Abstract:
A patch antenna is described that includes a ground plane, a first shorting structure in contact with the ground plane, a first conductor plate in contact with the first shorting structure. The patch antenna can also include a second shorting structure in contact with the ground plane, and a second conductor plate in contact with the second shorting structure and forming a radiation slot with the first conductor plate. Other devices and methods are herein provided for.

Description:
CROSS-REFERENCE TO RELATED APPLICATION  
       [0001]    This application claims priority to copending U.S. provisional application entitled, “SIZE-REDUCED FOLDED SHORTED-PATCH ANTENNA FOR WIRELESS COMMUNICATIONS,” having Ser. No. 60/340,977, filed 12/12/2001, which is entirely incorporated herein by reference. 
     
    
     
       TECHNICAL FIELD  
         [0002]    The present invention is generally related to communications, and, more particularly, is related to antennas.  
         BACKGROUND OF THE INVENTION  
         [0003]    In modern mobile and wireless communications systems, there is an increasing demand for smaller low-cost antennas. This is especially true for handheld wireless applications, such as in mobile phone handsets or Bluetooth chips, where a package-integrated antenna may be desirable. It is well known that planar structures such as microstrip patch antennas have a significant number of advantages over conventional antennas, such as low profile, light weight and low production cost. However, in some practical wireless communications systems such as Global System for Mobile Communications (GSM) 1800, Personal Communications Service (PCS) 1900, wideband code division multiple access standard IMT 2000, or Bluetooth ISM (Industrial, Scientific, and Medical), the physical size of planar structures may be too large for integration with radio frequency (RF) devices.  
           [0004]    One type of antenna suitable for use with personal communications devices is the conventional patch antenna  100 , shown in a side view in FIG. 1. The patch antenna  100  (here a λ 0 /2 patch antenna) comprises a ground plane  102 , a patch (or a conductor plate)  104 , and a feed  106 . It is well known that a conventional patch antenna operating at the fundamental mode, Transverse Magnetic (TM) mode TM 01 , has an antenna length of ˜λ 0 /2. The length of the patch is set in relation to a wavelength λ 0  associated with the resonant frequency f 0 . A number of techniques have been proposed to reduce the size of conventional half-wave (λ 0 /2, where λ 0  is the guide wavelength in the substrate) patch antennas. One approach is to use a high dielectric constant substrate (e.g., between the patch  104  and the ground plane  102 ). However, such an approach often leads to poor efficiency and narrow bandwidth.  
           [0005]    Shorting structures (e.g., shorting posts, shorting walls) also have been used in different arrangements to reduce the overall size of the patch antenna. Considering that the electric field is zero for the TM 01  mode at the middle of the patch  104 , the patch  104  along its middle line can be shorted with a metal wall without significantly changing the resonant frequency of the patch antenna  100 . FIG. 2 illustrates a conventional shorted patch antenna  200  that includes a patch  204  that is shorted to the ground plane  202  with a metal wall  208 . This shorted patch antenna  200  includes a patch  204  with a length of λ 0 /4. Further patch size reduction measures include using a shorting pin (not shown) near the feed  206 . The size-reduction technique using a shorting pin has been applied to the design of small patch antennas for 3G IMT-2000 mobile handsets.  
           [0006]    A planar invert-F antenna (PIFA) is one of the most well-known and documented small patch antennas. Actually, the PIFA can be viewed as a shorted-patch antenna. Therefore the antenna length of a PIFA is generally less than λ 0 /4. When a shorting post is located at a corner of a square plate, the length of the PIFA can be reduced to λ 0 /8. The size of a PIFA can be also reduced by loading it. Recent research efforts on the size reduction of patch antennas have focused on patch-shape optimization to increase the effective electric length of the patch. For example, by notching a rectangular patch, the antenna length can be reduced to less than λ 0 /8. A printed antenna with a surface area 75% smaller than a conventional microstrip patch was obtained by incorporating strategically positioned notches near a shorting pin. However, the demand for a further reduction in size while preserving or improving some performance characteristics of larger antennas still exists.  
           [0007]    Thus, a need exists in the industry to address the aforementioned and/or other deficiencies and inadequacies.  
         SUMMARY OF THE INVENTION  
         [0008]    The preferred embodiments of the present invention provide for a patch antenna. Briefly described, one embodiment of the patch antenna, among others, can be implemented as follows. The patch antenna includes a ground plane, a first shorting structure in contact with the ground plane, a first conductor plate in contact with the first shorting structure, a second shorting structure in contact with the ground plane, and a second conductor plate in contact with the second shorting structure and forming a radiation slot with the first conductor plate.  
           [0009]    The preferred embodiments of the present invention also include, among others, a method for making a patch antenna. One method can generally be described by the following steps: connecting a first conductor plate to a ground plane with a first shorting structure, the first conductor plate substantially parallel to the ground plane, the first conductor plate having an electrical length of approximately λ 0 /16; and connecting a second conductor plate to the ground plane with a second shorting structure, the second conductor plate substantially parallel to the first conductor plate, the second conductor plate having an electrical length of approximately λ 0 /16, the second conductor plate forming a radiation slot with the first conductor plate.  
           [0010]    Other systems, methods, features, and advantages of the present invention will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present invention, and be protected by the accompanying claims. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0011]    Many aspects of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.  
         [0012]    [0012]FIG. 1 is a side view of a prior art patch antenna.  
         [0013]    [0013]FIG. 2 is a side view of a prior art shorted patch antenna.  
         [0014]    FIGS.  3 A- 3 B are front and rear view schematic diagrams of a portable telephone that incorporates a folded shorted patch (FSP) antenna, in accordance with one embodiment of the invention.  
         [0015]    FIGS.  4 A- 4 B are side views demonstrating one method for making the FSP antenna of FIG. 3B, in accordance with one embodiment of the invention.  
         [0016]    [0016]FIG. 5A is an isometric view of the FSP antenna depicted in FIG. 4B, in accordance with one embodiment of the invention.  
         [0017]    [0017]FIG. 5B is a Smith chart showing the input impedance of the FSP antenna of FIG. 5A fed at different lower patch locations, in accordance with one embodiment of the invention.  
         [0018]    FIGS.  6 - 8  are graphs showing the effect on return loss and resonant frequency when modifying the shape parameters of the FSP antenna of FIG. 5A, in accordance with one embodiment of the invention.  
         [0019]    FIGS.  9 A- 9 B are graphs showing the radiation patterns of the FSP antenna of FIG. 5A after modifying the height parameters, in accordance with one embodiment of the invention.  
         [0020]    FIGS.  10 A- 10 C are side views illustrating the process of unfolding a folded shorted patch (S-P) antenna to arrive at a transmission model, in accordance with one embodiment of the invention.  
         [0021]    [0021]FIG. 10D is the transmission model of the unfolded S-P antenna derived from unfolding operations depicted in FIGS.  10 A- 10 C, in accordance with one embodiment of the invention.  
         [0022]    FIGS.  11 A- 11 C are Smith charts comparing the theoretical and numerical input impedance of the unfolded S-P antennas and folded S-P antennas depicted in FIGS.  10 A- 10 C, in accordance with one embodiment of the invention.  
         [0023]    [0023]FIG. 12 is a graphical illustration of the suseptance and capacitance versus various resonant frequencies of the unfolded S-P antennas and folded S-P antennas depicted in FIGS.  10 A- 10 C, in accordance with one embodiment of the invention.  
         [0024]    [0024]FIG. 13 is a graph showing the simulated results for input impedance versus frequency for the FSP antenna using a lumped capacitor, in accordance with an alternate embodiment of the invention.  
         [0025]    [0025]FIG. 14 is a graph showing the difference between simulated and measured return loss versus resonance frequency for one example FSP antenna implementation, in accordance with one embodiment of the invention.  
         [0026]    FIGS.  15 A- 15 B are graphs showing the radiation patterns of the simulated versus measured results of the FSP implementation described in association with FIG. 14, in accordance with one embodiment of the invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0027]    The preferred embodiments of the invention now will be described more fully hereinafter with reference to the accompanying drawings. One way of understanding the preferred embodiments of the invention includes viewing them within the context of a personal communications device, and more particularly within the context of an antenna for a portable telephone. However, it is noted that the preferred embodiments can be viewed within other contexts, such as for use in cellular handsets, sensors for monitoring, and wireless smart cards, among other example contexts that use antennas for transmitting and/or receiving signals over a medium.  
         [0028]    In the description that follows, a folded shorted patch (FSP) antenna will be described that is reduced in size compared to conventional patch antennas. By folding a shorted rectangular patch, the resonant length of the antenna can be reduced from ˜λ 0 /4 to ˜λ 0 /8. A further decrease of as much as more than 50% in the resonant length may be achieved through adjusting the width of the shorting walls and the heights of the folded patches. Thus the overall electrical length (less than λ 0 /16) of the FSP antenna can be eight times shorter than the length of a conventional patch (˜λ 0 /2). A brief note about the term electrical length can be described as follows. For example, if a patch with a physical length of 150 millimeters (mm) can operate at 1 gigahertz (GHz) (λ 0 =300 mm), then the electrical length of this patch will be understood to be λ 0 /2. But if the patch with the same physical length (150 mm) can operate at 500 megahertz (MHz) (λ 0 =600 mm), the electrical length of the same patch is now λ 0 /4.  
         [0029]    A structure of the FSP antenna for a personal communications device will be described below. One method for making the FSP antenna will also be described, as well as some numerical simulations described that are recorded in a series of graphs illustrating input impedance, radiation patterns, and the effect on return loss and resonant frequency when various elements of the FSP antenna are modified. This discussion is followed by a theoretical analysis based on a transmission-line model created by unfolding a folded shorted patch antenna, and then a comparison of the theoretical versus numerical simulations is discussed and illustrated. The FSP antenna operation for reducing resonant frequency is analyzed by considering the antenna as a shorted patch loaded with a capacitive device, followed by an example implementation of an FSP antenna.  
         [0030]    [0030]FIGS. 3A and 3B illustrate one example implementation for the FSP antenna. Specifically, FIG. 3A depicts a front view of a portable phone  300  having a speaker  308 , a microphone  312 , a display  316 , and a keyboard  320 , as well as internal transceiver circuitry not shown. FIG. 3B is a rear view of the portable phone  300  shown in FIG. 3A showing an FSP antenna  504  preferably mounted to the back of the portable phone  300  to reduce the specific absorption rate (SAR) potentially absorbed in the head of a user. The length of the FSP antenna  504  determines its resonant frequency. For example, a quarter wave (i.e., λ 0 /4) patch antenna having a length L will resonate at a frequency of c/4L, where c equals the speed of light. At or near the resonant frequency is where the FSP antenna  504 , or patch antennas in general, radiate most effectively.  
         [0031]    FIGS.  4 A- 4 B show a series of side views demonstrating one mechanism for making the FSP antenna structure via a series of folding operations, in accordance with one embodiment of the invention. FIG. 4A shows a folded shorted patch antenna  400  that demonstrates the steps of folding over the patch  404  together with the ground plane  402 . The example folded shorted patch antenna  400  includes a lower shorting wall  408  and a feed probe  406 . The total resonant length of the folded shorted patch antenna  400  is still ˜λ 0 /4. That is, the length spanning from the shorting wall formed by folding the ground plane  402  (referenced as the upper shorting wall  510  in FIG. 4B) to the radiating slot entrance is ˜λ 0 /4, which indicates that the resonant frequency of an FSP antenna  504  (FIG. 4B) is similar to that of a conventional shorted patch antenna  200  (FIG. 2), as is borne out in numerical simulations and theoretical analysis. The actual length (i.e., electrical length) of the folded patch  404  has been reduced through the folding operation by 50% to ˜λ 0 /8.  
         [0032]    With continued reference to FIG. 4A, and referring now to FIG. 4B, by adding a new piece of the ground plane to the right of the folded ground plane  402  and pressing the folded patch  404  together to form a lower patch  505 , a folded shorted patch antenna  504  is produced. Note that the original right part of the folded ground plane  402  (FIG. 4A) now serves as an upper shorting wall  510  and an upper patch  512  of the folded shorted patch antenna  504 . The space between the upper patch  512  and the lower patch  505  comprise a radiating slot from which electromagnetic energy is concentrated and transmitted and/or received.  
         [0033]    [0033]FIG. 5A depicts a general structure of the FSP antenna  504  shown in FIG. 4B. For simplicity, the discussions that follow will assume an implementation for the FSP antenna  504  in free space (i.e., an air dielectric substrate is approximated as a free space). The FSP antenna  504  includes a ground plane  502 , a lower patch  505 , an upper patch  512 , a lower shorting wall  508 , an upper shorting wall  510 , and a feed probe  506 . The ground plane  502  is preferably made of a conductive material such as aluminum, copper, and/or gold. The ground plane  502  is separated from the lower patch  505  by a dielectric substrate. The dielectric substrate described herein will be air, but can be glass or practically any other dielectric substrate.  
         [0034]    The lower patch  505  is approximately parallel to the ground plane  502 , and is shown with dimensions of width W 1 , length L 1 , and a height h 1  from the ground plane  502 . One end of the lower patch  505  is in contact with the ground plane  502  via the lower shorting wall  508 . The lower shorting wall  508  is shown with dimensions of width d 1 .  
         [0035]    A feed probe  506  can be electrically connected to the lower patch  505 . The feed probe  506 , which can be a coaxial cable, passes through the ground plane  502  and contacts the lower patch  505 . For example, a coaxial cable having an inner and outer conductor will be connected to the lower patch  505  using the inner conductor (e.g., feed probe, with no connection to the ground plane) and the outer conductor will connect to the ground plane  502 . The feed probe  506  connects a signal unit (not shown) to the lower patch  505  at various distances (y p ) from the lower shorting wall  508  in the y-direction. The signal unit can be connected to the lower patch  505  in other ways, such as via a microstrip or a transmission line. The signal unit provides a signal of a selected frequency band to the lower patch  505 , which creates a surface current in the lower patch  505 . The density of the surface current is high near the region of the lower patch  505  in proximity to where the feed probe  506  contacts the lower patch  505 . This current density decreases gradually along the length of the lower patch  505  in a direction away from the point where the feed probe  506  contacts the lower patch  505 .  
         [0036]    The FSP antenna  504  can be adjusted to match a defined feed input impedance, for example a 50-Ω feed, by changing the position of the feed probe  506 . The input impedance of the FSP antenna fed at different positions (y p ) is plotted in a Smith chart shown in FIG. 5B, with position adjustment in the x-direction having little effect on the impedance match. As shown, the impedance locus shrinks in size as the feed point moves closer to the lower shorting wall  508  (FIG. 5A). The asymmetry of the impedance locus about the x=0 axis in the Smith chart is due to the feed-probe reactance, which when read from the impedance locus is found to be near j25 Ω.  
         [0037]    Returning to FIG. 5A, the FSP antenna  504  also includes an upper patch  512  that is approximately parallel to the lower patch  505 . The upper patch  512  serves as a coupling patch (i.e., it is not fed by direct physical contact to a feed line or feed probe, but instead is excited through electromagnetic coupling). The upper patch  512  is shown with dimensions of width W 2 , length L 2 , and a height h 2  from the lower patch  505 . The upper patch  512  is in contact with the ground plane  502  via the upper shorting wall  510 . The upper shorting wall  510  is shown with a width of d 2 . The electric field of the FSP antenna  504  is concentrated in the gap (i.e., radiation slot) between the lower and upper patches ( 505 ,  512 ). Surface-current distributions primarily occur on the top face of the lower patch  505 , with smaller surface current distributions occurring on the inside face of the upper shorting wall  510 . An electric-field concentration also exists between the edge of the lower patch  505  (the edge closest to the upper shorting wall  510 ) and the upper shorting wall  510 . This is due at least in part to the effects of the relatively sharp edge of the lower patch  505  and the short distance between the edge and the upper shorting wall  510 . Increasing the distance between the edge and the upper shorting wall  510  (i.e., a shortened L 1 ) can improve the impedance bandwidth of the FSP antenna  504 .  
         [0038]    With continued reference to FIG. 5A throughout the discussion of FIGS.  6 - 8  that follow, the resonant frequency of the FSP antenna  504  can be lowered by slightly modifying the shape parameters of the FSP antenna  504 , such as by reducing the widths of the two shorting walls  508  and  510  and/or adjusting the heights h 1 , h 2  of the lower and upper patches  505 ,  512 . FIGS.  6 - 8  provide illustrations of the effects on return loss and resonant frequency when simulating the modification of these dimensions through numerical analysis (e.g., via well-known transmission line match (TLM) and finite differential time domain (FDTD) simulations). FIG. 6 shows the simulated effects on resonant frequency and return loss with a varying d 1  dimension. For example, the width (d 1 ) of the lower shorting wall  508  is reduced while setting and maintaining the width (d 2 ) of the upper shorting wall  510  to be d 2 =W 2  and the heights (h 1 =h 2 =1.5 millimeters (mm)) of the lower and upper patches  505 ,  512 . As shown, the resonant frequency (shown at the inverted peaks) decreases as the width (d 1 ) of the lower shorting wall  508  becomes narrower (i.e., from 10 mm to 2 mm). Continuing the analysis, while setting and maintaining d 1 =2 mm, the width of the upper shorting wall (d 2 ) can be changed, the effect of which is shown in FIG. 7. Again, the resonant frequency further decreases as d 2  reduces. One reason for the decrease of the resonant frequency with a reduction of the widths of the shorting walls ( 508 ,  510 ) is an increase in the inductance of the upper and lower patches ( 505 ,  512 ).  
         [0039]    [0039]FIG. 8 demonstrates the effects of simulating an adjustment in the height (h 1 ) of the lower patch  505  while setting and maintaining d 1 =d 2 =2 mm and the total FSP antenna height (h 1 +h 2 )=3 mm. The variation of the return loss with h 1  and the difference in resonance frequency is as shown. It is noted that a variation in h 1  has a more significant impact on the resonant frequency than changes in d 1  and d 2 . As the lower patch  505  moves toward the upper patch  512 , the resonant frequency decreases. When the distance between the lower and upper patches ( 505 ,  512 ) is less than ⅕ of the total FSP antenna height, the resonant frequency reduces by more than a half of 3.6 GHz. One reason for the decrease in the resonant frequency with increase in h 1  (or a decrease in the distance between the lower and upper patches ( 505 ,  512 )) is due to an enhancement of the capacitive coupling between the lower and upper patches ( 505 ,  512 ) as the upper and lower patches are brought closer to each other.  
         [0040]    The position of the feed probe  506  will typically be adjusted for different antenna shape parameters to match, for example, a 50-Ω feed. Usually the radiation resistance increases with a decrease in antenna thickness and patch width because the radiated power decreases. Thus, the resonant resistance increases as the resonant frequency decreases. For the FSP antenna  504 , the more the resonant frequency is reduced by varying the antenna shape parameters, the closer the feed probe position is shifted to the lower shorting wall  508 .  
         [0041]    The simulated radiation patterns at resonant frequencies for h 1 =0.5 mm at 3.63 GHz and with h 1 =2.5 mm at 1.65 GHz are shown in FIGS. 9A and 9B. As shown in FIG. 9A, the radiation pattern represents the far-zone field in the x-z plane of a Cartesian coordinate system (x,y,z) while FIG. 9B includes a radiation pattern that represents the far-zone field in the y-z plane. In each plane, the far-zone field includes two orthogonal components E φ  and E θ . E φ  in the y-z plane is zero due to symmetry, and thus there are only two lines indicated in FIG. 9B. For comparison, the radiation patterns at two different frequencies are plotted in each graph. The radiation patterns for the h 1 =0.5 mm case is depicted using a solid line, and the h 1 =2.5 mm case is depicted with a dotted line. The magnitude of electromagnetic energy, |E|, is in units of decibels (dB). The cross-polarized component is shown in FIG. 9A, and illustrates a more pronounced difference between the two cases: a lower h 1  corresponds to a higher cross-polarized level. Usually the cross polarized level increases with antenna thickness (i.e., total antenna height). When h 1  decreases, h 2  increases and the resonant frequency increases. As a result, the width of the radiating slot (h 2 ) further increases electrically, thus causing an increase in the cross-polarized level.  
         [0042]    In the section that follows, the FSP antenna  504  (FIG. 5A) is described analytically by employing a transmission-line model. Also a qualitative analysis of the resonant frequency of the FSP antenna  504  is presented of the FSP antenna operation.  
         [0043]    FIGS.  10 A- 10 C present the FSP antenna  504  with three different patch-height arrangements, shown in FIGS.  10 A- 10 C under the column heading, “folded S-P” (shorted patch): Case I (h 1 =h 2 =1.0 mm), Case II (h 1 =0.5 mm, h 2 =1.0 mm), and Case III (h 1 =1.0 mm, h 2 =0.5 mm). The “folded S-P” is unfolded to arrive at an “equivalent” (i.e., equivalent for transmission line analysis purposes) unfolded shorted patch (under the column heading, “unfolded S-P”) configuration associated with these three cases. Neglecting the effect of discontinuities, the “unfolded S-P” can be represented by a transmission-line equivalent circuit as shown in FIG. 10D. The input impedance of the “unfolded S-P” based on this equivalent circuit is obtained as follows:  
           Z   in   =jX   f   +Z   1   (1)  
         [0044]    where X f  is the feed-probe reactance given by  
               X   f     =         ω                   μ   0          h   1         2                 π            [       ln        (     2     β                   r   p         )       -   0.57721     ]               (   2   )                               
 
         [0045]    with β=2π/λ 0  and r p =the feed-probe radius. Z 1  (=1/Y 1 ) is obtained from the transmission-line equivalent circuit, that is,  
               Y   1     =         Y   01          1     j                   tan        (     β                   y   p       )             +       Y   01          Y   2       +       j                   Y   01          tan        [     β        (       L   1     -     y   p       )       ]             Y   01     +     j                   Y   2                     tan        [     β        (       L   1     -     y   p       )       ]                       (   3   )                 Y   2     =         Y   02          Y   s       +       j                   Y   02          tan        (     β                   L   1       )             Y   02     +     j                   Y   s                     tan        (     β                   L   1       )                       (   4   )                               
 
         [0046]    where Y 01  and Y 02  are respectively the characteristic admittance of the lower and upper patches, and Y s =G s +jB s . Here, G s  is the conductance associated with the power radiated from the radiating edge (or the radiating slot), and B s  is the susceptance due to the energy stored in the fringing field near the edge of the patch. In the calculations described herein, the following equations for Y(=Y 01  for h=h 1  or Y 02  for h=h 2 ), G s , and B s  were used:  
               Y   0     =             W   /   h     +   1.393   +     0.667                   ln        (       W   /   h     +   1.444     )             120                 π                     for                   W   /   h       ≥   1             (   5   )                 G   s     =     {               W   2     /     (     90                   λ   0   2       )           for         W   ≤     0.35                   λ   0                     W   /     (     120                   λ   0       )       -     1   /     (     60        λ   0   2       )             for           0.35                   λ   0       ≤   W   ≤     2        λ   0                   W   /     (     120                   λ   0       )           for           2                   λ   0       ≤   W                           (       h   2     ≤     0.02                   λ   0         )                 (   6   )                               
  B   s   =Y   02  tan(βΔ l )  (7)  
               Δ                 l     =           ς   1          ς   3          ς   5         ς   4            h   2               (   8   )                               
 
         [0047]    where W is the width of the patch and coefficients ζ 1 , ζ 3 , ζ 4 , ζ 5  can be found in the reference entitled, “Microstrip antenna design handbook”, by R. Garg et al., 2001, which is herein incorporated by reference.  
         [0048]    The theoretical results for the input impedance are obtained using the above analytical expressions and compared in FIGS.  11 A- 11 C with numerical simulations for the above three cases. Note that the numerical results are obtained for the “folded S-P” shown in FIGS.  10 A- 10 C. The theoretical and numerical results are in good agreement. The difference between the theoretical and simulated resonant frequencies is less than 3%. Also, it is again noted that the resonant frequency decreases as h 2 /h 1  decreases. This can be explained qualitatively as follows. For simplicity, the effects of Y S (Y S &lt;&lt;Y 0  in practice) and X f  (focusing on the resonance of the patch alone) are neglected. As a result the “unfolded S-P” becomes a shorted transmission line loaded with an open transmission line. Assume that the resonant frequency is almost independent of the feeding position, y p =L 1  Thus, Y 1  becomes  
               Y   1     =         Y   01          1     j                   tan        (     β                   L   1       )             +     j                   Y     02                       tan        (     β                   L   1       )                   (   9   )                               
 
         [0049]    At resonance, Y 1 =0 leads to  
           Y   01 /tan(β L   1 )= Y   02  tan(β L   1 ) or tan(β L   1 )={square root}{square root over ( Y   01   /Y   02 )}  (10)  
         [0050]    From equation 5 above, note that Y 0  is inversely proportional to h; therefore, from equation 10, it is determined that the resonant frequency varies proportionally with h 2 /h 1 . A graphical solution of equation 10 for resonant frequency is depicted in FIG. 12, where the intersection of the curves Y 01 /tan(βL 1 ) and Y 02  tan(βL 1 ) implies a resonant point. FIG. 12 includes a plot of suseptance versus βL 1 . Note that if Y 01 =Y 02 , then βL 1 =π/4 corresponds to an antenna length of L 1 =λ 0 /8. Also note that an increase in Y 02  leads to a decrease in βL 1  if Y 01  remains unchanged.  
         [0051]    With continued reference to FIGS.  10 A- 10 C, considering the upper patch as a capacitive load provides additional insight for the above analysis. Replacing the upper patch with a capacitor C (not shown), which is connected between the radiating edge of the lower patch and the ground plane of the folded S-P antenna shown in FIGS.  10 A- 10 C, equation 9 becomes  
           Y   01 /tan(β L   1 )=ω C.   (11)  
         [0052]    A graphical solution of equation 11 is also plotted in FIG. 12. As noted, the resonant frequency increases as the capacitance C increases. The resonant length of a capacitively loaded shorted patch will reduce to L 1 =λ 0 /8 if the loaded capacitance is C=Y 01 /ω 0 , where ω 0 =3π/(4L 1 )×10 8  rad-s −1  is obtained from βL 1 =/4π. A decrease in h 2  is equivalent to an increase in the coupling capacitance between the upper and lower patches, thus eventually leading to a decrease in the resonant frequency.  
         [0053]    Equation 11 suggests an alternate embodiment for the FSP antenna  504  (FIG. 5A), wherein the resonant frequency can be reduced using a lumped capacitive load (e.g., a lumped capacitor between the radiating edge of the lower patch  505  and the ground plane  502  of the FSP antenna  504  of FIG. 5A, as described above). The simulated results for input impedance versus frequency are shown in FIG. 13, wherein the resistance is shown with a sold line and the reactance is shown with a dashed line. As expected, the resonant frequency decreases with an increase in the loaded capacitance. Comparing FIGS. 12 and 13, it is noted that the proportional relationship of the resonant frequencies among C=0.3, 0.6, and 1.2 picofarad (pf) is very similar to that (about 3:4:5) read from the graphical solutions of equation 11 when C=(Y 01 /ω 0 )/2, C=Y 01 /ω 0 , and C=2Y 01 /ω 0 . This demonstrates agreement between the numerical investigation and theoretical analysis described above.  
         [0054]    As one example implementation, a test FSP antenna was integrated in the package of a Bluetooth chip operating in the Bluetooth ISM band (2.4-2.483 GHz). The test FSP antenna was fabricated with a brass sheet with a thickness of 0.254 mm. The following FSP antenna dimensions were chosen: 15 mm×15 mm (≈λ 0 /8×λ 0 /8). To achieve the bandwidth (near 4%) required by the Bluetooth specifications, the total thickness of the antenna was selected to be 6 mm. By adjusting the height (h 1 ) of the lower patch to 2.85 mm, the resonant frequency can be tuned to approximately 2.44 GHz. The simulated and measured results for the return loss are plotted in FIG. 14. As shown, good performance agreement is obtained, and both of the simulated and measured 10-dB return-loss bandwidths cover the Bluetooth band. The radiation patterns simulated and measured in the xz- and yz-planes at 2.44 GHz were compared, as shown in FIGS.  15 A- 15 B, and good agreement was again noted. There is a nearly omni-directional pattern for the co-polarized component, which is desirable for Bluetooth applications.  
         [0055]    It should be emphasized that the above-described embodiments of the present invention, particularly, any “preferred” embodiments, are merely possible examples of implementations, merely set forth for a clear understanding of the principles of the invention. Many variations and modifications may be made to the above-described embodiments of the invention without departing substantially from the spirit and principles of the invention. All such modifications and variations are intended to be included herein within the scope of this disclosure and the present invention and protected by the following claims.