Patent Publication Number: US-2022239154-A1

Title: Annular resonator and wireless power transmission device including annular resonator

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a Bypass Continuation Application of International Application No. PCT/KR2022/001118 designating the United States, which was filed on Jan. 21, 2022, and is based on and claims priority under 35 U.S.C. § 119 to Korean Patent Application No. 10-2021-0010259, which was filed in the Korean Intellectual Property Office on Jan. 25, 2021, the entire disclosure of each of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     1. Field 
     The disclosure relates generally to a power transmission device, and more particularly, to an annular resonator and a wireless power transmission device including an annular resonator 
     2. Description of Related Art 
     A wireless charging technology refers to the use of wireless power transmission/reception such that a battery of a mobile phone can be automatically charged when placed on a wireless power transmission device (for example, charging pad), without connecting the mobile phone to a separate charging connector. Such a wireless charging technology is advantageous in that no connector is necessary to supply power to an electronic product, thereby improving the waterproofing function, and no wired charger is necessary, thereby improving the portability of the electronic device. 
     Recent development of wireless charging technologies has been followed by research regarding methods for supplying power from a wireless power transmission device to wireless power reception devices, thereby charging the reception devices. Wireless charging technologies include an electromagnetic induction type using coils, a resonance type using resonance, and a radio frequency (RF)/microwave radiation type in which electric energy is converted into microwaves, which are then transferred. 
     Wireless charging technologies using the electromagnetic induction type or the resonance type have recently been widespread in connection with electronic devices such as smartphones. If a wireless power transmitting unit (PTU) (for example, wireless power transmission device) and a wireless power receiving unit (PRU) (for example, smartphone or wearable electronic device) contact or approach within a designated distance, the battery of the PRU may be charged by a method such as electromagnetic induction or electromagnetic resonance between the transmitting coil or resonator of the PTU and the receiving coil or resonator of the PRU. 
     A PTU or wireless power transmission device may include a resonator or coil capable of generating an inductive magnetic field if an electric current flows according to the resonance type or induction type. The resonance may have a varying shape causing varying characteristics regarding wireless power transmission. 
     For example, if the resonator is implemented as an annular resonator, the annular resonator may have a circular section and may be structured to have symmetry between the inner surface, which faces from the resonator surface to the center portion, and the outer surface, which faces the outer periphery of the resonator. 
     Magnetic fields may be formed through the annular resonator irrespective of the sectional structure of the annular resonator such that the type of a magnetic field formed on the inner surface of the annular resonator may differ from that of a magnetic field formed on the outer surface. 
     If the inner and outer surface types of the annular resonator are formed in a symmetric structure, there is no alignment with the magnetic field radiation type, thereby increasing current crowding. In addition, the flow of electric current is nonuniform, thereby increasing resistance. This causes degrading of the resonator efficiency. 
     As such, there is a need in the art for a resonator that mitigates the current crowding and increased resistance of the prior art resonator. 
     SUMMARY 
     The disclosure has been made to address at least the above-mentioned problems and/or disadvantages and to provide at least the advantages described below. 
     Accordingly, an aspect of the disclosure is to provide an annular resonator and a wireless power transmission device including an annular resonator, wherein the curvature of the inner surface of the annular resonator, which faces from the surface of the resonator towards the center portion, and the curvature of the outer surface of the annular resonator, which faces the outer periphery of the resonator, are aligned with the curvature of a magnetic field formed by the resonator, thereby improving the wireless power transmission efficiency of the resonator. 
     Another aspect of the disclosure is to provide an annular resonator and a wireless power transmission device including an annular resonator, wherein the curvature of the inner surface of the resonator section of the annular resonator and that of the outer surface of the annular resonator are aligned with the curvature of a magnetic field formed by the resonator, thereby reducing current crowding and providing a uniform flow of electric current which reduces resistance. 
     Another aspect of the disclosure is to provide an annular resonator and a wireless power transmission device including an annular resonator, wherein the curvature of the inner surface of the resonator section of the annular resonator and that of the outer surface of the annular resonator are aligned with the curvature of a magnetic field formed by the resonator, thereby increasing the quality (Q)-factor, improving the transmission efficiency of the wireless power transmission device, and increasing the transmission distance. 
     In accordance with an aspect of the disclosure, a resonator includes a conductor formed on a surface of an annular shaped structure and having a first end and a second end opposite to the first end, and a capacitor having a first end and a second end opposite to the first end, wherein a radius of curvature of a first side facing a center portion of the annular shaped structure is smaller than a radius of curvature of a second side facing an outer periphery of the annular shaped structure, and wherein the first end and the second end of the conductor are electrically connected to the first end and the second end of the capacitor, respectively. 
     In accordance with an aspect of the disclosure, a resonator includes an annular shaped structure, and conductor formed on a surface of the annular shaped structure, wherein, in a cross section of the annular shaped structure, a first area of a first region formed by a first side facing a center portion of the annular shaped structure among regions formed outside the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure is greater than a second area of a second region formed by a second side facing the outer periphery of the annular shaped structure. 
     In accordance with an aspect of the disclosure, a resonator includes an annular shaped structure, and a conductor formed on a surface of the annular shaped structure, wherein, in a cross section of the annular shaped structure, a maximum length in a first direction perpendicular to a direction from the annular shaped structure toward a center portion of the annular shaped structure is greater than a maximum length in a second direction corresponding to a direction facing the center portion of the annular shaped structure. 
     In accordance with an aspect of the disclosure, a wireless power transmission device includes an amplifying circuit configured to amplify input power, an impedance matching circuit electrically connected to the amplifying circuit, a feeding loop electrically connected to the impedance matching circuit, and a resonator electromagnetically coupled to the feeding loop, wherein the resonator comprises a conductor formed on a surface of the annular shaped structure and having a first end and a second end opposite to the first end, and the capacitor having a first end and a second end opposite to the first end, and wherein a radius of curvature of a first side facing a center portion of the annular shaped structure is smaller than a radius of curvature of a second side facing an outer periphery of the annular shaped structure, and the first end and the second end of the conductor and the first end and the second end of the capacitor are electrically connected to each other, respectively. 
     In accordance with an aspect of the disclosure, a wireless power transmission device includes an amplifying circuit configured to amplify input power, an impedance matching circuit, and a resonator, wherein the resonator comprises a conductor formed on a surface of the annular shaped structure, and wherein, in a cross section of the annular shaped structure, a first area of a first region formed by a first side facing a center portion of the annular shaped structure among regions formed outside the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure is greater than a second area of a second region formed by a second side facing the outer periphery of the annular shaped structure. 
     In accordance with an aspect of the disclosure, a wireless power transmission device includes an amplifying circuit configured to amplify input power, an impedance matching circuit, and a resonator, wherein the resonator comprises a conductor formed on a surface of the annular shaped structure, and wherein, in a cross section of the annular shaped structure, a maximum length in a first direction perpendicular to a direction facing a center portion of the annular shaped structure from the annular shaped structure is greater than a maximum length in a second direction facing the center portion of the annular shaped structure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, features, and advantages of certain embodiments of the disclosure will be more apparent from the following detailed description taken in conjunction with the accompanying drawings, in which: 
         FIG. 1A  illustrates a wireless power transmission device and a wireless power reception device according to an embodiment; 
         FIG. 1B  is a perspective view of an annular resonator according to an embodiment; 
         FIG. 2  illustrates the strength of a magnetic field formed around an annular resonator according to an embodiment; 
         FIG. 3  illustrates a cross section of an annular resonator according to an embodiment; 
         FIG. 4A  illustrates a cross section of an annular resonator according to an embodiment; 
         FIG. 4B  illustrates a cross section of an annular resonator according to an embodiment; 
         FIG. 5  illustrates the distance between a cross section and a center portion of an annular resonator according to an embodiment; 
         FIG. 6  illustrates the distance between a transmission-side resonator and a reception-side resonator according to an embodiment; 
         FIG. 7  illustrates a manufacturing method of an annular resonator according to an embodiment; 
         FIG. 8  illustrates a manufacturing method of an annular resonator according to an embodiment; 
         FIG. 9A  illustrates a wireless power transmission device including an annular resonator according to an embodiment; 
         FIG. 9B  illustrates a wireless power transmission device including an annular resonator according to an embodiment; 
         FIG. 10  illustrates the distance between a transmission-side resonator and a reception-side resonator according to an embodiment; 
         FIG. 11  illustrates a Q-factor and a coupling coefficient according to a cross section of an annular resonator according to an embodiment; and 
         FIG. 12  illustrates a Q-factor and a coupling coefficient according to a cross section of an annular resonator according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, embodiments of the disclosure will be described in detail with reference to the accompanying drawings. It should be noted that, in the drawings, the same or like elements are designated by the same or like reference signs as much as possible. In the following description and drawings, a detailed description of known functions or configurations that may make the subject matter of the disclosure unnecessarily unclear will be omitted. 
     It should be appreciated that embodiments of the disclosure and the terms used therein are not intended to limit the technological features set forth herein to particular embodiments and include various changes, equivalents, or alternatives for a corresponding embodiment. With regard to the description of the drawings, similar reference numerals may be used to designate similar or relevant elements. It is to be understood that a singular form of a noun corresponding to an item may include one or more of the items unless the relevant context clearly indicates otherwise. 
     As used herein, each of such phrases as “A or B,” “at least one of A and B,” “at least one of A or B,” “A, B, or C,” “at least one of A, B, and C,” and “at least one of A, B, or C,” may include all possible combinations of the items enumerated together in a corresponding one of the phrases. As used herein, such terms as “a first”, “a second”, “the first”, and “the second” may be used to simply distinguish a corresponding element from another and do not limit the elements in importance or order. It is to be understood that if an element (e.g., a first element) is referred to, with or without the term “operatively” or “communicatively”, as “coupled with,” “coupled to,” “connected with,” or “connected to” another element (e.g., a second element), this indicates that the element may be coupled/connected with/to the other element directly (e.g., wiredly), wirelessly, or via a third element. 
       FIG. 1A  illustrates a wireless power transmission device and a wireless power reception device according to an embodiment. Referring to  FIG. 1A , a wireless power transmission device  160  may transmit power  161  to a wireless power reception device  150  (hereinafter, an electronic device  150  or an external electronic device) wirelessly according to various charging methods. For example, the wireless power transmission device  160  may transmit power  161  according to an induction method, in which case the wireless power transmission device  160  may include a power source, a direct current-alternating current (DC-AC) conversion circuit, an amplifying circuit, an impedance matching circuit, at least one capacitor, at least one coil, and a communication modulation/demodulation circuit. The at least one capacitor may constitute a resonance circuit together with at least one coil. The wireless power transmission device  160  may operate in a method defined in a wireless power consortium (WPC) standard (or, Qi standard). 
     For example, the wireless power transmission device  160  may transmit power  161  according to a resonance type, wherein the wireless power transmission device  160  may include a power source, a DC-AC conversion circuit, an amplifying circuit, an impedance matching circuit, at least one capacitor, at least one resonator or coil, and an out band communication circuit (e.g., a Bluetooth™ low energy (BLE) communication circuit). At least one capacitor and at least one resonator or a coil may constitute a resonance circuit. The wireless power transmission device  160  may operate in a method defined in an alliance for wireless power (A4WP) standard (or an air fuel alliance (AFA) standard). The wireless power transmission device  160  may include a resonator or a coil capable of generating an inductive magnetic field when a current flows according to a resonance method or an induction type. The process in which the wireless power transmission device  160  generates an inductive magnetic field may be expressed as that the wireless power transmission device  160  wirelessly transmits power  161 . In addition, the electronic device  150  may include a coil configured to allow an induced electromotive force to be generated by a magnetic field, which is formed around the coil and varies in strength according to time. The process in which the electronic device  150  generates an induced electromotive force through a resonator or a coil may be expressed as that the electronic device  150  wirelessly receives power  161 . 
     The wireless power transmission device  160  may perform a communication with the electronic device  150  according to an in-band method. For example, the wireless power transmission device  160  or the electronic device  150  may be configured to change a load (or an impedance) in response to data to be transmitted according to an on/off keying modulation scheme. The wireless power transmission device  160  or the electronic device  150  may identify data to be transmitted from a counterpart device by measuring a load change (or an impedance change) based on changes in the magnitude of current, voltage or power of a resonator or a coil. 
     For example, the wireless power transmission device  160  may perform communication with the electronic device  150  according to an out-band (or out-of-band) method. The wireless power transmission device  160  or the electronic device  150  may transmit/receive data by using a short-distance communication module (e.g., a BLE communication module) separately provided with a resonator, a coil, or a patch antenna. 
       FIG. 1B  is a perspective view of an annular resonator according to an embodiment. Referring to  FIG. 1B , the resonator  100  applicable to the wireless power transmission device  160  may be configured in an annular shaped structure which, with reference to the A-A′ axis, a side from a surface toward a center portion of the annular shaped structure may be defined in an inner side of the annular shaped structure, and a side from the surface toward an outer periphery of the annular shaped structure may be defined in an outer side of the annular shaped structure. A slit  101  may be formed through at least a part of the annular shaped structure and may function as a capacitor. When the annular shaped structure is connected to a circuit part of the wireless power transmission device  160 , the annular shaped structure and a capacitor may be connected to the circuit part through both ends through which the slit  101  is formed. A conductor may be formed on the surface of the annular shaped structure. In the annular shaped structure, when a current is supplied to the both ends through which the slit  101  is formed, a high-frequency wave may be transmitted through the surface of the annular shaped structure. 
       FIG. 2  illustrates the strength of a magnetic field formed around an annular resonator according to an embodiment. Referring to  FIG. 2 , the forms of a magnetic field formed from the inner side toward a center portion toward among the surface of the annular resonator  100  and a magnetic field formed from the outer side toward an outer periphery among the surface of the annular resonator  100  may be different. For example, the strength of a magnetic field formed from the inner side toward the center portion of the annular resonator  100  may be larger than the strength of a magnetic field formed from the outer side toward the outer periphery of the annular resonator  100 . The curvature of a magnetic field formed from the inner side toward the center portion of the annular resonator  100  may be larger than the curvature of a magnetic field formed from the outer side toward the outer periphery of the annular resonator  100 . A radius of curvature of a magnetic field formed from the inner side toward the center portion of the annular resonator  100  may be smaller than a radius of curvature of a magnetic field formed from the outer side toward the outer periphery of the annular resonator  100 . 
     For example, when a resonator is implemented in an annular resonator, the cross section of the annular resonator may be a circle, and the inner side and the outer side of the resonator may be symmetrically formed. A magnetic field formed through the annular resonator may be irrelevant to the cross sectional structure of the annular resonator, and as illustrated in  FIG. 2 , the form of a magnetic field formed in the inner side of the annular resonator and the form of a magnetic field formed in the outer side of the annular resonator may be different. 
     When the shape of the inner side and the shape of the outer side of the annular resonator are formed in a symmetrical structure, the inner side and the outer side thereof may not be aligned with a radiation form of a magnetic field, which increases a current crowding phenomenon, and a flow of current is non-uniform, thereby causing decreased resonator efficiency as resistance increases. 
     In the annular resonator described herein, the wireless power transmission efficiency can be enhanced by aligning the curvatures of an inner side and an outer side of a resonator cross section with the curvature of a magnetic field formed by the resonator. 
       FIG. 3  illustrates a cross section of an annular resonator according to an embodiment. Referring to  FIG. 3 , with reference to the A-A′ axis in the annular resonator  100  of  FIG. 1B , a side toward a center portion among the surface of the annular shaped structure may be defined in an inner side of the annular shaped structure, and a side toward an outer periphery among the surface of the annular shaped structure may be defined in an outer side of the annular shaped structure. The cross section  300  of the annular resonator  100  may have an asymmetrically formed inner side and outer side in order to align with the curvature of a magnetic field. 
     The curvature of a first side facing the center portion of the annular shaped structure may be greater than the curvature of a second side facing the outer periphery of the annular shaped structure. For example, a radius of curvature of the first side facing the center portion of the annular shaped structure may be smaller than a radius of curvature of the second side facing the outer periphery of the annular shaped structure. For example, the ratio of the curvature of the first side to the curvature of the second side may be greater than 1. The ratio of the curvature radius of the first side to the curvature radius of the second side may be less than 1. 
     An area of an inner region  301  of the cross section  300  of the annular shaped structure may be expressed as A a . A minimum area rectangle configured to receive the cross section  300  of the annular shaped structure may have length W a  in a first direction and length W b  in a second direction. An area of the minimum area rectangle configured to receive the cross section  300  of the annular shaped structure may be W a ×W b . In the cross section of the annular shaped structure, the first direction may correspond to a direction perpendicular to a direction from the annular shaped structure toward the center portion of the annular shaped structure, and W a  may be a maximum length in the first direction of the cross section  300  of the annular shaped structure. In the cross section of the annular shaped structure, the second direction may correspond to a direction from the annular shaped structure toward the center portion of the annular shaped structure, and W b  may be a maximum length in the second direction of the cross section  300  of the annular shaped structure. 
     In the cross section  300  of the annular shaped structure, a first area A b  of a first region  303  formed by the first side facing the center portion of the annular shaped structure among a first region  303  and a second region  302  formed outside the cross section  300  excluding an area A a  of the cross section inner region  301  of the annular shaped structure within the minimum area rectangle configured to receive the cross section  300  of the annular shaped structure may be larger than a second area A c  of a second region  302  formed by the second side facing the outer periphery of the annular shaped structure. For example, the ratio of the first area A b  of the first region  303  formed by the first side facing the center portion of the annular shaped structure to the second area A c  of the second region  302  formed by the second side facing the outer periphery of the annular shaped structure may be greater than 1 as in the following Equation (1). 
     
       
         
           
             
               
                 
                   
                     
                       A 
                       b 
                     
                     
                       A 
                       c 
                     
                   
                   &gt; 
                   1 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The cross section  300  of the annular shaped structure may be formed in a curved surface as illustrated in  FIG. 3 , and alternatively, may be formed in a polygon as illustrated in  FIGS. 4A and 4B . 
     In the cross section  300  of the annular shaped structure, the maximum length W a  in a first direction perpendicular to a direction from the annular shaped structure toward the center portion of the annular shaped structure may be greater than the maximum length W b  in the second direction facing the center portion of the annular shaped structure. For example, the ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction corresponding to a direction facing the center portion of the annular shaped structure may be greater than 1 and less than 10 as in the following Equation (2). 
     
       
         
           
             
               
                 
                   1 
                   &lt; 
                   
                     
                       W 
                       a 
                     
                     
                       W 
                       b 
                     
                   
                   &lt; 
                   
                     1 
                     ⁢ 
                     0 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction facing the center portion of the annular shaped structure may be greater than 3 and less than 5. The ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction facing the center portion of the annular shaped structure may be greater than 1.5 and less than 5. The ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction facing the center portion of the annular shaped structure may be greater than 2 and less than 4.5. 
       FIGS. 4A and 4B  illustrate a cross section of an annular resonator formed in a polygonal shape according to an embodiment. 
     Referring to  FIG. 4A , in a cross section of the annular shaped structure formed in a polygon, a first area A b1  of a first region  413  formed by a first side facing a center portion of the annular shaped structure among a first region  413  and a second region  412  formed outside the cross section excluding an area A a1  of a cross section inner region  411  of the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure may be greater than a second area A c1  of a second region  412  formed by the second side facing the outer periphery of the annular shaped structure. For example, the ratio of the first area A b1  of the first region  413  formed by the first side facing the center portion of the annular shaped structure to the second area A c1  of a second region  412  formed by the second side facing the outer periphery of the annular shaped structure may be greater than 1 as in the following Equation (3). 
     
       
         
           
             
               
                 
                   
                     
                       A 
                       
                         b 
                         ⁢ 
                         1 
                       
                     
                     
                       A 
                       
                         c 
                         ⁢ 
                         1 
                       
                     
                   
                   &gt; 
                   1 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Referring to  FIG. 4B , in a cross section of the annular shaped structure formed in a polygon, a first area A b2  of a first region  423  formed by a first side facing a center portion of the annular shaped structure among a first region  423  and a second region  422  formed outside the cross section excluding an area A a2  of a cross section inner region  421  of the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure may be greater than a second area A c2  of a second region  422  formed by the second side facing the outer periphery of the annular shaped structure. For example, the ratio of the first area A b2  of the first region  423  formed by the first side facing the center portion of the annular shaped structure to the second area A c2  of the second region  422  formed by the second side facing the outer periphery of the annular shaped structure may be greater than 1 as in the following Equation (4). 
     
       
         
           
             
               
                 
                   
                     
                       A 
                       
                         b 
                         ⁢ 
                         2 
                       
                     
                     
                       A 
                       
                         c 
                         ⁢ 
                         2 
                       
                     
                   
                   &gt; 
                   1 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
       FIG. 5  illustrates the distance between a cross section and a center portion of an annular resonator according to an embodiment.  FIG. 6  illustrates the distance between a transmission side resonator and a reception side resonator according to an embodiment. 
     Referring to  FIGS. 5 and 6 , on a plane with line A-A′ as an axis, a maximum radius of an annular shaped structure may be referred to as a first radius R. In the annular shaped structure, with reference to a boundary between a first side facing a center portion of the annular shaped structure and a second side facing an outer periphery of the annular shaped structure, a radius of the annular shaped structure may be referred to as a second radius R e . 
     In a cross section  300  of the annular shaped structure, a Q-factor increases as a maximum length W b  in a second direction facing the center portion of the annular shaped structure increases, but the second radius R e  through which an average current flows decreases. Therefore, a coupling coefficient k between a resonator  100  of a wireless power transmission device and a resonator  600  of a wireless power reception device may decrease. A Q-factor increases as a maximum length W a  in a first direction perpendicular to a direction facing the center portion of the annular shaped structure increases, but when a minimum distance D real  between the resonator  100  of a wireless power transmission device and the resonator  600  of a wireless power reception device is fixed, as illustrated in  FIG. 6 , a distance D between a central axis of the resonator  100  of a wireless power transmission device and a central side of the resonator  600  of a wireless power reception device increases. Therefore, a coupling coefficient between resonators may decrease. 
     When the condition of the following Equation (5) is satisfied, an efficiency of a wireless power transmission device may relatively increase. 
     
       
         
           
             
               
                 
                   1 
                   &lt; 
                   
                     R 
                     
                       W 
                       a 
                     
                   
                   &lt; 
                   20 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
       FIG. 7  illustrates a manufacturing method of an annular resonator according to an embodiment. Referring to  FIG. 7 , in a resonator  100  of a wireless power transmission device, in the case of a high-frequency wave (e.g., 6.78 megahertz (MHz)), a current may flow only on a surface the resonator  100  of a wireless power transmission device. Therefore, a conductor  710  (e.g., copper) may be formed on the surface of the resonator  100 . To this end, as illustrated in  FIG. 7 , the conductor  710  may be plated or deposited on the surface of a resonator body  720 . 
       FIG. 8  illustrates a manufacturing method of an annular resonator according to an embodiment. Referring to  FIG. 8 , conductor  810  is press-molded by a mold  820 . For example, a lower conductor  810   a  is press-molded by a lower mold  820   a  and an upper conductor  810   b  is press-molded by an upper mold  820   b . An upper structure and a lower structure may then be joined to manufacture an annular resonator  100 . The manufacturing method of an annular resonator may vary, and may not be limited to the method illustrated in  FIG. 7 or 8 . 
       FIGS. 9A and 9B  illustrate a wireless power transmission device including an annular resonator according to an embodiment. Referring to  FIG. 9A , a wireless power transmission device may include an amplifying circuit  914 , an impedance matching circuit  913 , a feeding loop  912 , and an annular resonator  100 . The wireless power transmission device may amplify power to be transmitted, through the amplifying circuit  914 , and then may transmit the amplified power to the feeding loop  912  through the impedance matching circuit  913 . The feeding loop  912  may form a magnetic field by a supplied current, and the annular resonator  100  may be electromagnetically coupled to the feeding loop  912  and thus be magnetically induced. The annular resonator  100  may form a magnetic field by power induced through a coupling with the feeding loop  912  to transmit power to a wireless power reception device. A slit  101  may be formed through a side of the annular resonator  100 , and a capacitor  911  may be added to the slit  101 . 
     Referring to  FIG. 9B , a wireless power transmission device may include an amplifying circuit  923 , an impedance matching circuit  922 , and an annular resonator  100 . The wireless power transmission device may amplify power to be transmitted, through the amplifying circuit  923 , and then may transmit the amplified power to the annular resonator  100  through the impedance matching circuit  922 . The annular resonator  100  may form a magnetic field by a current supplied from the impedance matching circuit  922  to transmit power to a wireless power reception device. A slit  101  may be formed through a side of the annular resonator  100 , and a capacitor  921  may be added to the slit  101 . The capacitor  921  may be included in the impedance matching circuit  922 . 
       FIG. 10  illustrates the distance between a transmission-side resonator and a reception-side resonator according to an embodiment. Referring to  FIG. 10 , a transmission-side resonator of a wireless power transmission device and a reception-side resonator of a wireless power reception device may be disposed to be a predetermined distance spaced apart from each other in a z-axis direction. An induced electromotive force may be generated in a reception-side resonator by a magnetic field formed from a transmission-side resonator to transmit power from a wireless power transmission device to a wireless power reception. 
       FIG. 11  illustrates a Q-factor and a coupling coefficient according to a cross section of an annular resonator according to an embodiment. Referring to  FIG. 11 , in the cross section  300  of annular shaped structure illustrated in  FIG. 3 , a Q-factor and a coupling coefficient k may vary according to the ratio of the first area A b  of the first region  303  formed by the first side facing the center portion of the annular shaped structure to the second area A e  of the second region  302  formed by the second side facing the outer periphery of the annular shaped structure. 
     Referring to  FIG. 11 , it may be known that a Q-factor and a coupling coefficient k increase as A b /A c  increases. Therefore, in the cross section of the annular shaped structure, a Q-factor and a coupling coefficient may be increased by decreasing the radius of curvature of the inner side to be smaller than the radius of curvature of the outer side. For example, when A b /A c  is 1 rather than being less than 1, it may be known that a Q-factor and a coupling coefficient increase, and when A b /A c  is greater than 1 instead of being 1, it may be known that a Q-factor and a coupling coefficient increase. 
       FIG. 12  illustrates a Q-factor and a coupling coefficient according to a cross section of an annular resonator according to an embodiment. Referring to  FIG. 12 , in the cross section  300  of the annular shaped structure as described above in reference to Equation (2), a Q-factor and a coupling coefficient may increase as the maximum length W a  in a first direction perpendicular to a direction from the annular shaped structure toward the center portion of the annular shaped structure is greater than the maximum length W b  in the second direction facing the center portion of the annular shaped structure. 
     Referring to  FIG. 12 , as in Equation (2), when the ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction facing the center portion of the annular shaped structure is greater than 1 and is less than 10, a Q-factor and a coupling coefficient may increase. 
     When the ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction facing the center portion of the annular shaped structure is greater than 3 and less than 5, a Q-factor may closely approach a maximum value, and a coupling coefficient may be at least 0.012. 
     When the ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction facing the center portion of the annular shaped structure is greater than 1.5 and less than 5, a Q-factor may be at least 1200 and a coupling coefficient may be at least 0.012. 
     When the ratio of the maximum length W a  in the first direction to the maximum length W b  in the second direction facing the center portion of the annular shaped structure is greater than 2 and less than 4.5, a Q-factor may be at least 1225 and a coupling coefficient may be at least 0.0125. 
     As described above, a resonator includes a conductor formed on a surface of an annular shaped structure, wherein a radius of curvature of a first side facing a center portion of the annular shaped structure is smaller than a radius of curvature of a second side facing an outer periphery of the annular shaped structure. 
     In a cross section of the annular shaped structure, a first area A b  of a first region formed by the first side facing the center portion of the annular shaped structure among regions formed outside the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure is greater than a second area A c  of a second region formed by the second side facing the outer periphery of the annular shaped structure. 
     As described above, a resonator includes a conductor formed on a surface of an annular shaped structure in which a first area A b  of a first region formed by a first side facing a center portion of the annular shaped structure among regions formed outside the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure is greater than a second area A c  of a second region formed by a second side facing the outer periphery of the annular shaped structure. 
     The cross section of the annular shaped structure is formed in a curved surface. 
     The cross section of the annular shaped structure is formed in a polygon. 
     As described above, a resonator includes a conductor formed on a surface of an annular shaped structure in which a maximum length W a  in a first direction perpendicular to a direction from the annular shaped structure toward a center portion of the annular shaped structure is greater than a maximum length W b  in a second direction corresponding to a direction facing the center portion of the annular shaped structure. 
     A ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 3 and less than 5. 
     A ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 1 and less than 10. 
     A ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 1.5 and less than 5. 
     The ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 2 and less than 4.5. 
     As described above, a wireless power transmission device includes an amplifying circuit configured to amplify input power, an impedance matching circuit, and a resonator including a conductor formed on a surface of an annular shaped structure, and a radius of curvature of a first side facing a center portion of the annular shaped structure is smaller than a radius of curvature of a second side facing an outer periphery of the annular shaped structure. 
     In a cross section of the annular shaped structure, a first area A b  of a first region formed by the first side facing the center portion of the annular shaped structure among regions formed outside the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure is greater than a second area A c  of a second region formed by the second side facing the outer periphery of the annular shaped structure. 
     As described above, a wireless power transmission device includes an amplifying circuit configured to amplify input power, an impedance matching circuit, and a resonator including a conductor formed on a surface of an annular shaped structure, and in a cross section of the annular shaped structure, a first area A b  of a first region formed by a first side facing a center portion of the annular shaped structure among regions formed outside the annular shaped structure within a minimum area rectangle configured to receive the cross section of the annular shaped structure is greater than a second area A c  of a second region formed by a second side facing the outer periphery of the annular shaped structure. 
     The cross section of the annular shaped structure is formed in a curved surface. 
     The cross section of the annular shaped structure is formed in a polygon. 
     As described above, a wireless power transmission device includes an amplifying circuit configured to amplify input power, an impedance matching circuit, and a resonator including a conductor formed on a surface of an annular shaped structure, and in a cross section of the annular shaped structure, a maximum length W a  in a first direction perpendicular to a direction facing a center portion of the annular shaped structure from the annular shaped structure is greater than a maximum length W b  in a second direction corresponding to a direction facing the center portion of the annular shaped structure. 
     A ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 3 and less than 5. 
     A ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 1 and less than 10. 
     A ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 1.5 and less than 5. 
     The ratio of the maximum length in the first direction to the maximum length in the second direction is greater than 2 and less than 4.5. 
     Herein, each element (e.g., module or program) of the above-described elements may include a single entity or multiple entities, and some of the multiple entities may be separately disposed in another element. One or more of the above-described elements or operations may be omitted, or one or more other elements or operations may be added. Alternatively or additionally, a plurality of elements (e.g., modules or programs) may be integrated into a single element. In such a case, the integrated element may still perform one or more functions of each of the plurality of elements in the same or similar manner as they are performed by a corresponding one of the plurality of elements before the integration. Operations performed by the module, the program, or another element may be performed sequentially, in parallel, repeatedly, or heuristically, or one or more of the operations may be executed in a different order or omitted, or one or more other operations may be added. 
     While the present disclosure has been described with reference to various embodiments, various changes may be made without departing from the spirit and the scope of the present disclosure, which is defined, not by the detailed description and embodiments, but by the appended claims and their equivalents.