Patent Publication Number: US-2012044117-A1

Title: Planar antenna apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priorities from Japanese patent applications Nos. 2010-031222, filed on Feb. 16, 2010; 2010-037604, filed on Feb. 23, 2010; and 2010-287159, filed on Dec. 24, 2010, the disclosures of which are incorporated herein in their entirety by reference. 
    
    
     BACKGROUND 
     The present invention relates to a planar antenna apparatus which can be used for wireless communications. 
     Along with increased diversity in applications of a wireless communication apparatus, smaller size, higher performance, and higher efficiency are desired for the wireless communication apparatus. The size of the wireless communication apparatus largely depends on the size of the antenna. There is an increasing need of further improvement of radiation efficiency especially for a small size planar antenna that can be placed over a dielectric substrate as a layout pattern. 
     WO 2006/126320 discloses a nonresonant planar slot dipole antenna apparatus. A configuration and characteristics of this antenna apparatus are explained below.  FIG. 11  is a plan view illustrating the configuration of the antenna apparatus disclosed in WO 2006/126320.  FIG. 12  is a plan view showing an antenna unit  101  of the antenna apparatus shown in  FIG. 11 . The antenna apparatus shown in  FIG. 11  includes the antenna unit  101  and a matching unit  106 . The matching unit  106  performs impedance matching between the antenna unit  101  and an external circuit (signal source) which is not shown. 
     The antenna unit  101  as a slot dipole antenna is formed by providing openings (slots)  102  and  103  in a conductor  105  formed over a dielectric substrate. Accordingly, the lower layer dielectric substrate is exposed in the openings  102  and  103  shown in  FIGS. 11 and 12 . In the example of  FIGS. 11 and 12 , the antenna unit  101  is connected to the matching unit  106  via a Coplanar Waveguide (CPW). Since it is a tiny nonresonant antenna, in  FIGS. 11 and 12 , an antenna length L is far smaller than a wavelength λ. (that is, L&lt;&lt;λ). WO 2006/126320 discloses an analysis result of impedance Za of the antenna unit  101  by an electromagnetic field simulation. According to the analysis result, slopes of radiation resistance Ra and reactance Xa of the antenna unit  101  will be constant near a center frequency (for example, 5.0 GHz) of a radio signal. Accordingly, an equivalent circuit of this antenna unit  101  can be represented by a series circuit of the radiation resistance Ra and the reactance Xa as shown in  FIG. 13 . 
     The matching unit  106  includes a transmission line  104  and an inverter  107 . The transmission line  104  includes two parallel signal lines. As for these signal lines, one end is connected to the antenna unit  101 , and the other end is connected to an external circuit (signal source) via the inverter  107 . The matching unit  106  is designed using characteristic impedance Z 1  and electrical length θ 0  of the transmission line  104 . The characteristic impedance Z 1  is calculated according to a design formula of a formula (1). In the formula (1), Q e1  is external Q (coupling amount with an external circuit) of a resonator. The function Sinc(θ) is sinθ/θ. The design formula shown in the formula (1) is calculated based on the condition in which an antenna equivalent circuit with a matching circuit will be equivalent to a circuit based on the filter theory. 
     
       
         
           
             
               
                 
                   
                     Z 
                     1 
                   
                   = 
                   
                     
                       
                         X 
                         a 
                       
                        
                       tan 
                        
                       
                           
                       
                        
                       
                         
                           θ 
                           0 
                         
                         · 
                         
                           θ 
                           0 
                         
                       
                     
                     = 
                     
                       
                         1 
                         2 
                       
                        
                       
                         
                           Sinc 
                           
                             - 
                             1 
                           
                         
                          
                         
                           ( 
                           
                             
                               X 
                               a 
                             
                             
                               
                                 2 
                                  
                                 
                                   Q 
                                   
                                     e 
                                      
                                     
                                         
                                     
                                      
                                     1 
                                   
                                 
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                                   R 
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     SUMMARY 
     The present inventors have found a problem in the antenna apparatus disclosed in WO 2006/126320 is that it is difficult to improve the radiation efficiency of the antenna unit  101  when the antenna apparatus is mounted on a small size wireless communication apparatus. The reason is explained below. When incident power to the antenna is P A [W], radiation power of the antenna is P R [W], radiation resistance of the antenna is Ra[Ω], and loss resistance is R L [Ω], generally the radiation efficiency η is represented by a formula (2). 
     
       
         
           
             
               
                 
                   η 
                   = 
                   
                     
                       
                         P 
                         R 
                       
                       
                         P 
                         A 
                       
                     
                     = 
                     
                       Ra 
                       
                         Ra 
                         + 
                         
                           R 
                           L 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
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     The radiation resistance Ra[Ω] of the antenna unit  101  shown in  FIG. 12 , i.e., the nonresonant planar slot dipole antenna, is represented by a formula (3). In the formula (3), L[μm] is an antenna length and λ[μm] is a wavelength of a radio signal. Therefore, the radiation resistance of the nonresonant planar slot dipole antenna shown in  FIG. 12  depends on the antenna length L. 
         Ra =80π 2 ( L /λ) 2    (3)
 
     The characteristics of the slot dipole antenna are considered with peripheral conductors (peripheral conductors  111  to  114  of  FIGS. 11 and 12 ) placed around the slot as infinite, ideally. Thus, when assuming to place the planar antenna apparatus of  FIG. 11  in a limited area in order to reduce the size of the wireless communication apparatus, it is not easy to extend the antenna length L due to the limitation of area. Accordingly, it is difficult to improve the radiation resistance Ra shown in the formula (3), and it is difficult also to improve the radiation efficiency η that depends on the radiation resistance Ra. 
     An aspect of the present invention includes a planar antenna apparatus that includes a dielectric substrate, a ground conductor, and a transmission line. The ground conductor is formed by a conductor pattern placed to a surface of the dielectric substrate and includes a first and a second opening. The transmission line is also formed by the conductor pattern. The transmission line supplies a signal to a first and a second peripheral conductor respectively surrounding the first and the second opening. Further, the first and the second opening are arranged axis-symmetrically with respect to the transmission line. Furthermore, opening areas of the first and the second opening are determined so that, due to loop currents that are supplied by the transmission line and flow through the first and the second peripheral conductor, a region including the first opening and the first peripheral conductor operates as a first loop radiating element of a magnetic field radiation type, and a region including the second opening and the second peripheral conductor operates as a second loop radiating element of the magnetic field radiation type. 
     According to the aspect of the present invention mentioned above, by expanding the areas of the first and the second opening, it is possible to obtain magnetic field radiation type loop antenna characteristics in contrast to the antenna apparatus with electric field radiation type slot dipole antenna characteristics shown in  FIG. 11 . Note that the radiation efficiency η of the loop antenna depends on the loop area, that is, the opening area of the first and the second opening. Since the planar antenna apparatus according to the aspect of the present invention mentioned above is easy to expand the first and the second openings while suppressing the expansion of the antenna area, it is easy to improve the radiation efficiency η. 
     According to the aspect of the present invention mentioned above, the radiation efficiency η can be improved while suppressing the expansion of the antenna area. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other aspects, advantages and features will be more apparent from the following description of certain embodiments taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a plan view showing an example of a configuration of an antenna apparatus according to a first embodiment of the present invention; 
         FIG. 2  is a plan view showing a part of the antenna apparatus (i.e. an antenna unit  1 ) shown in  FIG. 1 ; 
         FIGS. 3A and 3B  are plan views of a planar antenna apparatus for which a simulation was performed; 
         FIG. 4  illustrates a simulation result of electric field distribution of a planar antenna apparatus according to a comparative example; 
         FIG. 5  illustrates a simulation result of current distribution of the planar antenna apparatus according to the comparative example; 
         FIG. 6  illustrates a simulation result of electric field distribution of the planar antenna apparatus according to the first embodiment of the present invention; 
         FIG. 7  illustrates a simulation result of current distribution of the planar antenna apparatus according to the first embodiment of the present invention; 
         FIG. 8  is a plan view showing an example of a configuration of the antenna apparatus according to a second embodiment of the present invention; 
         FIG. 9  is a plan view showing a state of current and a magnetic field flowing through the antenna unit  21  shown in  FIG. 8 ; 
         FIGS. 10A and 10B  are conceptual diagrams showing the magnetic field and magnetic flux density generated in the antenna unit  21  shown in  FIG. 8 ; 
         FIG. 11  is a plan view of an antenna apparatus according to a related art; 
         FIG. 12  is plan view showing a part of the antenna apparatus (i.e. an antenna unit  101 ) shown in  FIG. 11 ; and 
         FIG. 13  illustrates an equivalent circuit of the antenna unit  101  shown in  FIG. 12 . 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, specific embodiments incorporating the present invention are described with reference to the drawings. In each drawing, the same components are denoted by the same reference numerals, and repeated explanation is omitted as necessary for the clarity of the explanation. 
     First Embodiment 
       FIG. 1  is a plan view showing an example of a configuration of a planar antenna apparatus according to the first embodiment of the present invention. A schematic configuration of the antenna apparatus of  FIG. 1  is same as that of the planar antenna apparatus shown in  FIGS. 11 and 12 . To be specific, an antenna unit  1  is formed by providing openings (slots)  2  and  3  in a GND conductor  5  that is formed by a conductor pattern placed over a dielectric substrate  100 . The lower layer dielectric substrate  100  is exposed in the openings  2  and  3  shown in  FIG. 1 . The openings  2  and  3  are arranged axis-symmetrically with respect to a transmission line  4 . The antenna unit  1  is connected to an external circuit (signal source) via the transmission line  4  and an impedance matching circuit (not shown). In the example of  FIG. 1 , the transmission line  4  is a coplanar waveguide. The impedance matching circuit (not shown) may be similar to the inverter  107  or the like shown in  FIG. 11 . 
     However, specific arrangement, shape, and opening area of the openings  2  and  3  of the planar antenna apparatus according to this embodiment shown in  FIGS. 1 and 2  are different from the ones shown in  FIG. 11 . Specifically in this embodiment, a width of peripheral conductors (conductors  11  to  14 ) of the antenna unit  1  is narrowed to the extent that is not influenced by a skin effect, i.e. current reduction due to an insufficient surface depth, at a desired radio frequency. Then, the opening area of the openings  2  and  3  is expanded. By adopting such configuration, the radiation characteristics (that is, magnetic field radiation type) of a tiny loop antenna, not the radiation characteristics (that is, electric field radiation type) of a tiny dipole antenna, dominate the radiation characteristics of the antenna unit  1 . It is considered that this radiation characteristics are brought about by loop current (a first loop) which flows through the peripheral conductors  11  and  12  of the opening  2 , and loop current (a second loop) which flows through the peripheral conductors  13  and  14  of the opening  3 . Accordingly, the region including the opening  2  and its peripheral conductors  11  and  12  operates as a first loop radiating element, and the region including the opening  3  and its peripheral conductors  13  and  14  operates as a second loop radiating element. 
     As for the tiny loop antenna, the width of the peripheral conductors  11  to   14  should be determined not to block the flow of the loop current. Therefore, in the case of the tiny loop antenna, unlike the tiny slot dipole antenna, it is not necessary to reserve the width of the peripheral conductors  11  to  14  more than necessary. The radiation resistance of the tiny loop antenna is proportional to the opening area (i.e. area surrounded by the current loop). Thus, according to the antenna apparatus of this embodiment, the width of the peripheral conductors  11  to   14  is reduced so as to expand the openings  2  and  3  instead. Then the radiation efficiency can be improved while suppressing the area expansion of the planar antenna. Therefore, the antenna apparatus according to this embodiment is suitable for reducing the size of the wireless communication apparatus. 
     The state of magnetic field radiation of the antenna unit  1  is explained hereinafter.  FIG. 2  shows the loop current flowing through the antenna unit  1  and the magnetic field generated by the loop current. Forward current C 1  is supplied to the antenna unit  1  from the transmission line  4 . The forward current C 1  generates a forward magnetic field M 1 . The forward current C 1  is divided into return current C 2  which flows through the peripheral conductors  11  and  12  (the first loop) of the opening  2 , and return current C 3  which flows through the peripheral conductors  13  and  14  (the second loop) of the opening  3 . A return magnetic field M 2  in the first loop is generated by the return current C 2  which flows through the first loop. Similarly, a return magnetic field M 3  in the second loop is generated by the return current C 3  which flows through the second loop. Due to the return magnetic fields M 2 , M 3 , and the forward magnetic field M 1 , magnetic flux is localized in the antenna unit  1 , and strong electromagnetic waves are emitted to space. 
     Further, as shown in  FIGS. 1 and 2 , by adopting the layout of arranging the openings  2  and  3  axis-symmetrically with respect to the transmission line  4 , the return current C 2  and C 3  flows through the shortest path to the GND conductor  5  along the conductor edge due to the nature of high-frequency current. The flow of the current C 2  and C 3 , which is opposite direction to the forward current C 1 , suppresses propagation of the magnetic field in the transmission line  4  and disorder of electromagnetic wave radiation of the antenna unit  1 . 
     Hereinafter, a simulation result of the electric field distribution and the current distribution of the planar antenna apparatus according to this embodiment which has the loop antenna characteristics is explained. As a comparative example, a simulation result of the electric field distribution and the current distribution of the planar antenna apparatus which has the dipole antenna characteristics shown in  FIG. 11  is also explained.  FIGS. 3A and 3B  are plan views of the planar antenna apparatus for which the simulation was performed.  FIG. 3A  shows the planar antenna apparatus with the dipole antenna characteristics shown in  FIG. 11 .  FIG. 3B  shows the planar antenna apparatus according to this embodiment with the loop antenna characteristics. As compared with  FIG. 3A , in the antenna apparatus shown in  FIG. 3B , the area of the peripheral conductors  11  to   14  is reduced, and the openings  2  and  3  are expanded. The inverter  7  may have the same configuration as the inverter  107 . 
       FIG. 4  shows the simulation result of an electric field (absolute value) distribution of the planar antenna apparatus of the comparative example shown in  FIG. 3A .  FIG. 5  shows the simulation result of a current distribution of the planar antenna apparatus of the comparative example shown in  FIG. 3A . As can be seen from  FIG. 4  in the dotted line ellipses, large electric fields are generated along each long side of the slots (openings)  102  and  103 . Note that positive/negative is inverted around a ground potential (GND) between the two long sides of each slot. Although  FIG. 5  shows that current flows along a periphery of the slots  102  and   103 , a width of a current path around the slots  102  and  103  of  FIG. 5  is about  100   
     On the other hand,  FIG. 6  shows the simulation result of an electric field (absolute value) distribution of the planar antenna apparatus according to this embodiment shown in  FIG. 3B .  FIG. 7  shows the simulation result of a current distribution of the planar antenna apparatus according to this embodiment shown in  FIG. 3B . As can be seen from  FIG. 6  in the dotted line ellipses, electric fields generated along the long sides of the slots (openings)  2  and  3  (especially long sides of the upper part of  FIG. 6 ) are weaker as compared to  FIG. 4 . That is, in  FIG. 6 , the electric field distribution which appears in the slot dipole antenna does not exist. As can be seen from  FIG. 7 , current flows through the peripheral conductors  11  to  14  along the periphery of the slots  2  and  3 . A width of a current path around the slots  2  and  3  of  FIG. 7  is about 200 μm, and is expanded about twice the width in  FIG. 5 . Therefore, it is considered that the antenna apparatus of  FIG. 3B  has the radiation characteristics of the loop antenna which is based on the magnetic field. 
     The following conclusion can be drawn by the simulation results shown in  FIGS. 4 to 7 . Specifically, by expanding the area of the openings  2  and  3  as in the antenna apparatus of  FIG. 3B , a radiation characteristics changes from the slot dipole antenna operation to the loop antenna operation. 
     Next, an advantage in terms of the radiation efficiency of the planar antenna apparatus according to this embodiment is explained. As shown in the formula (3), the radiation resistance Ra of the planar slot dipole antenna depends on the antenna length L. However, the antenna length L cannot be sufficiently extended from the necessity of reserving the area of the peripheral conductor of the antenna unit  101  of  FIG. 11 . On the other hand, in the layout of the antenna unit  1  shown in  FIG. 1 , as the area of the peripheral conductors  11  to  14  is reduced in an attempt to expand the area of the openings  2  and  3 , the antenna length L 1  and the antenna width W 1  of  FIG. 1  can be extended respectively from the antenna length L and the antenna width W of  FIG. 11 . 
     Further, as for the radiation characteristics of the antenna unit  1 , the radiation resistance is proportional to the opening area and will be close characteristics to the loop antenna that does not require an infinite conductor. Suppose that both opening areas of the opening  2  (the first loop) and the opening  3   (the second loop) are A and the number of the openings (loops) is two, the radiation resistance R R  of the antenna unit  1 , which is considered to be a loop antenna, can be represented by a formula (4). Specifically, the radiation resistance R R  of the antenna unit  1  is proportional to the square of the opening area A of each of the first and second loop. 
     
       
         
           
             
               
                 
                   
                     R 
                     R 
                   
                   = 
                   
                     320 
                      
                     
                         
                     
                      
                     
                       π 
                       4 
                     
                      
                     
                       
                         
                           2 
                           2 
                         
                         · 
                         
                           A 
                           2 
                         
                       
                       
                         λ 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Next, if the loop antenna length L 1  of  FIG. 1  is assumed to be equal to the antenna length L of  FIG. 11 , a ratio of the radiation resistance Ra of the antenna unit  101  of  FIG. 11  to the radiation resistance R R  of the antenna unit  1  of  FIG. 1  is represented by a formula (5). 
         Ra/R   R   =L   2 ·λ 2 /16π 2   ·L   2 ·( W 1) 2    (5)
 
     From the formula (5), a condition of the antenna width W 1  for the radiation resistance R R  to exceed the radiation resistance Ra can be represented by a formula (6). 
       λ/4 π≦W 1   (6)
 
     In the formula (5), it is assumed that the antenna length L 1  of  FIG. 1  is equal to the antenna length L of  FIG. 11 . However, as described above, in this embodiment, since the width of the peripheral conductors  12  and  14  can be reduced, the antenna length L 1  of  FIG. 1  can be made longer than antenna length L of  FIG. 11 . Accordingly, when the antenna width W 1  of  FIG. 1  satisfies at least the condition shown in the formula (6), the radiation resistance R R  of the antenna unit  1  according to this embodiment will be larger than the radiation resistance R R  of the antenna unit  101  of  FIG. 11 . 
     Second Embodiment 
       FIG. 8  is a plan view showing an example of a configuration of a planar antenna apparatus according to the second embodiment of the present invention. A schematic configuration of the antenna apparatus of  FIG. 8  is the same as that of the planar antenna apparatus shown in  FIGS. 11 and 12 . To be specific, the antenna unit  21  is formed by providing openings (slots)  25  and  26  in a GND conductor  36 , which is formed by a conductor pattern placed over a dielectric substrate  200 . The lower layer dielectric substrate  200  is exposed in the openings   25  and  26  shown in  FIG. 8 . The openings  25  and  26  are arranged axis-symmetrically with respect to a transmission line  23 . In the example of  FIG. 8 , the transmission line  23  is a coplanar waveguide. The antenna unit  21  is connected to an external circuit (signal source) via a matching unit  22 . 
     However, specific arrangement, shape, and opening area of the openings  25  and  26  of the planar antenna apparatus according to this embodiment shown in  FIG. 8  are different from the ones shown in  FIG. 11 . More specifically, in this embodiment, a width of peripheral conductors (conductors  31  to  34 ) of the antenna unit  21  is narrowed to the extent that is not influenced by a skin effect, i.e. current reduction due to an insufficient surface depth, at a desired radio frequency. Then, the opening area of the openings  25  and  26  is expanded. By adopting such configuration, the radiation characteristics (that is, magnetic field radiation type) of a tiny loop antenna, not the radiation characteristics (that is, electric field radiation type) of a tiny dipole antenna, dominate the radiation characteristics of the antenna unit  21 . It is considered that this radiation characteristics are brought about by loop current (a first loop) which flows through the peripheral conductors   31  and  32  of the opening  25 , and loop current (a second loop) which flows through the peripheral conductors  33  and  34  of the opening  26 . 
     Further, the planar antenna apparatus of  FIG. 8  has a shape in which the conductors in the peripheral region (region A in  FIG. 8 ) of the transmission line  23  are removed, and elongate open stubs  35  project from the GND conductor  36  inside the openings  25  and  26 . The open stubs  35  are adjusted to the length which is shortened according to a perimeter length of the openings  25  and  26  on the basis of  ¼ of a desired radio signal wavelength (i.e. λ/4). By providing the open stub  35 , the shape of the loop antenna formed by the opening  25  and the stub  35  can be brought close to a quadrangle. Then the opening area of the openings  25  and  26  is further expanded. This applies to another loop antenna formed by the opening   26  and the stub  35 . 
     By appropriately changing the length of the open stub  35 , the electrical length of the loop antenna can be easily adjusted and it is easier to match the desired frequency (resonance frequency). Accordingly, the open stub  35  has a role of a return path for return current C 5  and C 6  described later, and also a role of matching the electrical length of the loop antenna to the desired frequency. As the electrical length of the loop antenna can be adjusted by the length of the open stub, advantages can be achieved, such as reduction of designing period. 
     The state of magnetic field radiation of the antenna unit  1  is explained hereinafter.  FIG. 9  shows loop current flowing through the antenna unit  21  and magnetic fields generated by the loop current when a signal is supplied to the antenna unit  21  from the signal line  24  via the matching unit  22 . In connection with the signal supply to the antenna unit  21 , the forward current C 1  is generated in the transmission line  23 . The forward current C 1  generates a forward magnetic field Ml. The forward current C 1  is divided into the return current C 2  which flows through the peripheral conductors  31  and  32  (the first loop) of the opening  25 , and the return current C 3  which flows through the peripheral conductors  33  and   34  (the second loop) of the opening  26 . A return magnetic field M 2  in the first loop is generated by the return current C 2  which flows through the first loop. Similarly, a return magnetic field M 3  in the second loop is generated by the return current C 3  which flows through the second loop. Due to the return magnetic fields M 2 , M 3 , and the forward magnetic field M 1 , magnetic flux is localized in the region in the antenna unit  1  excluding the transmission line  23  (the region not opposing the line  23  of the openings  25  and  26 ), and strong electromagnetic waves are emitted to space. 
     The magnetic field is cancelled out at the position of the matching unit  22  by the return magnetic field M 2  in the first loop and the return magnetic field M 3  in the second loop. Therefore, the layout of arranging the openings  25  and  26  axis-symmetrically with respect to the transmission line  23  reduces the influence of the magnetic field to the matching unit  22  from the antenna unit  21 . At this time, in order to reduce a leakage of the electromagnetic field in the matching unit   22 , the transmission line  23  is used. That is, the return current C 2  and C 3  flow through the shortest path to the GND conductor  36  along the conductor edge due to the nature of the high-frequency current. Therefore, the main return currents C 5  and C 6 , which are opposite direction to the forward current C 1 , flow the surface of the stub  35 . Then, it is possible to suppress propagation of the magnetic field M 4  in the transmission line  23  and also disorder of electromagnetic wave radiation of the antenna unit  21 . 
     Except for the case of performing a band design, characteristic impedance of the transmission line  23  is not important, but the electrical length θ is. For this reason, the width of the GND conductor (stub)  35  as the transmission line  23 , that is a coplanar waveguide, does not need twice the width of the conductor interval L 3  in the transmission line  23 . Accordingly, the necessary area of the matching unit  22  can be reduced. By placing the matching unit  22 , which has a reduced area due to the reduction of the width of the stub  35 , in the antenna unit  21 , it is possible to bring close the periphery of the two loop antennas formed by the first loop along the opening  25  and the second loop along the opening  26  to λ/2, and also to expand the opening area. Then, stronger resonance is obtained, and the forward current C 1 , the return current C 2  in the first loop, and the return current C 3  in the second loop increase. 
     Note that the width of the open stub  35  is conditional on not being influenced by the skin effect (current reduction due to the insufficient surface depth). Since the open stubs  35  are placed in the openings  25  and  26 , an electromagnetic field generated in the transmission line  23  does not influence the circumference. Further, the magnetic field from the first and the second loop has the weakest magnetic flux density in the intermediate position of these two loops. Therefore, even if the transmission line  23  is placed in the intermediate position of these two loops, the transmission line  23  and an antenna do not disturb operations each other. The transmission line  23  is sandwiched between the first and the second loop. Current with substantially the same direction and size, which is indicated by the return current C 2  in the first loop and the return current C 3  in the second loop in  FIG. 8  flows through the two loops. 
       FIG. 10A  illustrates the direction of the magnetic field of the antenna unit   21  in  FIG. 8 .  FIG. 10A  illustrates the magnetic field by the return current C 2  in the first loop and the direction thereof, and the magnetic field by the return current C 3  in the second loop and the direction thereof. As the direction of the magnetic field differs in the part where the two the magnetic fields by return currents C 2  and C 3  are intersect, that is, the part where the first and the second loop magnetic fields overlap, the magnetic field is cancelled out. 
       FIG. 10B  illustrates magnetic flux density of the part of the transmission line  23  in  FIG. 8 . A region surrounded by an ellipse  40  in  FIG. 10B  is corresponds to the position of the transmission line  23 . At the position of the transmission line  23 , the magnetic flux density is reduced by cancelling out the magnetic field from the first and the second loop. That is, the influence on the transmission line   23  is reduced. On the other hand, the directions of the return current C 2  in the first loop and the return current C 3  in the second loop are different from the direction of the forward current C 1  flowing through the transmission line  23 . Thus the magnetic flux density increases in the intermediate position between the two loops and the transmission line  23 , and the radiation of the magnetic field to space is increased. This achieves favorable loop antenna characteristics. Accordingly, there is no adverse effect to the magnetic field radiation characteristics by having provided the transmission line  23  (two stubs  35 ) in the openings  25  and  26 . 
     Next, an advantage in terms of the radiation efficiency of the planar antenna apparatus according to this embodiment is explained hereinafter. The radiation resistance R R  of the antenna unit  21  according to this embodiment is larger than the radiation resistance R R  of the antenna unit  101  of  FIG. 11  in a similar way as the antenna unit  1  according to the first embodiment. Therefore, as shown in the formula (3), the radiation resistance Ra of the planar slot dipole antenna depends on the antenna length L. However, the antenna length L cannot be sufficiently extended from the necessity of reserving the area of the peripheral conductor of the antenna unit  101  of  FIG. 11 . On the other hand, in the layout of the antenna unit  21  shown in  FIG. 8 , since the area of the peripheral conductors  31  to  34  is reduced in an attempt to expand the area of the openings  25  and  26 , the antenna length L 2  and the antenna width W 2  of  FIG. 8  can be extended respectively from the antenna length L and the antenna width W of  FIG. 11 . 
     Further, as for the radiation characteristics of the antenna unit  21 , the radiation resistance is proportional to the opening area and will be close characteristics to the loop antenna that does not require an infinite conductor. Suppose that both opening areas of the opening  25  (the first loop) and the opening   26  (the second loop) are A and the number of the openings (loops) is two, the radiation resistance R R  of the antenna unit  21 , which is considered to be a loop antenna, can be represented by a formula (7), in a similar manner as the abovementioned formula (4). Specifically, the radiation resistance R R  of the antenna unit  21  is proportional to the square of the opening area A of each of the first and the second loop. 
     
       
         
           
             
               
                 
                   
                     R 
                     R 
                   
                   = 
                   
                     320 
                      
                     
                         
                     
                      
                     
                       π 
                       4 
                     
                      
                     
                       
                         
                           2 
                           2 
                         
                         · 
                         
                           A 
                           2 
                         
                       
                       
                         λ 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Next, if the loop antenna length L 2  of  FIG. 8  is assumed to be equal to the antenna length L of  FIG. 11 , a ratio of the radiation resistance Ra of the antenna unit  101  of  FIG. 11  to the radiation resistance R R  of the antenna unit  21  of  FIG. 1  is represented by a formula (8). 
         Ra/R   R   =L   2 ·λ 2 /16π 2   ·L   2 ·( W 2) 2    (8)
 
     From the formula (8), a condition of the antenna width W 2  for the radiation resistance R R  to exceed the radiation resistance Ra can be represented by a formula (9). 
       λ/4π≦ W 2   (9)
 
     In the formula (8), it is assumed that the antenna length L 2  of  FIG. 8  is equal to the antenna length L of  FIG. 11 . However, as described above, in this embodiment, since the width of the peripheral conductors  32  and  34  can be reduced, the antenna length L 2  of  FIG. 8  can be made longer than antenna length L of  FIG. 11 . Accordingly, in a similar manner as the antenna unit  1  of  FIG. 1  explained in the first embodiment, when the antenna width W 2  of  FIG. 8  satisfies at least the condition shown in the formula (9), the radiation resistance R R  of the antenna unit  21  according to this embodiment will be larger than the radiation resistance R R  of the antenna unit  101  of  FIG. 11 . Moreover, in the configuration of  FIG. 8 , the conductors around the transmission line  23  (region A of  FIG. 8 ) are removed, and the width W 2  of the openings  25  and  26  is also extended. Therefore, the radiation resistance R R  of the antenna unit  21  can be further increased. 
     In order to bring the resonance frequency of the loop antenna close to the desired frequency, it is necessary to bring the perimeter length of the first loop and the second loop close to λ/2. A formula (10) represents the perimeter length of the slots  102  and  103  provided in the antenna unit  101  of  FIG. 11 . 
       2( L+W )   (10)
 
     In order to bring each perimeter length of each slot  102  and  103  to λ/2 while maintaining the same area as the antenna apparatus of  FIG. 11 , the peripheral conductor area of the transmission line  104  in  FIG. 11  may be removed, and the perimeter length of the removed peripheral conductor may be added to the perimeter length of the slots  102  and  103 . That is, the shape of the antenna unit   21  of the antenna apparatus ( FIG. 8 ) according to this embodiment may be adopted. 
     The length of the transmission line  23  including the open stub  35  may be determined by resonating with the antenna by multiplying a coefficient of contraction a, which is determined by the perimeter length of the antenna unit  21  and the antenna width W 2  or the like, by a reference value based on ¼ of the desired radio signal wavelength (λ/4). The perimeter of the openings (slots)  25  and  26  of  FIG. 8  can be respectively represented by formulas (11) and (12) using the antenna length L 2 , the antenna width W 2 , a part of the antenna perimeter length W 4 , and the coefficient of contraction α. If the formula (12) is compared with the formula (10), the formula (12) can extend the slot perimeter more than the formula (10), and it will be easy to bring the slot perimeter to λ/2. Accordingly, the resonance can flow larger current to the antenna unit  21 . 
         W 2=α(λ/4)+ W 4   (11)
 
       2( L 2 +W 2)≅λ/2   (12)
 
     In  FIG. 8 , the characteristic impedance of the transmission line  23  may be designed on the condition that the GND conductor  36  is an infinite planar conductor. However, in practice, since the GND conductor  36  is a finite conductor, it is preferable to take a deviation from a theoretical value into consideration. For example, the width of the open stub  35  may be twice or more than the GND conductor interval L 3  in the transmission line  23 . When it is not required to consider the characteristic impedance, only the length W 3  of the transmission line  23  is important. Thus the width of the open stub  35  may be further reduced to the width that is not influenced by the skin effect. The first and second embodiments can be combined as desirable by one of ordinary skill in the art. 
     While the invention has been described in terms of several embodiments, those skilled in the art will recognize that the invention can be practiced with various modifications within the spirit and scope of the appended claims and the invention is not limited to the examples described above. Further, the scope of the claims is not limited by the embodiments described above. Furthermore, it is noted that, Applicant&#39;s intent is to encompass equivalents of all claim elements, even if amended later during prosecution.