Abstract:
A line driver combining active impedance and filter in one stage for connection to a transmission line having a characteristic impedance. The line driver comprises an amplifier, a transformer with a primary to secondary winding ratio of 1:n, a reference impedance, an input impedance and two feedback impedances. The primary winding of the transformer has a first end connected to the output of the amplifier and the secondary winding is connectable to the transmission line. The reference resistor has an end connected to the second end of the first winding at a junction node and the feedback circuit is connected to the input and output of the amplifier and also to the junction node. The reference impedance has a value equal to n 2  /K times the characteristic impedance of the transmission line. The feedback circuit is arranged to produce a voltage at the output of the amplifier substantially equal to (K+1) times the voltage at the junction node, for a predetermined value of K. This results in output impedance equal to n 2  times the characteristic impedance of the transmission line. At the same time, the gain or filter function is set by the specifying the ratio of feedback impedance to the input impedance.

Description:
FIELD OF THE INVENTION  
         [0001]    This invention relates generally to line drivers and particularly to line drivers having desirable output impedance and filtering capabilities in a single amplifier stage.  
         BACKGROUND OF THE INVENTION  
         [0002]    DSL (digital subscriber line) is a technology for bringing high-bandwidth information to homes and small businesses over ordinary copper telephones lines. xDSL refers to different variations of DSL such as ADSL (asymmetric DSL), G.Lite DSL (ITU-T standard G-992.2), HDASL (high bit-rate DSL) and RADSL (rate-adaptive DSL).  
           [0003]    DSL modems are typically installed in pairs, with one of the modems installed in a home (customer&#39;s premises) and the other in the telephone company&#39;s central office servicing that home. The pair of xDSL modems are connected to the opposite ends of the same twisted-pair transmission line.  
           [0004]    Referring to FIG. 1 a conventional xDSL communication system  100  comprises a CO (central office)  101 . The CO  101  has a plurality of xDSL modems  102  (only one shown). The xDSL modem  102  has a D/A (digital to analog) converter  104 . An output of the D/A converter  104  is connected  105  to an input of an xDSL driver  106 . An output of the xDSL driver  106  is connected  107  to a 4-wire input of a hybrid  108 . A 4-wire output of the hybrid  108  is connected  109  to an input of an xDSL receiver  110 . An output of the xDSL receiver  110  is connected  111  to the input of an A/D (analog to digital) converter  112 . A 2-wire port of the hybrid  108  is connected to a transmission line  114 , such as copper twisted pair.  
           [0005]    The xDSL communication system  100  also comprises CPE (customer premises equipment)  126 . The CPE  126  has an xDSL modem  122 . The xDSL modem  122  has a D/A converter  124 . An output of the D/A converter  124  is connected  125  to an input of an xDSL driver  126 . An output of the xDSL driver  126  is connected  127  to a 4-wire input of a hybrid  128 . A 4-wire output of the hybrid  128  is connected  129  to an input of an xDSL receiver  130 . An output of the xDSL receiver  130  is connected  131  to an input of an A/D converter  132 . The 2-wire port of the hybrid  128  is connected to the transmission line  114 .  
           [0006]    Since an xDSL modem operates at frequencies higher than the voice-band frequencies, an xDSL modem may operate simultaneously with a voice-band modem or a telephone conversation. Referring to FIG. 2, there is shown an example of a frequency spectrum plan  200  for a G.Lite DSL system on the transmission line  114  of FIG. 1. The frequency range from 0.3 to 4 kHz  202  is occupied by conventional voice communications. The frequency range from 30 to 120 kHz 204 is occupied by upstream (CPE  126  to CO  101 ) data transmission. The frequency range from 150 kHz to approximately 500 kHz  206  is occupied by downstream (CO  101  to CPE  126 ) data transmission. The upper frequency limit of the downstream data transmission is determined by the length and quality of the transmission line  114 .  
           [0007]    Referring to FIG. 3, there is shown a conventional implementation of the xDSL driver  106  of FIG. 1. The input of the xDSL driver  106  is connected  105  to an input of a bandpass filter  302 . The output of the bandpass filter  302  is connected to a first non-inverting input  304  of a summation circuit  306 . The output of the summation circuit  306  is connected to an input  312  of an amplifier  314 . An output of the amplifier  314  is connected  316  to a first terminal of a reference resistor Re  318 . A second terminal of the reference resistor Re  318  is connected to the output of the xDSL driver  107 . A resistor R 1    320  is connected from a second non-inverting input  308  of the summation circuit to ground  328 . A resistor R 2    322  is connected from output  107  of the xDSL driver  106  to the second non-inverting input  308  of the summation circuit  306 . A resistor R 3    324  is connected from an inverting input  310  of the summation circuit  306  to ground  328 . A resistor R 4    326  is connected  316  from the output of the power amplifier  314  to the inverting input  310  of the summation circuit  306 .  
           [0008]    Referring to FIG. 4, there is shown a conventional implementation of the xDSL driver  126  of FIG. 1. The topology of the xDSL driver  126  is the same as the topology of the xDSL driver  106  of FIG. 3. The differences are in the upper and lower cut-off frequencies of the filters, a bandpass filter  302  in xDSL driver  106  and bandpass filter  402  in xDSL driver  126 . For example, in the case of G.Lite DSL, the lower cut-off frequency of filter  302  in xDSL driver  106  is 150 kHz, the upper cut-off frequency of filter  302  in xDSL driver  106  is 500 kHz, the lower cut-off frequency of filter  402  in xDSL driver  126  is 30 kHz and the upper cut-off frequency of filter  402  in xDSL driver  126  is 120 kHz. The gain and output impedance of xDSL driver  106  and xDSL driver  126  are substantially the same.  
           [0009]    Unfortunately, the performance characteristics such as gain and output impedance of the conventional xDSL drivers  106 ,  126  are severely affected by the tolerances of the components in the positive (R 1    320 ,  420 , R 2    322 ,  422 ) and negative (R 3    324 ,  424 , R 4    326 ,  426 ) feedback loops and in the reference resistor (R e    318 ,  418 ). Another disadvantage of this circuit is that the active impedance generation and filtering are realized in different stages.  
           [0010]    Thus there is a need in the industry to provide an xDSL driver that combines active impedance generation and filtering capabilities in a single amplifier stage. Furthermore, it would be advantageous to provide a line driver that would also have an independently specified gain and output impedance as well as gain that is relatively insensitive to component tolerances.  
         SUMMARY OF THE INVENTION  
         [0011]    The invention may be summarized according to a first broad aspect as a line driver having an amplifier, a transformer, a reference impedance, an input impedance, a first feedback impedance and a second feedback impedance. Preferably, the amplifier is an operational amplifier connected in an inverting configuration with an input and an output. The transformer has a primary winding and a secondary winding with a ratio of 1:n. The primary winding having a first terminal connected to the output of the amplifier and having a second terminal. The secondary winding is connectable to a transmission line having a characteristic impedance. The reference impedance is connected from the second terminal of the primary winding at a junction node to a ground reference. The input impedance having one terminal connected to the input of the amplifier and another terminal connectable to a voltage source. The first feedback impedance is connected from the junction node to the input of the amplifier and the second feedback impedance is connected from the output of the amplifier to the input of the amplifier. The second feedback impedance preferably has a value equal to (K−1) times the value of the first feedback impedance.  
           [0012]    In accordance with this first broad aspect of the invention, the reference impedance has a value equal to n 2 /K times the characteristic impedance of the transmission line and the feedback circuit is arranged to produce a voltage at the output of the amplifier substantially equal to (K+1) times the voltage at the junction node, for a predetermined value of K. The resulting output impedance will be equal to K times the reference impedance and the gain will be equal to half of the negative of the ratio of the value of the second feedback impedance to the value of the input impedance.  
           [0013]    According to a second broad aspect, the invention may be summarized as a line driver having a first amplifier, a transformer, a reference impedance, an input impedance, a first feedback impedance, a second feedback impedance and a second amplifier. Preferably, the first amplifier is an operational amplifier connected in an inverting configuration with a non-inverting input, an inverting input and an output and the second amplifier is an operational amplifier connected in a unity gain configuration with an input and an output. The transformer has a primary winding and a secondary winding with a ratio of 1:n. The primary winding having a first terminal connected to the output of the first amplifier and having a second terminal. The secondary winding is connectable to a transmission line having a characteristic impedance. The reference impedance is connected from the second terminal of the primary winding at a junction node to a ground reference. The input impedance having one terminal connected to the inverting input of the first amplifier and another terminal connectable to a voltage source. The first feedback impedance is connected from output of the second amplifier to the inverting input of the first amplifier and the second feedback impedance is connected from the output of the first amplifier to the inverting input of the first amplifier. The input to the second amplifier is connected to the junction node. The second feedback impedance preferably has a value equal to (K−1) times the value of the first feedback impedance.  
           [0014]    In accordance with this second broad aspect of the invention, the reference impedance has a value equal to  
         n   2     K                         
 
           [0015]    times the characteristic impedance of the transmission line. The resulting output impedance will be equal to K times the reference impedance and the gain will be equal to half of the negative of the ratio of the value of the second feedback impedance to the value of the input impedance.  
           [0016]    The invention may be summarized according to a third broad aspect as a line driver having an amplifier, a transformer, a reference impedance, an input impedance, a first feedback impedance and a second feedback impedance. Preferably, the amplifier is an operational amplifier connected in an inverting configuration with an input and an output. The transformer has a primary winding, a first secondary winding, a second secondary winding with a ratio of 1:n:m. The primary winding having a first terminal connected to the output of the amplifier and having a second terminal. The first secondary winding is connectable to a transmission line having a characteristic impedance. The second secondary winding having a first terminal connected to a ground reference and a second terminal. The primary winding and second secondary winding are arranged such that current flowing into the first terminal of the primary winding will cause current to flow into the second terminal of the second secondary winding. The reference impedance is connected from the second terminal of the primary winding at a junction node to the ground reference. The input impedance having one terminal connected to the input of the amplifier and another terminal connectable to a voltage source. The first feedback impedance is connected from the second terminal of the second secondary winding to the input of the amplifier and the second feedback impedance is connected from the output of the amplifier to the input of the amplifier. The second feedback impedance preferably has a value equal to  
         K   -   1     mK                         
 
           [0017]    times the value of the first feedback impedance.  
           [0018]    In accordance with this third broad aspect of the invention, the reference impedance has a value equal to  
         n   2     K                         
 
           [0019]    times the characteristic impedance of the transmission line and the feedback circuit is arranged to produce a voltage at the output of the amplifier substantially equal to (K+1) times the voltage at the junction node, for a predetermined value of K. The resulting output impedance will be equal to K times the reference impedance and the gain will be equal to half of the negative of the ratio of the value of the second feedback impedance to the value of the input impedance.  
           [0020]    The invention may be summarized according to a fourth broad aspect as a line driver having an amplifier, a transformer, a reference impedance, an input impedance, a first feedback impedance and a second feedback impedance. Preferably, the amplifier is an operational amplifier connected in an inverting configuration with an input and an output. The transformer has a primary winding, a first secondary winding, a second secondary winding with a ratio of 1:n:m. The primary winding having a first terminal connected to the output of the amplifier and having a second terminal. The first secondary winding is connectable to a transmission line having a characteristic impedance. The second secondary winding having a first terminal connected to a ground reference and a second terminal. The primary winding and second secondary winding are arranged such that current flowing into the first terminal of the primary winding will cause current to flow into the first terminal of the second secondary winding. The reference impedance is connected from the second terminal of the primary winding at a junction node to the ground reference. The input impedance having one terminal connected to the input of the amplifier and another terminal connectable to a voltage source. The first feedback impedance is connected from the second terminal of the second secondary winding to the input of the amplifier and the second feedback impedance is connected from the output of the amplifier to the input of the amplifier. The second feedback impedance preferably has a value equal to times  
       1   mK                         
 
           [0021]    the value of the first feedback impedance.  
           [0022]    In accordance with this fourth broad aspect of the invention, the reference impedance has a value equal to  
         n   2     K                         
 
           [0023]    times the characteristic impedance of the transmission line and the feedback circuit is arranged to produce a voltage at the output of the amplifier substantially equal to (K+1) times the voltage at the junction node, for a predetermined value of K. The resulting output impedance will be equal to K times the reference impedance and the gain will be equal to the ratio of the negative of the value of the second feedback impedance to the value of the input impedance.  
           [0024]    The invention may be summarized according to a fifth broad aspect as a line driver having an amplifier, a transformer, a reference impedance, an input impedance, a first feedback impedance and a second feedback impedance. Preferably, the amplifier is an operational amplifier connected in an inverting configuration with an input and an output. The transformer has a primary winding, a first secondary winding, a second secondary winding with a ratio of 1:n:m. The primary winding having a first terminal connected to the output of the amplifier and having a second terminal. The first secondary winding is connectable to a transmission line having a characteristic impedance. The second secondary winding having a first terminal connected to a ground reference and a second terminal. The primary winding and second secondary winding are arranged such that current flowing into the first terminal of the primary winding will cause current to flow into the first terminal of the second secondary winding. The reference impedance is connected from the second terminal of the primary winding at a junction node to the ground reference. The input impedance having one terminal connected to the input of the amplifier and another terminal connectable to a voltage source. The first feedback impedance is connected from the second terminal of the second secondary winding to the input of the amplifier and the second feedback impedance is connected from the output of the amplifier to the input of the amplifier. The second feedback impedance preferably has a value equal to  
           2      K     +   1     mK                         
 
           [0025]    times the value of the first feedback impedance.  
           [0026]    In accordance with this fifth broad aspect of the invention, the reference impedance has a value equal to  
         n   2     K                         
 
           [0027]    times the characteristic impedance of the transmission line and the feedback circuit is arranged to produce a voltage at the output of the amplifier substantially equal to (K+1) times the voltage at the junction node, for a predetermined value of K. The resulting output impedance will be equal to K times the reference impedance and the gain will be equal to the ratio of the value of the second feedback impedance to the value of the input impedance.  
           [0028]    Advantageously the output impedance of the xDSL driver is specified independently from the gain or filter function of the xDSL driver. Furthermore, the gain is a simple ratio of impedances that make the gain less sensitive to component and manufacturing variations.  
           [0029]    Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of the specific embodiments of the invention in conjunction with the accompanying figures. 
       
    
    
       [0030]    BRIEF DESCRIPTION OF THE DRAWINGS  
         [0031]    [0031]FIG. 1 is a block diagram of a conventional xDSL communication system;  
         [0032]    [0032]FIG. 2 is a frequency spectrum plan of a G.Lite DSL communication system;  
         [0033]    [0033]FIG. 3 is a circuit diagram of a conventional xDSL driver used in the CO of the xDSL communication system of FIG. 1;  
         [0034]    [0034]FIG. 4 is a circuit diagram of a conventional xDSL driver used in the CPE of the xDSL communication system of FIG. 1;  
         [0035]    [0035]FIG. 5 is a circuit diagram of a preferred embodiment of an xDSL line driver;  
         [0036]    [0036]FIG. 6 is a circuit diagram of an alternative embodiment of the xDSL line driver of FIG. 5;  
         [0037]    [0037]FIGS. 7A and 7B are circuit diagrams of alternative embodiments of the xDSL line driver of FIG. 5; and  
         [0038]    [0038]FIG. 8A, 8B and  8 C show in greater detail the input impedance, the second feedback impedance and the first feedback impedance respectively of FIG. 5 in accordance with an embodiment of the invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0039]    In order to combine active impedance generation and filtering capabilities in a single amplifier stage, the circuit of FIG. 5 is proposed. FIG. 5 shows an xDSL line driver  500  comprising an amplifier  502  that is preferably an opamp (operational amplifier) having a non-inverting input  504 , an inverting input  506  and an output  524 . The non-inverting input  504  of the opamp  502  is connected to a ground reference  528 . Assuming the opamp  502  to be ideal, a virtual ground exists at the inverting input  506 .  
         [0040]    The xDSL line driver also comprises a transformer  510  having a primary winding  512  and a secondary winding  514 . The primary winding  512  has a first terminal connected to the output  524  of the opamp  502  and a second terminal connected to a junction node  519 . The secondary winding  514  of the transformer  510  is connected across a 4-wire input of a hybrid (not shown) that has a characteristic impedance Z c .  
         [0041]    A reference impedance  516  is connected from the junction node  519  to a ground reference  518 . According to a preferred embodiment of the invention, the reference impedance  516  has a value of  
         Z   e     =         Z   c     K     .                           
 
         [0042]    The ratio  
       K   =       Z   c       Z   e                             
 
         [0043]    is a real number that preferably ranges from 1 to 10, although higher values may be used while remaining within the scope of the invention.  
         [0044]    In the transformer  510 , the ratio of primary  512  to secondary  514  turns in the transformer  510  is 1:1. Alternatively, the transformer ratio is 1:n where n≠1 and therefore  
       K   =           n   2          Z   c         Z   e       .                           
 
         [0045]    In alternative embodiment of the invention the transformer  510  is an integral part of the hybrid (not shown).  
         [0046]    The xDSL driver  500  also comprises a first feedback impedance  520  having a value of Z 3 , a second feedback impedance  522  having a value of Z 2  and an input impedance  526  having a value of Z 1 . The first feedback impedance  520  has a first terminal connected to the junction node  519  and a second terminal connected to the inverting input  506  of the opamp  502 . The second feedback impedance  522  has a first terminal connected to the output  524  of the opamp  502  and a second terminal connected to the inverting input  506  of the opamp  502 . The input impedance  526  has a first terminal connected to the inverting input  506  of the opamp  502  and a second terminal connectable to a voltage source such as a D/A converter (shown in dotted outline at  528 ).  
         [0047]    In an alternative embodiment, shown in FIG. 6, a second amplifier  601  having unity gain is inserted between the junction node  519  and the first terminal of the first feedback impedance  520  with the output  604  of the second amplifier  601  connected to the first terminal of the first feedback impedance  520 . Preferably the second amplifier  601  is an operational amplifier configured for unity gain with the inverting input  603  connected to the output  604  and the non-inverting input  602  connected to the junction node  519 . The rest of the topology of the xDSL driver  600  is identical to the topology of the preferred embodiment of the xDSL driver  500 .  
         [0048]    In another alternative embodiment, shown in FIG. 7A, the transformer  510  of FIG. 5 is replaced by a transformer  710  having a primary winding  512 , a first secondary winding  514  and a second secondary winding  715 . The primary winding  512  and the first secondary winding  514  of FIG. 7A are connected the same as the primary winding  512  and secondary winding  514  of FIG. 5. The second secondary winding  715  has a first terminal connected to the ground reference  518  and a second terminal connected to the first terminal of the first feedback impedance  520 . The rest of the topology of the xDSL driver  700  is identical to the topology of the preferred embodiment of the xDSL driver  500 . In this embodiment the preferred transformer ratio of the primary  512  turns to first secondary  514  turns to second secondary  715  turns is 1:1:1. Alternatively, the transformer ratio may be 1:n:m where n≠1 or m≠1 and hence:  
       K   =           n   2          Z   c         Z   e       .                           
 
         [0049]    The directions of the primary  512  and second secondary  715  windings are chosen such that current flowing into the first terminal of the primary winding  512  will cause current to flow into the second terminal of the second secondary winding  715 .  
         [0050]    Another alternative embodiment, shown in FIG. 7B, is identical to the circuit shown in FIG. 7A except that directions of the primary  512  and second secondary  715  windings are chosen such that current flowing into the first terminal of the primary winding  512  will cause current to flow into the first terminal of the second secondary winding  715 .  
         [0051]    In the preferred embodiment shown in FIG. 5 and the alternative embodiments shown in FIGS. 7A and 7B the first feedback impedance  520  is much greater and preferably two or more orders of magnitude greater than the reference impedance  516  ensuring that the voltage on the output  524  of the amplifier  502  is substantially equal to (K+1)V e . However, in the alternative embodiment of FIG. 6 this condition is unnecessary.  
         [0052]    The following derivation is valid for the embodiments shown in FIGS. 5 and 6. The gain is derived by applying Kirchhoff&#39;s Current Law at the virtual ground of the inverting input  506  to the opamp  502 :  
             V   in       Z   1       +     (         V   o     +     V   e         Z   2       )     +       V   e       Z   3         =   0                         
 
         [0053]    where V in  is the voltage between the second terminal of the input impedance  526  and the ground reference  518 ; V o  is the voltage between the first terminal and second terminal of the primary winding  512  of the transformer  510 ; and V e  is the voltage between the junction node  519  and ground reference  518 . Since Z 3  &gt;&gt;Z e  (only necessary for the embodiment of FIG. 5) and  
         K   =           Z   c       Z   e                     then                   V   e       =       V   o     K         ,                         
 
         [0054]    hence:  
             V   in       Z   1       +         V   o          (     1   +     1   K       )         Z   2       +       V   o       KZ   3         =       0                 solving                 for                 gain     =         V   o       V   in                       gives   :                               
 
           V   o       V   in       =     -       Z   2         Z   1          (     1   +     1   K     +       Z   2       KZ   3         )                     we                 choose                     Z   2       Z   3         =     K   -   1               therefore                     V   o       V   in         =     -       Z   2       2        Z   1                                 
 
         [0055]    The following derivation is valid for the embodiment shown in FIG. 7A. The gain is derived by applying Kirchhoff&#39;s Current Law at the virtual ground of the inverting input  506  to the opamp  502 :  
             V   in       Z   1       +       (       V   o     +     V   e       )       Z   2       +       mV   o       Z   3         =   0                         
 
         [0056]    where V in  is the voltage between the second terminal of the input impedance  526  and the ground reference  518 ; V o  is the voltage between the first terminal and second terminal of the primary winding  512  of the transformer  510 ; and m is the ratio of second secondary  715  turns to primary  512  turns. Since  
           V   e     =       V   o     K       ,                         
 
         [0057]    hence:  
             V   in       Z   1       +         V   o          (     1   +     1   K       )         Z   2       +       mV   o       Z   3         =       0                 solving                 for                 gain     =         V   o       V   in                       gives   :                               
 
           V   o       V   in       =     -       Z   2         Z   1          (     1   +     1   K     +       mZ   2       Z   3         )                     we                 choose                     Z   2       Z   3         =       K   -   1     mK               therefore                     V   o       V   in         =     -       Z   2       2        Z   1                                 
 
         [0058]    The following derivation is valid for the embodiment shown in FIG. 7B. The gain is derived by applying Kirchhoff&#39;s Current Law at the virtual ground of the inverting input  506  to the opamp  502 :  
             V   in       Z   1       +       (       V   o     +     V   e       )       Z   2       -       mV   o       Z   3         =   0                         
 
         [0059]    where V in  is the voltage between the second terminal of the input impedance  526  and the ground reference  518 ; V o  is the voltage between the first terminal and second terminal of the primary winding  512  of the transformer  510 ; and m is the ratio of second secondary  715  turns to primary  512  turns. Since  
           V   e     =       V   o     K       ,                         
 
         [0060]    hence:  
             V     i                 n         Z   1       +         V   o          (     1   +     1   K       )         Z   2       -       m                   V   o         Z   3         =   0             solving                 for                 gain     =         V   o       V     i                 n                         gives   :                             
 
           V   o       V     i                 n         =     -       Z   2         Z   1          (     1   +     1   K     -       mZ   2       Z   3         )                     we                 choose                     Z   2       Z   3         =     1   mK                 therefore                     V   o       V     i                 n           =     -       Z   2       Z   1           ,                         
 
         alternatively                 we                 can                 choose                     Z   2       Z   3         =         2      K     +   1     mK               and                 therefore                     V   o       V     i                 n           =       Z   2       Z   1                             
 
         [0061]    Note that the gain, for all of embodiments, is independent of the reference impedance  516  and the ratio K. As well, the gain is a simple ratio of impedances making the gain less sensitive to component tolerances and manufacturing variations.  
         [0062]    The following derivation of output impedance is applicable to the embodiments of FIGS. 5, 6,  7 A and  7 B. The output impedance of the xDSL line driver  500  is derived by applying Kirchhoff&#39;s Current Law to the junction node  519 :  
           I   o     -       V   e       Z   3       -       V   e       Z   e         =   0                         
 
         [0063]    where I o  is the current flowing into the first terminal of the primary winding  512  of the transformer  510 . Since Z 3 &gt;&gt;Z e  (unnecessary for the embodiment of FIG. 6),  
         V   e     =           V   o     K                   and                   Z   c       =     -       V   o       I   o                                 
 
         [0064]    and therefore: 
         
       Z 
       o 
       =KZ 
       e 
     
         [0065]    There are many possible gain functions, such as low-pass, high-pass, band-pass, band-reject or delay equalizer functions that can be realized by implementing the input impedance  526 , the second feedback impedance  522  and the first feedback impedance  520  as complex impedances (i.e. networks comprising resistors, capacitors and/or inductors). FIGS. 8A, 8B and  8 C show one of the possible implementations of the input impedance  526 , the second feedback impedance  522  and the first feedback impedance  520  respectively.  
         [0066]    Referring to FIG. 8A, the input impedance  526  comprises a first node  809  and a second node  810 . The input impedance  526  has a first resistor  801  having a value R 1 , a first terminal connected to the first node  809  of the input impedance  526  and a second terminal connected to a first junction node  807 . The input impedance  526  also has a second resistor  802  having a value R 2 , a first terminal connected to the first junction node  807  and a second terminal connected to the second node  810  of the input impedance  526 . The input impedance  526  also has a first capacitor  803  having a value C 1 , a first terminal connected to the first junction node  807  and a second terminal connected to a ground reference  518 . The input impedance  526  also has a second capacitor  804  having a value C 2 , a first terminal connected to the first node of  809  and a second terminal connected to a second junction node  808 . The input impedance  526  also has a capacitor 805 having a value C 3 , a first terminal connected to the second junction node  808  and a second terminal connected to the second node  810  of the input impedance  526 . The input impedance  526  also has a resistor  806  having a value R 3 , a first terminal connected to the second junction node  808  and a second terminal connected to the ground reference  518 .  
         [0067]    Referring to FIG. 8B, the second feedback impedance  522  has a first node  815  and a second node  816  with a first capacitor  814  having a value of C 4 , a first terminal connected to the first node  815  and a second terminal connected to the second node  816 . The second feedback impedance  522  also has a first resistor  812  having a value R 4 , a first terminal connected to the first node  815  and a second terminal connected to a junction node  817 . The second feedback impedance  522  also has a second resistor  813  having a value R 5 , a first terminal connected to the junction node  817  and a second terminal connected to the second node  816 . The second feedback impedance  522  has a capacitor  811  having a value C 5 , a first terminal connected to the junction node  817  and a second terminal connected to the ground reference  518 .  
         [0068]    Referring to FIG. 8C, the topology of the first feedback impedance  520  is identical to the second feedback impedance  522 . The first capacitor  824  has a value of C 6 , the second capacitor  821  has a value of C 7 , the first resistor  822  has a value of R 6  and the second resistor  823  has a value of R 7 .  
         [0069]    Since, in the preferred embodiment, Z 2 =(K−1)Z 3  then R 4 =(K−1)R 6 , R 5 =(K−1)R 7 , C 6 =(K−1)C 4  and C 7 =(K−1)C 5 .  
         [0070]    It is preferable that R 1 =R 2 , R 4 =R 5 , R 6 =R 7 , and C 2 =C 3 .  
         [0071]    As shown herein above, the gain of the preferred embodiment is:  
           V   o       V     i                 n         =     -       Z   2       2        Z   1                     Since                   Z   2       =     1       1       SR   4   2          C   5         +     SC   4                               
 
         [0072]    where the variable S represents complex frequency,  
         and                   Z   1       =     1       1         SR   1   2          C   1       +     2        R   1           +     1       1       S   2          R   3          C   2   2         +     2     SC   2                         therefore                     V   o       V     i                 n           =     -         1     R   1       ·     (       1         SR   1          C   1       +   2       +         S   2          R   1   2          C   2   2           2        SR   1          C   1       +       R   1       R   3             )           2     R   4       ·     (           S   2          R   4   2          C   5          C   4       +     2        SR   4          C   4       +   1           SR   4          C   5       +   2       )                                 
 
         [0073]    by choosing R 1 C 1= R 4 C 5 , C 1= 2C 2  and R 1= 2R 3 , then  
           V   o       V     i                 n         =       -       R   4       2        R   1           ·     (           S   2          C   2   2          R   1   2       +   1           S   2          R   4   2          C   5          C   4       +     2        SR   4          C   4       +   1       )                             
 
         [0074]    This equation is a well-known form of biquad that is useful for realizing band-reject, low-pass or high-pass filters.  
         [0075]    In an xDSL communication system it is advantageous to implement the xDSL driver  106  in the CO  101  as a high-pass filter and the xDSL driver  126  in the CPE  121  as a low-pass filter. In a G.Lite DSL communication, for example, the xDSL driver  106  in the CO  101  is a high-pass filter having a cut-off frequency of 150 kHz and the xDSL driver  126  in the CPE  121  is a low-pass filter having a cut-off frequency of 120 kHz. These filters can be designed using conventional design methodology known to those skilled in the art.  
         [0076]    While the preferred embodiment has been describe with respect to the xDSL communication system  100  of FIG. 1, those skilled in the art will appreciate that the invention is applicable to driving any transmission line having a characteristic impedance.  
         [0077]    While the preferred embodiment of the present invention has been described and illustrated, it will be apparent to persons skilled in the art that numerous modifications and variations are possible. The scope of the invention, therefore, is only to be limited by the claims appended hereto.