Patent Publication Number: US-7714791-B2

Title: Antenna with improved illumination efficiency

Description:
FIELD OF THE INVENTION 
   This invention generally relates to an antenna structure that provides reduced far-field radiation for an equivalent near field illumination for the activation of radio frequency identification tags. In particular, the antenna structure provides parallel radiators opposed in polarity to improve antenna efficiency and increase the useful range and area of coverage within the limitations imposed by various governmental RF emission rules. Furthermore, the antenna structure can efficiently use near-field inductive-coupling to energize remote devices. 
   BACKGROUND 
   Radio frequency identification (RFID) systems operating in the high-frequency range, typically at 13.56 Megahertz (MHz), are radiation limited by governmental regulations, such as the Federal Communications Commission (FCC) rules governing the industrial, scientific, and medical (ISM) operating bands commonly used for these unlicensed systems, in particular 47CFR15.225. These RFID systems are commonly known as vicinity readers because they are capable of reading credit card sized RFID tags to a distance of 60 centimeters (about two feet). 
   As is known in the art, antenna systems have near-field and far-field radiation regions. The near field is a region near an antenna where the angular field distribution depends upon the distance from the antenna. The near field is generally within a small number of wavelengths from the antenna and is characterized by a high concentration of energy and energy storage in non-radiating fields. In contrast, the far field is the region outside the near field, where the angular distributions of the fields are essentially independent of the distance from the antenna. Generally, the far-field region is established at a distance of greater than D 2 /λ from the antenna, where D is an overall dimension of the antenna that is large compared to wavelength λ. The far-field region is where radiation from the antenna is said to occur. 
   RFID systems use near fields for communications between the RFID tag and the RFID interrogator. Also, the energy stored in the near fields provides the power to drive a microchip imbedded in a passive RFID transponder tag. Many conventional RFID systems use loop-type radiators for interrogator antennas, for example, an antenna consisting of a figure-eight shaped conductor. 
   Conventional RFID systems are being increasingly used to enhance supply chain activities, security, and a myriad of other applications and industries. However, conventional RFID systems often have limited operating ranges, which limits their usefulness. Attempts to increase RFID system range, however, often result in the need for increasing input power, which violates FCC radiation limitations, generally because of proportional increases in far-field radiation. 
   It would, therefore, be useful to provide a RFID system that can increase near fields while simultaneously reducing far-field radiation. Such a RFID system would have an increased operating range while abiding by applicable governmental RF radiation regulations. 
   SUMMARY 
   In accordance with the present invention, an antenna comprises a first loop having at least one first conductor, the first loop having a first enclosed area defined by the area inside the perimeter of the first loop and having a first phase center point defined by the geometric center point of the first enclosed area; and a second loop having at least one second conductor, the at least one second conductor connected to the at least one first conductor, the second loop disposed a distance from and substantially parallel to the first loop, the second loop having a second enclosed area substantially equal in size to the first enclosed area and having a second phase center point, wherein a current supplied to the first and second loops is of equal magnitude and opposite polarity in the respective first and second loops. A line normal to the plane of the first loop passes through the first and second phase center points. 
   In another aspect of the present invention, an antenna comprises a first loop having at least one first conductor, the first loop having a first enclosed area defined by the area inside the perimeter of the first loop and having a first phase center point defined by the geometric center point of the first enclosed area; a second loop having at least one second conductor, coupled to the first loop and disposed a distance from and substantially parallel to the first loop, the second loop having a second enclosed area substantially equal in size to the first enclosed area; and an outer loop coupled to the first and second loops, the first and second loops having a total enclosed area equal to the sum of the first and second enclosed areas, and the outer loop substantially parallel to the first loop and having an outer enclosed area equal to the total enclosed area and an outer phase center point, wherein a current supplied to the antenna flows in a first polarity and has a first magnitude in the outer loop and flows in a second polarity and has a second magnitude in the first and second loops, the first and second polarities opposite to each other, and the first and second magnitudes equal to each other. A line normal to the plane of the first loop passes through the first loop, second loop, and outer loop phase center points. 
   With this particular arrangement, an antenna radiates power that is substantially cancelled in the far-field radiation region while being substantially maintained or increased in the near-field region. In this way, the antenna can extend the operating range of RFID systems and, therefore, the usefulness of RFID systems. 
   In one application, a RFID transponder can incorporate the antenna to extend the distance at which RFID tags can be reliably detected and identified. For example, the antenna can extend the operating range of systems using credit card sized RFID tags. In another application, the antenna is configured to be mountable in a low-profile environment, such as a ceiling or wall space, furniture, and other devices. A device may be positioned to maximize an amount of energy received from the antenna via inductive coupling. For example, a device may be positioned on a table top directly beneath the antenna mounted behind a ceiling tile. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing features of the antenna, techniques, and concepts described herein, may be more fully understood from the following description of the drawings in which: 
       FIG. 1  is a pictorial view of a supply chain and inventory tracking environment using an RFID system; 
       FIG. 2  is a pictorial view of an embodiment of an antenna of the invention; 
       FIG. 3  is a pictorial view of an alternative embodiment of the antenna shown in  FIG. 2 ; 
       FIG. 4  is a pictorial view of an embodiment of the antenna of the invention for energizing a device; 
       FIG. 5  is a pictorial view of an alternative embodiment of the antenna shown in  FIG. 2 ; 
       FIG. 6  is a pictorial view of a further embodiment of the antenna shown in  FIG. 2 ; 
       FIG. 7  is a pictorial view of an alternative embodiment of the antenna shown in  FIG. 2 ; 
       FIG. 8  is a pictorial view of a further embodiment of the antenna shown in  FIG. 7 ; 
       FIG. 9  is a pictorial view of an alternative embodiment of an antenna of the invention; 
       FIG. 10A  is a side view of a further embodiment of the antenna shown in  FIG. 9  having the inner loops on opposing sides of the outer loop; 
       FIG. 10B  is a side view of a further embodiment of the antenna in  FIG. 9  having the inner loops on the same side of the outer loop; 
       FIG. 10C  is a side view of a further embodiment of the antenna in  FIG. 9  having an insulation layer; 
       FIG. 11A  is a pictorial view of another alternative embodiment of the antenna shown in  FIG. 9 ; 
       FIG. 11B  is a side view of the antenna shown in  FIG. 11A ; 
       FIG. 12  is a pictorial view of still a further alternative embodiment of the antenna shown in  FIG. 9 ; 
       FIG. 13A  is a pictorial view of a conventional art single loop antenna; 
       FIG. 13B  is a pictorial view of a conventional art figure-eight loop antenna; 
       FIG. 14  is a graph of the H-field at a distance from the conventional art single loop antenna; 
       FIG. 15  is a graph of the H-field at a distance from the conventional art figure-eight loop antenna; 
       FIG. 16  is a graph of the H-field at a distance from an embodiment of an antenna shown in either of  FIG. 2  or  7 ; and 
       FIG. 17  is a graph of the H-field at a distance from an embodiment of the antenna shown in  FIG. 9 . 
   

   DETAILED DESCRIPTION 
   Referring to  FIG. 1 , a supply chain and inventory tracking environment in which an embodiment of the antenna  100  operates is shown. Inventory  190  may be boxed and labeled with an RFID tag  102  having a unique ID number for the inventory  190 . The unique ID number may be stored in an inventory database  180 . As the inventory  190  moves through the supply chain, a RFID system  110  tracks and records inventory location in an inventory tracking database  182 . 
   The RFID system  110  includes RFID tags  102  and RFID stations  184  having interrogators for radio communications with the tags. As a RFID tag  102  comes into operating range of a RFID station  184 , an initiate-communications signal may be transmitted from the RFID station  184  via a station antenna  100 . A receiver/transmitter on each of the RFID tags  102  responds to the initiate-communications signal by sending the tag&#39;s unique ID number to the RFID station  184 , which is received at the antenna  100 . The RFID system  110  may include authentication signals and may provide power to passive RFID tags  102 . 
   The antenna  100  may be located at various points along the supply chain to monitor advancements of inventory  190 . For example, the antenna  100  may be located along a factory conveyor belt  192  or loading dock  194 . The RFID station  184  may be coupled to an inventory tracking server  186  over a network  188 . As the inventory  190  advances through the supply chain  192 ,  194 , the RFID system  110  identifies pieces of inventory  190  by reading the unique ID number stored on the RFID tags  102  and tracks inventory location, which may be based on a location of an RFID station  184  currently reading the tags  102 . The RFID system  110  may send inventory attributes and location information over the network  188  to the RFID tracking server  186 , which may update the inventory tracking database  182 . 
   Referring to  FIG. 2 , an antenna  200  includes a first loop  210  and a second loop  220 . The first loop  210  includes at least one first electrical conductor  212  and has a first enclosed area  214  defined by an area inside the perimeter  211  of the first loop  210 . The first loop  210  has a first phase center point  216  defined by the geometric center point of the first loop  210 . A phase center point refers to the location from which phase is measured such that the electromagnetic fields spread spherically outward, with the phase of the signal being equal at any point on the sphere. 
   The second loop  220  includes at least one second electrical conductor  222  coupled to the at least one first electrical conductor  212  and has a second enclosed area  224  defined by an area inside the perimeter  221  of the second loop  220 . The second loop  220  has a second phase center point  226  defined by the geometric center point of the second loop  220 . 
   The first and second loops  210 ,  220  are placed a distance s  204  apart and are substantially parallel to each other. Furthermore, the first and second enclosed areas  214 ,  224  are substantially equal in area to each other and the first and second phase center points  216 ,  226  are substantially coincident with a line normal to them that passes through their geometric centers, as shown by the dotted lines designated by reference numeral  215 . 
   Preferably, a feed element  206  feeds a current  208  to the first and second loop  210 ,  220 . The feed element  206  may be coupled to an electric circuit for generating the current  208 . A return element  207  is also provided to return the current to, for example, the electric circuit. 
   The feed element  206  feeds the current  208  in a first polarity  218  to the first loop  210 . Polarity refers to a direction of current flow in a conductor. The current  208  traverses to the second loop  220  through a series element  202 . The series element  202  feeds the current  208  to the second loop  220  in a second polarity  228 . The second polarity  228  is opposite to the first polarity  218 . 
   With this configuration, an antenna  200  composed of two equal-sized, coincident loops positioned parallel to each other and spaced, for example, several inches apart, produces two substantially equivalent radiation fields. However, the current flow in the two loops is in opposition and slightly offset spatially. The opposition leads to the substantial reduction in experienced far-field power. This is because the far fields from the two loops are substantially identical and in opposition to each other at a great distance from the two loops, differing by only a small amount of phase in some directions. Further, in the particular directions where the maximum phase difference occurs, the individual loops do not radiate due to the loop geometries. At the point of greatest radiation experienced in a cone having an apex angle of 45 degrees centered on the normal to the planes of the loops, the directivity of the loops results in an additional far-field reduction effect of two (−3 decibels). 
   In the vicinity of the loops, the fields are not uniform, but vary significantly as a function of distance from each loop. This variation is substantially inversely proportional to the third power of the distance from each loop. Therefore, fields created by loops separated by only a small distance can result in a significant difference in strength. This effect causes the loop fields to differ significantly from each other at all locations of interest close by the antenna  200 . Thus, the summing of the fields does not result in a substantial reduction in the total field in this region. Further, because substantially less of the energy delivered to the antenna  200  escapes as far-field radiation, the antenna  200  is more efficient. This is especially important as antenna  200  size is increased to further extend communications range to the RFID tags. In this way, the antenna  200  can increase RFID system operating range while maintaining compliance with applicable governmental RF radiation regulations. 
   The antenna  200  may be defined by a single conductive element having different portions making up, in succession, the feed element  206 , the first loop  210 , the series element  202 , and the second loop  220 . In this configuration, the series element  202  can extend perpendicularly from the first loop  210 , and can couple perpendicularly to the second loop  220 . In this way, the first and second loops  210 ,  220  are configured to be parallel to each other, and spaced a distance apart from each other that is equal to the length of the interconnecting series element  202 . 
   The antenna  200  may be configured to interoperate with various types of RFID tags. For example, the antenna  200  may supply radiated power to a passive RFID tag. In another configuration, the RFID tag may be semi-passive in that the RFID tag is battery-powered instead of inductively powered, while the RFID tag modulates the incident RF energy to communicate with the interrogating device. For example, the RFID chip may be battery powered while the RFID transmitter may modulate the incident RF field. In still another configuration, the RFID tag is an active RFID tag driven by battery power and responding with an RF field created by the RFID tag. 
   Referring now to  FIG. 3 , in which like elements of  FIG. 2  are provided having like reference designations, a further embodiment of the antenna  300  includes a first array of first loops  310  and a second array of second loops  320 . Each of the first and second arrays  310 ,  320 , may include two or more respective first and second loops  210 ,  220 . The feed element  206  supplies a current in a first polarity  218  to the first array  310  and in a second polarity  228  to the second array  320 . The first and second polarities  218 ,  228  are opposite of each other. 
   Referring to  FIG. 4 , the antenna  400  is configured to energize a device  402  through inductive coupling, as shown by the line designated by reference numeral  401 . The device  402  can include, but is not limited to, a cell phone, a laptop, a hand-held game unit or other electronic device. The term energize includes providing instantaneous energy to the device  402  to enable use of the device  402 , for example, providing instantaneous energy to a smart phone during a call or to read email on the smart phone. Energize also includes providing energy over time to recharge a device&#39;s energy storage cell, for example, recharging a cell phone battery. A battery includes, but is not limited to, rechargeable electrochemical cells, also known in the art as secondary cells, for example, NiCd, NiMH, and rechargeable alkaline batteries. Other energy storage cells include those used to power electric vehicles. 
   In one environment, the antenna  400  is configured to be mountable in a low-profile environment, such as a ceiling or wall space, furniture, and other devices. The device  402  may be positioned to maximize an amount of energy received from the antenna  400  via inductive coupling. For example, the device  402  may be positioned on a table top directly beneath the antenna  400  mounted behind a ceiling tile. 
   Referring to  FIG. 5 , in another embodiment of the antenna  500 , the first and second loops  510 ,  520  have equal enclosed areas  514 ,  524 , and coincident phase center points  516 ,  526  (as shown by dotted lines designed by reference numeral  515 ), but are offset from each other at an angle of rotation a about the phase center points in the parallel planes of the loops. For example, as some in  FIG. 5 , the first and second loops  510 , 520  may be offset 45° from each other about their respective phase center points  514 ,  524 . 
   Referring again to  FIG. 5 , the first and second loops  510 ,  520  are both square-shaped, however, the first and second loops  510 ,  520  need not have the same overall shape, as long as the enclosed areas are equal and the phase center points are coincident. For example, one of the loops may be oval-shaped, and the other of the loops may be square-shaped. 
   Referring to  FIG. 6 , an alternative embodiment of the antenna  600  includes a third loop  630 . The third loop  630  is substantially parallel to and disposed midway between the first and second loops  610 ,  620 . For example, if the first and second loops  610 ,  620  are disposed a distance s  604  from each other, the third loop  630  would be disposed a distance s/2  605  from each of the loops. 
   Furthermore, the third loop  630  has a third enclosed area  634  substantially equal to the first enclosed area  614 , and a third phase center point  636  coincident to the first phase center point  616 . The third loop  630  may be configured as a receiving component of the antenna  600 , whereas the first and second loop  610 ,  620  are transmitting components of the antenna  600 . 
   With this configuration, the antenna  600  has a transmit and receive mode. One advantage of this configuration is that the wave patterns of the first and second loops  610 ,  620  will cancel each other at the vicinity of the third loop  630 . A second isolated feed  646  can be provided to the system receiver by the third loop  630 . The isolated feed  646  can be used to improve the isolation of the receive channel from the transmit channel of an antenna system to further improve operating range. In particular, as the range over which the RFID tag can be powered is increased; the sensitivity of the receiver must increase nearly proportionally. The sensitivity of the receive channel is dependent upon its ability to differentiate the very low power of the RFID tag&#39;s response from the very high power of the interrogating transmit signal. A substantial portion of this ability is provided by the frequency separation between the interrogation and response signals. However, substantially greater sensitivity is achievable with the addition of the frequency independent isolation provided by the geometry of the antenna  600 . 
   Referring now to  FIG. 7 , in another embodiment of the antenna  700 , at least one first conductor  712  of a first loop  710  includes a first and second conductor portion  712 A,  712 B. Also, at least one second conductor  722  of a second radiator  720  includes a third and fourth conductor portion  722 A,  722 B. The first and second loops  710 ,  720  are coupled using a series of joining elements  751 ,  752 ,  753 ,  754  forming dual u-shaped structures when viewed orthogonally to an x-z plane formed by an x-dimension  792  and a z-dimension  796 . The first and second loops  710 ,  720  extend in a y-dimension  794 . The dual u-shaped structures are adjacent to each other at the series of joining elements  751 ,  752 ,  753 ,  754 , which extend in the z-dimension  796 . 
   The first and third conductor portions  712 A,  722 A may be coupled to each other at opposing sides of the antenna  700  via a first joining element  751  and a second joining element  752 . Also, the second and fourth conductor portions  712 B,  722 B are coupled to each other at opposite ends via a third joining element  753  and a forth joining element  754 . The first and third joining elements  751 ,  753  are adjacent to each other and coupled to a first feed  706 A. The first feed  706 A supplies a current  708  to the antenna  700  in a first polarity  718  through second portion  712 B of first loop  710  and in a second polarity  728  through third portion  722 A in second loop  720 . The first and second polarities  718 ,  728  are opposite to each other. The second and fourth joining elements  752 ,  754  are adjacent to each other. The second joining element  752  supplies the current  708  in the first polarity  718  through first portion  712 A of the first loop  710 . The fourth joining element  754  supplies the current  708  in the second polarity  728  through forth portion  722 B of the second loop  720 . The loops of antenna  700  are comprised of disjoint portions which carry current  708  at the same polarity, forming a singular enclosed area. For example, the first loop  710  is comprised of disjoint first and second portions  712 A,  712 B which carry the current  708  at a first polarity  718  and form the first enclosed area  714 . 
   Referring now to  FIG. 8 , antenna  800  has a transmit mode and a receive mode and further includes a second feed  706 B that is coupled to a second joining element  852  and a fourth joining element  854 . Second feed  706 B supplies a receiver current  808  of the same polarity  818  to the first and second loops  810 ,  820 . 
   Referring to  FIG. 9 , in another embodiment, the antenna  900  includes a first loop  910  including at least one first conductor  912 , a second loop  920  including at least one second conductor  922 , and an outer loop  930  coupled to the first and second loops  910 ,  920 . The first loop  910  has a first enclosed area  914  defined by the area inside the perimeter of the first loop  910  and a first phase center point  916  defined by the geometric center point of the first enclosed area  914 . 
   The second loop  920  is coupled to the first loop  910  and disposed adjacent to and substantially parallel to the first loop  910 . The second loop  920  has a second enclosed area  924  substantially equal to the first enclosed area  914  and a second phase center point  926 . A line normal to the plane of the first loop  910  passes through the first phase center point  916  and the second center point  926 . 
   The outer loop  930  is substantially parallel to the first loop  910  and has an outer enclosed area  934  equal to the sum of the first and second enclosed areas  914 ,  924 . The outer loop  930  also has an outer phase center point  936  coincident to the first phase center point  916 . The antenna  900  may further include a coupler element  940  to couple the outer loop  930  to one of the first and second loops  910 ,  920 . Also, a feed element  906  supplies a current  908  in a first polarity  918  to the outer loop  930  and the coupler element  940  supplies the current  908  in a second polarity  928  to the one of the first and second loops  910 ,  920 . The second polarity  928  is opposite to the first polarity  918 . Optionally, a return element  907  is included to return the current  908  to, for example, an electric circuit. 
   With this configuration, characterized by an outer loop surrounding inner loops, the outer loop having an outer loop enclosed area equal in size to the sum of each of the inner loop enclosed areas, the far-field radiation is cancelled to a high degree, while the near-field energy is not as substantially impacted. Far-field radiation cancellation is dependent on the inner loops having substantially equal enclosed areas. The inner loops produce a substantially higher near-field energy peak along the axis coincident to the inner loops. Thus, the reduction in the near-field energy is not complete. Rather, a usable level of near-field energy can be produced at greater distances from the antenna  900  while maintaining radiation levels low enough to satisfy prevailing governmental RF radiation regulations. 
   In addition, the cancellation of the far-field results in higher system efficiency. The only limitation on RFID operating range is the accuracy of the sizing, the relative placement, and the orientation of the inner and outer loops such that respective enclosed areas are equal and phase center points coincident. 
   The antenna  900  can achieve far-field radiation cancellation on the order of 30 to 40 dB. The comparable reduction in the near-field is about two orders of magnitude less, leading to a 20 to 30 dB improvement in operating range. Generally, RFID system applications require an 18 dB improvement to realize a doubling of operating range. Thus, the antenna  900  can enhance operating ranges to values two or even three times that in the current state-of-the-art RFID systems. 
   Referring to  FIG. 10A  showing a side view of the antenna  900 ′, the first and second loops  910 ′,  920 ′ may be disposed on opposites sides of the plane formed by the outer loop  930 ′. Alternatively, as shown in  FIG. 10B , the first and second loops  910 ″,  920 ″ of the antenna  900 ″ may be disposed on the same side of the plane formed by the outer loop  930 ″. 
   Referring to  FIG. 10C , the antenna  1000  can further include an electrically insulating material  1050  to insulate the first and second loops  1010 ,  1020  from each other to minimize an overall thickness  1052  of the antenna  1000 . With this configuration, the antenna  1000  can be made as thin as possible for mounting in narrow spaces behind walls, floors, ceilings, etc. 
   In an alternative embodiment shown in  FIGS. 11A and 11B , an antenna  1100  can be substantially flat and disposed a plane designated by reference numeral  1150 . The antenna  1100  includes first loop  1110 , a second loop  1120 , and a third loop  1130  which are substantially coplanar in plane  1150 . A coupler element  1140  supplies a current from the third loop  1130  to one of the first and second loops  1110 ,  1120 . In the configuration shown in  FIGS. 11A and 11B , the coupler element  1140  juts out a distance from the plane  1150  in order to couple the third loop  1130  to the second loop  1120 . An inner loop element  1142 , disposed in plane  1150 , couples the first and second loops  1110 ,  1120 . 
   The current flows in a first polarity through the third loop  1130 , and in a second polarity opposite to the first polarity in first and second loops  1110 ,  1120 . The loops  1110 ,  1120 ,  1130  may be disposed on a single side of an insulating material, such as a printed circuit panel, for ease of fabrication. 
   Referring now to  FIG. 12 , in a further embodiment, an antenna  1200  includes a first inner loop  1210  and a second inner loop  1220 . The second inner loop  1220  comprises at least one first inner loop  1210 . The antenna  1200  also includes an outer loop  1230  coupled to one of the first and second inner loops  1210 ,  1220 . The first and second inner loops  1210 ,  1220  have a total enclosed area equal to the sum of a first inner loop enclosed area  1214  and a second inner loop enclosed area  1224 . Also, an outer loop enclosed area  1234  is substantially equal to the total enclosed area of the first and second inner loops  1210 ,  1220 . For example, as shown in  FIG. 12 , the inner loops include a first inner loop  1210  and a second inner loop  1220  including five inner loops. In this instance, the outer loop enclosed area  1234  will equal total enclosed area of the first inner loop  1210  plus the five loops of the second inner loop  1220 . The outer enclosed area A outer  can be computed using the following equation:
 
 A   outer   =A   inner   *n  
 
In this equation, A inner  is the enclosed area of each of the inner loops and n is the number of inner loops.
 
   The near-field energy (H-field) of alternate embodiments of the antenna of the invention can be computed and compared with conventional art antennas. The general characteristics of RFID transponder antennas include an operating frequency of 13.56 MHz. Other general characteristics of the antennas and the operating environment include the following: 
   Wavelength in free-space at the operating frequency:
 
λ≡sol/13.56 MHz; wherein sol equals the speed of light
 
FCC E-field radiation-limit E 0  at radius r≡30 meters:
 
E 0 ≡15.849 milli-volts/meter
 
Characteristic impedance of free-space Z 0 :
 
Z 0 ≡377 ohms
 
Scalar magnitude of the E-field E c  of a one-square meter loop at 30 meter:
 
 E   c ≡(1.5 1/2   *Z   0 *π)/( r*λ   2 ).
 
A function to calculate the equivalent radius a of a loop having a rectangular cross section height×width:
 
 a (height,width)=(height*width/π) 1/2 .  Function 1:
 
A function to compute the radiation-limited current I FCC  in a loop of radius a, having n turns:
 
 I   FCC ( a,n )≡ E ( n*E   c   *π*a   2 ) −1   Function 2:
 
A function to compute the quadi-static H-field H z  of a loop of radius a at a distance of z:
 
 H   z ( I,n,a,z )≡( I*n*a   2 )/(2*(( a   2   +z   2 ) 3 ) 1/2 )  Function 3:
 
A function to compute the cancellation factor for two loops of opposite polarity spaced apart by a distance of 2*S:
 
canc( S )≡2*sin(2 *π*S /λ)  Function 4:
 
   The H-field at distances from the conventional single loop conventional antenna  1300  shown in  FIG. 13A  can be computed using the following equations.
 
Width of a square single loop: W 0 =9 inches
 
Equivalent radius a 0  of the single loop using Function 1 above:
 
 a   0   =a ( W   0   ,W   0 )=5.1 inches
 
Radiation-limit current I 0  in single loop (n=1) using Function 2 above:
 
 I   0 =min( I   FCC ( a   0   ,n   0 ))=3.1 amperes
 
The single loop H-field H 0  can be now computed as a function of distance along the center line of the single loop using Function 3 above:
 
 H   0   =H   z ( I   0   ,n   0   ,a   0   ,z )
 
   The H-field at distances near the single loop antenna  1300  is the bell-curve shown  FIG. 14 . An H-field value of 100 milli-Amperes/meter (shown by line  1400 ) is achieved at a distance of 24 inches (shown by line  1402 ) from the antenna. 
   The H-field at distances from the conventional figure-eight antenna f 8    1302  shown in  FIG. 13B  can be computed using the following equations.
 
Width of figure-eight loops: W f8 =36 inches
 
Height of half the figure-eight: H f8 =0.5 W f8 =18 inches
 
Equivalent radius a f8  of the figure-eight antenna using Function 1:
 
 a   f8   =a ( W   f8   ,H   f8 )=14.4 inches
 
A function to compute the cancellation factor C f8  for two equal-sized loops of opposite polarity, where the loops are spaced one above the other, therefore, having a separation of their geometric centers equal to half the height of the loops is as follows:
 
 C   f8 =−20*log(canc( H   f8 /2))=17.7 dB
 
The radiation-limit current I 0  of an equivalent single loop can be computed using Function 2:
 
 I   0   =I   FCC ( a   f8   ,n   f8 )=0.38 amperes
 
A function to calculate the radiation limited current I CANC  for a system having a given cancellation factor, C f , in decibels (dB) is as follows:
 
 I   CANC ( I   FCC   ,C   f )≡ I   FCC *10 0.05*Cf   Function 5:
 
The radiation-limit current I f8  of the figure-eight antenna accounting for far-field cancellation of the loops using Function 5 is as follows:
 
 I   f8   =I   CANC ( I   0   ,C   f8 )=3 amperes
 
   The H-field of the figure-eight antenna  1302  can be computed as a function of distance along the center line of the single loop using modified Function 3:
 
 H   f8 =0.5 H   z ( I   f8   ,a   f8   ,x )
 
   The H-field H f8  at distances near the conventional figure-eight antenna  1302  is the bell-curve shown  FIG. 15 . An H-field value of 100 milli-Amperes/meter (shown by reference line  1500 ), which corresponds to the field strength generally needed to activate a commercially available ID sized RFID tag, is achieved at a distance of 36 inches (shown by reference line  1502 ) from the antenna  1302 . Note that the resulting operating range improvement of the conventional figure-eight antenna  1302  over the conventional single loop antenna  1300  equals (36 inches/24 inches)−1, or 50%. 
   The H-field at distances from exemplary embodiments of the antenna  200  and  700 , shown in  FIGS. 2 and 7 , can be computed using the following equations.
 
Typical spacing s between the back-to-back loops: 12 inches
 
Width and height of back-to-back loops:  W   b2b ( H   b2b )=37 inches
 
Equivalent radius a b2b  of the back-to-back antenna using Function 1 above:
 
 a   b2b   =a ( W   b2b   ,H   b2b )=20.9 inches
 
A function to compute the cancellation factor C b2b  for back-to-back loops of opposite polarity:
 
 C   b2b =−20*log(canc(0.5 s )*2 −1/2 )=23.3 dB
 
The radiation-limit current I 0  of an equivalent single loop can be computed using Function 2 above:
 
 I   0 =min( I   FCC ( a   b2b   ,n   b2b ))=0.18 amperes
 
The radiation-limit current I b2b  of the back-to-back antenna accounting for far-field cancellation using Function 4 above:
 
 I   fb2b   =I   CANC ( I   0   ,C   b2b )=3 amperes
 
The near-field H-field of the leftmost loop H L , spaced to the left of the rightmost loop by s can be computed using Function 3 above:
 
 H   L   =H   z (− I   b2b   ,a   b2b   ,x+s )
 
The near-field H-field of the rightmost loop H R , having a current of opposite polarity to the leftmost loop and placed at x=0 can be computed using Function 3 above:
 
 H   R   =H   z ( I   b2b   ,a   b2b   ,x )
 
The resulting total H-field of both loops as a function of distance along the centerline can be computed as follows:
 
 H   L   =H   R   +H   L  
 
   The H-field at distances near exemplary embodiments  200 ,  700  is the bell-curve shown  FIG. 16 . An H-field value of 100 milli-Amperes/meter (shown by reference line  1600 ) is achieved at a distance of 44 inches (shown by reference line  1602 ) from the antenna  200 ,  700 . Note that the resulting operating-range improvement of antenna  200 ,  700  over the conventional single loop antenna  1300  equals (44 inches/24 inches)−1, or 83%. The improvement over the conventional figure-eight antenna  1302  equals (44 inches/36 inches)−1, or 22%. 
   The H-field of the exemplary inner-outer loop antenna  900  shown in  FIG. 9 , can be compared with the H-field for exemplary antennas  200 ,  700 . An inner-outer loop antenna with an outer loop width of 91 inches, and inner loop width of 64.35 inches, has a current of 3 amperes of opposite polarity in the inner and outer loops, and a cancellation factor of 40 dB. The H-field at distances near the inner-outer loop antenna  900  is represented by the bell-curves shown in  FIG. 17 . H-field value of 100 milli-Amperes/meter (shown by reference line  1700 ) is achieved at a distance of 66 inches (shown by reference line  1702 ) from the antenna. Note that the resulting operating-range improvement of the inner-outer loop antenna relative to exemplary embodiments  200 ,  700  equals (66 inches/44 inches)−1, or 50%. 
   The operating-range improvement of the inner-outer loop antenna over the conventional single loop antenna  1300  equals (66 inches/24 inches)−1 or 175%. Further, the operating-range improvement of the inner-outer loop antenna over the conventional figure-eight antenna  1302  equals (66 inches/36 inches)−1, or 83%. 
   All of the embodiments of the antenna are compatible with known techniques of resonating, tuning, and/or matching of RFID antennas for the purpose of coupling to transmitters and/or receivers to achieve efficient operation. For example, passive, lumped elements; such as capacitors, inductors, or transformers; could be added in series and/or parallel combinations at the feed point of any of the embodiments of the antenna to achieve a suitable drive point impedance match with conventional art amplifiers. That is, no special provisions are required to apply embodiments of the antenna to existing or future systems. 
   Having described exemplary embodiments of the invention, it will now become apparent to one of ordinary skill in the art that other embodiments incorporating their concepts may also be used. The embodiments contained herein should not be limited to disclosed embodiments but rather should be limited only by the spirit and scope of the appended claims. All publications and references cited herein are expressly incorporated herein by reference in their entirety.