Abstract:
A center frequency of an adjustable filter is controlled to achieve a compromise between DC offset rejection and image rejection.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of U.S. patent application Ser. No. 10/865,951, filed Jun. 14, 2004, now U.S. Pat. No. 7,596,195, which is a continuation-in-part of U.S. patent application Ser. No. 10/813,270, filed Mar. 31, 2004, now U.S. Pat. No. 7,603,098, all of which are incorporated herein by reference in their entirety. 
     This application is also a continuation-in-part of U.S. patent application Ser. No. 10/840,271, filed May 7, 2004, now U.S. Pat. No. 7,603,085, which is a continuation-in-part of U.S. patent application Ser. No. 10/813,270, filed Mar. 31, 2004, now U.S. Pat. No. 7,603,098, all of which are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND 
     1. Field of the Invention 
     This invention relates generally to wireless communication systems, and more particularly, but not exclusively, to a programmable IF frequency filter that enables a compromise between DC offset rejection and image rejection. 
     2. Related Art 
     Communication systems are known to support wireless and wire line communications between wireless and/or wire line communication devices. Such communication systems range from national and/or international cellular telephone systems to the Internet to point-to-point in-home wireless networks. Each type of communication system is constructed, and hence operates, in accordance with one or more communication standards. For instance, wireless communication systems may operate in accordance with one or more standards including, but not limited to, IEEE 802.11, Bluetooth, advanced mobile phone services (AMPS), digital AMPS, global system for mobile communications (GSM), code division multiple access (CDMA), and/or variations thereof. 
     Depending on the type of wireless communication system, a wireless communication device, such as a cellular telephone, two-way radio, personal digital assistant (PDA), personal computer (PC), laptop computer, home entertainment equipment, et cetera communicates directly or indirectly with other wireless communication devices. For direct communications (also known as point-to-point communications), the participating wireless communication devices tune their receivers and transmitters to the same channel or channel pair (e.g., one of the plurality of radio frequency (RF) carriers of the wireless communication system) and communicate over that channel or channel pair. For indirect wireless communications, each wireless communication device communicates directly with an associated base station (e.g., for cellular services) and/or an associated access point (e.g., for an in-home or in-building wireless network) via an assigned channel. To complete a communication connection between the wireless communication devices, the associated base stations and/or associated access points communicate with each other directly, via a system controller, via the public switch telephone network, via the internet, and/or via some other wide area network. 
     For each wireless communication device to participate in wireless communications, it includes a built-in radio transceiver (i.e., receiver and transmitter) or is coupled to an associated radio transceiver (e.g., a station for in-home and/or in-building wireless communication networks, RF modem, etc.). As is known, the receiver receives RF signals, removes the RF carrier frequency from the RF signals directly or via one or more intermediate frequency stages, and demodulates the signals in accordance with a particular wireless communication standard to recapture the transmitted data. The transmitter converts data into RF signals by modulating the data to RF carrier in accordance with the particular wireless communication standard and directly or in one or more intermediate frequency stages to produce the RF signals. 
     However, two issues complicate the selection of an RF receiver IF frequency: DC offset rejection and image rejection. Increasing the IF frequency will improve DC offset rejection while decreasing the IF frequency will improve image rejection. 
     Accordingly, a new circuit and method is required that enables a compromise between DC offset rejection and image rejection. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES 
       The accompanying drawings illustrate the present invention and, together with the description, further serve to explain the principles of the invention and to enable one skilled in the pertinent art to make and use the invention. 
         FIG. 1  is a block diagram illustrating a network system according to an embodiment of the present invention; 
         FIG. 2  is a circuit diagram illustrating a receiver; 
         FIG. 3  is a chart illustrating an IF frequency shift to transform a low pass filter into a bandpass filter; 
         FIGS. 4A and 4B  are diagrams illustrating a channel select filter (bandpass filter) of the receiver IF section of  FIG. 2  and its electrical equivalent, respectively; 
         FIG. 5A  and  FIG. 5B  are charts illustrating shifting the IF frequency of the channel select filter (bandpass filter) to overcome DC offset rejection and image rejection, respectively; 
         FIG. 6  is a flowchart illustrating a method for IF frequency selection according to an embodiment of the invention; 
         FIG. 7A  and  FIG. 7B  are charts illustrating a variable gain in the bandpass filter of the receiver of  FIG. 2  and corresponding noise figures; 
         FIGS. 8A and 8B  are diagrams illustrating a channel select filter (bandpass filter) of the receiver IF section of  FIG. 2  and its electrical equivalent, respectively; 
         FIG. 9  is a flowchart illustrating a method for variable gain selection in the filter; 
         FIG. 10A-10D  are diagrams illustrating BPF center frequency based on down conversion frequency; 
         FIG. 11  is a diagram illustrating a channel select filter (bandpass filter) of the receiver IF section of  FIG. 2 ; 
         FIGS. 12A and 12B  are diagrams illustrating the switching devices of the BPF when polarity is not reversed; 
         FIGS. 13A and 13B  are diagrams illustrating a signal flow diagram of the BPF without reversed polarity and the center frequency of the BPF; 
         FIGS. 14A and 14B  are diagrams illustrating the switching devices of the BPF when polarity is not reversed; 
         FIGS. 15A and 15B  are diagrams illustrating a signal flow diagram of the BPF without reversed polarity and the center frequency of the BPF; 
         FIGS. 16A and 16B  are simulation charts illustrating the center frequency of the BPF without and with reversed polarity, respectively; and 
         FIG. 17  is a flowchart illustrating a method of changing a center frequency of a BPF by reversing polarity. 
     
    
    
     The present invention will now be described with reference to the accompanying drawings. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. The drawing in which an element first appears is indicated by the leftmost digit(s) in the reference number. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The following detailed description of the present invention refers to the accompanying drawings that illustrate exemplary embodiments consistent with this invention. Other embodiments are possible, and modifications may be made to the embodiments within the spirit and scope of the invention. Therefore, the detailed description is not meant to limit the invention. Rather, the scope of the invention is defined by the appended claims. 
     References in the specification to “one embodiment,” “an embodiment,” “an example embodiment,” etc., indicate that the embodiment described may include a particular feature, structure, or characteristic, but every embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection with an embodiment, it is submitted that it is within the knowledge of one skilled in the art to effect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described. 
     Furthermore, it should be understood that spatial descriptions (e.g., “above,” “below,” “up,” “left,” “right,” “down,” “top,” “bottom,” “vertical,” “horizontal,” etc.) used herein are for purposes of illustration only, and that practical implementations of the structures described herein may be spatially arranged in any orientation or manner. Likewise, particular bit values of “0” or “1” (and representative voltage values) are used in illustrative examples provided herein to represent information for purposes of illustration only. Information described herein may be represented by either bit value (and by alternative voltage values), and embodiments described herein may be configured to operate on either bit value (and any representative voltage value), as would be understood by persons skilled in the relevant art(s). 
     The example embodiments described herein are provided for illustrative purposes, and are not limiting. Further structural and operational embodiments, including modifications/alterations, will become apparent to persons skilled in the relevant art(s) from the teachings herein. 
       FIG. 1  is a block diagram illustrating a network system  10  according to an embodiment of the present invention. The system  10  includes a plurality of base stations and/or access points  12 - 16 , a plurality of wireless communication devices  18 - 32  and a network hardware component  34 . The wireless communication devices  18 - 32  may be laptop host computers  18  and  26 , personal digital assistant hosts  20  and  30 , personal computer hosts  24  and  32  and/or cellular telephone hosts  22  and  28 . 
     The base stations or access points  12  are operably coupled to the network hardware  34  via local area network connections  36 ,  38  and  40 . The network hardware  34 , which may be a router, switch, bridge, modem, system controller, etc. provides a wide area network connection  42  for the communication system  10 . Each of the base stations or access points  12 - 16  has an associated antenna or antenna array to communicate with the wireless communication devices in its area. Typically, the wireless communication devices register with a particular base station or access point  12 - 14  to receive services from the communication system  10 . For direct connections (i.e., point-to-point communications), wireless communication devices communicate directly via an allocated channel. 
     Typically, base stations are used for cellular telephone systems and like-type systems, while access points are used for in-home or in-building wireless networks. Regardless of the particular type of communication system, each wireless communication device includes a built-in radio and/or is coupled to a radio. The radio includes a transmitter capable of adjusting power amplifier output power and therefore has characteristics of reduced power requirements, thereby extending the life of an associated power supply. 
       FIG. 2  is a circuit diagram illustrating a receiver  200  with low-intermediate frequency, which is 100 KHz in this embodiment. An antenna  205  is coupled to a low noise amplifier (LNA)  210 , which is coupled to down converters (mixers)  220  and  225 . The down converters  220  and  225  are coupled to bandpass filters (BPFs)  230  and  235 , respectively, which are coupled to programmable gain stages  240  and  245 , respectively. The gain stages  240  and  245  are coupled to gain stages  250  and  255  respectively, which output analog signals to measurement circuits  285  and  290 , respectively. Further, an LO generator  280  is coupled to the down converters  220  and  225 . A wideband radio signal strength indicator (WRSSI)  215  is coupled to connections between the down converters  220  and  225  and the bandpass filters  230  and  235 . 
     The antenna  205  receives signals and passes the signals to the LNA  210 , which amplifies the received signals and passes them to the down converters  220  and  225 , which shifts the frequency of the received signals downwards. The BPFs  230  and  235  discriminate against unwanted frequencies outside of a selected band. The BPFs  230  and  235  also perform channel selection to compromise between image rejection and DC offset rejection, as will be discussed in further detail below. 
     In an embodiment of the invention, each BPF  230  and  235  can comprise 3 biquads with configurations as shown in Table I below. 
     
       
         
               
             
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE I 
               
             
             
               
                   
               
               
                 (Center Frequency of 100 KHz) 
               
             
          
           
               
                   
                 Biquad1 
                 Biquad2 
                 Biquad3 
               
               
                   
                   
               
             
          
           
               
                 Center 
                 100 
                 KHz 
                 186 
                 KHz 
                 13.4 
                 KHz 
               
               
                 Frequency 
               
               
                 BW 
                 200 
                 KHz 
                 100 
                 KHz 
                 100 
                 KHz 
               
             
          
           
               
                 Q 
                 0.5 
                 1.866 
                 0.134 
               
             
          
           
               
                 Gain Setting 
                 20 dB, 0 dB 
                 10 dB, 0 dB 
                 0 
                 dB 
               
             
          
           
               
                 30 dB 
                 20 
                 dB 
                 10 
                 dB 
                 0 
                 dB 
               
               
                 20 dB 
                 20 
                 dB 
                 0 
                 dB 
                 0 
                 dB 
               
               
                 10 dB 
                 0 
                 dB 
                 10 
                 dB 
                 0 
                 dB 
               
               
                  0 dB 
                 0 
                 dB 
                 0 
                 dB 
                 0 
                 dB 
               
             
          
           
               
                 Current 
                 1.7 mA (I and Q) 
                 1.7 mA (I and Q) 
                 1.7 mA (I and Q) 
               
               
                   
               
             
          
         
       
     
     Each BPF  230  and  235  can have gain settings of 30 dB, 20 dB, 10 dB and 0 dB. IF can be centered at 112 KHz, 108 KHz, 104 KHz, and 100 KHz. Further, the BPFs  230  and  235  can change the IQ polarity. 
     Control words will vary the coupling resistor 410 values, which is Rx in  FIG. 4 , and change the IF frequency of the channel select filter  400 . Control words for changing the channel selection (frequency selection) of the BPFs  230  and  235  are shown in Table II below. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE II 
               
               
                   
                   
               
               
                   
                   
                 Center Frequency 
               
               
                   
                 BPF Center Frequency 
                 Control Word (4 bit) 
               
               
                   
                   
               
             
             
               
                   
                 112 KHz 
                 1000 
               
               
                   
                 108 KHz 
                 0100 
               
               
                   
                 104 KHz 
                 0010 
               
               
                   
                 100 KHz 
                 0001 
               
               
                   
                   
               
             
          
         
       
     
     The LO generator  280  determines how to bring an incoming RF signal received at the antenna  205  down to 100 KHz. The gain stages  240 - 255  increase the gain of the BPFs  230  and  235  output. The measurement circuits  285  and  290  measure the DC offset rejection and image rejection of the filtered signals and provide feedback to the BPFs  230  and  235  so that a new IF frequency can be chosen to form a better compromise between DC offset rejection and image rejection. 
       FIG. 3  is a chart illustrating an IF frequency shift  300  to transform a low pass filter into a bandpass filter. The transformation can be done by the variation of resistance in the BPFs  230  and  235  as derived below based on the circuits shown in  FIG. 4A  and  FIG. 4B  below. The transformation also enables IF frequency shifting to compensate for DC offset rejection and image rejection. 
     For a low pass filter: 
                 y   x     =     Gain     1   +     j   ⁢     ω     ω   0               ,         
wherein ω 0  is the corner frequency.
 
For a bandpass filter:
 
                 y   x     =     Gain     1   +     j   ⁢       (     ω   -     ω   c       )       ω   0               ,         
wherein ω C  is the center frequency.
 
Therefore, for the channel select filter electrical equivalent  420  ( FIG. 4B ):
 
     
       
         
           
             
               
                 
                   
                     y 
                     x 
                   
                   = 
                     
                   ⁢ 
                   
                     1 
                     
                       
                         j 
                         ⁢ 
                         
                           ω 
                           
                             ω 
                             0 
                           
                         
                       
                       + 
                       1 
                       - 
                       
                         j 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Q 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     1 
                     
                       1 
                       + 
                       
                         j 
                         ⁡ 
                         
                           ( 
                           
                             
                               ω 
                               
                                 ω 
                                 0 
                               
                             
                             - 
                             
                               2 
                               ⁢ 
                               Q 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     1 
                     
                       1 
                       + 
                       
                         j 
                         ⁢ 
                         
                           
                             ω 
                             - 
                             
                               2 
                               ⁢ 
                               Q 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ω 
                                 0 
                               
                             
                           
                           
                             ω 
                             0 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1 
                       
                         1 
                         + 
                         
                           j 
                           ⁢ 
                           
                             
                               ω 
                               - 
                               
                                 ω 
                                 c 
                               
                             
                             
                               ω 
                               0 
                             
                           
                         
                       
                     
                     . 
                   
                 
               
             
           
         
       
       
         
           
             Therefore 
             , 
             
               
 
             
             ⁢ 
             
               
                 ω 
                 0 
               
               = 
               
                 1 
                 
                   
                     R 
                     f 
                   
                   ⁢ 
                   C 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 ω 
                 C 
               
               = 
               
                 1 
                 
                   
                     R 
                     x 
                   
                   ⁢ 
                   C 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             and 
           
         
       
       
         
           
             Q 
             = 
             
               
                 
                   ω 
                   c 
                 
                 
                   2 
                   ⁢ 
                   
                     ω 
                     0 
                   
                 
               
               . 
             
           
         
       
     
       FIG. 4A  and  FIG. 4B  are diagrams illustrating a channel select filter  400  (e.g., bandpass filters  230  and  235 ) and its electrical equivalent, respectively. The filter  400  is an active RC filter that enables achievement of a high dynamic range. The filter  400  comprises two cross coupled low pass filters having cross coupled variable resistors  410 , each having a resistance R X . As derived above, variation of R X  shifts the bandpass filter IF frequency up or down. Specifically, the IF frequency of the filter  400  is inversely proportional to R X . 
     During operation of the filter  400 , a signal is filtered by the filter  400  with the resistors  410  set to an initial default value. The filtered signals are then transmitted to the measurement circuits  285  and  290  where image rejection and DC offset rejection are measured. The circuits  285  and  290  provide feedback to the resistors  410 , which are then adjusted and the measurements repeated after filtering again. This process is repeated until a compromise is established between DC offset rejection and image rejection (e.g., wherein image rejection meets minimum pre-specified requirements and the DC offset rejection is within acceptable tolerances). 
       FIG. 5A  and  FIG. 5B  are charts  500 A and  500 B illustrating shifting the IF frequency of the channel select filter  400  (e.g., bandpass filters  230  and  235 ) to overcome DC offset rejection and image rejection, respectively. During the operation of the filter  400 , the IF frequency of the filter  400  is shifted upwards to improve DC offset rejection (as shown in  FIG. 5A ) and downwards to improve image rejection (as shown in  FIG. 5B ) until a compromise is reached. 
       FIG. 6  is a flowchart illustrating a method  600  for IF frequency selection according to an embodiment of the invention. The IF receiver section  200  may implement the method  600 . First, the IF center frequency is adjusted ( 610 ) by varying resistance of the resistors  410 . A received signal is then filtered ( 620 ) using a bandpass filter using the adjusted frequency. Image rejection and DC offset rejection of the filtered signal is then measured ( 630 ,  640 ). It is then determined ( 650 ) if the measurements are within a specific tolerance (e.g., DC offset rejection is within acceptable tolerances and image rejection meet minimum pre-specified requirements). If the measurements are within the tolerances, the method  600  ends. Otherwise, the center frequency is then adjusted ( 610 ) again and the method  600  repeats. 
     Control words also vary R f  and R i  ( FIG. 8A ) values to change the gain of the bandpass filter  230  and  235 . As shown in  FIG. 7A , in an embodiment of the invention, the BPFs  230  and  235  can have variable gain from 0 db to 30 db in 10 db steps. Control words for the varying gain are shown in Table III below. It will be appreciated by one of ordinary skill in the art that the gain settings are not limited to the values shown in Table III. 
     
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE III 
               
               
                   
               
               
                 Gain 
                 Gain Control Word (2 bit) 
                 Noise Figure @ 100 KHz 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 30 db 
                 11 
                 18.9 
               
               
                 20 db 
                 10 
                 21 
               
               
                 10 db 
                 01 
                 39 
               
               
                  0 db 
                 00 
                 41 
               
               
                   
               
             
          
         
       
     
     The LO generator  280  determines how to bring an incoming RF signal received at the antenna  205  down to 100 KHz. The PGAs  240  and  245  increase the gain of the BPFs  230  and  235  output. The baseband digital processing circuits  285  and  290  convert analog signals from the PGAs  240  and  245  to digital data and determine if the current gain is adequate (e.g., if signal to noise ratio too low). The baseband digital processing circuits  285  and  290  then adjust the BPF  230  and  235  gain function accordingly by varying R f  and R i  ( FIG. 8A ). In an embodiment of the invention, the receiver  200  can include measurement circuits (not shown) in place of or in addition to the baseband digital processing circuits  285  and  290  that measure the DC offset rejection and image rejection of the filtered signals and provide feedback to the BPFs  230  and  235  so that a new IF frequency can be chosen to form a better compromise between DC offset rejection and image rejection. 
       FIG. 7A  is a chart illustrating variable gain in the bandpass filter of the receiver of  FIG. 2 . Gain can be varied by the variation of resistance in the BPFs  230  and  235  as derived below based on the circuits shown in  FIG. 8A  and  FIG. 8B  below. Resistance variation (for resistors  810  in  FIG. 8A ) also enables IF frequency shifting to compensate for DC offset rejection and image rejection. 
     For a low pass filter: 
                 y   x     =     Gain     1   +     j   ⁢     ω     ω   0               ,         
wherein ω 0  is the corner frequency.
 
For a bandpass filter:
 
                 y   x     =     Gain     1   +     j   ⁢       (     ω   -     ω   c       )       ω   0               ,         
wherein ω C  is the center frequency.
 
Therefore, for the channel select filter electrical equivalent  820  ( FIG. 8B ):
 
     
       
         
           
             
               
                 
                   
                     y 
                     x 
                   
                   = 
                     
                   ⁢ 
                   
                     Gain 
                     
                       
                         j 
                         ⁢ 
                         
                           ω 
                           
                             ω 
                             0 
                           
                         
                       
                       + 
                       1 
                       - 
                       
                         j 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Q 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     Gain 
                     
                       1 
                       + 
                       
                         j 
                         ⁡ 
                         
                           ( 
                           
                             
                               ω 
                               
                                 ω 
                                 0 
                               
                             
                             - 
                             
                               2 
                               ⁢ 
                               Q 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     Gain 
                     
                       1 
                       + 
                       
                         j 
                         ⁢ 
                         
                           
                             ω 
                             - 
                             
                               2 
                               ⁢ 
                               Q 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ω 
                                 0 
                               
                             
                           
                           
                             ω 
                             0 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       Gain 
                       
                         1 
                         + 
                         
                           j 
                           ⁢ 
                           
                             
                               ω 
                               - 
                               
                                 ω 
                                 c 
                               
                             
                             
                               ω 
                               0 
                             
                           
                         
                       
                     
                     . 
                   
                 
               
             
           
         
       
       
         
           
             Therefore 
             , 
             
               
 
             
             ⁢ 
             
               
                 ω 
                 0 
               
               = 
               
                 1 
                 
                   
                     R 
                     f 
                   
                   ⁢ 
                   C 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 ω 
                 C 
               
               = 
               
                 1 
                 
                   
                     R 
                     x 
                   
                   ⁢ 
                   C 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             and 
           
         
       
       
         
           
             Q 
             = 
             
               
                 
                   ω 
                   c 
                 
                 
                   2 
                   ⁢ 
                   
                     ω 
                     o 
                   
                 
               
               . 
             
           
         
       
     
       FIG. 7B  are charts showing noise figures for the BPFs  230  and  235 . As gain is increased, noise decreases, thereby improving the signal to noise ratio. 
       FIG. 8A  and  FIG. 8B  are diagrams illustrating a BPF  800  (e.g., the bandpass filters  230  and  235 ) and its electrical equivalent  820 , respectively. The filter  800  is an active RC filter that enables achievement of a high dynamic range. The filter  800  comprises two cross coupled low pass filters having cross coupled variable resistors  810 , each having a resistance R X . As derived above, variation of R X  shifts the bandpass filter IF frequency up or down. Specifically, the IF frequency of the filter  800  is inversely proportional to R X . In addition, variation of a feedback resistor, R f , and of an input resistor, R i , enable changes in gain of the filter  800  as gain is equal to 
     
       
         
           
             
               
                 R 
                 f 
               
               
                 R 
                 i 
               
             
             . 
           
         
       
     
     R f  and R i  are set to default values (e.g., zero gain) initially and gain, if any, is applied. After filtering and amplification (by the PGAs  240 ,  245 ), the baseband digital processing circuits  285  and  290  determine if the gain is adequate based on the signal to noise ratio. If the gain is insufficient because of BPF  230  or  235  noise is being amplified, then the baseband digital processing circuits  285  and  290  provide feedback to the BPFs  230  and  235  and R f  and R i  are adjusted to increase gain in the BPFs  230  and  235 . 
       FIG. 9  is a flowchart illustrating a method  900  for variable gain selection in the filter  800 . In an embodiment of the invention, the filter  800  (e.g., the BPFs  230  and  235 ) and the baseband digital processing circuits  285  and  290  perform the method  900 . First, gain in the filter  800  is set ( 910 ) to a default setting (e.g., 0 by setting R f  and R i  to be equal to each other). Next, the signal is amplified ( 920 ) according to the setting. The signal to noise ratio is then measured ( 930 ). If ( 940 ) it is determined that the gain is sufficient because the signal to noise ratio is sufficient, the method  900  then ends. Otherwise, the gain setting is adjusted ( 950 ) upwards and the amplifying ( 920 ), measuring ( 930 ), and determining ( 940 ) are repeated until the signal to noise ratio is adequate. 
     In an embodiment of the invention, the measuring ( 930 ) can determine if the gain is appropriate (too high or too low) and the adjusting ( 950 ) can adjust the gain up or down accordingly. 
     Further, the BPFs  230  and  235  can change the IQ polarity, as will be discussed further below. Control words for changing IQ polarity are shown in Table IV below. 
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE IV 
               
             
             
               
                   
               
               
                 (Control Words for IQ Polarity) 
               
             
          
           
               
                   
                 IQ_select 
                 IQ Polarity 
                 BPF Shape 
               
               
                   
                   
               
               
                   
                 1 
                 I = I, Q = Q 
                 Wif = 100 KHz 
               
               
                   
                 0 
                 I = I, Q = Qbar 
                 Wif = −100 KHz 
               
               
                   
                   
               
             
          
         
       
     
     The LO generator  280  determines how to bring an incoming RF signal received at the antenna  205  down to 100 KHz. The PGAs  240  and  245  increase the gain of the BPFs  230  and  235  output. The baseband digital processing circuits  285  and  290  convert analog signals from the PGAs  240  and  245  to digital data and determine if the current gain is adequate (e.g., if signal to noise ratio too low). The baseband digital processing circuits  285  and  290  then adjust the BPF  230  and  235  gain function accordingly by varying R f  and R i  ( FIG. 11 ). In an embodiment of the invention, the receiver  200  can include measurement circuits (not shown) in place of or in addition to the baseband digital processing circuits  285  and  290  that measure the DC offset rejection and image rejection of the filtered signals and provide feedback to the BPFs  230  and  235  so that a new IF frequency can be chosen to form a better compromise between DC offset rejection and image rejection. 
       FIG. 10A-10D  are diagrams illustrating BPF center frequency based on down conversion frequency. As shown in  FIG. 10A , when Wlo (LO frequency) is greater than Wrf (received frequency), Wif=Wlo−Wro will be positive. Accordingly, a BPF with a positive center frequency will be required to filter Wif. Further, as shown in  FIG. 10C , when Wlo&lt;Wrf, then Wif=Wlo−Wrf will be negative, necessitating the need for a BPF with a negative center frequency. 
     For a low pass filter: 
                 y   x     =     Gain     1   +     j   ⁢     ω     ω   0               ,         
wherein ω 0  is the corner frequency.
 
For a bandpass filter:
 
                 y   x     =     Gain     1   +     j   ⁢       (     ω   -     ω   c       )       ω   0               ,         
wherein ω C  is the center frequency.
 
For the channel select filter electrical equivalent  1300  ( FIG. 13A ):
 
                     y   x     =       ⁢     Gain       j   ⁢     ω     ω   0         +   1   -     j   ⁢           ⁢   2   ⁢           ⁢   Q                     =       ⁢     Gain     1   +     j   ⁡     (       ω     ω   0       -     2   ⁢   Q       )                       =       ⁢     Gain     1   +     j   ⁢       ω   -     2   ⁢   Q   ⁢           ⁢     ω   0           ω   0                           =       ⁢     Gain     1   +     j   ⁢       ω   -     ω   c         ω   0               ,                   where                 ω   0     =     1       R   f     ⁢   C         ,     
     ⁢       ω   C     =     1       R   x     ⁢   C         ,     
     ⁢     Q   =       ω   c       2   ⁢     ω   o           ,     
     ⁢   and               Gain   =         R   f       R   i       .           
In contrast, for the channel select filter equivalent  1500  ( FIG. 15A ):
 
     
       
         
           
             
               
                 
                   
                     y 
                     x 
                   
                   = 
                     
                   ⁢ 
                   
                     Gain 
                     
                       
                         j 
                         ⁢ 
                         
                           ω 
                           
                             ω 
                             0 
                           
                         
                       
                       + 
                       1 
                       + 
                       
                         j 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Q 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     Gain 
                     
                       1 
                       + 
                       
                         j 
                         ⁡ 
                         
                           ( 
                           
                             
                               ω 
                               
                                 ω 
                                 0 
                               
                             
                             + 
                             
                               2 
                               ⁢ 
                               Q 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     Gain 
                     
                       1 
                       + 
                       
                         j 
                         ⁢ 
                         
                           
                             ω 
                             + 
                             
                               2 
                               ⁢ 
                               Q 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ω 
                                 0 
                               
                             
                           
                           
                             ω 
                             0 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   
                     = 
                       
                     ⁢ 
                     
                       Gain 
                       
                         1 
                         + 
                         
                           j 
                           ⁢ 
                           
                             
                               ω 
                               + 
                               
                                 ω 
                                 c 
                               
                             
                             
                               ω 
                               0 
                             
                           
                         
                       
                     
                   
                   , 
                 
               
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               
                 ω 
                 0 
               
               = 
               
                 1 
                 
                   
                     R 
                     f 
                   
                   ⁢ 
                   C 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 ω 
                 C 
               
               = 
               
                 - 
                 
                   1 
                   
                     
                       R 
                       x 
                     
                     ⁢ 
                     C 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               Q 
               = 
               
                 
                   ω 
                   c 
                 
                 
                   2 
                   ⁢ 
                   
                     ω 
                     o 
                   
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               Gain 
               = 
               
                 
                   R 
                   f 
                 
                 
                   R 
                   i 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             and 
           
         
       
       
         
           
             
               y 
               x 
             
             = 
             
               
                 Gain 
                 
                   1 
                   + 
                   
                     j 
                     ⁢ 
                     
                       
                         ( 
                         
                           ω 
                           + 
                           
                             ω 
                             c 
                           
                         
                         ) 
                       
                       
                         ω 
                         0 
                       
                     
                   
                 
               
               . 
             
           
         
       
     
     The filter  1100  is an active RC filter that enables achievement of a high dynamic range. The filter  1100  comprises two cross coupled low pass filters having cross coupled variable resistors  410 , each having a resistance R X . As derived above, variation of R X  shifts the bandpass filter IF frequency up or down. Specifically, the IF frequency of the filter  1100  is inversely proportional to R X . In addition, variation of a feedback resistor, R f , and of an input resistor, R i , enable changes in gain of the filter  1100  as gain is equal to 
     
       
         
           
             
               
                 R 
                 f 
               
               
                 R 
                 i 
               
             
             . 
           
         
       
     
     R f  and R i  are set to default values (e.g., zero gain) initially and gain, if any, is applied. After filtering and amplification (by the PGAs  240 ,  245 ), the baseband digital processing circuits  285  and  290  determine if the gain is adequate based on the signal to noise ratio. If the gain is insufficient because of BPF  230  or  235  noise is being amplified, then the baseband digital processing circuits  285  and  290  provide feedback to the BPFs  230  and  235  and R f  and R i  are adjusted to increase gain in the BPFs  230  and  235 . 
     In order to reverse polarities to move the BPF  1100  center frequency from positive to negative, the BPF  1100  includes switching devices  1120  and  1130 . The switching device  1120  is coupled to the inputs of a first LPF that is a cross-coupled to a second LPF to form the BPF  1100 . The switching device  1130  is coupled to the second LPF. In an embodiment of the invention, the BPF  1100  does not include the switching device  1120 . Each switching device  1120  and  1130  include 4 (four) switches s 1 -s 4 . Switches s 2  and s 3  of each switching device  1120  and  1130  enable the cross-coupling of inputs while the switches s 1  and s 4  enable straight input without cross-coupling. Specifically, the switches s 2  and s 3  of the switching device  1120  reverse the inputs of V IIP  and V IIN , while the switches s 2  and s 3  of the switching device  1130  reverse the inputs of V QIP  and V QIN . 
       FIGS. 12A and 12B  are diagrams illustrating the switching devices  1120  and  1130  of the BPF  1100  when polarity is not reversed (i.e., IQ_select=1). When polarity is not reversed (e.g., the BPF  1100  center frequency is positive), the switches s 1  and s 4  of both the switching devices  1120  and  1130  are activated to enable straight pass through of signals to the BPF  1100  with no cross-coupling. Accordingly, I out =I in  and Q out =Q in . 
       FIGS. 13A and 13B  are diagrams illustrating a signal flow diagram of the BPF  1100  without reversed polarity and the center frequency of the BPF. When IQ_select=1, the signal flow diagram of the BPF  1100  becomes the circuit  1300  as shown in  FIG. 13A . Therefore, the center frequency of the BPF is positive, as shown in  FIG. 13B . 
       FIGS. 14A and 14B  are diagrams illustrating the switching devices  1120  and  1130  of the BPF  1100  when polarity is reversed (i.e., IQ_select=0). When polarity is reversed (e.g., the BPF  1100  center frequency is negative), the switches s 1  and s 4  of the switching devices  1120  are activated to enable straight pass through of signals to the BPF  1100  with no cross-coupling. However, the switches s 2  and s 3  of the switching device  1130  is activated to enabling cross-coupling, thereby reversing the inputs of Qin. Accordingly, I out =I in  and Q out =−Q in . 
       FIGS. 15A and 15B  are diagrams illustrating a signal flow diagram of the BPF  1100  with reversed polarity and the center frequency of the BPF. When IQ_select=0, the signal flow diagram of the BPF  1100  becomes the circuit  1500  as shown in  FIG. 15A . Therefore, the center frequency of the BPF is negative, as shown in  FIG. 15B . 
       FIGS. 16A and 16B  are simulation charts illustrating the center frequency of the BPF  1100  without and with reversed polarity, respectively. When IQ_select=1 (high side injection), the center frequency of the BPF  1100  is positive, as shown in  FIG. 16A . When IQ_select=0 (low side injection), the center frequency of the BPF  1100  is negative, as shown in  FIG. 16B . Accordingly, the BPF  1100  can perform filtering for either high side or low side injection. 
       FIG. 17  is a flowchart illustrating a method  1700  of changing a center frequency of a BPF by reversing polarity. First, a heterodyne receiver determines ( 1710 ) to use either high side injection or low side injection. If ( 1720 ) high injection is used then Wlo is set to be higher than the Wrf, and then Wif will be greater than 0. Accordingly IQ_select is set ( 1730 ) to 1 to center the BPF at a positive frequency. Else if low injection is used then Wlo is set to be lower than the Wrf, and then Wif will be less than 0. Accordingly, IQ_select is set ( 1740 ) to 0 to center the BPF at negative frequency. The method  1700  then ends. 
     CONCLUSION 
     While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example, and not limitation. It will be apparent to persons skilled in the relevant art(s) that various changes in form and detail may be made therein without departing from the spirit and scope of the invention. Thus the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.