Abstract:
A low noise apparatus for receiving an input current and producing an output current which mirrors the input current significantly increases accuracy and signal-to-noise ratio by greatly reducing the effects resulting from threshold voltage mismatches and 1/ƒ noise. The apparatus comprises two cascode current mirrors. Further, the apparatus comprises a switching network which, in turn, comprises a plurality of switches formed within either a first or second electrical path. A first clock controls the switches formed within the first electrical path, while a second clock controls the switches formed within the second electrical path. When the first clock is in its first state and the second clock is in its second state, the switches formed within the first electrical path close to form the first cascode current mirror. However, the switches formed within the second electrical path remain open. Conversely, when the first clock is in its second state and the second clock is in its first state, the switches formed within the second electrical path close to form the second cascode current mirror. However, the switches formed within the first electrical path remain open. Consequently, the apparatus modulates a significant percentage of the threshold voltage mismatch up to the operating frequency of the two clocks. As a result, the first order error term resulting from the threshold voltage mismatch is eliminated and 1/ƒ noise is reduced.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to current mirrors and, more particularly, but not by way of limitation, to a low noise apparatus for producing an output current which mirrors the input current. 
     2. Description of the Related Art 
     Audio chips presently enable personal computers, compact disk players, and other portable audio devices to execute high quality, low power audio applications. Audio chips usually comprise digital circuitry which occupies approximately 75-80% of the audio chip&#39;s silicon space and analog circuitry which occupies the remaining 20-25%. Typically, the analog circuitry comprises an analog-to-digital converter, a digital-to-analog converter, and some output amplifiers. The analog circuitry converts an analog audio input signal into a digital format suitable for processing by the digital circuitry. Also, the analog circuitry converts the digital signals back into an analog format suitable to drive a load, such as a speaker. The digital circuitry occupies the majority of the silicon area and typically performs digital signal processing, such as filtering, noise shaping, and synthesizing on the converted analog signals. The primary function of these audio chips is to implement an entire audio system on one piece of silicon. 
     The above-described analog circuitry typically comprises current mirrors. These current mirrors serve several important functions, such as providing reference currents and reference voltages to other components in the analog circuitry. Therefore, these current mirrors must have very good matching characteristics and low noise (i.e., must have a large signal to noise ratio) to improve, illustratively, the output swing of the output amplifiers and the overall reliability and accuracy of the analog circuitry. 
     FIG. 1 illustrates current mirror 100, which is a conventional cascode current mirror comprising N-channel transistors 110, 120, 130, and 140. Transistors 110, 120, 130, and 140 are enhancement-type, metal-oxide silicon field effect transistors (i.e., MOSFETs). For the output current (i.e., I OUT ) Of current mirror 100 to exactly match (i.e., mirror) the input current (i.e., I IN ), transistors 110 and 130 must have identical threshold voltage drops (i.e., V T ) and gate-to-source voltage drops (i.e., V GS ). Similarly, transistors 120 and 140 must have identical threshold voltage drops (i.e., V T ) and gate-to-source voltage drops (i.e., V GS ). These requirements for current mirror 100 will become evident from the equations defining I OUT  and I IN  (described herein). 
     Transistors 120 and 140 have identical V GS  because their sources are connected to a reference voltage (e.g., ground) and their gates are connected to each other. Similarly, transistors 110 and 130 have nearly identical V GS  because their gates are connected to each other and they have identical drain currents. 
     Moreover, to have identical V GS  and V T  drops, transistors 110 and 130 must be equal in size (i.e., width and length) and transistors 120 and 140 must be equal in size. Therefore, transistors 110 and 130 and transistors 120 and 140 are fabricated to be as close in size as possible. Unfortunately, however, two exactly sized transistors cannot be fabricated due to inherent errors associated with currently available fabrication techniques. Consequently, the V T  of transistors 120 and 140 and transistors 110 and 130 are not identical. A first-order model of this threshold voltage mismatch (i.e., ΔV T ) between transistors 120 and 140 is illustrated in FIG. 2. 
     Referring to FIG. 2, the input current I IN  of current mirror 100 can be approximated by the following equation: 
     
         I.sub.IN =(k&#39;)(w/l)(V.sub.GS -V.sub.T).sup.2               (1) 
    
     where k&#39; is a process parameter, w/l is the size (i.e., width and length) of transistor 120, V T  is the threshold voltage of transistor 120, and V GS  is the gate-to-source voltage of transistor 120. 
     The voltage at the gates of transistors 120 and 140 (i.e., V A ) can be approximated by the following equation: 
     
         V.sub.A =ΔV.sub.T +V.sub.GS                          (2) 
    
     Therefore, substituting equation (2) into equation (1) and solving for V A  : 
     
         I.sub.IN =(k&#39;)(w/l)[V.sub.A -ΔV.sub.T -V.sub.T ].sup.2 
    
     
         V.sub.A =ΔV.sub.T +V.sub.T +[I.sub.IN /(k&#39;(w/l))].sup.1/2 (3) 
    
     Similarly, I OUT  may be approximated by the following equation: 
     
         I.sub.OUT =(K&#39;)(w/l)(V.sub.GS -V.sub.T).sup.2              (4) 
    
     where k&#39; is the process parameter, w/l is the size (i.e., width and length) of transistor 140, V T  is the threshold voltage of transistor 140, and V GS  is the gate-to-source voltage of transistor 140. Substituting equation (2) into equation (4) and solving: 
     
         I.sub.OUT =(k&#39;)(w/l)[V.sub.A -V.sub.T ].sup.2              (5) 
    
     Substituting equation (3) into equation (5) and solving: ##EQU1## Accordingly, the first order and second order terms 2(k&#39;)(w/l)(ΔV T )[I IN  /(k&#39;(w/l))] 1/2  and k&#39;(w/l)(ΔV T ) 2  (see equation 6) are error terms resulting from the threshold voltage mismatch ΔV T . 
     Illustratively, if I IN  =50 μA, k&#39;=43×10 -6  A/V 2 , w/l=100/10, and ΔV T  =10 mV, then: 
     
         I.sub.OUT =50×10.sup.-6 +2.61×10.sup.-6 +0.034×10.sup.-6 
    
     
         I.sub.OUT =52.644 μA 
    
     Thus, for an input current of 50 μA, the output current of current mirror 100 is 52.644 μA. This disparity in input and output currents produces an error rate of 5.3% The majority of this error is attributable to the first order error term in equation 6. Therefore, if a new and improved current mirroring apparatus could be designed which would significantly reduce the mismatch/noise and, thus, the error rate resulting from the threshold voltage mismatch ΔV T , the overall reliability and accuracy of the analog circuitry would be greatly increased. 
     SUMMARY 
     The first and second embodiments of the present invention comprise a new and improved low noise current mirroring apparatus having an input for receiving an input current and an output for producing an output current which mirrors the input current. This apparatus significantly increases the signal-to-noise ratio by greatly reducing low frequency noise (i.e., 1/ƒ) and mismatch resulting from threshold voltage mismatches. In a first embodiment, the apparatus comprises four transistors, each having a control terminal and a first and second terminal, and a switching network comprising a plurality of switches formed within either a first or second electrical path. In a second embodiment, this apparatus comprises: 1) four transistors, each having a control terminal and a first and second terminal; 2) two bias transistors which bias the gates of the first and second transistors; and 3) a switching network comprising a plurality of switches formed within either a first or second electrical path. 
     In the first embodiment, a first clock controls the switches formed within the first electrical path, while a second clock controls the switches formed within the second electrical path. When the first clock is in its first state and the second clock is in its second state, the switches formed within the first electrical path close to connect the second terminal of the first and second transistors to the second terminal of the third and fourth transistors, respectively. Further, the second terminal of the third transistor connects to the control terminals of the third and fourth transistors. However, the switches formed within the second electrical path remain open. 
     Conversely, when the first clock is in its second state and the second clock is in its first state, the switches formed within the second electrical path close to connect the second terminal of the first and second transistors to the second terminal of the fourth and third transistors, respectively. Further, the second terminal of the fourth transistor connects to the control terminals of the third and fourth transistors. However, the switches formed within the first electrical path remain open. 
     In the second embodiment, a first clock controls the switches formed within the first electrical path, while a second clock controls the switches formed within the second electrical path. When the first clock is in its first state and the second clock is in its second state, the switches formed within the first electrical path close to connect the first terminal of the first transistor to both the input and the control terminals of the third and fourth transistors. Further, the first terminal of the second transistor connects to the output. However, the switches formed within the second electrical path remain open. 
     Conversely, when the first clock is in its second state and the second clock is in its first state, the switches formed within the second electrical path close to connect the first terminal of the first transistor to the output. Further, the first terminal of the second transistor connects to both the input and the control terminals of the third and fourth transistors. However, the switches formed within the first electrical path remain open. 
     Consequently, both embodiments of the apparatus modulate a significant percentage of the threshold voltage mismatch up to the operating frequency of the two clocks. As a result, the first order error term resulting from the threshold voltage mismatch ΔV T  is eliminated. 
     It is therefore an object of the present invention to provide a current mirroring apparatus having a large signal-to-noise ratio. 
     It is another object of the present invention to provide a current mirroring apparatus which is capable of eliminating the first order error term resulting from a threshold voltage mismatch. 
     It is a further object of the present invention to provide a current mirroring apparatus which switches the connections of a plurality of transistors using a switching network. 
     It is still another object of the present invention to provide a current mirroring apparatus which mitigates the adverse effects of threshold voltage mismatches. 
     These and other objects, features, and advantages of the present invention will become evident to those skilled in the art in light of the following drawings and detailed description of the preferred embodiment. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a conventional, prior art current mirror. 
     FIG. 2 is a schematic diagram of the conventional, prior art current mirror of FIG. 1 further illustrating a threshold voltage mismatch. 
     FIG. 3 is a schematic diagram of a first embodiment for a low noise apparatus for receiving an input current and producing an output current which mirrors the input current. 
     FIG. 4 is a timing diagram of the two clocks utilized with the low noise apparatus of FIGS. 3, 5, 6, 7, 8, 9, and 10. 
     FIG. 5 is a schematic diagram of the low noise apparatus of FIG. 3 during a positive cycle of one clock. 
     FIG. 6 is a schematic diagram of the low noise apparatus of FIG. 3 during the positive cycle of the other clock. 
     FIG. 7 is a schematic diagram illustrating the low noise apparatus of FIG. 3 having two chopped pairs of transistors. 
     FIG. 8 is a schematic diagram of a second embodiment for a low noise apparatus for receiving an input current and producing an output current which mirrors the input current. 
     FIG. 9 is a schematic diagram of the low noise apparatus of FIG. 8 during a positive cycle of one clock. 
     FIG. 10 is a schematic diagram of the low noise apparatus of FIG. 8 during the positive cycle of the other clock. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     All transistors in the preferred embodiments of the present invention are enhancement-type, metal-oxide silicon field effect transistors (i.e., MOSFETs). DC power is supplied by power supply V DDA  and reference potential V SSA  (e.g. ground). The output paths I OUT  (described herein) of the preferred embodiments connect between the reference potential V SSA  and other analog circuitry (not shown). 
     FIG. 3 illustrates a first embodiment of the present invention. Apparatus 300 comprises: 1) an input node 360 for receiving an input current I IN  ; 2) an output node 350 for delivering an output current I OUT  which mirrors I IN  ; 3) N-channel cascode transistors 310 and 330; 4) N-channel sinking transistors 320 and 340; and 5) a switching network comprising switches 335 and 345 formed within electrical paths φ1 and φ2, respectively (herein referred to as paths). Any suitable device capable of generating an oscillating signal, such as an oscillator, may activate/deactivate switches 335 and 345. For example, switches 335 may be activated and switches 345 deactivated during a first state of the signal, while switches 335 may be deactivated and switches 345 activated during a second state of the signal. However, in this preferred embodiment, clock φ1 (not shown) controls switches 335 and clock φ2 (not shown) controls switches 345. FIG. 4 illustrates a timing diagram of clocks φ1 and φ2, which are inverses of each other. 
     Again referring to FIG. 3, any suitable switch may implement switches 335 and 345, such as CMOS transmission gates or field effect transistors. However, in this preferred embodiment, switches 335 and 345 are implemented using N-channel MOSFETs (not shown). The gates (not shown) of the MOSFETs which implement switches 335 and 345 connect to clocks φ1 and φ2, respectively. 
     For every positive cycle of clock φ1 and negative cycle of clock φ2 (e.g., clock φ1 is in its first state and clock φ2 is in its second state), switches 335 close, while switches 345 remain open. By closing switches 335 and opening switches 345, transistor 310 connects to transistor 320, the gate of transistor 320 connects to its drain, and transistor 330 connects to transistor 340, thereby forming a first cascode current mirror. The first cascode current mirror receives the input current I IN  at input node 360. The input current I IN  flows through a reference current path (i.e., transistors 310 and 320), while I OUT (φ1) flows through an output path (i.e., transistors 330 and 340). In this manner, the output current I OUT (φ1) at output node 350 mirrors the input current I IN  at input node 360. 
     Conversely, for every positive cycle of clock φ2 and negative cycle of clock φ1, (e.g., clock φ2 is in its first state and clock φ1 is in its second state), switches 345 close, while switches 335 remain open. By closing switches 345 and opening switches 335, transistor 310 connects to transistor 340, the gate of transistor 340 connects to its drain, and transistor 330 connects to transistor 320, thereby forming a second cascode current mirror. The second cascode current mirror receives the input current I IN  at input node 360. The input current I IN  flows through a reference current path (i.e., transistors 310 and 340), while I OUT (φ2) flows through an output path (i.e., transistors 330 and 320). In this manner, the output current I OUT (φ2) at output node 350 mirrors the input current I IN  at input node 360. 
     However, for the output current I OUT  of apparatus 300 to exactly mirror the input current I IN , transistors 310 and 330 must have identical threshold voltage drops (i.e., V T ). Similarly, transistors 320 and 340 must have identical threshold voltage drops (i.e., V T ). TO accomplish this, transistors 310 and 330 must be equal in size and transistors 320 and 340 must be equal in size. Consequently, transistors 310 and 330 and transistors 320 and 340 are fabricated to be as close in size as possible. Unfortunately, as previously described, two exactly sized transistors cannot be fabricated due to inherent errors associated with currently available fabrication techniques. Consequently, the V T  Of transistors 320 and 340 and transistors 310 and 330 are not identical. A first-order model of this threshold voltage mismatch ΔV T  between transistors 320 and 340 is illustrated in FIG. 3. 
     The repeated cycles of opening and closing switches 335 and 345 to connect and disconnect transistors 320 and 340 to/from transistors 310 and 330 can be thought of as alternately chopping transistors 320 and 340. By alternately chopping transistors 320 and 340, the transistor with the threshold voltage mismatch ΔV T  (e.g., transistor 320) is alternately switched from the reference current path to the output current path at a sufficiently high rate such that the average output current at output node 350 accurately represents the input current at input node 360 (described by equations herein). 
     FIG. 5 illustrates the first cascode current mirror of apparatus 300 which is formed during positive cycles of clock φ1. FIG. 5 also illustrates the first order model of the threshold voltage mismatch ΔV T  between transistors 320 and 340. As shown in FIGS. 1 and 5, the structure of apparatus 300 during positive cycles of clock φ1 is identical to the structure of prior art current mirror 100. Consequently, I OUT (φ1) for apparatus 300 is identical to I OUT  for prior art current mirror 100: 
     
         I.sub.OUT(φ1) =I.sub.IN +2(k&#39;)(w/l)(ΔV.sub.T)[I.sub.IN /(k&#39;(w/l))].sup.1/2 +k&#39;(w/l)(ΔV.sub.T).sup.2        (7) 
    
     where k&#39; is the process parameter, w/l is the size of transistor 340, and ΔV T  is the threshold voltage mismatch between transistors 320 and 340. FIG. 6 illustrates the second cascode current mirror of apparatus 300 during positive cycles of clock φ2. FIG. 6 also illustrates the first order model of the threshold voltage mismatch ΔV T  between transistors 320 and 340. During positive cycles of φ2, the input current I IN  and output current I OUT (φ2) for apparatus 300 can be approximated by solving the following equations: 
     
         I.sub.IN =k&#39;(w/l)[V.sub.A -V.sub.T ].sup.2 
    
     where k&#39; is the process parameter, w/l is the size of transistor 340, V T  is the threshold voltage of transistor 340, and V A  is the voltage at the gate of transistors 320 and 340. Solving for V A  : 
     
         V.sub.A =[I.sub.IN /(k&#39;(w/l))].sup.1/2 +V.sub.T            (8) 
    
     During positive cycles of φ2, the output current I OUT (φ2) for apparatus 300 can be approximated by solving the following equations: 
     
         V.sub.GS1 =V.sub.A -ΔV.sub.T 
    
     
         I.sub.OUT(φ2) =k&#39;(w/l)[V.sub.GS1 -V.sub.T ].sup.2 
    
     where k&#39; is the process parameter, w/l is the size of transistor 320, V GS1  is the gate-to-source voltage across transistor 320, V T  is the threshold voltage of transistor 320, and V A  is the voltage at the gate of transistors 320 and 340. Therefore: 
     
         I.sub.OUT(φ2) =K&#39;(w/l)[V.sub.A -ΔV.sub.T -V.sub.T ].sup.2 (9) 
    
     Substituting equation 8 into 9: ##EQU2## 
     Accordingly, the average DC current lava for apparatus 300 is: 
     
         I.sub.AVG =[I.sub.OUT(φ1) +I.sub.OUT(φ2) ]/2       (11) 
    
     However, comparing I OUT (φ1) with I OUT (φ2) : 
     
         I.sub.OUT(φ1) =I.sub.IN +2(k&#39;)(w/l)(ΔV.sub.T)[I.sub.IN /(k&#39;(w/l))].sup.1/2 +k&#39;(w/l)(ΔV.sub.T).sup.2 ; 
    
     
         I.sub.OUT(φ2) =I.sub.IN -2(k&#39;)(w/l)(ΔV.sub.T)[I.sub.IN /(k&#39;(w/l))].sup.1/2 +k&#39;(w/l)(ΔV.sub.T).sup.2 ; 
    
     Thus, when I OUT (φ1) and I OUT (φ2) add together in equation 11, the first order error term 2(k&#39;)(w/l)(ΔV T )[I IN  /(k&#39;)(w/l)] 1/2  is eliminated. Accordingly: 
     
         I.sub.AVG =[2I.sub.IN +2(k&#39;)(w/l)(ΔV.sub.T).sup.2 ]/2 
    
     
         I.sub.AVG =I.sub.IN +k&#39;(w/l)ΔV.sub.T.sup.2 
    
     Using the identical parameters as those given in the Background of the Invention, namely ##EQU3## Thus, for an input current of 50 μA, the output current of apparatus 300 is 50.034 μA, which is an error rate of 0.068% This error rate is a significant improvement over conventional current mirrors. This significant improvement occurs because the first order error term cancels when transistors 320 and 340 are chopped. In effect, apparatus 300 modulates a substantial percentage of the threshold voltage mismatch ΔV T  and low frequency noise (i.e., 1/ƒ) up to the operating frequency of clocks φ1 and φ2. The resulting high frequency noise may then be filtered out using any suitable low pass filter. 
     The present invention overcomes the limitations in the related art and is particularly effective when configured and employed as described herein. However, those skilled in the art will readily recognize that numerous variations and substitutions may be made to the invention to achieve substantially the same results as achieved by the preferred embodiment. For example, although cascode transistors 310 and 330 contribute only to the second order error, they may be chopped as well. FIG. 7 illustrates apparatus 400 having two sets of chopped transistors, namely transistors 310 and 330 and transistors 320 and 340. Switches 335 and 435 are controlled by clock φ1 and switches 345 and 445 are controlled by clock φ2. The operation of chopping transistors 310 and 330 is identical to the operation of chopping transistors 320 and 340. 
     FIG. 8 illustrates a second embodiment of the present invention. Apparatus 200 comprises: 1) input node 260 for receiving an input current; 2) output node 250 for producing an output current which mirrors the input current; 3) N-channel cascode transistors 210 and 230 and N-channel sinking transistors 220 and 240; 4) N-channel bias transistors 215 and 225; and 5) a switching network comprising switches 235 and 245 formed within electrical paths φ1 and φ2, respectively (herein referred to as paths). Bias transistor 215 operates in its saturation region, while bias transistor 225 operates in its triode region. Together, bias transistors 215 and 225 bias the gates of cascode transistors 210 and 230 such that the voltage on output node 250 is capable of swinging nearly rail-to-rail. Further, transistor 225 is sized such that the drain-to-source voltage drops (i.e., V DS ) across transistors 220 and 240 are slightly larger than the voltage drop required for transistors 220 and 240 to operate in their saturation region. Transistors 220 and 240 have identical V GS  because their sources are connected to a reference voltage (e.g., ground) and their gates are connected to each other. Similarly, transistors 210 and 230 have nearly identical V GS  because their gates are connected to each other and they have nearly identical drain currents (described herein). 
     Any suitable device capable of generating an oscillating signal, such as an oscillator, may activate/deactivate switches 235 and 245. For example, switches 235 may be activated and switches 245 deactivated during a first state of the signal, while switches 235 may be deactivated and switches 245 activated during a second state of the signal. However, in this preferred embodiment, clock φ1 (not shown) controls switches 235 and clock φ2 (not shown) controls switches 245. FIG. 4 illustrates a timing diagram of clocks φ1 and φ2, which are inverses of each other. 
     Again referring to FIG. 8, any suitable switch may implement switches 235 and 245, such as CMOS transmission gates or field effect transistors. However, in this preferred embodiment, switches 235 and 245 are implemented using N-channel MOSFETs (not shown). The gates (not shown) of the MOSFETs which implement switches 235 and 245 connect to clocks φ1 and φ2, respectively. 
     For every positive cycle of clock φ1 and negative cycle of clock φ2 (e.g., clock φ1 is in its first state and clock φ2 is in its second state), switches 235 close, while switches 245 remain open. By closing switches 235 and opening switches 245, the drain of transistor 210 connects to both input node 260 and the gates of transistors 220 and 240, while the drain of transistor 230 connects to output node 250, thereby forming a first cascode current mirror. The first cascode current mirror receives the input current I IN  at input node 260. The input current I IN  flows through a reference current path (i.e., transistors 210 and 220), while I OUT (φ1) flows through an output path (i.e., transistors 230 and 240). In this manner, the output current I OUT (φ1) at output node 250 mirrors the input current I IN  at input node 260. 
     Conversely, for every positive cycle of clock φ2 and negative cycle of clock φ1, (e.g., clock φ2 is in its first state and clock φ1 is in its second state), switches 245 close, while switches 235 remain open. By closing switches 245 and opening switches 235, the drain of transistor 210 connects to output node 250, while the drain of transistor 230 connects to both input node 260 and the gates of transistors 220 and 240, thereby forming a second cascode current mirror. The second cascode current mirror receives the input current I IN  at input node 260. The input current I IN  flows through a reference current path (i.e., transistors 230 and 240), while I OUT (φ2) flows through an output path (i.e., transistors 210 and 220). In this manner, the output current I OUT (φ2) at output node 250 mirrors the input current I IN  at input node 260. 
     However, for the output current (i.e., I OUT ) of apparatus 200 to exactly mirror the input current I IN , transistors 210,215, and 230 must have identical threshold voltage drops (i.e., V T ). Similarly, transistors 220 and 240 must have identical threshold voltage drops (i.e., V T ). To accomplish this, transistors 210, 215, and 230 must be equal in size and transistors 220 and 240 must be equal in size. Consequently, transistors 210, 215, and 230 and transistors 220 and 240 are fabricated to be as close in size as possible. Unfortunately, as previously described, two exactly sized transistors cannot be fabricated due to inherent errors associated with currently available fabrication techniques. As a result, the threshold voltage V T  of transistors 220 and 240 and transistors 210, 215, and 230 are not identical. FIG. 8 illustrates the first order model of this threshold voltage mismatch ΔV T  between transistors 220 and 240. 
     The repeated cycles of opening and closing switches 235 and 245 to connect and disconnect transistors 210 and 230 to/from input node 260 and output node 250 can be thought of as alternately chopping transistors 210 and 220 with transistors 230 and 240. By alternately chopping these transistors, the transistor with the threshold voltage mismatch ΔV T  (e.g., transistor 220) is alternately switched from the reference current path to the output current path at a sufficiently high rate such that the average output current at output node 250 accurately represents the input current at input node 260 (described by equations herein). 
     FIG. 9 illustrates the first cascode current mirror of apparatus 200 which is formed during positive cycles of clock φ1. FIG. 9 also illustrates the first order model of the threshold voltage mismatch ΔV T  between transistors 220 and 240. During positive cycles of clock φ1, the I OUT (φ1) of the second embodiment is identical to the I OUT (φ1) of the first embodiment. Therefore: 
     
         I.sub.OUT(φ1) =I.sub.IN +2(k&#39;)(w/l)(ΔV.sub.T)[I.sub.IN /(k&#39;(w/l))].sup.1/2 +k&#39;(w/l)(ΔV.sub.T).sup.2        (7) 
    
     where k&#39; is the process parameter, w/l is the size of transistor 240, and ΔV T  is the threshold voltage mismatch between transistors 220 and 240. 
     FIG. 10 illustrates the second cascode current mirror of apparatus 200 during positive cycles of clock φ2. FIG. 10 also illustrates the first order model of the threshold voltage mismatch ΔV T  between transistors 220 and 240. During positive cycles of φ2, the input current I IN  and output current I OUT (φ2) for apparatus 200 can be approximated by solving the following equations: 
     
         I.sub.IN =(k&#39;)(w/l)[V.sub.A -V.sub.T ].sup.2 
    
     where k&#39; is the process parameter, w/l is the size of transistor 240, V T  is the threshold voltage of transistor 240, and V A  is the voltage at the gate of transistors 220 and 240. Solving for V A  : 
     
         V.sub.A =[I.sub.IN /(k&#39;(w/l))].sup.1/2 +V.sub.T            (8) 
    
     During positive cycles of φ2, the output current I OUT (φ2) for apparatus 200 can be approximated by solving the following equations: 
     
         V.sub.GS1 =V.sub.A -ΔV.sub.T 
    
     
         I.sub.OUT(φ2) =k&#39;(w/l)[V.sub.GS1 -V.sub.T ].sup.2 
    
     where k&#39; is the process parameter, w/l is the size of transistor 220, V A  is the gate-to-source voltage across transistor 220, V T  is the threshold voltage of transistor 220, and V A  is the voltage at the gate of transistors 220 and 240. Therefore: 
     
         I.sub.OUT(φ2) =k&#39;(w/l)[V.sub.A -ΔV.sub.T -V.sub.T ].sup.2 (9) 
    
     Substituting equation 8 into 9: ##EQU4## 
     Accordingly, the average DC current I AVG  for apparatus 300 is: 
     
         I.sub.AVG =[I.sub.OUT(φ1) +I.sub.(OUT(φ2) ]/2      (11) 
    
     However, comparing I OUT (φ1) with I OUT (φ2) : 
     
         I.sub.OUT(φ1) =I.sub.IN +2(k&#39;)(w/l)(ΔV.sub.T)[I.sub.IN /(k&#39;(w/l))].sup.1/2 +k&#39;(w/l)(ΔV.sub.T).sup.2 ; 
    
     
         I.sub.OUT(φ2) =I.sub.IN -2(k&#39;)(w/l)(ΔV.sub.T)[I.sub.IN /(k&#39;(w/l))].sup.1/2 +k&#39;(w/l)(ΔV.sub.T).sup.2 ; 
    
     Thus, when I OUT (φ1) and I OUT (φ2) add together in equation 11, the first order error term 2(k&#39;)(w/l)(ΔV T )[I IN  /(k&#39;)(w/l)] 1/2  is eliminated. Accordingly: 
     
         I.sub.AVG =[2I.sub.IN +2(k&#39;)(w/l)(ΔV.sub.T).sup.2 ]/2 
    
     
         I.sub.AVG =I.sub.IN +k&#39;(w/l)ΔV.sub.T.sup.2 
    
     Using the identical parameters as those given in the Background of the Invention, namely I IN  =50 μA, k&#39;=43×10 -6  A/V 2 , w/l=100/10, and ΔV T  =10 mV, then: 
     
         I.sub.OUT =50×10.sup.-6 +0.034×10.sup.-6 ; 
    
     
         I.sub.OUT =50.034 μA 
    
     Thus, for an input current of 50 μA, the output current of apparatus 200 is 50.034 μA, which is an error rate of 0.068%. This error rate is a significant improvement over conventional current mirrors. This significant improvement occurs because the first order error term cancels when transistors 210 and 220 and transistors 230 and 240 are chopped. In effect, apparatus 200 modulates a substantial percentage of the threshold voltage mismatch ΔV T  and low frequency noise (i.e., 1/ƒ) up to the operating frequency of clocks φ1 and φ2. The resulting high frequency noise may then be filtered out using any suitable low pass filter. 
     The present invention overcomes the limitations in the related art and is particularly effective when configured and employed as described herein. However, those skilled in the art will readily recognize that numerous variations and substitutions may be made to the invention to achieve substantially the same results as achieved by the preferred embodiments. Although the present invention has been described in terms of the foregoing preferred embodiments, this description has been provided by way of explanation only and is not necessarily to be construed as a limitation of the invention. Illustratively, while the preferred embodiments are implemented in a P-well process, numerous CMOS processes, including twin tub and N-well, are suitable as well. Furthermore, while CMOS technology is used to advantage in the embodiments shown, any semiconductor circuitry which exhibits similar or even more advantageous characteristics could be substituted. For example, improved logic structures and innovative integrated circuit technology such as silicon-on-insulator structures could be substituted to improve circuit operation speed and reduce power consumption. Accordingly, various other embodiments and modifications and improvements not described herein may be within the spirit and scope of the invention, as defined by the following claims.