Abstract:
A magnetic air core apparatus that includes a first toroid formed of a plate like structure wrapped in a helical shape and including an air core, further the plate like structure has an outer peripheral surface and an inner peripheral surface, a second toroid that substantially envelopes the first toroid in a concentric manner. The first and second toroids have a first air gap provided therebetween. A start terminal is connected to the first toroid and a return terminal is connected to the second toroid, the start and return terminals enable connections to other electrical devices.

Description:
BACKGROUND 
       [0001]    1. Field of the Disclosure 
         [0002]    This application relates generally to air core magnetic components. More particularly the present disclosure relates to high frequency cores made of a toroidal magnetic material that can be energized by passing electric current. 
         [0003]    2. Description of the Related Art 
         [0004]    A magnetic core is an important component of electrical, electromechanical and magnetic devices. The magnetic core confines and guides magnetic fields in a circuit. For example, a typical inductor consists of a coil that creates flux, a magnetic core that directs flux, and an air gap, that stores magnetic energy. The air gap is made of two flat faces of iron within the magnetic core. Several factors define the performance characteristics of a magnetic core including the geometry, permeability and hysteresis properties, amount of air gap, operating frequency, magnetic material, etc. Magnetic cores are available in many shapes each having different characteristic behavior. Typically, it is desired to select a magnetic core having highest efficiency, and low flux leakage. 
         [0005]    Toroid shape magnetic cores are often found very effective for many wide band frequency application, power transformers, and inductors. The toroidal core is formed either by winding a thin strip of magnetic material continuously, like a tape, or by using powder iron that is pressed and compacted into toroidal shape. An ideal coil is distributed evenly all around the circumference of the toroid. The symmetry of this geometry creates a magnetic field of circular loops inside the core, and the lack of sharp bends will constrain virtually the entire magnetic field to the core. 
         [0006]    SiC or GaN wide-band gap (WBG) semiconductors permit power electronics to have an operation frequency at least ten times higher than conventional Si device circuits, up to several MHz. Further, due to the AC characteristics of WBG semiconductors, fewer passive components are required. However, core materials for transformers have frequency limits. 
         [0007]    Core losses are an important limitation in most high frequency applications for transformer. Common core losses occur due to a changing magnetic field such as hysteresis loss due to expansion and contraction of magnetic domain from changing magnetic field, eddy current losses due to induced circulating loops of current that generates heat and adds to the resistivity of the core, and skin effect due to increased current concentration at the surface of the conductor thus reducing its effective surface area in turn increasing the resistivity. Further, electromagnetic interference and electromagnetic compatibility are other issues related to high frequency devices. 
         [0008]    A toroid shaped magnetic core offers lower core losses compared to other shapes. A wire wound toroid is widely used in several applications. However, the wire winding process can be expensive and results in a sub-optimal toroid configuration. More advanced toroidal core designs offering high quality factor, commonly referred to as Q-factor, which are needed with the increased demand of high frequency operation. 
       SUMMARY 
       [0009]    According to an embodiment of the present disclosure, there is provided an magnetic core apparatus. A magnetic air core apparatus that includes a first toroid formed of a plate like structure wrapped in a helical shape and including an air core, further the plate like structure has an outer peripheral surface and an inner peripheral surface, a second toroid that substantially envelopes the first toroid in a concentric manner. The first and second toroids have a first air gap provided therebetween. A start terminal is connected to the first toroid and a return terminal is connected to the second toroid, the start and return terminals enable connections to other electrical devices. 
         [0010]    The width of each turn of the plate-like structure has a varying width. The width of the outer peripheral surface of the first toroid is greater than the width of the inner peripheral surface. Each turn of the plurality of turns of the first toroid is separated by a second gap creating a second capacitor. The first air gap between the second toroid and the first toroid creates a first capacitor having a first capacitance. The first capacitance of the first capacitor can be controlled by varying the first air gap. 
         [0011]    The second toroid includes at least one toroidal slot to enable access to the first toroid, at least one poloidal slot to enable access to the first toroid, and at least one terminal slot to connect a terminal to the first toroid and the second toroid. 
         [0012]    Further, the first toroid can be configured to allow a first current flow in first direction and the second toroid can be configured to allow current flow in a second direction. 
         [0013]    The forgoing general description of the illustrative implementations and the following detailed description thereof are merely exemplary aspects of the teachings of this disclosure, and are not restrictive. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1  is a graph illustrating basic characteristics of ferrite magnetic cores. 
           [0015]      FIG. 2  illustrates a coil design for high accuracy Rogowski current sensor. 
           [0016]      FIG. 3A  is a perspective view of an exemplary surfaced air core according to an embodiment of the present disclosure. 
           [0017]      FIGS. 3B and 3C  are a cross-sectional view illustrating the geometry of the surfaced air core. 
           [0018]      FIG. 3D  is a cross-sectional view illustrating the internal structure of the surfaced air core. 
           [0019]      FIG. 3E  is a cross sectional view of the surfaced air core illustrating the current flow direction. 
           [0020]      FIG. 4A  illustrates a stray capacitor between coil windings of a wired toroidal core according to an exemplary embodiment of the present disclosure. 
           [0021]      FIG. 4B  illustrates the stray capacitor between coil windings of a surface air core toroid according to an exemplary embodiment of the present disclosure. 
           [0022]      FIGS. 5A and 5B  illustrate an intrinsic effect of a current flowing through a typical wired toroidal core and a surfaced air core toroid respectively according to an exemplary embodiment of the present disclosure. 
           [0023]      FIG. 6A  shows exemplary simulation results of magnetic flux density generated in a wired toroidal core according to an exemplary embodiment of the present disclosure. 
           [0024]      FIG. 6B  shows exemplary simulation results of magnetic flux density generated in a surface air core according to an exemplary embodiment of the present disclosure. 
           [0025]      FIG. 6C  illustrates the difference in magnetic flux density in a wired toroidal core and a surface air core toroid according to an exemplary embodiment of the present disclosure. 
           [0026]      FIG. 7A  illustrates a step with excitation current applied to a coil according to an exemplary embodiment of the present disclosure. 
           [0027]      FIGS. 7B and 7C  shows exemplary simulation results of magnetic flux density generated in a wired toroidal core and a surface air core respectively according to an exemplary embodiment of the present disclosure. 
           [0028]      FIG. 7D  is a graph that illustrates the difference in magnetic flux density in a wired toroidal core and a surface air core toroid according to an exemplary embodiment of the present disclosure. 
           [0029]      FIG. 8A  is an exemplary application of the surfaced air core as a transformer according to an exemplary embodiment of the present disclosure. 
           [0030]      FIG. 8B  illustrates the operation circuit of the transformer in  FIG. 8A  according to an exemplary embodiment of the present disclosure. 
           [0031]      FIG. 8C  shows an exemplary magnetic flux distribution for the transformer setup in  FIG. 8A  according to an embodiment of present disclosure. 
           [0032]      FIG. 8D  compares the coupling ratio of a flat wire and a toroidal wire core structures used in a transformer according to an exemplary embodiment of present disclosure. 
           [0033]      FIG. 9A  illustrates an operation circuit employing a surfaced air core toroid for magnetic resonance wireless power transmission operation according to an embodiment of the present disclosure. 
           [0034]      FIG. 9B  shows a sample simulation result of magnetic flux density distribution in a surfaced air core toroid used in  FIG. 9A . 
           [0035]      FIG. 9C  is a graph that illustrates the magnetic flux distribution, the power transmission and the efficiency as the capacitance varies according to an exemplary embodiment of present disclosure. 
           [0036]      FIG. 10  illustrates a near field wireless power transfer step up employing surfaced air core toroid transformer with multiple outputs. 
           [0037]      FIGS. 11A-11C  illustrate power control graphs of a near field wireless power transfer having multiple inputs and multiple outputs according to an exemplary embodiment of present disclosure. 
           [0038]      FIGS. 12A-12D  illustrate a 3D printing based manufacturing of a surfaced air core toroid according to an exemplary embodiment of present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0039]    In the drawings, like reference numerals designate identical or corresponding parts throughout the several views. Further, as used herein, the words “a”, “an” and the like generally carry a meaning of “one or more”, unless stated otherwise. The drawings are generally drawn to scale unless specified otherwise or illustrating schematic structures or flowcharts. 
         [0040]    A high frequency magnetic device can be implemented as a solid toroid using a ferrite material or a toroid with an air core. A device having a ferrite material core has a saturation limit which bounds the maximum flux carried by the ferromagnetic material. Typically, as the magnetic flux increases the ferrite-core&#39;s permissivity, the ferrite-core&#39;s ability to support formation of a magnetic field decreases. The ferrite-core&#39;s permissivity is also affected by the frequency of the operation; however, the permissivity-frequency relationship is highly complex. See for instance  FIG. 1 . 
         [0041]    On the other hand, a high frequency magnetic device having an air core has no ferrite material in the path of the magnetic field. Consequently, it has potentially low losses during a high frequency operation. Further, such a device using an air core does not have a flux saturation limit. Thus, a higher magnetic flux can be support by the air core and multiple inputs and outputs can be connected to one transformer. Further, the high efficiency of the air core and the higher mutual inductance capacity enables design of a contactless, multiple input and output power transmitting device. 
         [0042]      FIG. 1  illustrates sample frequency vs. permeability characteristics of Mn—Zn and Ni—Zn ferrite cores. Lines L 107   a  and L 107   b  illustrate the permeability of the ferrite cores as a function of frequency. The ferrite materials offer a trade-off called ‘snakes limit’, indicated by line L 105 , beyond which the permeability decreases as the frequency increases. 
         [0043]    A high frequency designed transformer not only has a coil with a large number of turns for maintaining exciting inductance, but also has large AC loss caused by the core itself and skin effect. Referring back to  FIG. 1 , the high-permeability and low-loss materials (Mn—Zn) have a frequency limit around 500 kHz (region R 101  of  FIG. 1 ). The lower permeability and larger loss materials composed of Ni—Zn ferrites have a higher frequency limit around 1 MHz (region R 103 ). Consequently most DC-DC converters have an operating frequency under 1 MHz. In contrast, a WBG semiconductor is able to operate over 1 MHz switching. To utilize the WBG switching capability, use of an air core for magnetic components is disclosed herein. 
         [0044]    Any poor mutual coupling associated with an air core transformer is overcome by use of resonant inductive coupling, sometimes referred to as LC resonance. Resonant inductive coupling consists of two high quality (Q) coils wound around the same core with capacitors across the winding creating two LC circuits, which may be distributed in the same device or different devices. When an oscillating current is passed through the coil, the LC circuit generates an oscillating magnetic field which produces resonance in the coil. In a resonant coil, any energy placed in the coil dies away relatively slowly over several cycles. If a second coil is brought near the resonant coil, the energy is transferred to the second coil before it is lost, even if the coils are apart. The efficiency equation 1 summarizes the basic operation of the wireless power transfer technology. 
         [0000]    
       
         
           
             
               
                 
                   Efficiency 
                   ∝ 
                   
                     1 
                     + 
                     
                       1 
                       
                         2 
                         * 
                         K 
                         * 
                         
                           
                             
                               Q 
                               1 
                             
                             * 
                             
                               Q 
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The efficiency equation 1, indicates that efficiency increases monotonically and approaches 100% with an increase in coupling factor K and quality factors Q 1  and Q 2  of primary and secondary coils, respectively. 
         [0045]    According to the present disclosure, high K and Q factors are achieved by designing a coil with a physical layout which generates the magnetic flux path, while reducing the stray resistances, which are dominant especially for high frequency devices. 
         [0046]      FIG. 2  illustrates a conventional coil design composed of wound wire particularly designed for a Rogowski current sensor. A toroidal structure is created from the wire which begins at a start terminal  201  and is wrapped in direction  203   a  to form a helical shaped toroidal wire  201 . A return wire  205  is connected to the end of the toroidal wire  201  at  201   c  and is wrapped in a reverse direction  203   b  inside the toroidal wire  201  such that the return wire  205  ends at the return terminal  201   e . This turn method cancels Z axis flux interference so it is able to increase the signal to noise ratio if used in a sensor. Alternately, the conventional coil may be composed of a wire wound around a toroidal core made of magnetic material. 
         [0047]      FIG. 3A  is a perspective view of an exemplary surfaced air core according to the present disclosure. The surfaced air core  300  includes a toroidal winding  301  formed using a plate-like structure, a return winding  303  that encapsulates the toroidal winding, and start terminal and return terminals  305  and  307 , respectively. The return winding  303  is a hollow toroid concentric with the toroidal winding  301  and placed outside the toroidal winding  301 . 
         [0048]    The return winding  303  has a toroidal slot  310 , a poloidal slot  320 , and a terminal slot  330  (not visible in  FIG. 3A , see  FIG. 3D  instead). The toroidal slot  310  restricts the current circulation in a poroidal direction. The poloidal slot  320  restricts the current circulation in a toroidal direction. The terminal slot  330  is provided to access the start terminal  305 . 
         [0049]      FIGS. 3B and 3C  is a cross-sectional view illustrating a geometry of the surfaced air core  300 . The toroidal winding has a toroidal radius of R from center O, a poloidal radius r from center O′ and a thickness Tt. The toroidal winding  301  is positioned inside and concentric with the return winding  303  and separated by a gap d. The start and the return terminals  305  and  307  are separated from each other. The return winding  303  has a toroidal radius R, a poloidal radius r′ and a thickness Tr. The poloidal radius r′ may also be calculated as r+d. 
         [0050]    The toroidal slot  310  on the return winding  303  has a width Wts. The width Wts may be constant or vary along the toroidal direction. As illustrated in  FIG. 3B , the toroidal slot  310  is provided at a poloidal angle θ equal to 180 degrees, which represents the inner radius, R-r′, of the return winding  303  and runs through the entire perimeter; however, the toroidal slot  310  may be provided at a different poloidal angle θ from the center e.g., 0=90 degrees, and may not cover the entire perimeter of the return winding  303 . The poloidal angle θ is measured from the x or y axis (or horizontal plane) towards the z-axis. The poloidal slot  320  on the return winding  303  has a width Wps. The width Wps may be constant or vary along the poloidal direction. 
         [0051]    In one embodiment the gap d between the toroidal winding  301  and return winding  303  may be varied. For instance, a circular clip may be attached on the outside of the return winding  303 . The circular clip, such as a hose clamp, can be tightened or loosened thus decreasing or increasing the gap d, respectively. The circular clip enables variability of the gap d, which in turn enables a dynamic capacitance control of the surfaced air core  300 . 
         [0052]    Further in another embodiment the return winding can be manufactured by connecting small sections such as small circular pipes to create a complete toroidal shape. The sections can be detachable and may be used to change the size of the poroidal slot  320  by removing one or more of the sections. The sectional toroid design enables variability of the width Wps, which in turn enables a dynamic capacitance control of the surfaced air core  300 . 
         [0053]      FIG. 3D  is a cross-sectional view illustrating the internal structure of the surfaced air core  300 . The toroidal winding has a plate-like spiral winding along the toroidal direction. The plate-like spiral winding is twisted in a clockwise direction from the starting point  305 C and is continuous along the toroidal direction until it returns to the starting point  305 C. A small gap d 1  is maintained between the two adjacent windings. The gap d 1  provides separation between two consecutive turns of the toroidal winding. Further, the gap d 1  is a factor in determining the capacitance of the surfaced air core  300 . The toroidal winding can have a varying width along the toroidal radius R. For each turn, the outer width Wta towards the outer peripheral surface is wider than the inner width Wtb towards the inner peripheral surface. The gap d 1  between plates is usually maintained constant and smaller than the outer width Wta, thus increasing the surface area of a turn. All the turns of the toroidal winding  301  are separated by the gap d between the toroidal winding  301  and return winding  303 . The return winding  303  has a continuous surface and is positioned outside the toroidal winding  301 . 
         [0054]    The start terminal  305  is connected to the return winding  303  and can have a rectangular cross-section. Alternatively, the start terminal  305  may be a hollow circular cross-section. The return terminal  307  is connected to the toroidal winding  301  and can also have a rectangular cross-section. Alternatively, the return terminal  307  may be a hollow circular cross-section. Further, the toroidal winding  301  and the return winding  303  are connected at the connection point  330   a  visible from the terminal slot  330 . The start and the return terminals  305  and  307  are used as inputs and can be connected to a power source (not shown). When the power source is activated, a current starts flowing through the surface air core. Additional terminals may also be provided to connect to multiple inputs or outputs. 
         [0055]      FIG. 3E  is a cross sectional view of the surfaced air core which illustrates the current flow direction. When a power source (not shown) is connected to the surfaced air core, a current IA flows in the clockwise direction along the toroidal winding  301  in the helical direction  310   a  and a current IB flows in the counter-clockwise direction and along the toroidal direction  310   b  in the return winding  303 . Thus, the currents IA and IB are flowing in opposite directions. The current IA generates a magnetic force FA directed towards the center of the toroidal winding  301  and a magnetic field BA (not illustrated). Current IB generates a magnetic force FB directed away from the center of the return winding  303  and a magnetic field BB (not illustrated). Due to the closed loop form of the surfaced air core and the symmetry of the structure, the magnetic fields BA and BB are confined within the toroid. 
         [0056]    According to an embodiment of the present disclosure, the surfaced air core is a plate-like current carrying conductor and does not include wires wound around a core. As shown in  FIG. 3 , the surface area of the structure of the return is non-negligible, and it covers the toroidal winding with the narrow gap d. For the surfaced air core, the self-inductance L s  and internal capacitance C s  can be calculated using equations 2 and 3 as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     s 
                   
                   = 
                   
                     
                       μ 
                       0 
                     
                      
                     
                       μ 
                       r 
                     
                      
                     
                       
                         
                           N 
                           2 
                         
                          
                         
                           r 
                           2 
                         
                       
                       
                         2 
                          
                         
                             
                         
                          
                         R 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     C 
                     s 
                   
                   = 
                   
                     
                       ∈ 
                       0 
                     
                      
                     
                       ∈ 
                       r 
                     
                      
                     
                       
                         4 
                          
                         
                           π 
                           2 
                         
                          
                         rR 
                       
                       d 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0057]    In the above equations 2 and 3, N is the toroidal turn number, R is the toroidal radius, r is the poroidal radius, μ 0  is a constant for the permeability of space, μ r  is the relative permeability of the core, ∈ 0  is the electric constant, ∈ r  is the relative static permittivity of the material between the plates, and d is the distance between the toroidal surface and the return structure. 
         [0058]    At a resonant point the resonant frequency f res  and quality factor Q can be calculated using equations 4 and 5 as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     res 
                   
                   = 
                   
                     1 
                     
                       2 
                        
                       π 
                        
                       
                         
                           
                             L 
                             s 
                           
                            
                           
                             C 
                             s 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   Q 
                   = 
                   
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         L 
                         s 
                       
                     
                     
                       R 
                       s 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0059]    In the above equations 4 and 5, R, is the total stray resistance of L s  and C s . The surfaced air core according to the present disclosure has three features to create high KQ for LC resonance operation including: a low equivalent series resistance (ESR) capacitor (high Q operation), a reduced intrinsic effect (high Q operation), and a flux packing effect (high K operation). 
         [0060]    Sample parameters used are presented in table 1 for the surfaced air core according to the present disclosure. 
         [0000]    
       
         
               
             
               
               
             
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Sample parameters of the surfaced air core 
               
             
          
           
               
                   
                 Parameter 
               
             
          
           
               
                   
                 R 
                   
                   
                   
                   
                   
                 Ls 
                   
                 f res   
               
               
                   
                 (mm) 
                 r (mm) 
                 d (mm) 
                 N 
                 Lr 
                 Er 
                 (nH) 
                 Cs (nF) 
                 (MHz) 
               
               
                   
                   
               
             
          
           
               
                 Value 
                 9 
                 4.5 
                 0.01 
                 12 
                 1 
                 2.2 
                 118 
                 23 
                 3 
               
               
                   
               
             
          
         
       
     
         [0061]    To achieve LC resonance, conventional wired winding requires additional capacitance to set the operation frequency. Consequently, the stray resistance caused by the terminals or capacitor ESR decrease Q. Referring to  FIG. 4 , the surfaced air core structure according to the present disclosure creates an internal capacitance C s  without the need for additional capacitance. Further, the internal capacitance of the surface air core may be adjusted by varying gap size d 1  or inserting a dielectric material within the core. Further, the toroidal winding resistance and the resistance of the capacitor Cx, generated due to the gap d between the toroidal winding and return winding, are shared. For example, the resistance from Cx 1 , Cx 2 , Cx 3  are shared between the toroidal winding  301  and return winding  303 . So, the total stray resistance for the surfaced air core is smaller than for the wired coil. Also, the surfaced air core according to the present disclosure integrates LC into one object while maintaining a high Q value. 
         [0062]      FIGS. 5A and 5B  illustrate the intrinsic effect caused by the magnetic force between the two different directional currents in a toroid core.  FIG. 5A  shows the intrinsic effect for the toroid wire  201  of the wired coil  200 . The wired coil impedance is increased since the skin effect at higher frequency causes a significant increase in the resistance and the current is concentrated at the inner portion of the toroidal conductor. An increased surface area of the current carrying conductor reduces the resistance. As such, the surfaced air core  300  has a lower resistance Rs, which in turn increases the Q-factor as defined in equation 5. 
         [0063]      FIG. 5B  illustrates simulation results confirming the intrinsic effect reduction obtained by the surfaced air core structure of the present disclosure. When the current IB is flowing in a counter-clockwise direction in the return wire  303 , a magnetic force-field FB is created in an outward direction, i.e. away from the center of the circle. Similarly, when the current IA is flowing in a clockwise direction in the toroidal winding  301 , a magnetic force-field FA is created in an inward direction (i.e., towards the center of the circle). The direction of the magnetic force-fields FB and FA are in opposite direction, hence they have a cancelling effect and the effective magnetic force field in the surfaced air core is reduced. 
         [0064]    In general, for a conductor carrying current, a magnetic force is inversely proportional to the distance from the conductor and directly proportional to the current density. A lower magnetic force indicates a lower current density in a conductor. A lower current density implies a higher surface is available for the current to flow, as such a lower resistance is observed. It is well known that resistance is directly proportional to the length and inversely proportional to the surface area. Further, the current density of return winding  303  should be lower than the current density of the toroidal winding  301 . So, effectively, the surfaced air core will have more balanced current density in the toroidal coil and the effective resistance of the surfaced air core is low. This effect contributes to a high Q enabling efficient power transmission. 
         [0065]      FIGS. 6A-6C  illustrate differences in the flux density effect when current is passed through the conventional wired core and the surfaced air core according to the present disclosure, respectively. The amount of current passed through the conventional wired coil  200  and the surfaced air core coil  300  according to the present disclosure is the same. The frequency is set to the resonant point, which can be determined from the LC value of the surfaced air core.  FIG. 6A  illustrates that the wired core  200  with inside return wire  205  (not shown) has an uneven distribution of flux. A higher flux density is observed close to the windings, maximum but unevenly distributed flux is observed in the innermost part of the wired coil.  FIG. 6B  shows that the surface air core  300  has regulated flux and less leakage compared to the wired coil type. Maximum flux is uniformly distributed at the innermost part of the surfaced air core.  FIG. 6C  further illustrates the flux density distribution with respect to the distance X. Along the X axis a coil  601  with center O is marked. The coil  601  may be of wired or surfaced air core type. The circles  605   a  and  605   b  represent the cross-section of the coil  601 . The flux is distributed around the coil  601 . The graphs illustrates that the flux distribution of conventional wired coil, curve  610 , is irregular and has a higher flux density, more than 20 mT, outside the wired coil region. On the other hand, curve  620  indicates that the surfaced air core has a lower flux density outside the coil, less than 5 mT, increases sharply within the toroid and falls sharply towards the center of the coil. Less leakage flux outside the surfaced air core coil indicates low electromagnetic interference to outside devices, and lower disturbances from outer material such as windings, circuit boards, and other metallic material. 
         [0066]      FIGS. 7A-7D  illustrate differences in the flux density effect when an excitation from an outer winding is applied to the conventional wired core and the surfaced air core according to the present disclosure.  FIG. 7A  illustrates the setup for measuring the flux density effect for the conventional wired core. An excitation coil  701  is driven by a current of 1 ampere. The frequency is set as the resonant point f res  determined by the LC value of the surfaced air core coil.  FIG. 7B  shows that the magnetic flux density is minimized at the center of wired core  201  and is maximum where the excitation coil  701  is connected.  FIG. 7C  shows that the magnetic flux density at the surfaced air core  300  is maximum in the toroidal winding  301  and minimum in the return winding  303 . The flux density distributions of  FIGS. 7B and 7C  are further illustrated in the graph of  FIG. 7D . The curve  710  in the graph indicates the wired coil has a higher percentage of flux density concentrated around the primary coil i.e., from 0 to 45 degrees and from 325 to 360 degrees, while away from the primary coil i.e., from 90 to 270 degrees, the flux density in the coil is almost zero. On the other hand, the curve  720  indicates the surfaced air core has much more regulated flux density throughout the coil. 
         [0067]    As discussed above, the surfaced air core according to the present disclosure is highly efficient and can potentially have several applications such as a sensor, an induction motor, a high frequency transformer, a wireless charger, a filter etc. For instance, sensors with higher measurement accuracy can be created using the surfaced air core. The sensor can measure current through a conductor carrying current placed in the vicinity of the surfaced air core by measuring the change in magnetic flux around the current. Because of its metal plate characteristics, the sensor will sense only the magnetic flux inside of the toroid as opposed to a wired coil configuration. 
         [0068]      FIGS. 8A-8C  illustrate application of the surfaced air core coil to a transformer.  FIG. 8A  illustrates the physical setup for a transformer operation. A primary winding  801   a  is attached around the surfaced air core  300  and a secondary winding  803   b , opposite to the primary winding  801   a , is attached around the surface air core  300 .  FIG. 8B  illustrates the circuit diagram in which the primary and secondary windings  801   b  and  803   b , respectively, are wound on the surfaced air core  300 , and input voltage V 1  excites primary coil  801   a  at V 1 =10 V. The secondary winding  803   b  has a voltage V 2  proportionate to the crossed magnetic flux excited by the primary winding  801   b .  FIG. 8C  show the simulation results of the circuit in  FIG. 8B . In this study, a coupling ratio K between primary coil and surfaced air core coil reached greater than 0.8, approximately 0.88. 
         [0069]      FIGS. 8C and 8D  and show a comparison of the coupling ratio for other types of core structure such as wire wound in helical form, in  FIG. 8C , and wire wound in a circular form, in  FIG. 8D . For instance, referring to  FIG. 8C , the K-value for a toroidal wire coil connected to a primary  801   d  and a secondary  803   d  is 0.5. On the other hand, referring to  FIG. 8D , the K-value for wires wound in a circular form  801   e  and  803   e  is 0.1. Thus, for a surfaced air core according to the present disclosure, the coupling ratio K approximately equal to 0.88 is significantly higher than the other air core designs such as wire wound in helical form and wire wound in a circular form. 
         [0070]      FIGS. 9A-9C  illustrate application of the surfaced air core structure to a wireless power transmission application.  FIG. 9A  is a circuit diagram for wireless power transmission using the surfaced air core. The primary and secondary windings  901  and  903  connect series capacitors C 1  and C 2 , respectively, for wireless transmission operation. AC power transmits from primary winding  901  to secondary winding  903  through the surfaced air core coil  300 , which acts as a repeating coil. The power is repeatedly transferred from primary winding  901  to secondary winding  903  via magnetic induction.  FIG. 9B  shows the simulation result for the magnetic flux density distribution. The magnetic flux is packed inside the toroidal winding  301  when it is operated as a repeating coil. A maximum flux density is observed in the center of the toroidal winding  301 , while in the rest of the toroid the flux is evenly distributed with very little leakage flux.  FIG. 9C  illustrates variation in the transmitting power and the efficiency as the secondary capacitance C 2  changes. The efficiency reaches 86% at resonant frequency when a secondary capacitance of 24 nF is used. The transmitting power can be controlled by changing the secondary (receiver side) capacitance C 2 . For instance, as the secondary capacitance C 2  is increased the power transmitted decreases exponentially. Hence, a lower secondary capacitance C 2  is desired for higher power transmission. 
         [0071]      FIG. 10  illustrates application of the surface air core to a multiple input and multiple output power transfer configuration. In this example, three modules are each fitted with a frequency selectable rectifier and a very high frequency (VHF) inverter. Module M 1  is the source of power and modules M 2  and M 3  are receivers. From module M 1  the primary DC power  1010  is converted to AC through a very high frequency (VHF) inverter  1001   a , where the AC current is set at the resonant frequency f res  by the frequency selectable rectifier  1003   a . The AC current has a resonant frequency which creates a resonant magnetic flux  1005  in the surfaced air core. The power transmission has a peak efficiency at the resonant frequency f res , as discussed earlier, with reference to  FIG. 9C . Modules M 2  and M 3  are connected to a frequency selectable receiver  1003   b  and  1003   c , respectively, and a VHF inverter  1001   b  and  1001   c  respectively. Module M 2  receives AC power from the surfaced air core  300  and is rectified to produce DC power via the frequency selectable rectifier  1003   b . Similarly, module M 3  receives AC power from the surfaced air core  300  and is rectified to produce DC power via the frequency selectable rectifier  1003   c . The above setup can produce various modes of operation based on the receiving  1  frequency of modules M 2  and M 3 . For example, in complete mismatch mode both M 2  and M 3  are set at a frequency outside the frequency range of module M 1 . In partial mismatch mode, module M 2  is set close to the resonant frequency f res , while module M 3  is set at a frequency outside the frequency range of the module M 1 . In energy distribution mode both modules M 2  and M 3  are set at frequencies within the frequency bandwidth of module M 1 . The power transmission characteristics of each mode are illustrated in  FIGS. 11A-11C . 
         [0072]      FIG. 11A  illustrates the power distribution for complete mismatch mode. In this mode, modules M 2  and M 3  are outside the frequency bandwidth of module M 1  or out-of-phase with module M 1 . All the power is stored as reactive power and there is no net transfer of energy.  FIG. 11B  is the case where module M 2  is set at the same resonating frequency as module M 1  or in other words module M 2  is in phase with module M 1 , while module M 3  is out-of-phase with module M 1 . In this case, energy transmits from module M 1  to module M 2 . Module M 2  absorbs most all of the AC power while no power is transferred to module M 3 .  FIG. 11C  illustrates the power distribution in the energy distribution mode. Modules M 2  and M 3  are using different frequency receivers both within the frequency bandwidth of module M 1 . In this case, power is partially absorbed by module M 2  and partially by module M 3 . 
         [0073]      FIGS. 12A-12D  illustrate a sample fabrication of the surfaced air core using a three-dimension (3D) printing technique. First a 3D computer assisted drawing (CAD) model of the toroidal winding  301  and return winding are constructed. The geometry of the surfaced air core inductor was illustrated in  FIG. 3 . Then the 3D CAD model of the surface air core is printed using a 3D printer. The 3D printer may employ a metal, plastic or other suitable material to produce a physical 3D artifact. The physical artifact may be manufactured as a single unit or in parts. Individual parts may be 3D printed and assembled to produce the final physical 3D artifact. In an embodiment of the present disclosure the surfaced air core is manufactured in parts and assembled to produce the final physical 3D artifact of the surfaced air core.  FIGS. 12A-12C  are images of different parts of the surfaced air core  300 . The return winding is manufactured in two parts  303   a  and  303   b  as shown in  FIGS. 12A and 12C , while the toroidal winding  300  is manufactured as a single unit as shown in  FIG. 12B . Referring to  FIG. 12D , the return winding halves  303   a  and  303   b  are assembled around the toroidal winding  301  to build the surfaced air core  300 . The return winding halves  303   a  and  303   b  can be joined together using various joining methods such as welding or laser sintering. Further, each part of the surfaced air core can be fabricated using different materials or a combination of materials such as sterling silver and copper, two very good electrically and thermally conductive material. 
         [0074]    Alternatively, the 3D printer can use a castable material such as plastic to produce the physical 3D artifact of the surfaced air core. A plastic mold of the toroidal winding and the return winding of the surfaced air core may be created. The inductor can be printed in resin using a low cost stereo-lithography or laser sintering 3D printer. Further, the plastic mold of the toroidal winding and the return winding of the surfaced air core inductor can be used in the casting process to fabricate the surface air core from desired material such as ferrite. 
         [0075]    The surface air core manufacturing is not limited to 3D printing techniques. Alternatively, several other techniques may be used to manufacture the surface air core. For instance, a toroidal winding of desired geometry can be fabricated by passing a sheet metal of sterling silver, for instance, through rollers followed by molding or 3D printing of the return winding over the toroidal winding. Depending on the material used, additional heat treatment may be required before passing the sheet metal through the rollers or before the molding process. The simulation results of this model is shown in  FIG. 9B . 
         [0076]    It should be understood that this technology when embodied is not limited to the above-described embodiments and that various modifications, variations and alternatives may be made of this technology so far as they are within the spirit and scope described thereof.