Patent Publication Number: US-8525730-B2

Title: Multi-band printed circuit board antenna and method of manufacturing the same

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This patent application claims priority, and the benefit of, U.S. Provisional Patent Application Ser. No. 61/163,022 filed on Mar. 24, 2009, the entirety of which is hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The embodiments described herein are related to a multi-band printed circuit board antenna and, more particularly, to a multi-band printed circuit board antenna with a first trace operative in a low frequency band on a first surface of the printed circuit board, and a second trace operative in a high frequency band on an opposing second surface of the printed circuit board. 
     2. Description of the Related Art 
     Portable communication devices that communicate with wireless services frequently operate in different frequency bands. Different frequency bands may be used, for example, in different geographical regions, for different wireless providers, and for different wireless services. Pagers, data terminals, mobile phones, other wireless devices and combined function wireless devices therefore often require an antenna or multiple antennas responsive to multiple frequency bands. As an example of a need for multi-band reception and transmission, at least some “world” mobile phones must accommodate the following bands: Global System for Mobile Communication or Group Special Mobile (GSM); Digital Cellular Systems (DCS); and Personal Communication Services (PCS). 
     Although there are several designs available for external multi-band antennas, conventional portable communication devices house antennas internally or within a device housing on a printed circuit board (PCB). However, conventional PCB antennas are incapable of achieving four bandwidths, such as 850 MHz, 900 MHz, 1800 MHz, and 1900 MHz simultaneously. Further, conventional PCB antennas cannot achieve very low bandwidths, such as 824 MHz, without extending an antenna to interact with further components within a device. One factor causing conventional PCB antennas to be incapable of achieving multi-band capabilities is that traces on conventional PCB antennas include more than four bends (e.g., four 90° turns) forming, for example, a spiral shape. However, the more bends a trace makes, the less effective of a radiator it will be because the trace will interact with material in the PCB and therefore dissipate more energy into the PCB rather than radiating the energy. 
       FIG. 12  is an example of a conventional system  1200  designed to transfer a ground to a motherboard  1202 . Conventional apparatus  1200  comprises two coax cables  1204  and  1205  and an antenna  1206  with a ground end soldered to a ground of a motherboard  1202 . In addition, a coax cable ground  1210  is soldered to an edge of the motherboard  1202 , thus allowing only a center conductor to make contact with a base of antenna  1206 . Conventional apparatus have several problems when connecting, for example, antenna  1206  to a radio  1212 . For example, radio  1212  is a secondary PCB having a ground that is poorly connected to motherboard  1202 . 
     Additionally, conventional apparatuses neglect an effect of a coax cable. Therefore, unless there is a balun at the base of the antenna or unless the antenna is fed with a truly differential transmission line, radio frequency currents flow on an outside of the coax cable and radiate, which is undesirable. 
     BRIEF DESCRIPTION OF THE INVENTION 
     In one aspect, a multi-band antenna for a printed circuit board (PCB) is provided. The multi-band antenna comprises a first trace coupled to a first surface of the PCB and extending along at least a portion of a length of a first side of the PCB and along at least a portion of a length of a second side of the PCB intersecting the first side, wherein the first trace is positioned proximate a perimeter of the PCB partially defined by the first side and the second side. 
     In a further aspect, a communication device is provided. The communication device comprises a printed circuit board (PCB) having a perimeter at least partially defined by a first side, a second side, and a third side. An antenna is coupled to the PCB, and comprises a first trace of conductive material coupled to a first surface of the PCB. The first trace extends along at least a portion of a length of the first side proximate the perimeter and at least a portion of a length of the second side proximate the perimeter. A second trace of conductive material is coupled to a second surface of the PCB opposing the first surface. The second trace extends along at least a portion of a length of the third side proximate the perimeter and along at least a portion of the length of the second side proximate the perimeter. 
     In yet another aspect, a method is provided for manufacturing a multi-band antenna that is coupled to a printed circuit board (PCB) having a perimeter at least partially defined by a first side, a second side, and a third side. The method comprises forming a first trace of conductive material on a first surface of the PCB. The first trace extends along at least a portion of a length of the first side proximate the perimeter and at least a portion of a length of the second side proximate the perimeter. A second trace of conductive material is formed on a second surface of the PCB. The second trace extends along at least a portion of a length of the third side proximate the perimeter and at least a portion of a length of the second side proximate the perimeter. 
     In yet another aspect, a two sided antenna is provided. The two sided antenna comprises a dielectric substrate having a first surface and a second surface. A first radiator is positioned on the first surface and is configured to radiate a first frequency band. A second radiator is positioned on the second surface to overlap the first radiator and is configured to radiate a second frequency band. The overlap allows a weak coupling to occur between the first radiator and the second radiator, and to combine with the dielectric material and a band to split a resonate mode. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Non-limiting and non-exhaustive embodiments are described with reference to the following figures, wherein like reference numerals refer to like parts throughout the various views unless otherwise specified. 
         FIG. 1  is a block diagram of an exemplary wireless communication network. 
         FIG. 2  is a block diagram of an exemplary wireless communication device. 
         FIG. 3  is a schematic view of a first surface of an exemplary printed circuit board including a first trace. 
         FIG. 4  is a schematic view of a second surface of an exemplary printed circuit board including a second trace. 
         FIG. 5  is a schematic view of a first surface of an exemplary printed circuit board including a first trace. 
         FIG. 6  is a schematic view of a second surface of an exemplary printed circuit board including a second trace. 
         FIG. 7  is a schematic view of a first surface of an exemplary printed circuit board including a first trace. 
         FIG. 8  is a schematic view of a second surface of an exemplary printed circuit board including a second trace. 
         FIG. 9  is a graph showing a maximum available efficiency verses return loss for a multi-band PCB antenna. 
         FIG. 10  is a graph showing return loss measurements. 
         FIG. 11  is a portion of the graph shown in  FIG. 10 . 
         FIG. 12  is an illustrative example of a conventional apparatus designed to transfer a ground to a motherboard. 
         FIGS. 13 and 14  are illustrative examples of an exemplary apparatus for transferring a ground to a motherboard in accordance with embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring initially to  FIG. 1 , a block diagram of an exemplary wireless communication network is shown and designated generally as wireless network  100 . In one embodiment, wireless network  100  may be any wireless communication network that comprises two or more wireless communication devices  102  and  104 . Wireless network  100  may be used to communicate any type or combination of information in any suitable format including, without limitation, audio, video, and/or data format. In one embodiment, communication devices  102  and  104  can communicate either directly or indirectly (e.g., through one or more of wireless devices  102  and  104  acting as a wireless router) with a wireless communication system  106 , although such communication is not required. 
     Additionally, wireless communication system  106  may be any publicly accessible or any proprietary system, and can use any appropriate access and/or link protocol to communicate with wireless communication devices  102  and  104  including, without limitation, analog, digital, packet-based, time division multiple access (TDMA), code division multiple access (CDMA), such as direct sequence CDMA, frequency hopping CDMA, wideband code division multiple access (WCDMA), frequency division multiple access (FDMA), spread spectrum or any other known or developed access or link protocol or methodology. The wireless communication system  106  can further use any of a variety of networking protocols, such as, for example, User Datagram Protocol (UDP), Transmission Control Protocol/Internet Protocol (TCP/IP), APPLETALK, Inter-Packet Exchange/Sequential Packet Exchange (IPX/SPX), Network Basic Input Output System (Net BIOS), or any proprietary or non-proprietary protocol, to communicate digital voice, data and/or video information with wireless devices  102  and  104  and/or other networks to which wireless communication system  106  can be connected. For example, wireless communication system  106  can be connected to one or more wide area networks, such as Internet  108  and/or a public switched telephone network  118 . 
     Each wireless communication device  102  and  104  can be, for example, a cellular telephone, a mobile data terminal, a two-way radio, a personal digital assistant (PDA), a handheld computer, a laptop or notebook computer, a wireless e-mail device, a two way messaging device, or any combination thereof which has been modified or fabricated to include functionality of the described subject matter. In the following description, the term “wireless communication device” refers to any of the devices mentioned above and any suitable device that operates in accordance with the described subject matter. 
     Each wireless communication device  102  and  104  as shown comprises at least one embodiment of a multi-band printed circuit board (PCB) antenna  110 , together with various other components as described in more detail below with respect to  FIG. 2 . Multi-band PCB antenna  110  is configured to receive and transmit messages and other signals in at least one low frequency band and in at least one high frequency band. In one embodiment, multi-band PCB antenna  110  is also covered by a protective shell (not shown), such as a shroud. 
     Referring now to  FIG. 2 , a block diagram of an exemplary wireless communication device operating in wireless communication network  100  is shown and designated generally as wireless communication device  200 . In one embodiment, all communication devices in wireless network  100  may be configured in a manner identical to or at least substantially similar to the configuration of wireless communication device  200 . 
     Wireless communication device  200  comprises the aforementioned multi-band PCB antenna  110  and a processor  204 , a memory  206 , and a user interface  208 . In one embodiment, wireless communication device  200  further comprises a display  210  and/or an alert circuit  212 , as well as other conventional components (not shown). 
     As noted above, the exemplary multi-band PCB antenna  110  is configured to transmit message signals to and/or receive message signals from another wireless device and/or wireless communication system  106 . The message signals can be, for example, radio signals, and/or modulated audio, video, and/or data signals. In one embodiment, the message signals are communicated over pre-established channels within a selected frequency band, for example, frequency bands established by Global System for Mobile Communication or Group Special Mobile (GSM) (e.g., 824 MHz, 850 MHz, and 900 MHz); Digital Cellular Systems (DCS) (e.g., 1800 MHz); and Personal Communication Services (PCS) (e.g., 1900 MHz). Unlike conventional PCB antennas, multi-band PCB antenna  110  described herein is capable of having enough bandwidth to switch between two frequency bands and four frequency bands, for example, two low frequency bands and two high frequency bands. 
     In one embodiment, multi-band PCB antenna  110  employs demodulation techniques for receiving incoming message signals transmitted by another wireless device or by communication system  106 , as well as modulation and amplification techniques to convey outgoing message signals to other communication devices and/or wireless communication system  106 . In one embodiment, processor  204  is configured to send message signals to another communication device or wireless communication system  106  via multi-band PCB antenna  110 . The transmitted message signal can, for example, comprise one or more data packets containing radio signals, audio, textual, graphic, and/or video information. 
     Referring to  FIGS. 3 and 4 , multi-band PCB antenna  110  comprises a first surface  302  and an opposing second surface  304 . A first side  306 , a second side  308 , a third side  310 , and a fourth side  312  at least partially define a periphery of PCB  320 . Although PCB  320  is shown in  FIGS. 3 and 4  as a rectangle, PCB  320  may have any suitable shape and/or configuration including, without limitation, any suitable polygon, circular or other suitable shape and/or configuration. 
     In one embodiment, first surface  302  comprises a first trace  314  of conductive material coupled to and extending along, or with respect to, at least a portion of a length of first side  306  proximate to, e.g., at or near, perimeter  301  of PCB  320  and at least a portion of a length of second side  308  intersecting the first  306 . In one embodiment, first trace  314  is printed on first surface  302  and comprises a conducting material made of at least one of the following: copper and/or enig plated (which is Electroless), and gold plated over nickel (which prevents oxidation and maintains high conductivity, low resistivity, and therefore high antenna efficiency). Thus, unlike conventional traces that form a spiral shape, or comprise multiple bends (e.g., five or more bends at 90°) without extending along perimeter of two or more sides of a PCB antenna, such as shown in  FIG. 3 , first trace  314  bends one time and extends along the length of first side  306  and the length of second side  308  along perimeter  301  of PCB  320 . Thus, utilizing the outer perimeter  301  of PCB  320 , first trace  314  only requires one bend. It has been found by the inventors of the present disclosure, that the less bends a trace has, the less the trace will interact with material in PCB  320 , and therefore, less energy will dissipate into PCB  320  and more energy will be radiated. Radiation of energy (e.g., power) is desirable because energy is not reflected back toward a generator. Further, the number of bends a particular trace may have depends upon a length of a trace and/or one or more dimensions of PCB  320 . In a particular embodiment, PCB  320  has a measured length relative to the length shown in  FIGS. 3 and 4  sufficient to comprise a substantially linear trace having no bends to facilitate radiating energy through an antenna. 
     An antenna is a reciprocal device, meaning an antenna performs equally well at the same frequency whether it is used as a receive antenna or a transmit antenna. In the embodiments described herein, an antenna is characterized as a receive antenna, and therefore return loss (e.g., the ratio of power reflected by the antenna divided by the total power sent to the antenna) measured in decibels (dB) is used as an indicator of antenna performance. As a relative measurement, transmitted power and received power may be measured in one direction and may be equal to a total radiated power. 
     In a further embodiment, second surface  304 , as shown in  FIG. 4 , comprises a second trace  316  of conductive material coupled to second surface  304  and extending along or with respect to at least a portion of a length of third side  310  proximate to, e.g., at or near, perimeter  301  of PCB  320  and at least a portion of the length of second side  308  proximate to, e.g., at or near, perimeter  301  of PCB  320 . In a particular embodiment second trace  316  is printed on second surface  304  and includes a suitable conducting material, such as described above in reference to first trace  304 . Similar to first trace  314 , unlike conventional traces, second trace  316  comprises only one bend in the embodiment as shown in  FIGS. 3 and 4 . In one embodiment, a portion  318  of first trace  314  overlaps a portion  322  of second trace  316 . The overlap of the portion of first trace  314  and second trace  316  provides a weak coupling between first trace  314  and second trace  316 , thus allowing an interaction between first trace  314  and second trace  316  that further enhances an ability of multi-band PCB antenna  110  to achieve multi-band frequencies, such as 824 MHz, 850 MHz, 900 MHz, 1800 MHz, and 1900 MHz without a need for interaction with another component within wireless communication device  200 . However, excessive overlap may result in a large increase in coupling which will result in excessive resonant mode splitting that is undesirable. In addition, too little overlap and mode splitting will achieve such a small amount of coupling, if any, that the coupling is not distinguishable from, for example, two independent widely separated traces, and thus provides no interaction between the traces. However, when first trace  314  and second trace  316  achieve an appropriate overlap, the appropriate overlap is precisely tuned so as to provide a suitable amount of coupling between resonances. When this occurs, a proper amount of mode splitting also occurs. 
     Bandwidth of an antenna is a function of the proximity to the ground. In certain embodiments, multi-band PCB antenna  110  may be oriented parallel to a ground plane or perpendicular to the ground plane. However, when an antenna, for example, multi-band PCB antenna  110  is oriented parallel to the ground plane, the closer the antenna is located to ground the narrower radiation bandwidth the antenna will have and the poorer the radiator the antenna becomes, and thus conventionally, this was not possible. However, by taking advantage of mode splitting due to the weak coupling between resonators (e.g., antenna, traces, and radiators), as described above, it is possible to achieve a higher bandwidth antenna in a smaller space because the bandwidth of each mode actually widens, and therefore, a multi-band antenna that is parallel to the ground plane is now possible. 
       FIGS. 5 and 6  show an alternative embodiment of a multi-band antenna  110  coupled to a PCB, for example, PCB  320 . PCB  320  comprises first surface  302  having first trace  314  extending along at least a portion of the length of first side  306 , at least a portion of the length of second side  308 , and at least a portion of a length of fourth side  312 . Referring further to  FIG. 6 , second surface  304  may comprise second trace  316  extending along at least a portion of the length of second side  308 , at least a portion of the length of third side  310 , and at least a portion of the length of fourth side  312 . 
       FIGS. 7 and 8  show yet another alternative embodiment of a multi-band antenna  110  coupled to a PCB, for example, PCB  320 . PCB  320  comprises first surface  302  having first trace  314  extending along at least a portion of the length of first side  306 , at least a portion of the length of second side  308 , at least a portion of the length of fourth side  312 , and at least a portion of the length of third side  310 . Referring further to  FIG. 8 , second surface  304  may comprise second trace  316  extending along at least a portion of the length of second side  308 , at least a portion of the length of third side  310 , at least a portion of the length of fourth side  312 , and at least a portion of the length of first side  306 . 
     In a further embodiment, a method for manufacturing a multi-band antenna coupled to a PCB having a perimeter at least partially defined by first side  306 , second side  308 , and a third side  310 . In one embodiment, the method comprises forming first trace  306  of conductive material on first surface  302  of PCB  320 , first trace  314  extending along at least a portion of a length of first side  306  proximate perimeter  301  and at least a portion of a length of second side  308  proximate perimeter  301 . The method further comprises forming second trace  316  of conductive material on second surface  304  of PCB  320 , second trace  316  extending along at least a portion of a length of third side  310  proximate perimeter  301  and at least a portion of a length of second side  308  proximate perimeter  301 . In one embodiment, first trace  314  and second trace  316  are etched into PCB  320 . 
     With reference to  FIGS. 3-8 , any combination of design for first trace  314  and second trace  316  is within the scope of the present disclosure. For example, multi-band PCB antenna  110  may have first surface  302  as shown in  FIG. 7 , with second surface  304  as shown in  FIG. 4 . 
     In one embodiment, manufacturing a printed circuit board antenna, for example, multi-band PCB antenna  110 , comprises coupling (e.g., embedding) first trace  314  to first surface  302  of multi-band PCB antenna  110  and coupling second trace  316  to second surface  304  of PCB via, for example, printing, etching, or any suitable coupling method or technique. 
     As mentioned above, multi-band PCB antenna  110  is capable of achieving multiple band frequencies. However, as one or more dimensions and/or a shape of a PCB (e.g., PCB  320 ) varies from device to device, and as requirements for particular band frequencies vary, when manufacturing a multi-band PCB antenna, one should take each of the these factors into consideration to produce a multi-band PCB antenna that is capable of achieving multiple band frequencies. 
     An exemplary process will now be described for manufacturing a multi-band PCB antenna that operates on multiple desired band frequencies. 
     In one embodiment, a relationship between a return loss (dB) and a maximum available efficiency for a multi-band PCB antenna with a first trace operative in a low frequency band on a first surface of a PCB, and a second trace operative in a high frequency band on a second surface of the PCB opposite the first surface, may be shown as:
 
[Efficiency=1−(10 (((return     —     loss)(dB))/10) )]  Equation (1)
 
       FIG. 9  is a graph  900  showing efficiency  901  versus return loss (db)  902 . As shown in  FIG. 9 , a maximum available efficiency rises with an increasing return loss. Therefore, to achieve an efficient multi-band PCB antenna that is capable of communicating in multiple bands, frequencies of interest and bandwidth requirements should be taken into consideration in determining a return loss and an efficiency of a multi-band PCB antenna. An exemplary set of frequencies of interest and bandwidth requirements, as well as the calculated desired return loss and desired efficiency at each corresponding channel in the frequencies of interest is shown in Table 1 below. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                   
                   
                 Desired 
                 Desired 
               
               
                   
                   
                   
                   
                 Return Loss 
                 Efficiency 
               
               
                   
                 Channel 
                 TX (MHz) 
                 RX (MHz) 
                 &lt; 
                 &gt; 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 GSM 850 
                 128 
                 824 
                 869 
                 −6 
                 0.75 
               
               
                   
                 189 
                 836.2 
                 881.2 
                 −6 
                 0.75 
               
               
                   
                 251 
                 849 
                 894 
                 −6 
                 0.75 
               
               
                 GSM 900 
                 975 
                 880.2 
                 925.2 
                 −6 
                 0.75 
               
               
                   
                 37 
                 897.4 
                 942.4 
                 −6 
                 0.75 
               
               
                   
                 124 
                 914.8 
                 959.8 
                 −6 
                 0.75 
               
               
                 DCS 1800 
                 512 
                 1710 
                 1805 
                 −6 
                 0.75 
               
               
                   
                 698 
                 1747.2 
                 1842.2 
                 −6 
                 0.75 
               
               
                   
                 885 
                 1785 
                 1880 
                 −6 
                 0.75 
               
               
                 PCS 1900 
                 512 
                 1850 
                 1930 
                 −6 
                 0.75 
               
               
                   
                 661 
                 1880 
                 1960 
                 −6 
                 0.75 
               
               
                   
                 810 
                 1910 
                 1990 
                 −6 
                 0.75 
               
               
                   
               
            
           
         
       
     
     For example, the first column of Table 1 lists exemplary frequencies of interest, column 2 lists exemplary channels at each of the frequencies of interest, columns 3 and 4 list transmitted frequencies (TX(MHz)) and received frequencies (RX(MHz)), respectively, for each of the corresponding channels in column 2, and columns 5 and 6 list desired return loss and desired efficiency, respectively, for each of the corresponding channels in column 2. 
     In one embodiment, a design choice is based upon summing or multiplying return loss values over frequencies of interest utilizing GSM, DCS, and PCS standards. Thus, in a case of multiplication (assuming absolute value for clarity) a largest positive number is a “best antenna.” In a case of summing, a largest negative value is the “best antenna.” 
     Experiments were constructed for various lengths of a low band first trace, e.g., L1_LB, and high band second trace, e.g., L2_HB (wherein L1 is a length of a first trace, and L2 is a length of a second trace, and LB represents a Low Band and HB represent a High Band). Table 2 (below) provides values for L1 and L2 (where L1 is a length of a first trace, and L2 is a length of a second trace) at the various lengths. Return loss at each frequency was measured for each antenna. Each antenna corresponds to a particular “S” file as shown in table 2 (below), which also provides values for L1_LB and L2_HB at the various lengths. The file name and the results of a return loss at each value of L1_LB and L2_HB at a frequency of 824 MHz are also shown. Return loss can be calculated using the following equation:
 
returnloss=const+
 
+ A *( L 1 —   LB )+ B *( L 2 —   HB )
 
+ C *( L 1 —   LB*L 2 —   HB )
 
+ D *( L 1 —   LB^ 2)+ E ( L 2 —   HB^ 2)  Equation (2)
 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 L1_LB 
                 L2_HB 
                 file 
                 824.00 MHz 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 24.75 
                 11.45 
                 S_1 
                 −7.36 
               
               
                   
                 25.25 
                 11.95 
                 S_2 
                 −9.58 
               
               
                   
                 24.25 
                 11.95 
                 S_3 
                 −7.62 
               
               
                   
                 25.25 
                 10.95 
                 S_4 
                 −7.84 
               
               
                   
                 24.25 
                 10.95 
                 S_5 
                 −6.76 
               
               
                   
                 24.75 
                 11.45 
                 S_6 
                 −8.95 
               
               
                   
                 25.25 
                 11.95 
                 S_7 
                 −7.87 
               
               
                   
                 24.25 
                 11.95 
                 S_8 
                 −7.73 
               
               
                   
                 25.25 
                 10.95 
                 S_9 
                 −7.42 
               
               
                   
                 24.25 
                 10.95 
                 S_10 
                 −7.87 
               
               
                   
                 24.25 
                 10 
                 S_11 
                 −7.28 
               
               
                   
                 25.25 
                 10 
                 S_12 
                 −7.61 
               
               
                   
                 26.25 
                 10 
                 S_13 
                 −9.75 
               
               
                   
                 26.25 
                 10.95 
                 S_14 
                 −9.70 
               
               
                   
                 26.25 
                 11.95 
                 S_15 
                 −11.36 
               
               
                   
                 24.75 
                 10.475 
                 S_16 
                 −8.36 
               
               
                   
                 25.75 
                 10.475 
                 S_17 
                 −8.60 
               
               
                   
                 25.75 
                 11.45 
                 S_18 
                 −9.31 
               
               
                   
                 24.25 
                 10 
                 S_19 
                 −7.88 
               
               
                   
                 25.25 
                 10 
                 S_20 
                 −8.06 
               
               
                   
                 26.25 
                 10 
                 S_21 
                 −8.21 
               
               
                   
                 26.25 
                 10.95 
                 S_22 
                 −9.48 
               
               
                   
                 26.25 
                 11.95 
                 S_23 
                 −9.95 
               
               
                   
                 24.75 
                 10.475 
                 S_24 
                 −8.05 
               
               
                   
                 25.75 
                 10.475 
                 S_25 
                 −8.45 
               
               
                   
                 25.75 
                 11.45 
                 S_26 
                 −9.38 
               
               
                   
                   
               
            
           
         
       
     
     The coefficients A, B, C, D, and E in Tables 3 and 4 (below) were determined (e.g., utilizing Equation 2) by a least squared error fit to the measured return loss data. 
     
       
         
           
               
               
             
               
                   
                 TABLE 3 
               
             
            
               
                   
                   
               
               
                   
                 Freq (MHz) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 824 
                 836.5 
                 849 
                 869 
                 880.2 
                 897.4 
                 914.6 
                 920 
                 959.6 
                 960 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
            
               
                 const 
                 −354.30 
                 −196.80 
                 −196.80 
                 69.40 
                 918.50 
                 802.20 
                 540.30 
                 480.70 
                 198.40 
                 189.10 
               
               
                 A 
                 22.25 
                 13.77 
                 13.77 
                 −1.88 
                 −57.07 
                 −48.78 
                 −36.39 
                 −34.40 
                 −17.98 
                 −17.18 
               
               
                 B 
                 14.78 
                 5.75 
                 5.75 
                 −6.22 
                 −37.14 
                 −38.35 
                 −19.27 
                 −13.49 
                 1.39 
                 1.29 
               
               
                 C 
                 −0.43 
                 −0.06 
                 −0.06 
                 0.30 
                 1.40 
                 1.01 
                 0.47 
                 0.36 
                 −0.01 
                 −0.01 
               
               
                 D 
                 −0.37 
                 −0.28 
                 −0.28 
                 −0.06 
                 0.81 
                 0.76 
                 0.64 
                 0.62 
                 0.38 
                 0.36 
               
               
                 E 
                 −0.20 
                 −0.21 
                 −0.21 
                 −0.08 
                 0.11 
                 0.62 
                 0.37 
                 0.23 
                 −0.04 
                 −0.03 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
             
               
                   
                 TABLE 4 
               
             
            
               
                   
                   
               
               
                   
                 Freq (MHz) 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 1710 
                 1747.4 
                 1785 
                 1795 
                 1805 
                 1843 
                 1850 
                 1880 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 const 
                 2734.20 
                 1522.80 
                 701.50 
                 654.30 
                 651.20 
                 776.00 
                 812.20 
                 1150.60 
               
               
                 A 
                 −162.91 
                 −100.71 
                 −50.73 
                 −47.81 
                 −47.73 
                 −53.13 
                 −55.20 
                 −82.22 
               
               
                 B 
                 −122.81 
                 −49.77 
                 −14.81 
                 −13.12 
                 −12.73 
                 −23.12 
                 −25.23 
                 −28.99 
               
               
                 C 
                 3.84 
                 1.55 
                 0.46 
                 0.39 
                 0.39 
                 0.62 
                 0.68 
                 0.79 
               
               
                 D 
                 2.37 
                 1.67 
                 0.91 
                 0.87 
                 0.87 
                 0.92 
                 0.95 
                 1.49 
               
               
                 E 
                 1.14 
                 0.51 
                 0.19 
                 0.19 
                 0.17 
                 0.37 
                 0.40 
                 0.48 
               
               
                   
               
            
           
         
       
     
     The rows in Table 3 and Table 4 represent regression components of the coefficients A, B, C, D, and E. The columns in Table 3 and Table 4 are frequencies in Megahertz (MHz). Table 3 and Table 4 illustrate calculated regression components, which indicate a sensitivity of the components to return loss to determine a sensitivity of an antenna corresponding to a change in length, for example, L1_LB and L2_HB, which are the lengths of, for example, first trace  314  and second trace  316  on a respective side of multi-band PCB antenna  110 . 
     Table 3 and Table 4 can be extended by fitting a model for frequency at every frequency of interest and varying L1_LB and L2_LB in a parametric way to find a combination with a best return loss over a frequency range of interest, as shown in  FIG. 10 . For example, in Table 3, a production variation of a multi-band PCB antenna etching process is assumed to be 0.001 inches=1 mil. 
       FIG. 10  is a graph  1000  showing return loss measurements of selected test antennas  1001  verses frequency  1003  for a selected set of test antennas (e.g.,  FIG. 10  illustrates four curves represented by four selected antennas (e.g., four “S” files) in Table 2). As mentioned above, coupling that occurs between a low band arm and a high band arm (e.g., first trace  314  and second trace  316 ) causes mode splitting, which is shown, for example, at graph area  1002  and in  FIG. 11 , which is a magnification of graph area  1002 . Due to mode splitting, a low band arm resonance  1004  and a high band arm resonance  1006  actually become four resonances  1004 ,  1006 ,  1008 , and  1010 , for example; two closely tuned low band resonances and two closely tuned high band resonances. Thus, unlike conventional multi-band PCB antennas that can only be reduced to a particular size because the antenna is unable to achieve a proper bandwidth when the antenna is too small, overlap between the low band arm and the high band arm provides coupling, and therefore will result in mode splitting which allows the low band arm and the high band arm to appear wider, thereby increasing the bandwidth. Therefore, a smaller, more narrow multi-band PCB antenna, which may have been unable to achieve proper bandwidth conventionally, by the embodiments described herein is able resonate between bands of interest, for example, between about 824 MHz to about 960 MHz, and from about 1710 MHz to about 1990 MHz, as shown at resonant points  1004  and  1006 , the lowest points on the graph in  FIG. 10 . 
     Radio and Motherboard Stack Analysis 
     To overcome the deficiencies described above with the conventional apparatus, the embodiments described herein for transferring a ground to a motherboard not only capacitively couple the grounds between a radio and a motherboard, provide mechanical restraint for an antenna, and increase capacitive coupling to ground and, thus, reduce series inductance along an outside of coax cable, but also require only one coax cable which reduces the cost to nearly one half of a cost of conventional apparatus which require two coax cables. 
       FIG. 13  is an example of an apparatus  1300  for transferring a ground to a motherboard  1302 . Apparatus  1300  comprises motherboard  1302 , a radio  1312  having a first end  1307  and a second end  1308 , and a first connector  1310  (e.g., radio frequency connector) proximate first end  1307  of radio  1312 . First connector  1310  is configured to couple radio  1312  and motherboard  1302 . Apparatus  1300  further comprises a coax cable  1304  having a first end  1314  coupled to radio  1312 . First connector  1310  and an opposing second end  1316 , and an antenna  1306  (e.g. multi-band PCB antenna  110 ) coupled to second end  1316  of coax cable  1304 . 
     In one embodiment, radio frequency ground currents are transferred to a top edge  1320  of motherboard  1302  through direct contact with coax cable  1304 . For example, at least a portion of a length of coax cable  1304  may be in direct contact with motherboard  1302 . In one embodiment, coax cable  1304  may be secured to motherboard  1302  to increase capacitive coupling to ground and, thus, reduce series inductance along the outside of coax cable  1304 . 
     In one embodiment, antenna  1306  can be coupled to second end  1316  of coax cable  1304  with a ground pad solder point on a base of antenna  1306  for mechanical restraint, although other coupling means are also possible. 
     In one embodiment, first connector  1310  is in physical contact with each of radio  1312  and motherboard  1302  and, thus, capacitively couples the grounds between radio  1312  and motherboard  1302 . In one embodiment, radio  1312  is secured to motherboard  1302  with any suitable fastener, for example, a screw. 
       FIG. 14  shows a more detailed example of an apparatus  1400  for transferring a ground to a motherboard  1402 . For example,  FIG. 14  shows components between a radio  1412  and motherboard  1402 . One advantage of apparatus  1400  is that apparatus  1400  provides direct/indirect physical contact with each component to radio  1412  and/or motherboard  1402 . For example, a distance between radio  1412  and motherboard  1402  is configured to allow a battery  1406  to have direct physical contact with radio  1412  and motherboard  1402 . 
     To achieve a distance between radio  1412  and motherboard  1402  that enables physical contact with one or more components between radio  1404  and motherboard  1402 , in one embodiment, a connector  1407  (for example, a radio frequency connector) has a connector height  1408  less than a maximum height of battery  1406 . In a further embodiment, connector height  1408  equals a total height  1410  minus a radio thickness  1413 . In yet another embodiment, connector height  1408  is greater than a gap  1414  (e.g., a distance between radio  1412  and motherboard  1402 ), and is also equal to total height  1410  minus radio thickness  1413 . In a further embodiment, total height  1410  minus radio thickness  1413  minus connector height  1408  is greater than zero. 
     This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any device or system and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.