Abstract:
Dynamic matching of a source impedance to a load impedance or the complex conjugate of the load impedance. An embodiment of the invention is a device for active impedance matching comprising a voltage driver having an output connected to a load, means for detecting an output current from the voltage driver to the load, means for scaling the detected output current by a scaling value, and means for subtracting a value representing the scaled detected output current from an input signal of the voltage driver. Another embodiment is a device for active impedance matching comprising a current driver having an output connected to a load, means for detecting an output voltage from the current driver to the load, means for scaling the detected output voltage by a scaling value, and means for subtracting a value representing the scaled detected output voltage from an input signal of the current driver.

Description:
[0001]    This application claims the benefit of U.S. Provisional Application No. 60/185,656, filed on Feb. 29, 2000. 
     
    
     
       BACKGROUND  
         [0002]    The invention relates generally to transmission lines and, more particularly, to adjusting the terminating and driving impedance of a transmission line to match the characteristic impedance of the transmission line.  
           [0003]    It is well known to skilled practitioners in the electrical arts that if a source impedance is matched to a complex conjugate of a load impedance, maximum power transfer between the source and the load is achieved. However, it is difficult to match the imaginary part of the complex impedance and half of the power is lost in the matched source impedance when using passive components for impedance matching. Although this is a characteristic of many electrical circuits, it may take on greater significance where transmission lines are considered. With transmission lines, the primary objective is to avoid reflections in the transmission line, so the characteristic impedance is assumed to be resistive.  
           [0004]    Transmission lines, where the transmission line length is large with respect to the wavelength of the lowest transmission frequency, are commonly used for transmission of data between two or more locations. It is well known in the art of transmission lines, and particularly transmission lines for transmitting information at high data rates, that in order to maximize the efficiency of information transfer with minimum loss and dispersion effects, the terminating impedance of a receiver and the driving impedance of a transmitter must match the characteristic impedance Z 0  of the transmission line over the frequency range of interest. That is, it is desirable to maintain a uniform characteristic impedance Z 0  along the length of the signal carrying line. Any mismatch in the characteristic impedance across interconnect interfaces will cause reflection of the signal at the interface, resulting in losses and distortion of the signal in the form of attenuation, echo and cross-talk. Furthermore, multiple reflections from multiple interfaces only compound the deleterious affect on the information-carrying signal. The classical solution to the impedance matching problem involves attempting to match the distributed-parameter impedance of the transmission line with lumped-parameter impedances of resistor, capacitor and inductor circuit elements.  
           [0005]    Wide band communication channels, like ADSL modulation over telephone conventional lines or other wideband modulation schemes, require matching of line impedances that are complex, where amplitude and phase are dependent on frequency. Telephone subscriber loops with bridged taps present impedance variations at the receiver end that are difficult to match using simple circuits. Furthermore, the impedances variations may change from loop to loop, making it impossible to design a matching circuit using generic discrete circuit components. The use of full-duplex techniques, where bi-directional transmission is conducted concurrently only further complicates the difficulty of matching interface impedances to the characteristic impedance of the transmission line.  
           [0006]    There have been a number of different approaches to solving the characteristic impedance matching problem. In the most simple and rudimentary form, fixed resistor elements are connected across the transmission line interfaces to match the interface impedance with the characteristic impedance of the transmission line. More complex impedance matching circuits using combinations of resistor and capacitor elements are often found connected to transmission lines. Impedance matching circuits using passive components may dissipate half of the available power at the transmitter, oftentimes reducing its dynamic range by half. Although power is seldom a major consideration on a standard data transmission line, loss in dynamic range can result in excessive signal clipping with high peak to average ratios that are typical of Quadrature Amplitude Modulated signals and Discrete Multi-Tone signals, used in many modern data transmission systems.  
           [0007]    One of the oldest and widely used approaches to match a transmitter-receiver to a transmission line is a hybrid circuit that makes use of two transformers and a balance impedance network Z L  that, when matched to the characteristic impedance Z 0  of the transmission line, results in very high isolation between transmitter and receiver circuits. This circuit provides a line termination that matches the characteristic impedance of the line and results in no reduction in dynamic range. However, only half the power delivered by the transmitter is sent to the transmission line, the other half being wasted on the balancing impedance network Z L . In addition to loss of transmitted power, the balancing impedance network Z L  cannot perfectly match a line with bridged taps or multiple interfaces. It is impractical to add switching circuits to adapt the impedance to different lines, where each line has a different configuration of taps or interfaces along the length of the line. Furthermore, this hybrid circuit makes use of multiple magnetic circuits that have inherent non-linear characteristics that produce distortion, which adversely affects signals with high peak to average ratios. These transformers also exhibit parasitic capacitance and leakage inductance that may impair circuit operation and reduce useful bandwidth.  
           [0008]    Another approach that has received increased interest is the use of a differential driver circuit having two outputs, where each output is connected through an impedance matching resistor to each of the two terminals, respectively, of the primary winding of a transformer. The secondary winding of the transformer is connected to the transmission line. However, not only is half of the transmitter power dissipated in the two impedance matching resistors, but half of the signal amplitude is also dropped across these resistors. This results in reducing the dynamic range of the signal at the transmitter by one-half and reducing the maximum power available to drive the transmission line by one-fourth. The transformer provides for scaling the line impedance to compensate for this reduction and for generating enough peak voltage without excessive clipping. Two amplifiers, each connected across a terminating resistor receive the signal on the transmission line. This circuit may only perform better than the hybrid circuit described above in the high frequency range, where the line impedance will be mostly resistive in nature. Although more complex networks may replace these terminating resistors, the resultant configuration would also suffer from the same limitations as the hybrid circuit described above, namely low power efficiency and reduced dynamic range.  
           [0009]    All of these solutions assume that the characteristic impedance of the transmission line is fixed and known, and therefore terminated accordingly. These solutions result in reduced power available to the transmission line, reduced dynamic range of the signal, and losses and distortion in the signal. Although more pronounced with transmission lines, these problems apply to many electrical circuits.  
           [0010]    For the foregoing reasons, it is desirable to have a method and device for driving and receiving signals on a transmission line that does not exhibit loss of the available transmitter power to drive the line, does not suffer from a reduction in dynamic signal range, and dynamically matches the driving and terminating impedance at the interfaces to the characteristic impedance of the transmission line.  
         SUMMARY  
         [0011]    The present invention is directed to a method and device for driving a load with active impedance matching that satisfies these needs. The present invention is particularly suitable for providing a method and device for driving and receiving signals on a transmission line that does not exhibit loss of the available transmitter power to drive the line, does not suffer from a reduction in dynamic signal range, and dynamically matches the transmission line interface driving and terminating impedance to the characteristic impedance of the transmission line.  
           [0012]    In a voltage driver version of the present invention, a means is provided for sensing the current provided to a load by a voltage source, and the magnitude of the voltage source is automatically adjusted by negatively feeding back a voltage to an input that represents a scaled value of the sensed current multiplied by an impedance that matches the load impedance. The result is a voltage source having an effective internal impedance that matches the load impedance, but yet maintains full dynamic signal range without a loss of transmitted power to the load.  
           [0013]    In a current driver version of the present invention, a means is provided for sensing the voltage provided to a load by a current source, and the magnitude of the current source is automatically adjusted by negatively feeding back a current to an input that represents a scaled value of the sensed voltage divided by an impedance that matches the load impedance. The result is a current source having an effective internal impedance that matches the load impedance, but yet maintains full dynamic signal range without a loss of transmitted power to the load.  
           [0014]    Although the present method and device is applicable to many electrical circuits, its application is particularly suitable to transmission lines.  
           [0015]    A device having features of the present invention is a device with active impedance matching for driving a load that comprises a voltage driver having an output connected to a load, means for detecting an output current from the voltage driver to the load, means for scaling the detected output current by a scaling value, and means for subtracting a value representing the scaled detected output current from an input signal of the voltage driver. The means for scaling the detected output current may be a multiplier having an input comprising the detected output current and another input comprising the scaling value, an output of the multiplier representing the scaled output current. The device of claim  2 , wherein the scaling value is a value representing a load impedance to be matched. The means for scaling the detected output current may be an amplifier having an input comprising the detected output current and a gain equal to the scaling value, an output of the amplifier representing the scaled output current. The means for detecting an output current may be a transformer having a primary winding in series with the output current. The means for detecting an output current may be a resistor in series with the output current and an amplifier with inputs connected to terminals of the resistor. The means for subtracting may be a summing junction of an operational amplifier. The load may be a transmission line. The scaling value may be a characteristic impedance of the transmission line. The means for scaling and the means for subtracting may comprise a digital signal processor.  
           [0016]    In an alternative embodiment of the present invention, a device with active impedance matching for driving a load comprises a current driver having an output connected to a load, means for detecting an output voltage from the current driver to the load, means for scaling the detected output voltage by a scaling value, and means for subtracting a value representing the scaled detected output voltage from an input signal of the current driver. The means for scaling the detected output voltage may be a multiplier having an input comprising the detected output voltage and another input comprising the scaling value, an output of the multiplier representing the scaled output voltage. The scaling value may be a value representing a load impedance to be matched. The means for scaling the detected output voltage may be an amplifier having an input comprising the detected output voltage and a gain equal to the scaling value, an output of the amplifier representing the scaled output voltage. The means for detecting an output voltage may be an amplifier with inputs connected to the outputs of the current driver. The means for detecting an output voltage may be a transformer with primary terminals connected to the outputs of the current driver. The means for subtracting may be a summing junction of an operational amplifier. The load may be a transmission line. The scaling value may be a characteristic impedance of the transmission line. The means for scaling and the means for subtracting may comprise a digital signal processor.  
           [0017]    In another alternative embodiment of the present invention, a method for driving a load with active impedance matching, comprises connecting an output of a voltage driver to a load, detecting an output current from the voltage driver to the load, scaling the detected output current by a scaling value, and subtracting a value representing the scaled detected output current from an input signal of the voltage driver. Scaling the detected output current may comprise multiplying the detected output current by the scaling value, an output of the multiplication representing the scaled output current. The scaling value may be a value representing a load impedance to be matched. The detected output current may comprise amplifying the detected output current by the scaling value for obtaining a value representing the scaled output current. Detecting an output current may comprise connecting a primary winding of a transformer in series with the output current. Detecting an output current may comprise connecting a resistor in series with the output current and connecting inputs of an amplifier to terminals of the resistor. Subtracting may comprise summing currents into a summing junction of an operational amplifier. The load may be a transmission line. The scaling value may be a characteristic impedance of the transmission line. Scaling and subtracting may comprise processing instructions of a digital signal processor.  
           [0018]    In another alternative embodiment of the present invention, a method for driving a load with active impedance matching comprises connecting an output of a current driver to a load, detecting an output voltage from the current driver to the load, scaling the detected output voltage by a scaling value, and subtracting a value representing the scaled detected output voltage from an input signal of the current driver. Scaling the detected output voltage may comprise multiplying the detected output voltage by the scaling value, an output of the multiplication representing the scaled output voltage. The scaling value may be a value representing a load impedance to be matched. Scaling the detected output voltage may comprise amplifying the detected output voltage by the scaling value for obtaining a value representing the scaled output voltage. Detecting an output voltage may comprise connecting inputs of an amplifier to outputs of the current driver. Detecting an output voltage may comprise connecting a primary winding of a transformer to the outputs of the current driver. Subtracting may comprise summing currents into a summing junction of an operational amplifier. The load may be a transmission line. The scaling value may be a characteristic impedance of the transmission line. Scaling and subtracting may comprise processing instructions of a digital signal processor.  
           [0019]    In another alternative embodiment of the present invention, a method for driving a load with active impedance matching comprises connecting an output of a voltage driver to a load, detecting an output current value from the voltage driver to the load, connecting the detected output current to an analog-to-digital converter, converting the detected output current value to a digital representation by the analog-to-digital converter, connecting the digital representation of the output current at an output of the analog-to-digital converter to an input of a digital signal processor, connecting a digital representation of an input signal to another input of the digital signal processor, executing a program in the digital signal processor, providing an digital representation output from the digital signal processor to a digital-to-analog converter, and connecting an output of the digital-to-analog converter to an input of the voltage driver. The method may further comprise interposing an anti-aliasing low-pass filter between the detected current output and the analog-to-digital converter. The method may further comprise interposing an interpolation low-pass filter between the output of the digital-to-analog converter and the input of the voltage driver. The step of connecting a digital representation of an input signal may comprise connecting an input signal to another input of the voltage driver. The step of executing a program in the digital signal processor may further comprise executing an initialization routine, reading an input voltage value, associating a time value with the input voltage value, adjusting the time value with a time domain filter delay, reading an output current value from the analog-to-digital converter, applying the output current value to the time domain filter, subtracting the filtered output current value from the adjusted input voltage value, outputting the result of the subtraction to a digital-to-analog converter, repeating steps b. through h. if the program is not terminated, and ending the process if the program is terminated. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0020]    These and other features, aspects, and advantages of the present invention will become understood with regard to the following description, appended claims, and accompanying drawings where:  
         [0021]    [0021]FIG. 1A shows a half duplex configuration of a transmitter/receiver circuit;  
         [0022]    [0022]FIG. 1B shows a full duplex configuration of a transmitter/receiver circuit;  
         [0023]    [0023]FIG. 2A shows a Thevenin equivalent of a voltage transmitter circuit;  
         [0024]    [0024]FIG. 2B shows an equivalent circuit of the circuit shown in FIG. 2A;  
         [0025]    [0025]FIG. 3A shows a Norton equivalent of a current transmitter circuit;  
         [0026]    [0026]FIG. 3B shows an equivalent circuit of the circuit shown in FIG. 3A;  
         [0027]    [0027]FIG. 4 shows a block diagram of a voltage transmitter circuit;  
         [0028]    [0028]FIG. 5 shows a block diagram of a current transmitter circuit;  
         [0029]    [0029]FIG. 6A shows a circuit diagram of an a voltage transmitter using an inductive sensor;  
         [0030]    [0030]FIG. 6B shows a circuit diagram of a voltage transmitter using a resistive sensor;  
         [0031]    [0031]FIG. 7 shows a circuit diagram of a DSP implementation of a voltage transmitter;  
         [0032]    [0032]FIG. 8A shows a flow diagram of a program executed in the DSP of FIG. 7; and  
         [0033]    [0033]FIG. 8B shows a flow diagram of an initialization routine. 
     
    
     DETAILED DESCRIPTION  
       [0034]    Turning now to FIG. 1A, FIG. 1A shows a half duplex configuration  10  of transmitter/receiver circuit connected to a transmission line  140 . This configuration is well known to skilled practitioners in the relevant art. In the half duplex configuration of FIG. 1A, a transmit input signal  112  is connected to an input of a differential transmitter  102 . An output of the transmitter is connected to a switch  106 . A receive output signal  114  is provided by an output of a differential receiver  104 . An input of the receiver  104  is connected to the switch  106 . A transmission line signal  108 ,  110  is connected to the switch  106  such that the when the switch  106  is in position A, the transmission line signal  108 ,  110  is connected to the output of the transmitter  102 , for transmitting a transmission line signal  108 ,  110 . Alternatively, when the switch is in position B, the transmission line signal  108 ,  110  is connected to the input of the receiver  104 , for receiving a transmission line signal  108 ,  110 . Although the switch  106  is depicted as an electromechanical device, skilled practitioners would recognize that a semiconductor device would normally provide this function for half duplex operation. In half duplex operation, a transmission line  140  is transmitting signals in one direction at a time.  
         [0035]    Turning now to FIG. 1B, FIG. 1B shows a full duplex configuration  12  of transmitter/receiver circuit connected to a transmission line  140 . This configuration is also well known to skilled practitioners in the relevant art. In the half duplex configuration of FIG  1 B, a transmit input signal  112  is connected to an input of a differential transmitter  102 . An output of the transmitter is connected to a transmission line signal  108 ,  110  through one port  128  of a hybrid coil or four-to-two wire converter  126 . A receive output signal  114  is provided by an output of a differential receiver  104 . An input of the receiver  104  is connected the transmission line signal  108 ,  110  through another port  130  of the hybrid coil or four-to-two wire converter  126 . In this full duplex configuration  12 , the transmission line  140  may transmit signals in both directions simultaneously, the directional coupling and line termination being performed by the hybrid coil or four-to-two wire converter  126 .  
         [0036]    The subsequent descriptions of embodiments of the present invention pertain to the transmitter  102  of FIG. 1A and FIG. 1B. Skilled practitioners will recognize that embodiments of the present invention may be used with a receiver  104  in either a half duplex configuration of FIG. 1A or the full duplex configuration of FIG. 1B, eliminating the need for the switch  106  or the hybrid coil or four-to-two wire converter.  
         [0037]    Turning now to FIG. 2A and FIG. 2B, FIG. 2A shows a Thevenin equivalent circuit  20  of a voltage transmitter circuit and FIG. 2B shows an equivalent circuit  22  of the circuit  20  shown in FIG. 2A. In FIG. 2A, a voltage generator V g    202  represents a Thevenin equivalent open circuit voltage source and an impedance Z g    204  represents a Thevenin equivalent impedance. The circuit has an output voltage V o    208  and an output current I o    206  connected to a load impedance Z L    240 . By measuring the output current I o    206  and negatively feeding it back with an appropriate gain required to synthesize the impedance Z g    204 , the equivalent circuit  22  shown in FIG. 2B is formed. FIG. 2B comprises a voltage generator  222  having a value of  
         
       V 
       o 
       =V 
       g 
       −Z 
       g 
       I 
       o  
     
         [0038]    that provides the output voltage V o    208  and the output current I o    206  connected to a load impedance Z L    240 . Note that V o    208  and I o    206  are the same in FIG. 2A and FIG. 2B. If the value of V g  is set to zero (short-circuit) and a current generator of unity value is connected to the outputs of the circuits shown in both FIG. 2A and FIG. 2B, the value of the voltage V o =Z g  is the same in both circuits. This example illustrates the principle of operation of one of the embodiments of the present invention. That is, in a voltage transmitter circuit, the source impedance Z g    204  may be matched to a load impedance Z L    240  by measuring the output current from the circuit and negatively feeding back a scaled part of the output current determined by the value of the load impedance Z L    240 . In this manner, maximum power transfer may be achieved by setting Z g    204 =Z L    240  without power loss in Z g    204 .  
         [0039]    Turning now to FIG. 3A and FIG. 3B, FIG. 3A shows a Norton equivalent circuit  30  of a current transmitter circuit and FIG. 3B shows an equivalent circuit  32  of the circuit  30  shown in FIG. 3A. In FIG. 3A, a current generator I g    302  represents a Norton equivalent short circuit current source and an impedance Z g    304  represents a Norton equivalent impedance. The circuit has an output voltage V o    308  and an output current I o    306  connected to a load impedance Z L    340 . By measuring the output voltage V o    306  and negatively feeding it back with an appropriate gain required to synthesize the admittance 1/Z g    304 , the equivalent circuit  32  shown in FIG. 3B is formed. FIG. 3B comprises a current generator  322  having a value of  
         
       I 
       o 
       =I 
       g 
       −V 
       o 
       /Z 
       g  
     
         [0040]    that provides the output voltage V o    308  and the output current I o    306  connected to the load impedance Z L    340 . Note that V o    308  and I o    306  are the same in FIG. 3A and FIG. 3B. If the value of I g  is set to zero (open-circuit) and a voltage generator of unity value is connected to the outputs of the circuits shown in both FIG. 3A and FIG. 3B, the value of the current I o =1/Z g  is the same in both circuits. This example illustrates the principle of operation of one of the embodiments of the present invention. That is, in a current transmitter circuit, the source impedances Z g    304  may be matched to a load impedance Z L    340  by measuring the output voltage from the circuit and negatively feeding back a scaled part of the output voltage, determined by the value of the load admittances 1/Z L    340 . In this manner, maximum power transfer may be achieved by setting Z g    304 =Z L    340  without power loss in Z g    304 .  
         [0041]    Turning now to FIG. 4, FIG. 4 shows a block diagram of a voltage transmitter circuit  40  connected to a transmission line  440  having a characteristic impedance Z o    442 . The block diagram  40  illustrates a use of current feedback  418  from the an output of a voltage driver  410  to synthesize a driver circuit whose Thevenin equivalent is a voltage generator of amplitude 2V in  in series with an impedance Z o , similar to the circuit shown in FIG. 2A. The input voltage V in    402  is summed with a negative feedback voltage V fb    420  to provide an input voltage of V in −V fb  to the voltage driver  410 . Since the voltage driver  410  has a voltage gain of two, the output voltage V o    408  of the voltage driver  410  is V o =2V in −2V fb . A transformer  412  having a turns ratio of n senses the output current I o    406  and provides the signal I o /n to one input to a multiplier  414 . Another input signal to the multiplier is the constant value nZ o /2  516 . Therefore, the output signal of the multiplier  414  is V fb =(I o /n)(nZ o /2)=I o Z o /2  420 . By substituting this value of V fb    420  into the expression above for the output voltage V o    408 , the output voltage  
           V   o =2V in −I o Z o    
         [0042]    This expression for the output voltage V o    408  has the form of the output voltage of FIG. 2A and FIG. 2B, and illustrates how the driving source impedance may be matched to the characteristic impedance of a transmission without the use of power consuming components. Summarizing, the output current  406  is measured, scaled and multiplied by an impedance nZ o /2, resulting in the feedback voltage V fb    420 . The feedback voltage V fb    420  is subtracted from the input voltage V in    402  and fed to an input of the voltage driver  410 , which has a gain of two. The scaling and multiplication may be accomplished on a current-to-voltage converter, the output driver, or through use of digital filtering techniques in a Digital Signal Processor (DSP). Note that the voltage driver  410  will only generate the voltage seen by the line V o , even if the Thevenin equivalent circuit has a voltage generator of twice this value. This method achieves the objective of impedance matching without wasting power or dropping a voltage in an impedance-matching resistor. This method is also adaptable to the use of a DSP to enable more accurate and adaptive matching through digital signal processing techniques. It also allows full duplex communication over the same transmission line.  
         [0043]    Turning now to FIG. 5, FIG. 5 shows a block diagram of a current transmitter circuit  50  connected to a transmission line  540  having a characteristic impedance Z o    542 . The block diagram  50  illustrates a use of output voltage feedback V o    508  from an output of a transconductance driver  510  to synthesize a driver circuit  50  whose Norton equivalent circuit is a current generator of amplitude I o =kV in    506  having an internal shunt impedance Z g =Z o , the characteristic impedance of the line, and a transconductance of k, similar to FIG. 3A. The input voltage V in    502  is summed with a negative feedback voltage V fb    520  to provide an input voltage of V in −V fb  to the transconductance driver  510 . Since the transconductance driver  510  has a transconductance of 2k, the output current I o    506  of the transconductance driver  510  is I o =2kV in −2kV fb . An amplifier  512  senses the output voltage V o    508  and provides this signal V o    508  to one input of a multiplier  514 . Another input signal to the multiplier is the constant value ½kZ o    516 . Therefore, the output signal of the multiplier  514  is V fb =V o 2kZ o    520 . By substituting this value of V fb    520  into the expression above for the output current I o    506 , the output current  
           I   o =2 kV   in   −V   o   /Z   o    
         [0044]    This expression for the output current I o    506  has the form of the output current of FIG. 3A and FIG. 3B, and illustrates how the driving source impedance may be matched to the characteristic impedance of a transmission without the use of power consuming components. Summarizing, the output voltage  508  is measured and multiplied by an admittance ½kZ o , resulting in the feedback voltage V fb    520 . The feedback voltage V fb    520  is subtracted from the input voltage V in    502  and fed to an input of the transconductance driver  510 , which has a gain of 2k, where k is the transconductance of the transconductance driver  510 . The scaling and multiplication may be accomplished on an amplifier, the output driver, or through use of digital filtering techniques in a Digital Signal Processor (DSP). This method achieves the objective of impedance matching without wasting power or dropping a voltage in an impedance-matching resistor. This method is also adaptable to the use of a DSP to enable more accurate and adaptive matching through digital signal processing techniques. It also allows full duplex communication over the same transmission line.  
         [0045]    Turning now to FIG. 6A, FIG. 6A shows a circuit diagram  60  of a voltage transmitter circuit using an inductive sensor connected to a transmission line  640  having a characteristic impedance Z o    642 . The voltage transmitter circuit of FIG. 6A comprises a first operational amplifier  614  and a second operational amplifier  616  having input and outputs connected to a resistor network  618 . An input voltage V in    602  is connected to one terminal of an input impedance nZ o /4  603 . Another terminal of the input impedance nZ o /4  603  connects a summing junction  620 . An output voltage V o    608  is derived between an output terminal of the first amplifier  614  and an output terminal of the second amplifier  616 . The voltages at the output terminals of the amplifiers are mirror images of each other. That is, when the output terminal of the first amplifier is at given voltage, the output terminal of the second amplifier is at an equal voltage of opposite polarity. The magnitude of the voltage at the output terminal of each amplifier  614 ,  616  is V o /2. A terminal of a feedback impedance nZ o /2  604  is connected to the output terminal of the second amplifier  616  and another terminal of the feedback impedance nZ o /2  604  is connected to the summing junction  620 . A transformer  612  senses the output current I o    606  and provides a scaled feedback current I fb =I o /n  622  to the summing junction  620 . By summing the currents into the summing junction, an expression for the output voltage may be derived  
           V   o =4 V   in   −I   o   Z   o    
         [0046]    This expression for the output voltage V o    608  has the form of the output voltage of FIG. 2A and FIG. 2B, and illustrates how the driving source impedance may be matched to the characteristic impedance of a transmission without the use of power consuming components.  
         [0047]    Turning now to FIG. 6B, FIG. 6B shows a circuit diagram  65  of a voltage transmitter circuit using a resistive sensor connected to a transmission line  690  having a characteristic impedance Z o    692 . FIG. 6B is similar to FIG. 6A, except that a current sensing resistor R s    662 , a differential amplifier  660  with a gain of A and a resistor nR s /A  674  have replaced the current sensing transformer of FIG. 6A. The inputs of the amplifier  660  are connected to the terminals of the sensing resistor R s    662 . The output current I o    656  through the sensing resistor R s    662  creates a voltage that is detected by the amplifier  660 . The output of the amplifier  660  is connected to a terminal of the resistor nR s /A  674  and another terminal of the resistor nR s /A  674  is connected to a summing junction  670 . The voltage transmitter circuit of FIG. 6B further comprises a first operational amplifier  664  and a second operational amplifier  666  having input and outputs connected to a resistor network  668 . An input voltage V in    652  is connected to one terminal of an input impedance nZ o /4  653 . Another terminal of the input impedance nZ o /4  653  connects the summing junction  670 . An output voltage V o    658  is derived between an output terminal of the first amplifier  664  and an output terminal of the second amplifier  666 . The voltages at the output terminals of the amplifiers are mirror images of each other. That is, when the output terminal of the first amplifier is at given voltage, the output terminal of the second amplifier is at an equal voltage of opposite polarity. The magnitude of the voltage at the output terminal of each amplifier  664 ,  666  is V o /2. A terminal of a feedback impedance nZ o /2  654  is connected to the output terminal of the second amplifier  666  and another terminal of the feedback impedance nZ o /2  654  is connected to the summing junction  670 . By summing the currents into the summing junction, an expression for the output voltage may be derived:  
           V   o =4 V   in   −I   o   Z   o    
         [0048]    This expression for the output voltage V o    658  has the form of the output voltage of FIG. 2A and FIG. 2B, and illustrates how the driving source impedance may be matched to the characteristic impedance of a transmission without the use of power consuming components.  
         [0049]    Turning now to FIG. 7, FIG. 7 shows a circuit diagram  70  of a DSP implementation of a voltage transmitter connected to a transmission line  740  having a characteristic impedance Z o    742 . The amplifiers  714 ,  716 , resistor network  718 , input resistor  703 , feedback resistor  704 , and transformer  712  are similar to those corresponding elements shown in FIG. 6A. The voltage transmitter circuit of FIG. 7 comprises a first operational amplifier  714  and a second operational amplifier  716  having input and outputs connected to a resistor network  718 . An input resistor  703  connects between an output of an interpolation filter  728  and a summing junction  734 . A feedback resistor  704  connects between the summing junction  734  and an output of the second amplifier. An output voltage V o    708  is derived between an output terminal of the first amplifier  714  and the output terminal of the second amplifier  716 . The voltages at the output terminals of the amplifiers are mirror images of each other. That is, when the output terminal of the first amplifier is at given voltage, the output terminal of the second amplifier is at an equal voltage of opposite polarity. The magnitude of the voltage at the output terminal of each amplifier  714 ,  716  is V o /2. A transformer  712  senses the output current I o    706  and provides a scaled feedback current I o /n to the summing junction  736  of an I/V converter  730 . A feedback resistor  732  connects between an output of the I/V converter  730  and the summing junction  736  of the I/V converter  730 . The output of the I/V converter  730  is connected to the input of an anti-aliasing filter  720 . An output of the anti-aliasing filter  720  is connected to an input of an analog-to-digital (A/D) converter  722 . Outputs from the A/D converter  722  are connected to a DSP  724 . Outputs from the DSP  724  are connected to the inputs of a digital-to-analog (D/A) converter  726 . An output from the D/A converter  726  is connected to the interpolation filter  728 . Normally the DSP generates the signals to be transmitted over the transmission line, functioning as a modem. Alternatively, a digital input voltage V in    702  is connected an input terminal of the DSP. By performing scaling and feedback functions in a DSP  724 , intelligence is added to the process that allows sophisticated and adaptive matching of the characteristic impedance Z o  of the transmission line. The DSP  724  may send a voltage signal V o  to the line, measure the resulting current and calculate a transfer function, such as nV/I. With sufficient over-sampling to avoid excessive phase shift, the line impedance may be matched by multiplying the line current I o  by a suitable transfer function and subtracting the result from twice the intended output signal V o . For full duplex operation, the received signal may be obtained by digitally subtracting the transmitted signal from the line voltage V o  measured by a receiver. Since the invention requires the use of line impedance models, with a DSP, these models are no longer limited to simple passive network elements.  
         [0050]    Turning now to FIG. 8A, FIG. 8A shows a representative flow diagram  80  of a program executed in the DSP of FIG. 7. The DSP is started  802  whenever it is initially powered on or reset. A first step is an execution of an initialization routine  804 . The details of the initialization routine  804  are described in the description of FIG. 8B. The DSP then reads a value representing an input voltage  806 , associates a current time value with the input voltage  808 , and adjusts the time value for a time domain filter delay  810 . Concurrently with these steps, the DSP reads a value representing an output current I o /n from an A/D converter  812 , calculates an error from a predicted current and updates time domain filter  813 , and applies the output current value to a nZ o /2 time domain filter  814 . The DSP then subtracts the filtered output current value from the input voltage value  816 , and provides the resultant value to a D/A converter. If the DSP operation is to be terminated  820 , the process is ended  822 . If not terminated  820 , the process beginning with concurrently reading input voltage values  806  and reading output current values  812  is repeated. As an alternative to the initialization routine  804  described in FIG. 8B, the initialization routine may be limited to setting initial parameters of the time domain filter for synthesizing an output impedance of approximate value. Then, referring to FIG. 8A, the DSP would read the output current  812 , calculate an error from a predicted current and update the time domain filter  813  with a fraction of the error to improve the matching in a recursive manner. These updated values would then be used to adjust the output voltage  816 .  
         [0051]    Turning now to FIG. 8B, FIG. 8B shows a flow diagram  85  of an initialization routine depicted as step  804  in FIG. 8A. If the DSP requires initialization, as described in the description of FIG. 8A, the initialization routine is started  850 . A value of the characteristic impedance Z o  of the transmission line is set to approximately match the transmission line and this value is applied to a time domain filter  852 . For example, an approximate value of 600 ohms is used for telephone lines, 120 ohms for twisted pair, or 50 ohm for coaxial cable. The DSP then initiates a request to a receiver at the opposite end of the transmission line to present a short-circuit for a fixed amount of time  854 , simulates a short-circuit output by setting an output voltage to a constant  856 , and measures the value of an output current to find values for a short-circuit impedance Z is  versus frequency  858 . The DSP then initiates a request to the receiver at the opposite end of the transmission line to present an open-circuit for a fixed amount of time  860 , simulates an open-circuit output by setting an output voltage to zero and setting Z o  to a high value  862 , and measures the value of the output current to find values for an open circuit impedance Z io  versus frequency  864 . The DSP then computes values for the characteristic impedance Z o =(Z is Z os ) ½  versus frequency  866  and sets time domain filter parameters to match Z o  versus frequency  869 . Control is then returned to the main program  870 .  
         [0052]    Although the present invention has been described in detail with reference to certain preferred embodiments, it should be apparent that modifications and adaptations to those embodiments may occur to persons skilled in the art without departing from the spirit and scope of the present invention as set forth in the following claims.