                           7 
                         
                       
                        
                       
                         ρ 
                         
                           1 
                           / 
                           7 
                         
                       
                     
                     
                       
                         15 
                         
                           1 
                           / 
                           7 
                         
                       
                        
                       
                          
                         
                           13 
                           / 
                           7 
                         
                       
                        
                       
                         
                           π 
                           
                             2 
                             / 
                             7 
                           
                         
                         [ 
                         
                           
                             
                               c 
                               
                                 4 
                                 / 
                                 7 
                               
                             
                              
                             
                               μ 
                               
                                 4 
                                 / 
                                 7 
                               
                             
                              
                             
                               ρ 
                               
                                 4 
                                 / 
                                 7 
                               
                             
                           
                           + 
                           
                             6 
                              
                             
                               r 
                               c 
                               
                                 4 
                                 / 
                                 7 
                               
                             
                              
                             
                               N 
                               
                                 1 
                                 / 
                                 7 
                               
                             
                              
                             
                               
                                 
                                   
                                     c 
                                     
                                       8 
                                       / 
                                       7 
                                     
                                   
                                    
                                   
                                     μ 
                                     
                                       8 
                                       / 
                                       7 
                                     
                                   
                                    
                                   
                                     ρ 
                                     
                                       8 
                                       / 
                                       7 
                                     
                                   
                                 
                                 
                                   
                                     r 
                                     c 
                                     
                                       8 
                                       / 
                                       7 
                                     
                                   
                                    
                                   
                                     N 
                                     
                                       2 
                                       / 
                                       7 
                                     
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
         [0047]    Therefore, if a helix is designed to operate at the global maximum Q-factor it will yield the maximum possible wireless efficiency for the corresponding SCMR system. In order to verify the global maximum design of (17), we assume that an arbitrary ratio of r/r c =t, and solve (13) and (17) to obtain the r and r c  given the number of turns, N, and the desired frequency of operation, f o : 
         [0000]    
       
         
           
             
               
                 
                   
                     r 
                     
                       c 
                       max 
                     
                   
                   = 
                   
                     
                       c 
                        
                       
                           
                       
                        
                       
                         μ 
                         
                           1 
                           / 
                           8 
                         
                       
                        
                       
                         ρ 
                         
                           1 
                           / 
                           8 
                         
                       
                     
                     
                       
                         2 
                         · 
                         
                           2 
                           
                             3 
                             / 
                             4 
                           
                         
                         · 
                         
                           15 
                           
                             1 
                             / 
                             4 
                           
                         
                       
                        
                       
                         N 
                         
                           1 
                           / 
                           4 
                         
                       
                        
                       
                         f 
                         o 
                         
                           7 
                           / 
                           8 
                         
                       
                        
                       
                         π 
                         
                           11 
                           / 
                           8 
                         
                       
                        
                       
                         t 
                         
                           3 
                           / 
                           4 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   
                     r 
                     max 
                   
                   = 
                   
                     
                       c 
                        
                       
                           
                       
                        
                       
                         μ 
                         
                           1 
                           / 
                           8 
                         
                       
                        
                       
                         ρ 
                         
                           1 
                           / 
                           8 
                         
                       
                        
                       
                         t 
                         
                           1 
                           / 
                           4 
                         
                       
                     
                     
                       
                         2 
                         · 
                         
                           2 
                           
                             3 
                             / 
                             4 
                           
                         
                         · 
                         
                           15 
                           
                             1 
                             / 
                             4 
                           
                         
                       
                        
                       
                         N 
                         
                           1 
                           / 
                           4 
                         
                       
                        
                       
                         f 
                         o 
                         
                           7 
                           / 
                           8 
                         
                       
                        
                       
                         π 
                         
                           11 
                           / 
                           8 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
         [0048]    Based on (19) and (20), SCMR systems were designed and simulated in Ansoft HFSS for different ratios r/r c  (2≦t≦50) and assuming the number of turns, N=5, distances, l 1 =l 3 =2 cm, l 2 =10 cm (see  FIG. 2A ), and operational frequency, f o =46.5 MHz. The efficiency of these designs is compared in  FIG. 2C . The results clearly illustrate that the maximum efficiency is achieved for a ratio of t=9.52 that matches our derived global maximum condition of (17). 
         [0049]    The following are guidelines for designing helical TX and RX elements of SCMR wireless powering systems. An SCMR system based on helices will not be optimal unless the spacing, s, is picked so that the helices exhibit the appropriate capacitance in order to resonate at the desired operating frequency of the system. The spacing, s of an SCMR helix is an important parameter that should be picked to ensure optimal wireless power transfer efficiency. The capacitance formula for closely wound helix is as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                     t 
                   
                   = 
                   
                     
                       2 
                        
                       
                           
                       
                        
                       
                         π 
                         2 
                       
                        
                       r 
                        
                       
                           
                       
                        
                       
                         ɛ 
                         0 
                       
                     
                     
                       ln 
                       [ 
                       
                         
                           
                             s 
                             / 
                             2 
                           
                            
                           
                               
                           
                            
                           
                             r 
                             c 
                           
                         
                         + 
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     s 
                                     / 
                                     2 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     r 
                                     c 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             - 
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where r is the radius of the helix, r c  is the cross sectional wire radius, ε 0  is the permittivity of free space, s is the spacing between adjacent turns of the helix, C t  is the total distributed capacitance of the helix, and t is the thickness of the insulation coating. 
         [0050]    The capacitance formula of (21) is valid when s/2r c ≦2 and t&lt;&lt;s−2r c . In order to resonate the helix at a desired frequency f, the spacing between two adjacent turns, s, can be adjusted to provide the required capacitance calculated from (1) as: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                     t 
                   
                   = 
                   
                     1 
                     
                       4 
                        
                       
                           
                       
                        
                       
                         π 
                         2 
                       
                        
                       
                         f 
                         2 
                       
                        
                       
                         L 
                         helix 
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
         [0051]    Then equation (21) can be solved for the spacing, s, as follows: 
         [0000]    
       
         
           
             
               
                 
                   s 
                   = 
                   
                     
                       
                         [ 
                         
                           
                              
                             
                               ( 
                               
                                 
                                   4 
                                    
                                   
                                       
                                   
                                    
                                   
                                     π 
                                     4 
                                   
                                    
                                   
                                     r 
                                     2 
                                   
                                    
                                   
                                     ɛ 
                                     0 
                                     2 
                                   
                                 
                                 
                                   C 
                                   t 
                                   2 
                                 
                               
                               ) 
                             
                           
                           + 
                           1 
                         
                         ] 
                       
                        
                       
                         r 
                         c 
                       
                     
                     
                        
                       
                         ( 
                         
                           
                             2 
                              
                             
                                 
                             
                              
                             
                               π 
                               2 
                             
                              
                             r 
                              
                             
                                 
                             
                              
                             
                               ɛ 
                               0 
                             
                           
                           
                             C 
                             t 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Equation (23) is valid when s/2r c ≦2 and t&lt;&lt;s−2r c . Therefore, the spacing, s, can be adjusted using (23) independently from the other geometrical parameters to achieve the necessary capacitance and without affecting the frequency where a short helix or solenoid (2r&gt;h) exhibits maximum Q-factor since (13) shows that the f max  does not depend on s. 
         [0052]    As shown in  FIG. 3 , the planar resonant source element  110  and the planar resonant load element  120  could each be a conductive spiral  302 , which could be in the form of a conductive material that has been printed on a planar substrate. In such an embodiment, the spirals  302  have an inherent capacitance and the design of the spiral is chosen so that each spiral resonator  302  resonates at the frequency where the loop naturally exhibits its maximum Q-factor. Given the complexity of the capacitance associated with the spirals  302 , their design would typically be accomplished through simulation. Similarly, as shown in  FIG. 4 , the planar resonant source element  110  and the planar resonant load element  120  could each include two coplanar conductive bifilar spirals  416  and  418 . Because such spirals are self-resonant, they would not exhibit the same sort of capacitor loss associated with embodiments in which a capacitor is added to a conductive loop. 
         [0053]    One embodiment, as shown in  FIG. 5 , maintains efficiency even when the source unit  510  and the load unit  530  are not in alignment through the use of a three dimensional symmetric source unit  510  and load unit  530 . In this embodiment, the source element  512  includes a first loop  514  and an electrically contiguous second loop  516  that is orthogonal to the first loop  514 . Similarly, the first resonator unit  520  includes a first loop  522  and an orthogonal second loop  524 . The source unit  512  is disposed inside the first resonator unit  520 . The receiver unit  530  is configured similarly, having a load element  532  with a first loop  534  and a second orthogonal loop  536 , and having a second resonator element  540  with a first loop  542  and an orthogonal second loop  544 . More complex structures may be employed and as the spherical symmetry of the resonators increases, the effect of misalignment also decreases. A photograph of an experimental embodiment of a resonator element  1010  according to this embodiment is shown in  FIG. 10A , a source element  1020  is shown in  FIG. 10B  and an assembled source unit  1000  is shown in  FIG. 10C . 
         [0054]    One approach to making such a three-dimensional structure is shown in  FIGS. 6A-6C . In this embodiment a conductive ink  612  (such as a metallic ink) is printed on a non-conductive substrate  614  (such as a plastic or a paper) to form the conductive elements of the source element  610 , as shown in  FIG. 6A . Similarly, as shown in  FIG. 6B , a conductive ink  622  is printed on a non-conductive substrate  624  to form the conductive elements of the first resonator element  620 . These shapes are then folded into cubes to form the source unit  600 . A similar process can be employed to form the load unit (not shown). Also, conductive ink can be printed directly onto a three dimensional object (such as the interior of the casing of a cellular telephone, etc.) to form the load unit and the first resonator unit. 
         [0055]    As shown in  FIGS. 7A-7B , the inefficiency resulting from a load unit  730  being misaligned with a source unit  710  can be reduced by increasing the spherical symmetry of each unit. One way in which this can be accomplished, as shown in  FIG. 7A , is to use conductive elements  700  (i.e., source, first resonating, second resonating and load) that include a first loop  702 , an electrically contiguous second loop  704  and an electrically contiguous third loop  706 . In this embodiment, each loop is substantially planar and is substantially orthogonal to the other two loops. As shown in  FIG. 7B , one embodiment employs a source unit  710  with a three orthogonal loop source element  712  disposed inside of a first three orthogonal loop resonator element  720 , and a load unit  730  with a three orthogonal loop load element  732  disposed inside of a second three orthogonal loop resonator element  734 . A photograph of one experimental embodiment of a source unit  1110  and a load unit  1120  employing elements with three orthogonal loops is shown in  FIG. 11 . As will be appreciated by those of skill in the art, three dimensional structures of greater complexity can increase the spherical symmetry of the elements, thereby reducing inefficiency caused by misalignment of the units. 
         [0056]    In other embodiments, multiple source and resonator elements can be employed to tune the system to more than one different frequency. Such embodiments can facilitate, for example, the transfer of both power and data from the source to the load. This ability may be useful in such situations as when it is desirable to charge a cell phone (or other type of digital device, such as a tablet) which updating some of the data stored on the device. For example, one embodiment, as shown in  FIGS. 8A-8B , includes a source unit  810  with a source element  812  and two separate resonator elements: a first source resonator element  814  and a second source resonator element  816 . Similarly, the load unit  820  includes a load element  822  and two resonator elements: a first load resonator element  824  that has substantially the same resonant frequency as the first source resonator element  814 , and a second load resonator element  826  that has substantially the same resonant frequency as the second source resonator element  816 . Use of multiple resonator elements allows the system to be tuned to multiple specific frequencies. For example, efficiency as a function of frequency is shown in  FIG. 8B  for an embodiment in which the distance between the units was 7 cm, the radii of the source loop  812  and the load loop  822  were 1.5 cm, the radii of the a first source resonator element  814  and the first load resonator element  824  were 2.2 cm, the radii of the second source resonator element  816  and the second load resonator element  826  and the cross-sectional radius of the wires used in each element was 2.2 mm. As can be seen, efficiency peaks at two distinct frequencies with this embodiment. 
         [0057]    In another embodiment, as shown in  FIGS. 9A and 9B , the source unit  910  can include two different source elements  914  and  918  and three different source resonator elements  912 ,  916  and  920 . Similarly, the load unit  930  includes two load elements  934  and  938  and three different load resonator elements  932 ,  936  and  940 . As shown in  FIG. 9B , an experimental embodiment using this configuration resulted in a more complex efficiency versus frequency graph. This embodiment allows for control over the bandwidth of the system, which facilitates transfer of signals (such as digital signals) during a power transfer event. This embodiment employed the following parameters: distance=10 cm; first source/load loops radius=4.7 cm; second source/load loop2 radius=8.5 cm; first TX &amp; RX resonator loops radius=2.2 cm; second TX &amp; RX resonator loops radius=6.5 cm; third TX &amp; RX resonator loops radius=11.5 cm; and wire cross-sectional radius=2.2 mm. Many other combinations of source/load elements and resonator elements are possible. 
         [0058]    The above described embodiments, while including the preferred embodiment and the best mode of the invention known to the inventor at the time of filing, are given as illustrative examples only. It will be readily appreciated that many deviations may be made from the specific embodiments disclosed in this specification without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is to be determined by the claims below rather than being limited to the specifically described embodiments above.