Abstract:
An antenna that includes a first element extending from a connection point, and has a curvature such that a first tip end of the first element extends in a direction toward the connection point. A second element is connected to the connection point, and has a second tip end that extends in a direction away from the connection point, the second tip being disposed within an outer periphery of the first element. A distance between a portion of the first element that is parallel to the second element is greater than λ gx /100, where λ gx  represents an effective wavelength of a first anti-resonance frequency.

Description:
BACKGROUND 
     Technical Field 
     The present disclosure relates to an antenna device and a corresponding terminal for the antenna device. 
     Description of Related Art 
     Terminal devices, such as cellular phones, smart phones, and tablet devices, typically include an antenna apparatus with which to transmit and receive voice and/or data signals. The frequency bandwidth utilization is increasing in these terminal devices. In order to cope with the increase in bandwidth, there exists a method of providing multiple antennas to accommodate a wider frequency spectrum. Additionally, there exists a method of carrying out bandwidth increases utilizing a single antenna. 
     When a single antenna is used, it is preferable that any increase in bandwidth capacity does not unnecessarily increase the antenna size. Additionally, when carrying out a bandwidth increase using a single antenna, it is preferable not only to ensure favorable performance of each frequency band, but also to optimize Specific Absorption Rate (SAR) of each band to counter effects of SAR that are detrimental to antenna and/or terminal device performance. Previously, conventional cellular phone design was mainly concerned with reducing SAR of a user&#39;s head during a telephone call. However, in the case of a smart phone, a design should consider not only reducing SAR of the user&#39;s head during telephone calls, but also SAR of the user&#39;s body at the time of a data transmission (e.g., Internet transmissions, streaming, etc.), which are often being performed while the smart phone is stored close to the body (e.g., in the pocket of a coat). 
     U.S. Pat. No. 7,990,321 describes an exemplary multi-band antenna. The antenna as described in this literature is made to support multiple frequency bands (e.g., Global System for Mobile Communications (GSM), Global Positioning System (GPS), Digital Cellular Service (DCS), Personal Communication Service (PCS)) using one antenna feeding portion for passing electromagnetic signals in a plurality of frequency bands. Since a coupled grounding portion is provided in the case of the antenna, it is a premise of the literature to arrange and use the multi-band antenna on a circuit board substrate. For this reason, the countermeasure against SAR is left to the circuit side of a terminal device. This arrangement is problematic because any adjustments needed in the circuit board components involve undesirable increases in manufacturing and materials costs, as well as new printed circuit board (PCB) layout design labor costs. 
     SUMMARY 
     Among other things, the present disclosure describes an antenna and corresponding terminal device for providing multi-band frequency response, while countering against the effects of SAR. 
     An antenna of the present disclosure may include a first element extending from a connection point. The first element may have a curvature such that a first tip end of the first element extends in a direction toward the connection point. The antenna may include a second element that is connected to the connection point. The second element may have a second tip end that extends in a direction away from the connection point. The second tip may be disposed within an outer periphery of the first element. A distance between a portion of the first element that is parallel to the second element may be greater than λ gx /100, where λ gx  represents an effective wavelength of a first anti-resonance frequency. 
     The foregoing general description of the illustrative embodiments 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 
       A more complete appreciation of this disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
         FIG. 1  shows an exemplary terminal device and antenna arrangement; 
         FIG. 2  illustrates a top-view perspective of the arrangement in  FIG. 1 ; 
         FIG. 3  illustrates a disassembled view of the  FIG. 2  elements; 
         FIG. 4  illustrates a perspective view showing an exemplary antenna; 
         FIG. 5  shows the exemplary antenna of  FIG. 4  from an alternate perspective; 
         FIG. 6  illustrates a block diagram of an exemplary terminal device; 
         FIG. 7  illustrates dimensional features of an exemplary antenna; 
         FIGS. 8A and 8B  respectively illustrate current phasors and magnetic field vectors of an exemplary antenna; 
         FIGS. 9A and 9B  respectively illustrate current phasors and magnetic field vectors of another exemplary antenna; 
         FIGS. 10A-D  illustrate SAR simulations for an exemplary antenna; 
         FIGS. 11A-D  illustrate SAR simulations for another exemplary antenna; 
         FIGS. 12A and 12B  illustrate directivity characteristics for an exemplary antenna; 
         FIGS. 13A and 13B  illustrate directivity characteristics for another exemplary antenna; 
         FIGS. 14A and 14B  show impedance characteristics for exemplary antennas; 
         FIG. 15  illustrates radiation efficiency for the antennas of  FIGS. 14A and 14B ; 
         FIG. 16  illustrates radiation efficiency for an alternate condition using the antennas of  FIGS. 14A and 14B ; 
         FIGS. 17A and 17B  illustrate directivity features for an antenna without a second element; 
         FIGS. 18A and 18B  illustrate directivity features for an antenna that includes a second element; 
         FIG. 19  shows exemplary SAR measurements in tabular form for the case in which an exemplary antenna does not include a second element, as well as the case in which the second element is included; 
         FIGS. 20A-20N  illustrate exemplary modifications for a second element on an exemplary antenna; 
         FIGS. 21A-21I  illustrate exemplary modifications for a first element on an exemplary antenna; 
         FIGS. 22 and 23  illustrate exemplary configurations of an antenna using alternate configurations of first and second elements; 
         FIG. 24  illustrates current phasors of the exemplary antenna shown in  FIG. 22 ; 
         FIG. 25  illustrates magnetic field vectors generated in the exemplary antenna shown in  FIG. 22 ; 
         FIGS. 26A-D  illustrate antenna directivity characteristics for an exemplary antenna; 
         FIGS. 27A-D  illustrate antenna directivity characteristics for an exemplary case in which the first element the antenna from  FIGS. 26A-D  is modified; 
         FIGS. 28A-B  and  29 A-B illustrate directivity characteristics resultant from modifying parameters of the antenna of  FIG. 27A ; 
         FIGS. 30A and 30B  show impedance characteristics for exemplary antennas; 
         FIG. 31  provides a graph illustrating radiation efficiency for exemplary antennas; 
         FIG. 32  provides a graph illustrating radiation efficiency of the antennas of  FIG. 31  under alternate conditions; 
         FIGS. 33A-B  and  34 A-B illustrate directivity for the cases shown in  FIGS. 30A and 30B ; 
         FIGS. 35A and 35B  show impedance characteristics for exemplary antennas; 
         FIG. 36  provides a graph illustrating radiation efficiency for exemplary antennas; 
         FIG. 37  provides a graph illustrating radiation efficiency of the antennas of  FIG. 36  under alternate conditions; 
         FIGS. 38A-B  and  39 A-B illustrate directivity for two cases shown in  FIGS. 35A and 35B ; 
         FIGS. 40A and 40B  show impedance characteristics for exemplary antennas; and 
         FIGS. 41A-B  and  42 A-B illustrate directivity for two cases shown in  FIGS. 40A and 40B . 
     
    
    
     DETAILED DESCRIPTION 
     Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views. 
       FIG. 1  illustrates an example of a terminal device  1 , which shows one aspect of an exemplary antenna arrangement. Terminal device  1  includes a circuit board  10 , which may include communication processing circuitry described in later paragraphs. The circuit board  10  includes an edge part corresponding to an electric power feeding circuit  11  for an antenna  30 . The antenna  30  includes a first element  31  and a second element  32 , which are formed on an elongated circuit board substrate  20 . Elements included in the antenna  30  are electrically connected via conductors, such as copper. The substrate  20  may be connected to the circuit board  10  in such a manner that it “floats” on the substrate  20  surface. The height at which the substrate  20  floats from the circuit board  10  corresponds to the length of a third element  33 , which will be described in further detail in later paragraphs. As a non-limiting example of the multi-band characteristics associated with the antenna  30 , a low frequency band of the antenna  30  may perform transmission and reception at 900 MHz, and a high frequency band of the antenna  30  may perform transmission and reception at 2 GHz. However, it should be appreciated that the present disclosure may easily be adapted such that other frequency bands are used. 
     For illustration purposes,  FIG. 2  illustrates a top-view perspective of the terminal device  1 , and  FIG. 3  illustrates a disassembled view of the circuit board  10  and the substrate  20 . 
     Next,  FIG. 4  illustrates a perspective view showing detail of the antenna  30 . 
     Referring to  FIG. 4 , the three axes dX, dY, and dZ illustrate an orientation of the various elements in the figure. The exemplary antenna  30  may include the first element  31 , the second element  32 , and the third element  33 . The first element  31  may have an elongated structure extending along a first axis (e.g., the dX axis) while bending from a connection point  31   a  to connect with the second element  32  such that the structure of the second element  32  may be enclosed within the first element  31 . A connection point  33   a  of the end of the third element  33  of the antenna  30  may be connected to the electric power feeding circuit  11  of the circuit board  10 . 
     The first element  31  may comprise multiple linear electrically conductive sub-elements, including components  31   b ,  31   c ,  31   d , and  31   e . Each component  31   b ,  31   c ,  31   d , and  31   e  are shown in  FIG. 4  being connected at right angles; however, other arrangements may easily be used, and this configuration is not limiting. The component  31   b  includes the connection point  31   a  and is extended along the longitudinal direction (dX) on a surface  21  of the antenna substrate  20 . The component  31   c  is connected to the component  31   b , and extends in the width direction (dY) on the surface  21  of the antenna substrate  20 . The component  31   c  and the connected component  31   d  are arranged on a side surface  23  of the antenna substrate  20 . The component  31   d  and the connected component  31   e  are arranged on the surface  21  of the antenna substrate  20 . 
     The second element  32  may be L-shaped, where components  32   a  and  32   b  are connected at a right angle. As mentioned above and illustrated in  FIG. 4 , the second element  32  may be arranged such that the components of the first element  31  are positioned around the second element  32 . A tip of the component  31   e  is separated from a tip of the component  32   b.    
     The third element  33  may be connected to the second element  32 . The third element  33  may be a shape that extends along a side surface  22  of the antenna substrate  20  from a lower surface of the antenna  30 . An upright tip of the third element  33  corresponds to the connection point  33   a , which connects with the electric power feeding circuit  11 . Length L3 shown in  FIG. 4  shows the length of the third element  33 . The definition of length L3 of the third element  33  is discussed in further detail in later paragraphs. 
     For illustration purposes,  FIG. 5  shows the exemplary antenna  30  from an alternate perspective. 
     Next,  FIG. 6  illustrates a block diagram of the exemplary terminal device  1 . Terminal device  1  may, e.g., be a mobile phone, a smart phone, a personal digital assistant (PDA), a tablet computer, or the like. 
     Referring to  FIG. 6 , the terminal device  1  may be equipped with the antenna  30 , which may connect to a controller  102  via the electric power feeding circuit  11  and a communication processing circuit  101 . The terminal device  1  may also include an operating portion  103 , a memory  104 , a display  105 , a speaker  106 , a microphone  107 , and a voice processing section  108 . The communication processing circuit  101  processes voice and data signals transmitted to/from the antenna  30 . The processing of the communication processing circuit  101  may include modulating and demodulating signals supplied to/from the antenna  30 . As a non-limiting example, the communication processing circuit  101  may utilize 900 MHz and 2 GHz frequency bands in the processing, and may transmit/receive signals via radio and/or wireless paths to other devices and/or base stations. For example, the terminal device  1  may communicates according to the Long Term Evolution (LTE) specification. 
     The controller  102  is comprised, e.g., of a Central Processing Unit (CPU), which may include one or more processors that are programmed to execute instructions stored in the memory  104  when performing the various features of the terminal device  1 . 
     The operating portion  103  may include various interface elements for performing input on the terminal device  1 . For example, the operating portion  103  may interface with external buttons and/or a touch screen, where detected inputs on these interface elements may generate an operation signal, which the operating portion  103  and/or the controller  102  may utilize for further processing. 
     The memory  104  may consist of a Read Only Memory (ROM), a Random Access Memory (RAM), or combination thereof. For example, data that needs to be stored/memorized for later use may be stored in ROM, while RAM may be used as working memory, e.g., in the case where the controller  102  performs control processing. 
     The display  105  may be a liquid crystal panel, an organic Electro Luminescence (EL) panel, or the like. The display  105  may perform display features regarding, e.g., transmission or receipt of voice and data signals. For example, the display  105  may display information regarding a telephone call, a Web page, a text message, images, or the like. 
     The speaker  106  and the microphone  107  are connected to the voice processing section  108 . The speech-processing part  108  may perform a modulation process to audio data received by the communication processing circuit  101 , and supply it to the speaker  106 . Moreover, the speech-processing part  108  may modulate voice signals acquired with the microphone  107  to generate audio data for transmission via the communication processing circuit  101 . 
     Next,  FIG. 7  illustrates exemplary dimensional features of the antenna  30 . It should be appreciated that the features discussed with regard to  FIG. 7  are merely provided for illustration purposes; however these features are not limiting, and other dimensional features may easily be incorporated in a multi-band antenna of the present disclosure. 
     Referring to  FIG. 7 , the length from the connection point  31   a  of the first element  31  to the component  31   e  at a tip of the first element  31  is set to L1. The length of the second element  32  is set to L2. The length L2 of the second element  32  corresponds to the length from where the connection point  31   a  meets the element  32   a , to a tip of the component  32   b . The length of the component  32   b  of the second element  32  is set to La. The space between the component  32   b  of the second element  32  and the component  31   b  of the first element  31  is set to X. The space between the component  32   b  of the second element  32  and the component  31   d  of the first element  31  is set to Y. 
     Spacing length Y is defined as follows:
 
 Y&gt;λ   gx /100
 
Here, λ gx  is the effective wavelength of the first anti-resonance frequency f x , and Y is defined in meters.
 
     Specific Example of Spacing Length Y: 
     First anti-resonance frequency f x =1.4 GHz
 
λ gx   =C/f   x *1 /√{square root over (∈r)},  
 
where C is the speed of light in a vacuum, and ∈r is a dielectric constant of a medium. Although the elements  31  and  32  are arranged on the medium of a dielectric material, since a single surface of the medium is open, there are few wavelength shortening effects. Therefore, based on a simulator result, ∈r is set to a value at which 1/√{square root over (∈r)}=0.85, which yields:
 
λ gx =214.3*0.85≈0.18 m
 
λ gx /100=0.0018 m=1.8 mm
 
Therefore, with first anti-resonance frequency f x =1.4 GHz, the resultant spacing length Y becomes Y&gt;1.8 mm using the above-defined inequality.
 
     Length L1 of the first element  31  should satisfy the conditions of following inequality:
 
5*(2 n+ 1)*λ g1 /8&lt; L 1&lt;7*(2 n+ 1)*λ g1 /8,
 
where λ g1  is the effective wavelength (in meters) corresponding to a minimum frequency f 1  of a countermeasure frequency band, and n is a positive integer or 0.
 
     Length L2 of the second element  32  should satisfy the conditions of following inequality:
 
 L 2&lt;=(2 n+ 1)*λ g1 /4
 
     An adjustment of the impedance of the minimum frequency simplifies the derivation of length L3 of the third element  33 . Specifically, length L3 is made to satisfy:
 
Voltage Standing Wave Ratio (VSWR)&lt;7.
 
The point to which an adjustment of the impedance is preferred is the point at which the first element  31  is connected. If the second element  32  is short enough with respect to the wavelength of the low frequency band (e.g., 900 MHz), the antenna  30  including elements  31 ,  32 , and  33  that satisfies such conditions may exhibit the same behavior as the case of only a single element.
 
     It should be noted that although the definition of the spacing length X is not shown, the length may be made to correspond to spacing length Y. 
     In order to demonstrate the high performance characteristics of an antenna according to the present disclosure, such as antenna  30 , features of an antenna without the second element  32  are first shown in  FIGS. 8A and 8B , and features of the antenna  30  with the second element  32  included are shown in  FIGS. 9A and 9B . 
     First,  FIG. 8A  shows current phasors I1 and I2 of an antenna comprising only the first element  31 . The perspective of  FIG. 8A  corresponds to the direction of arrow A in  FIG. 4 , which also shows the first element  31 . The current phasor I1 is generated by the component  31   d . The current phasor I2 is generated by the component  31   b . Current phasors I1 and I2 are the same direction. 
       FIG. 8B  shows magnetic field vectors H1 and H2 of the antenna comprising only the first element  31  (i.e., resultant magnetic field vectors from current vectors I1 and I2 of  FIG. 8A ). The perspective of  FIG. 8B  corresponds to the direction of arrow B of  FIG. 4 , which also shows the first element  31 . The direction of arrow B is a direction which is slightly inclined with respect to the surface  21  of the antenna substrate  20 . As shown in  FIG. 8B , partial H0 is mutually negated due to the direction of generated magnetic field vectors H1 and H2. 
     Next,  FIG. 9A  shows current phasors I1, I2, and I3 of the antenna  30 , which includes both first element  31  and the second element  32 .  FIG. 9A  shows the antenna  30  from a perspective corresponding to arrow A of  FIG. 4 . The current phasor I1 is generated by the component  31   d  of the first element  31 . The current phasor I2 is generated by the component  31   b  of the first element  31 . The current phasor I3 is generated by the component  32   b  of the second element  32 . Current phasors I1 and I2 are in the opposite direction of the current phasor I3. 
       FIG. 9B  shows magnetic field vectors H1, H2, and H3 of the antenna (i.e., resultant magnetic field vectors from current vectors I1, I2, and I3 of  FIG. 9A ).  FIG. 9B  shows the antenna  30  from a perspective corresponding to arrow B of  FIG. 4 . As evident in  FIG. 9B , magnetic field vectors H1 and H3 overlap between the component  31   d  and the component  32   b , and the magnetic field vector H2 and the magnetic field vector H3 overlap between the component  32   b  and the component  31   b . Due to the direction of the overlapping vectors, the overlapping magnetic field vectors may be added. As a result of this overlap, the magnitude of electric current amount of current phasors I1, I2, I3 becomes large. In particular, the current phasor I3 corresponding to the overlapped magnetic field vector H3 is predominant in this example. Additionally, the first element  31  and the second element  32  are electromagnetically coupled, and the extent of the coupling is controlled by spacing lengths X and Y ( FIG. 7 ), and the magnitude of the electric current I3 ( FIG. 9A ) of the second element  32 . The resonant frequency in this case occurs when the electric current amount  13  becomes the highest, and when length L2 of the second element  32  is in the λg/4 vicinity. 
     The direction of each magnetic field vector can also be changed by adjusting the electric current I3, spacing lengths X and Y, and the length L2 of the second element  32 . In this case, magnetic field directivity begins to change with a frequency in the λg/4 vicinity. For this reason, appropriate element sizing should be chosen while confirming SAR of the antenna  30 . Spacing Y may especially experience a first anti-resonance frequency (e.g., 1400-1700 MHz), and since the wavelength shortening effect can be present, it is possible to show an element long. Therefore, what is necessary is to decide on the conditions satisfied while also confirming the characteristic that the wavelength shortening effect is acquired. 
     Next,  FIGS. 10A-D  illustrate exemplary SAR simulations for an antenna without the second element  32  (see, e.g.,  FIG. 10A ), and  FIGS. 11A-D  illustrate exemplary SAR simulations for an antenna that includes the second element  32  (see, e.g.,  FIG. 11A ). These simulations were performed according the following conditions. 
     Calculation of λ g1    
     Lengths L1 and L2 are respectively matched with the minimum frequency band (900 MHz) and an LTE countermeasure band (2500-2570 MHz), and λ g1  is computed. 
                     λ     g   ⁢           ⁢   1       =       ⁢       C   /     f   1       *     1   /       ɛ   ⁢           ⁢   r                       =       ⁢         (     300   *     10   8       )     /     (     2500   *     10   6       )       *     1   /       ɛ   ⁢           ⁢   r                       =       ⁢     120   *     1   /       ɛ   ⁢           ⁢   r                       
Here, C is the speed of light in a vacuum, f 1  is a minimum frequency of the countermeasure band, ∈r is a dielectric constant of a medium, and λ g1  is calculated in millimeters.
 
     Although the first element  31  and the second element  32  are arranged on the surface of the antenna substrate  20 , which is a dielectric material, since a single surface is open, there are few wavelength shortening effects present. Therefore, based on a simulator result, ∈r is set to a value at which 1/√{square root over (∈r)}=0.85, which yields:
 
λ g1 =120*0.85=102 mm
 
     Dimension conditions are then computed as follows: 
     Length of the First Element  31  (L1):
 
63.75 mm&lt; L 1&lt;89.25 mm
 
     Length of the Second Element  32  (L2):
 
 L 2&lt;=25 mm
 
     As mentioned earlier, the directivity shown in  FIGS. 10A-D  is an example where only the first element  31  is present in the antenna. The directivity of this antenna is characteristically emitted from the +Y-axis to the +Z-axis.  FIG. 10B  shows antenna directivity in a case with a frequency of 2.55 GHz. The maximum directivity value in this case is 2.5 dBi.  FIGS. 10C and 10D  show an S parameter (S11) of the antenna with only the first element  31 , where S11 is defined by the following formula:
 
 S 11=10 log [10]*(reflective electric power)/(incident electric power to an antenna)
 
 FIG. 10C  is a Smith chart showing impedance from 0.5 GHz to 3.0 GHz, with a normalization impedance of 50 ohms.  FIG. 10D  shows VSWR for the frequency range of  FIG. 10C , where the VSWR value of 1 is illustrated (ideal state), as well as states with much higher loss levels, which is undesirable. As shown in  FIG. 10D , a first anti-resonance frequency exists at 1500 MHz, with the VSWR value quite high at 11 or more.
 
     Next,  FIGS. 11A-D  provide corresponding illustrations to  FIG. 10A-D  for the case where the antenna  30  has both the first element  31  and the second element  32 . The exemplary illustrations of  FIGS. 11A-D  assume the following parameters:
 
 La= 20.0 mm
 
 X= 2.0 mm
 
 Y= 2.0 mm
 
 FIG. 11B  shows the antenna directivity from  FIG. 11A  in a case with a frequency of 2.55 GHz. The maximum directivity value in this case is 3.5 dBi.  FIGS. 11C and 11D  show the S parameter (S  11 ) of the antenna.  FIG. 11C  is a Smith chart showing impedance from 0.5 GHz to 3.0 GHz, with a normalization impedance of 50 ohms.  FIG. 11D  shows VSWR for the frequency range of  FIG. 11C . As illustrated in  FIG. 11D , the directivity at the 2.5 GHz frequency band, which is the frequency band that needs countermeasures against SAR, is changing a lot so that it may turn out that the directivity of  FIG. 11B  is comparable with the directivity of  FIG. 10B . Moreover, as shown in  FIG. 11D , a first anti-resonance frequency exists at 1200 MHz, and VSWR(s) are typically 3 or less and at low values. Thus, under this condition, favorable directional characteristics are acquired, and the antenna  30  has a high performance improvement in the frequency band of 1500 MHz.
 
       FIGS. 12A and 12B  illustrate antenna  30  directivity characteristics in a case with the following parameters:
 
 La= 21.0 mm
 
 X= 2.0 mm
 
 Y= 2.0 mm
 
The directivity in this case is shown in  FIG. 12A , and  FIG. 12B  shows corresponding VSWR for the frequency range of  FIG. 12A . As illustrated in these figures, directivity and VSWR are changing from the example of  FIGS. 11A-D , which illustrates the effect changing the above parameters has on antenna performance. In the example of  FIGS. 12A and 12B , directivity is getting worse relative to the example of  FIGS. 11A-D . Moreover, VSWR at 2550 MHz has deteriorated to approximately 4 or 5.
 
       FIGS. 13A and 13B  illustrate antenna  30  directivity characteristics in a case with the following parameters:
 
 La= 21.0 mm
 
 X= 0.5 mm
 
 Y= 3.5 mm
 
The directivity in this case is shown in  FIG. 13A , and  FIG. 13B  shows corresponding VSWR for the frequency range of  FIG. 13A . As illustrated in these figures, directivity is not optimal under these conditions, and VSWR at 2550 MHz is also high.
 
     Next,  FIGS. 14A and 14B  show impedance characteristics (Rb and Jb) of an antenna having only the first element  31  (i.e., no second element  32 ), and impedance characteristics of an antenna having both the first element  31  and the second element  32  (Ra and Ja).  FIGS. 14A and 14B  assume the following parameters:
 
 La= 20.5 mm
 
 X= 2.0 mm
 
 Y= 3.0 mm
 
 FIG. 14A  shows the real portion of impedance characteristics Ra and Rb, and  FIG. 14B  shows the imaginary portion of impedance characteristics Ja and Jb. As shown in these figures, in the case of the antenna with only the first element  31  (i.e., impedance Rb and Jb), a first anti-resonance condition exists at 1250 MHz, and this high impedance state continues to the 1600 MHz vicinity. On the other hand, in the case of the antenna which has the second element  32  (i.e., impedance Ra and Ja), the first anti-resonance has moved to 1100 MHz. Although the high impedance state continues to the 1300 MHz vicinity, the impedance is comparatively low at greater than 1400 MHz relative to the case with only the first element  31 .
 
     Next,  FIG. 15  shows radiation efficiency α11 of an antenna having both the first element  31  and the second element  32 , such as the antenna  30 , and the radiation efficiency α12 of and antenna having only the first element  31 . The exemplary radiation efficiency characteristics shown in  FIG. 15  assume power is supplied to the antenna under perfect adjustment conditions. As shown in the figure, the radiation efficiency α11 is significantly improved compared with the radiation efficiency α12 in the 1.4 GHz vicinity. Moreover, the antenna having the second element  32  exhibits a gentler change in reactance in the 1.4 GHz vicinity, and its change of real impedance is also relatively gentle. Thus, these exemplary graphs show that the bandwidth increase of the direction of the antenna that has the second element  32  is carried out. 
     Next,  FIG. 16  illustrates radiation efficiency in a condition with 50 ohms in impedance without a matching circuit, and when transmission power is supplied to an antenna. In this case, the radiation efficiency α21 in the case of the antenna that has both the first element  31  and the second element  32  (e.g., antenna  30 ) has been significantly improved in the 1.4 GHz vicinity compared with the radiation efficiency α22, which does not have the second element  32 . 
     Next,  FIGS. 17A and 17B  illustrate directivity features for an antenna without the second element  32 , and  FIGS. 18A and 18B  illustrate directivity features for an antenna that includes the second element  32  (e.g., antenna  30 ). These figures assume the following parameters:
 
 La= 20.0 mm
 
 X= 2.0 mm
 
 Y= 3.0 mm
 
 FIGS. 17A-B  and  18 A-B respectively illustrate directivity features of the same antenna, but  FIG. 17 / 18 B shifts the axes dY and dZ relative to  FIG. 17 / 18 A. As seen in the exemplary graphs of  FIGS. 18A and 18B , the inclusion of the second element  32  results in increased directivity dispersion along the various axes.
 
     Next,  FIG. 19  shows exemplary SAR measurements in tabular form for the case in which the antenna does not include the second element  32 , as well as the case in which the second element  32  is included, such as in the antenna  30 . Calculated values are shown for both cases when the antenna is positioned 10 mm and 15 mm from a human body. As shown in the table, for both distances, SAR is significantly reduced when the second element  32  is included in the antenna. 
     Next,  FIGS. 20A through 20N  illustrate exemplary modifications for a second element, such as the second element  32  of  FIG. 4 , which can be used in an antenna for balancing increased bandwidth with SAR countermeasures. It should be noted that the exemplary second element configurations are merely examples presented for illustration purposes, and other configurations could easily be implemented within the scope of the present disclosure. 
     Referring first to  FIG. 20A , an exemplary second element  210  is shown with a component  211  and a component  212  connecting in an L-shape. Additionally, the component  212  includes an opening part  213 , which may be provided in substantially the entire elongated length of the component  212 . 
     Next,  FIG. 20B  shows an exemplary second element  220 . The second element  220  includes a component  221  connected with a component  222  to form an L-shape. Additionally, the component  222  includes an opening part  223 , which is provided at a front end of the component  222 . 
     Next,  FIG. 20C  shows an exemplary second element  230 . The second element  230  includes a component  231  connected with a component  232  to form an L-shape. Additionally, the component  232  includes an opening part  233 , which is provided in the component  232  in the vicinity of a connection portion (i.e., an adjacent edge) of the component  231 . 
     Next,  FIG. 20D  shows an exemplary second element  240 . The second element  240  includes a component  241  connected with a component  242  to form an L-shape. Additionally, the component  242  includes an inclination part  243  at a front tip of the component  242 . 
     Next,  FIG. 20E  shows an exemplary second element  250 . The second element  250  includes a component  251 , a component  252 , a component  253 , and a component  254 , which may be respectively connected at right angles. 
     Next,  FIG. 20F  shows an exemplary second element  260 . The second element  260  includes a component  261  connected with a component  262  to form an L-shape. Additionally, the component  262  has a thin component  263  and thin component  264 , which bifurcate the component  262  at a front tip. 
     Next,  FIG. 20G  shows an exemplary second element  270 . The second element  270  includes a component  271  connected with a component  272  to form an L-shape. The second element  270  is similar to the second element  210  of  FIG. 20A , but the component  272  is wider than the component  212 . Additionally, the component  272  is equipped with an opening part  273 , which may be provided in substantially the entire elongated length of the component  272 , and may be centered or offset in a width direction of the component  272 . 
     Next,  FIG. 20H  shows an exemplary second element  280 . The second element  280  includes a component  281  connected with a component  282  to form an L-shape. The second element is similar to the second element  210  of  FIG. 20A , but with an opening part  283  in the component  282  that is narrower than the opening part  213 . 
     Next,  FIG. 20I  shows an exemplary second element  290 . The second element  290  includes a component  291 , a component  292 , the component  293 , a component  294 , and a component  295 . The component  291  and the component  292  are connected to form an L-shape. The component  293  is connected at a front tip of the component  292 . The component  294  has a length that is shorter than the component  292 , and the component  294  is connected at a front tip of the component  293 . Moreover, the component  295  is connected to an edge of the component  291  such that a front tip of the component  294  opposes a front tip of the component  295 . 
     Next,  FIG. 20J  shows an exemplary second element  300 . The second element  300  includes a component  301 , a component  302 , a component  303 , a component  304 , and a component  305 . The component  301  and the component  302  are connected to form an L-shape. The component  303  is connected at a front tip of the component  302 . The component  304  is connected to an edge of the component  301 . The component  305  is connected at the front tip of the component  304 . The component  305  may curve from the front tip of the component  304  in a direction corresponding to, or opposing, the component  303 . 
     Next,  FIG. 20K  shows an exemplary second element  310 . The second element  310  includes a component  311  connected with a component  312  to form an L-shape. Additionally, the second element  310  includes a component  313  and a component  314 , which are arranged substantially in parallel with the component  312 . The component  313  and the component  314  are connected to an edge of the component  311 . 
     Next,  FIG. 20L  shows an exemplary second element  320 . The second element  320  includes a component  321  connected with a component  322  to form an L-shape. Additionally, the second element  310  includes a component  323  is arranged substantially in parallel with the component  322 . The component  323  is connected to an edge of the component  321 , and the component  323  is shorter than the component  322 . 
       FIG. 20M  shows an exemplary second element  330 . The second element  330  includes a component  331  connected with a component  332  to form an L-shape. Additionally, the second element  330  includes a component  333  arranged substantially in parallel with the component  332 . The component  333  is connected to an edge of the component  331 , and the component  333  is shorter and wider than the component  332 . 
       FIG. 20N  shows an exemplary second element  340 . The second element  340  includes a component  341  connected with a component  342  to form an L-shape. Additionally, the second element  330  includes a component  343  connected at a front tip of the component  342 . 
     As stated previously, the second elements  210 - 340  described above with respect to  FIGS. 20A to 20N , or any combination of elements thereof, may be utilized as a second element when forming a multi-band antenna of the present disclosure, such as the antenna  30  of  FIG. 4 . 
     Next,  FIGS. 21A to 21C  illustrate exemplary modifications for a first element, such as the first element  31  of  FIG. 4 , which can be used in an antenna for balancing increased bandwidth with SAR countermeasures. It should be noted that the exemplary first element configurations are merely examples presented for illustration purposes, and other configurations could easily be implemented within the scope of the present disclosure. 
     Turning first to  FIG. 21A , an exemplary first element  410  includes components  411 ,  412 ,  413 ,  414 ,  415 ,  416 ,  417 , and  418 . An end  411   a  of the component  411  may be connected to a second element (e.g., the second element  32 ). Components  411  through  418 , in order, may be connected at right angles (i.e., the component  411  connects to the component  412 , the component  412  connects to the component  413 , etc.). 
       FIG. 21B  illustrates an exemplary first element  420 , which includes components  421 ,  422 ,  423 ,  424 ,  425 , and  426 . An end  421   a  of the component  421  may be connected to a second element (e.g., the second element  32 ). The component  423  and the component  424  are connected along an edge of the component  422 . Further, the components  423  and  424  are arranged substantially in parallel with the components  421  and  425 . 
       FIG. 21C  illustrates an exemplary first element  430 , which includes components  431 ,  432 ,  433 ,  434 , and  435 . An end  431   a  of the component  431  may be connected to a second element (e.g., the second element  32 ). The component  433  is connected along an edge of the component  432 . Further, the component  433  is arranged in parallel with the components  431  and  434 . 
       FIG. 21D  illustrates an exemplary first element  1000 , which includes components  1001 ,  1002 ,  1003 ,  1004 ,  1005 ,  1006 ,  1007 ,  1008 , and  1009 . An end  1001   a  of the component  1001  may be connected to a second element (e.g., the second element  32 ). Components  1001  through  1009 , in order, may be connected at right angles (i.e., the component  1001  connects to the component  1002  and  1003 , the component  1002  connects to the component  1008 , the component  1003  connects to the component  1009 , etc.). 
       FIG. 21E  illustrates an exemplary first element  1100 , which includes components  1101 ,  1102 ,  1103 ,  1104 ,  1105 ,  1106 , and  1107 . An end  1101   a  of the component  1101  may be connected to a second element (e.g., the second element  32 ). The component  1102  and the component  1103  are each connected along an edge of the components  1104  and  1105 , respectively. 
       FIG. 21F  illustrates an exemplary first element  1200 , which includes components  1201 ,  1202 ,  1203 ,  1204 ,  1205 ,  1206 ,  1207 ,  1208 ,  1209 , and  1210 . An end  1201   a  of the component  1201  may be connected to a second element (e.g., the second element  32 ). The component  1210  is connected along an edge of the component  1204 . Further, the component  1210  is arranged in parallel with the components  1202 ,  1203 ,  1206 , and,  1207 . 
       FIG. 21G  illustrates an exemplary first element  1300 , which includes components  1301 ,  1302 ,  1303 ,  1304 ,  1305 ,  1306 ,  1307 , and  1308 . An end  1301   a  of the component  1301  may be connected to a second element (e.g., the second element  32 ). The component  1306  is connected along an edge of the component  1304 . Further, the component  1306  is arranged in parallel with the components  1302 ,  1303 , and  1307 . 
       FIG. 21H  illustrates an exemplary first element  1400 , which includes components  1401 ,  1402 ,  1403 ,  1404 ,  1405 ,  1406 ,  1407 ,  1408 ,  1409 ,  1410 , and  1411 . An end  1401   a  of the component  1401  may be connected to a second element (e.g., the second element  32 ). The components  1410  and  1411  are connected along an edge of the component  1404 . Further, the components  1410  and  1411  are arranged in parallel with the components  1402 ,  1403 ,  1406 , and  1407 . 
       FIG. 21I  illustrates an exemplary first element  1500 , which includes components  1501 ,  1502 ,  1503 ,  504 ,  1505 ,  1506 ,  1507 ,  1508 , and  1509 . An end  1501   a  of the component  1501  may be connected to a second element (e.g., the second element  32 ). The component  1508  and  1509  are connected along an edge of the component  1504 . Further, the component  1508  and  1509  are arranged in parallel with the components  1502 ,  1503 , and  1506 . 
     Next,  FIGS. 22 and 23  illustrate exemplary configurations of the antenna  30  of  FIG. 4  using alternate configurations of first and second elements, such as those described above for  FIGS. 20A through 21C . As a non-limiting example,  FIG. 22  shows the antenna  30  of  FIG. 4  modified with the first element  430  of  FIG. 21C .  FIG. 23  shows a top-view perspective of  FIG. 22 , where it can be seen that the component  32   b  of the second element  32 , and the component  433  of the first element  430 , are separated by a predetermined clearance gap, and the two components overlap a common plane. Referring to  FIG. 23 , a length S is set to the elongated length of the component  433 , a width W is set to the width between the an edge of component  430  and an edge of component  433 , and a width Q is set to the width between an edge of the component  434  and an edge of the component  433 . 
     Next,  FIG. 24  illustrates an exemplary current phasor diagram of the antenna shown in  FIG. 22 . Here, the current phasor of the component  433  is set to I3a, and the current phasor of the component  32   b  of the second element  32  is set to I3b. In this example, the direction of the current phasor I3a and I3b is the same. For this reason, as shown in  FIG. 24 , an in-phase coupling C is generated by the component  433  and the component  32   b . The current phasors I3a and I3b become large when the inductance L and capacitance C formed by the spacing of the two elements resonates. In addition, current phasors I1 and I2 have opposing phases relative to the current phasors I3a and I3b. 
     Generally there exists the following relationship between the resonant frequency f c , the inductance L, and the capacitance C (Equation A): 
               f   c     ∝     1       L   *   C               
Here, since the denominator of Equation A will become large by the increased capacitance C when the structure of  FIG. 24  is used, the resonant frequency f c  becomes small. That is, it becomes possible to move the resonant frequency f 1  to a low frequency while keeping the length of the second element set. Thus, an arrangement such as that shown in  FIG. 24  contributes to size reduction of a corresponding antenna.
 
       FIG. 25  illustrates magnetic field vectors H1, H2, and H3 generated in the antenna shown in  FIG. 22  (i.e., the magnetic field vectors resultant from the current phasors of  FIG. 24 ). As shown in  FIG. 25 , the magnetic field vector H1 and the magnetic field vector H3 overlap, and the magnetic field vector H2 and the magnetic field vector H3 overlap. As a result of these overlaps, the overlapping magnetic field vectors may be added. 
     Next,  FIGS. 26A-D  illustrate antenna directivity characteristics for an exemplary case in which the first element of  FIG. 22  does not include the component  433 , and  FIGS. 27A-D  illustrate antenna directivity characteristics for an exemplary case in which the first element of  FIG. 22  does include the component  433 . 
     Referring to  FIGS. 26A-D , the figures assume the following parameters:
 
 La= 19.0 mm
 
 X= 4.0 mm
 
 Y= 3.0 mm
 
The directivity of the antenna shown in  FIG. 26A  is illustrated in  FIG. 26B  for a frequency of 1.95 GHz. The maximum directivity value in this case is 3.9 dBi.  FIGS. 26C and 26D  show S parameter (S11) of the antenna in  FIG. 26A . In particular,  FIG. 26C  is a Smith chart that shows impedance from 0.5 GHz to 3.0 GHz, and  FIG. 26D  illustrates VSWR for a corresponding frequency range. As shown in  FIG. 26D , a first anti-resonance frequency exists at 1500 MHz for this exemplary case, and VSWR is a value quite high at 11 or more.
 
     Turning to  FIGS. 27A-27D , the directivity characteristics shown in illustrate the case of an antenna with the component  433  (e.g.,  FIG. 27A ). The example of  FIGS. 27A-27D  assumes the following parameters:
 
 La= 19.0 mm
 
 X= 4.0 mm
 
 Y= 3.0 mm
 
 S= 12.0 mm
 
 Q= 5.0 mm
 
 W= 2.0 mm
 
The directivity characteristics of the antenna shown in  FIG. 27A  are illustrated in  FIG. 27B  for a case with a frequency of 1.95 GHz. The maximum directivity value in this case is 4.3 dBi.  FIGS. 27C and 27D  show S parameter (S11) of the antenna in  FIG. 27A . In particular,  FIG. 27C  is a Smith chart which shows the impedance from 0.5 GHz to 3.0 GHz, and  FIG. 27D  shows VSWR for a corresponding frequency range. As evidenced in comparing  FIGS. 26B and 27B , the presence or absence of the component  433  in the antenna&#39;s first element may result in large changes in directivity. Moreover, as shown in  FIG. 27D , VSWR improves relative to the case of  FIG. 26D  at the 1.5 GHz resonance frequency vicinity, with values below 4.
 
     Thus, the exemplary illustrations of  FIGS. 26A-27D  show that the directivity of an antenna can be changed by adding the component  433  to a first element, while providing wide bandwidth properties for the antenna. 
     For further illustration purposes,  FIGS. 28A and 28B  illustrate a second case where the component  433  is included in an antenna&#39;s first element, as in  FIG. 27A . This second non-limiting example assumes the following parameters:
 
 La= 19.0 mm
 
 X= 4.0 mm
 
 Y= 3.0 mm
 
 S= 14.0 mm
 
 Q= 5.0 mm
 
 W= 2.0 mm
 
The directivity in this case is shown in  FIG. 28A , and  FIG. 28B  illustrates VSWR for the 0.5 GHz to 3.0 GHz frequency range. A comparison of  FIGS. 28B and 27D  illustrates the impact of changing the length S of the component  433 .
 
     For further illustration purposes,  FIGS. 29A and 29B  illustrate a third case where the component  433  is included in an antenna&#39;s first element, as in  FIG. 27A . This third non-limiting example assumes the following parameters:
 
 La= 19.0 mm
 
 X= 4.0 mm
 
 Y= 3.0 mm
 
 S= 12.0 mm
 
 Q= 6.0 mm
 
 W= 1.0 mm
 
The directivity in this case is shown in  FIG. 28A , and  FIG. 28B  illustrates VSWR for the 0.5 GHz to 3.0 GHz frequency range. A comparison of  FIGS. 29B and 27D  illustrates the impact of changing widths Q and W on antenna performance.
 
     Next,  FIGS. 30A and 30B  show real and imaginary impedance characteristics (R21 and J21, respectively) of an antenna without the component  433  on the first element (e.g., antenna  30  shown in  FIG. 4 ), and real and imaginary impedance characteristics (R22 and J22, respectively) of an antenna with the component  433  included on the first element, such as in  FIG. 23 . The parameters of the antenna for this example are as follows:
 
 La= 21.0 mm
 
 X= 4.0 mm
 
 Y= 3.0 mm
 
 S= 14.0 mm
 
 Q= 5.0 mm
 
 W= 2.0 mm
 
As shown in the exemplary figures, an antenna without the component  433  exhibits a first anti-resonance frequency at the 1000 MHz vicinity, with a high impedance state continuing to the 1300 MHz vicinity; however, the impedance is comparatively low at 1400 MHz or more. Moreover, reactance becomes zero at a point near the 2500 MHz vicinity.
 
     On the other hand, in the case in which the antenna has the first element  430  with the component  433 , together with the second element  32 , the first anti-resonance frequency has moved to the 960-MHz vicinity. Although the high impedance state continues to 1300 MHz vicinity in this case, impedance is comparatively low at 1400 MHz or more. Further, the point at which reactance becomes zero moves to the 2040 MHz vicinity. In addition, the change in the real portion other than the first anti-resonance frequency is gentle irrespective of the presence or absence of the component  433 . Thus, when the component  433  is present, the frequency f c  at which a reactance component becomes zero is lower relative to the case where the component  433  is not present. 
     Next,  FIG. 31  provides an exemplary graph illustrating radiation efficiency α31 of an antenna without the component  433  (e.g., antenna  30  of  FIG. 4 ), and radiation efficiency α32 of an antenna with the component  433  (e.g., antenna  30  of  FIG. 23 ).  FIG. 31  assumes transmission power is supplied to the antennas in a perfect adjustment condition. Referring to the graph, although a decline in radiation efficiency α32 is shown at the 2.05 GHz vicinity, the decrease is small and therefore, this condition is satisfactory. In the low frequency region, although the efficiency at 950 MHz is falling, this can be improved by shortening the length of the first element. Since a fall in efficiency is not seen at the first anti-resonance frequency vicinity, the antenna is operating in a wide bandwidth condition. 
       FIG. 32  shows a corresponding radiation efficiency graph as in  FIG. 31 , but with a normalization impedance of 50 ohms. Under these alternate conditions,  FIG. 32  illustrates radiation efficiency α41 of an antenna without the component  433  (e.g., antenna  30  of  FIG. 4 ), and radiation efficiency α42 of an antenna with the component  433  (e.g., antenna  30  of  FIG. 23 ). 
       FIGS. 33A-B  and  34 A-B illustrate directivity for the cases shown in  FIGS. 30A and 30B . Specifically,  FIGS. 33A and 33B  illustrate directivity in the case where no component  433  exists on the first element, and  FIGS. 34A and 34B  illustrate directivity in the case where the component  433  is included on the first element.  FIG. 33B  illustrates the graph of  FIG. 33A  with the Y-axis and Z-axis shifted to the opposite side. Likewise,  FIG. 34B  illustrates the graph of  FIG. 34A  with the Y-axis and Z-axis shifted to the opposite side. 
     Next,  FIGS. 35A and 35B  show real and imaginary impedance characteristics (R41 and J41, respectively) of an antenna with a second element and the component  433  included on the first element (e.g., antenna  30  shown in  FIG. 4 ); real and imaginary impedance characteristics (R42 and J42, respectively) of an antenna with a first element including component  433 , but no second element; and real and imaginary impedance characteristics (R43 and J43, respectively) of an antenna with a second element and a first element that does not include the component  433 .  FIG. 35A  illustrates the real portion of impedance for each case, and  FIG. 35B  illustrates the imaginary portion of impedance for each case. In addition, these figures assume the second element is similar to the second element  320  in which components  322  and  323  are extended from component  321  in parallel, such as in  FIG. 20L . However, in contrast to  FIG. 20L ,  FIGS. 35A and 35B  assume components  322  and  323  are the same length. Moreover, for the case with the antenna of impedance characteristics R41 and J41, the component  433  of the first element  430  is arranged between the components  322  and  323 . 
     Referring to the graphs, there is no frequency at which the reactance component J42 becomes zero for the antenna without a second element. The frequencies at which the reactance component J43 for the antenna without the component  433  becomes zero are 2450 MHz, 2780 MHz, 2880 MHz, and 2930 MHz. The frequencies at which the reactance component J41 for the antenna with the component  433  included becomes zero are 2030 MHz, 2440 MHz, 2630 MHz, 2690 MHz. Thus, as evident in the graphs, the presence and position of the component  433  is shown to change the frequency at which reactance becomes zero. 
     Next,  FIG. 36  provides an exemplary graph illustrating radiation efficiency α51 of an antenna without the second element, of the three cases shown in  FIGS. 35A and 35B ; and radiation efficiency α52 of an antenna with the component  433  included on the first element, of the three cases shown in  FIGS. 35A and 35B . Referring to the graphs, although efficiency is shown to decline somewhat at the 2.05 GHz vicinity for α52, the decline is small and therefore, the result is satisfactory. Moreover, in the low frequency region, although the efficiency at 950 MHz is falling, this can be improved by shortening the length of the first element. Since a fall in efficiency is not seen at the first anti-resonance frequency vicinity, the antenna is operating in a wide bandwidth condition. 
       FIG. 37  shows a corresponding radiation efficiency graph as in  FIG. 36 , but with a normalization impedance of 50 ohms. Under these alternate conditions,  FIG. 37  illustrates radiation efficiency α61 of the antenna without the second element, and radiation efficiency α62 of an antenna with the second element and the component  433  included on the first element. 
       FIGS. 38A-B  and  39 A-B illustrate directivity for two cases shown in  FIGS. 35A and 35B . Specifically,  FIGS. 38A and 38B  illustrate directivity in the case where the antenna does not include a second element; and  FIGS. 39A and 39B  illustrate directivity in the case where the antenna includes the second element, and the component  433  is included on the first element.  FIGS. 38A and 39A  show directivity at 2.15 GHz, and  FIGS. 38B and 39B  show directivity at 2.55 GHz. Thus, as evidenced by these directivity illustrations, directivity can be changed on the two frequencies based on the presence and location of the second element and the component  433 . 
     Next,  FIGS. 40A and 40B  show real and imaginary impedance characteristics of the antenna  30  shown in  FIG. 4  (R51 and J51), and the antenna of  FIG. 4  modified with the second element  320  shown in  FIG. 20L  (R52 and J52). In the second exemplary case, the components  322  and  323  are different lengths, as in  FIG. 20L , and the component  323  of the second element  320  is assumed to be shorter. Referring to the graphs, the reactance component J51 becomes zero at 2470-2820 MHz, and the reactance component J52 becomes zero at 2470 MHz, 2800 MHz, 3400 MHz, 3500 MHz. That is, the frequency at which the reactance component becomes zero has increased to 2470 MHz under these conditions. 
       FIGS. 41A-B  and  42 A-B illustrate directivity for two cases shown in  FIGS. 40A and 40B . Specifically,  FIGS. 41A and 41B  illustrate directivity in the case of antenna  30  from  FIG. 4 ; and  FIGS. 42A and 42B  illustrate directivity in the case where the antenna  30  is modified by using the second element  320  of  FIG. 20L .  FIGS. 41A and 42A  show directivity at 2.55 GHz, and  FIGS. 41B and 42B  show directivity at 3.35 GHz. Thus, as evidenced by these directivity illustrations, directivity can be changed on the two frequencies based on the configuration of the second element. 
     Obviously, numerous modifications and variations of the present disclosure are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the present disclosure may be practiced otherwise than as specifically described herein. For example, advantageous results may be achieved if components in the present disclosure were combined in a different manner, or if the components were replaced or supplemented by other components. The functions, processes, and algorithms described herein may be performed in hardware or software executed by hardware, including computer processors and/or programmable circuits configured to execute program code and/or computer instructions to execute the functions, processes and algorithms described herein. Additionally, some implementations may be performed on modules or hardware not identical to those described. Accordingly, other implementations are within the scope that may be claimed. 
     The functions and features described herein may also be executed by various distributed components of a system. For example, one or more processors may execute these system functions, wherein the processors are distributed across multiple components communicating in a network. The distributed components may include one or more client and/or server machines, in addition to various human interface and/or communication devices (e.g., display monitors, smart phones, tablets, personal digital assistants (PDAs)). The network may be a private network, such as a LAN or WAN, or may be a public network, such as the Internet. Input to the system may be received via direct user input and/or received remotely either in real-time or as a batch process. 
     It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise.