Abstract:
A transimpedance amplifier circuit includes a first amplifier with an input, an output and a first transconductance. A second amplifier has an input that communicates with the output of the first amplifier, an output and a second transconductance. A first resistance has one end that communicates with the input of the first amplifier. An inverter has an input that communicates with the output of the second amplifier and an output that communicates with an opposite end of the first resistance. A second resistance has one end that communicates with the input of the second amplifier and an opposite end that communicates with the output of the second amplifier. A third resistance has one end that is connected to the output of the second amplifier. A first capacitance has one end that communicates with the one end of the first resistance and an opposite end that communicates with the opposite end of the first resistance.

Description:
FIELD OF THE INVENTION 
   The present invention relates to amplifier circuits, and more particularly to multi-stage amplifier circuits. 
   BACKGROUND OF THE INVENTION 
   Referring now to  FIGS. 1 and 2 , a transimpedance amplifier (TIA) circuit is shown and includes an inverting amplifier having a transconductance g m , a load resistance R L , and a feedback resistance R f . As is known, the TIA circuit converts an input current I in  to an output voltage V o . Several characteristics of the amplifier circuit in  FIG. 1  are described below, including gain, input impedance, output impedance, and noise. The gain of the amplifier circuit: 
           Gain   =         v   o       i   in       =       -     R   f       +       1     g   m       .               
For many implementations, R f  is much larger than
 
           1     g   m           
such that the gain is essentially equal to —R f .
 
   The input impedance R in  of the amplifier circuit of  FIG. 1  is as follows: 
             R   in     =       1     g   m       ⁢     (     1   +       R   f       r   L         )             
Thus, the input impedance R in  is a function of the load resistance R L , as well as the feedback resistance R f  and the transconductance g m . The output impedance R o  is equal to
 
           1     g   m           
at low frequency. However, due to parasitic capacitance C 1 , the output impedance increases to the value of the feedback resistance R f  for frequencies greater than
 
             1       R   f     ⁢     C   1         ,         
as is illustrated generally in  FIG. 2 .
 
   Assuming the feedback resistance R f  is much greater than 
             1     g   m       ,         
the noise at the input of the amplifier circuit is:
 
           Noise   =       4   ⁢           ⁢   K   ⁢           ⁢   T       g   m             
Thus, the noise is independent of the feedback resistance R f  and the load resistance R L , and inversely related to the transconductance g m . Note that K is Boltzmann&#39;s constant and T is temperature. Therefore, reducing noise generally involves increasing the transconductance g m .
 
   One advantage of the amplifier circuit of  FIG. 1  is that while noise is closely related to the transconductance g m , the input impedance R in  is not. Therefore, noise can be set to a desired level by adjusting the transconductance g m . The desired input impedance R in  can then be obtained by adjusting the feedback and load resistances R f  and R L , respectively. In this sense, the noise and input impedance of the amplifier circuit of  FIG. 1  are relatively independent. 
   In contrast, the input impedance and noise of differential TIAs are both dependent on the transconductance g m . Specifically, the input impedance R in  is equal to 
           1     g   m           
and the noise is equal to
 
               4   ⁢           ⁢   K   ⁢           ⁢   T       g   m       .         
Accordingly, adjusting the noise level will affect the input impedance and vice versa in differential TIAs.
 
   Referring now to  FIG. 3 , it is difficult to obtain high gain from a transimpedance amplifier while maintaining relatively flat input impedance and noise levels at high frequencies. As noted above, to have low noise, the transconductance g m  must be relatively large. For most transistors, the transconductance g m  is given by the following equation: 
             g   m     =         2   ⁢           ⁢   K   ⁢           ⁢   I   ⁢           ⁢   W     L             
Where W is width, L is length, and I is current. To increase the transconductance g m , the width W of the device and/or the current I can be increased. As can be seen from the following equations, however, the width W is proportional to the parasitic capacitances C 1  and C 2 :
 C 1 =C ox WL; and C 2 ocW. 
Where C ox  is oxide capacitance. Thus, increasing the width W to increase the transconductance g m  also increases the parasitic capacitances C 1  and C 2 . The effects of the larger parasitic capacitances on circuit performance (specifically input impedance, gain, and bandwidth) are discussed further below.
 
   Referring now to  FIG. 4 , the general equation for input impedance is set forth above. However, if the value of capacitance C 2  increases, at some frequency it shunts the load resistance R L  such that the equation for input impedance becomes: 
             R   in     =       1     g   m       ⁢     (     1   +         R   L     ⁢     C   2           R   L     +     C   2           )               FIG. 4  illustrates this relationship. As shown therein, the input impedance is initially flat. As frequency increases, the impedance of capacitor C 2  decreases and begins to reduce the impedance of the parallel combination of capacitor C 2  and the load resistance R L . This, in turn, increases the input impedance R in  starting at a frequency of about
 
             1       C   2     ⁢     R   L         .         
At even higher frequencies, the input impedance may drop off due to circuit performance, as shown in  FIG. 4 . Thus, one problem with the amplifier circuit of  FIG. 1  is that reducing noise also requires increasing the transconductance g m . Increasing the transconductance g m , in turn, increases the parasitic capacitance and can adversely impact the input impedance R in  at certain frequencies.
 
   Referring now to  FIG. 5 , to achieve high gain, a high feedback resistance R f  is typically needed. However, the transistor has an output impedance r o  and a load impedance R L . Usually R L  is much greater than r o . The equation for r o  is: 
             r   o     =         T   ·   L       g   m       .           
Where T represents a constant typically having a value of about 100 and L represents the length of the device. Therefore, given a value for
 
           1     g   m           
of 5 ohms and a device length of 0.25 microns, r o  will be approximately 125 ohms. Assuming the load impedance R L  is infinite, the equation for input impedance R in  is:
 
             R   in     =         1     g   m       ⁢   1     +       (         R   f     ⁡     (       R   L     +     r   o       )           R   L     ⁢     r   o         )     .             
If an input impedance of 50 ohms is used, the feedback resistance R f  is limited to approximately 1125 ohms.
 
   Increasing the size of the device adversely impacts the input impedance R in  at high frequencies because of the increased capacitance. Increasing the size of the device also limits the value of the load impedance R L . Limiting R L  also limits the value of the feedback resistance R f  and adversely impacts the gain at DC. 
   Referring now to  FIG. 6 , in order to derive the bandwidth of an amplifier with feedback, an open loop response technique is used to provide information relating to the bandwidth and maximum achievable bandwidth of a circuit. The DC gain of the open loop response is determined by opening the feedback loop and attaching a voltage source to one end of the feedback loop as shown in  FIG. 6 . The output voltage is sensed at the other end of the feedback loop. 
   To derive the bandwidth, the DC gain of the open loop response and the first dominant pole P 1  are found. Assuming stable operation, there is only one pole P 1  that is located below a crossover frequency. The crossover frequency is the product of the DC gain of the open loop response and the first dominant pole P 1 . The crossover frequency defines the bandwidth of the closed loop amplifier. The maximum available bandwidth is related to the second non-dominant pole P 2 . 
   Referring now to  FIG. 7 , the response of the amplifier circuit of  FIG. 6  is shown. The DC gain of the open loop response is g m R L  and the circuit has a dominant pole at 
             1       R   f     ⁡     (       C   1     +     C   2       )         .         
Multiplying the DC gain of the open loop response with P 1  provides a crossover frequency of
 
                 g   m     ⁢     R   L           R   f     ⁡     (       C   1     +     C   2       )         .         
Further the circuit arrangement has a non-dominant pole at
 
             1       C   L     ⁢     R   2         ,         
which relates to a barrier frequency or maximum achievable bandwidth. Increasing the transconductance g m  increases the parasitic capacitances C 1 , C 2 . If the load impedance R L  is less than the feedback resistance R f , then the second component of the equation
 
           (       i   .   e   .     ,       R   L       R   f         )         
is less than unity. Thus, it should be understood that there is a maximum bandwidth that can be obtained, which is basically
 
               g   m     C     ,         
which limits the speed of the circuit.
 
   SUMMARY OF THE INVENTION 
   A transimpedance amplifier circuit comprises a first amplifier with an input, an output and a first transconductance. A second amplifier has an input that communicates with the output of the first amplifier, an output and a second transconductance. A first resistance has one end that communicates with the input of the first amplifier. An inverter has an input that communicates with the output of the second amplifier and an output that communicates with an opposite end of the first resistance. 
   In other features, the first transconductance is greater than the second transconductance. A second resistance has one end that communicates with the input of the second amplifier and an opposite end that communicates with the output of the second amplifier. A third resistance has one end that is connected to the output of the second amplifier. 
   In still other features, a first capacitance has one end that communicates with the one end of the first resistance and an opposite end that communicates with the opposite end of the first resistance. 
   A transimpedance amplifier circuit comprises a first amplifier with an input, an output and a first transconductance. A second amplifier has an input that communicates with the output of the first amplifier, an output and a second transconductance. A first resistance has one end that communicates with the input of the first amplifier. A third amplifier has an input that communicates with the output of the second amplifier, an output and a third transconductance. A fourth amplifier has an input that communicates with the output of the third amplifier, an output and a fourth transconductance. An inverter has an input that communicates with the output of the fourth amplifier and an output that communicates with an opposite end of the first resistance. 
   In other features, the first transconductance is greater than the second transconductance and the second transconductance is greater than the third and fourth transconductances. The second transconductance is approximately equal to one-fourth of the first transconductance. The third and fourth transconductances are approximately equal to one-twelfth of the first transconductance. 
   In yet other features, a second resistance has one end that communicates with the input of the second amplifier and an opposite end that communicates with the output of the second amplifier. A third resistance has one end that communicates with the input of the fourth amplifier and an opposite end that communicates with the output of the fourth amplifier. A first capacitance has one end that communicates with the one end of the first resistance and an opposite end that communicates with an opposite end of the first resistance. 
   A differential transimpedance amplifier circuit comprises a first amplifier with an input, an output and a first transconductance. A second amplifier has an input that communicates with the output of the first amplifier, an output and a second transconductance. A first resistance has one end that communicates with the input of the first amplifier. A second resistance has one end that communicates with the input of the second amplifier and an opposite end that communicates with the output of the second amplifier. A third amplifier has an input, an output and a third transconductance. A fourth amplifier has an input that communicates with the output of the third amplifier, an output and a fourth transconductance. A third resistance has one end that communicates with the input of the third amplifier. A fourth resistance has one end that communicates with the input of the fourth amplifier and an opposite end that communicates with the output of the fourth amplifier. An opposite end of the first resistance communicates with the opposite end of the fourth resistance. An opposite end of the third resistance communicates with the opposite end of the second resistance. 
   In other features, the first and third transconductances are greater than the second and fourth transconductances, respectively. A first capacitance has one end that communicates with the one end of the first resistance and an opposite end that communicates with the opposite end of the first resistance. A second capacitance has one end that communicates with the one end of the third resistance and an opposite end that communicates with the opposite end of the third resistance. 
   A differential transimpedance amplifier circuit comprises a first amplifier with an input, an output and a first transconductance. A second amplifier has an input that communicates with the output of the first amplifier, an output and a second transconductance. A first resistance has one end that communicates with the input of the first amplifier. A second resistance has one end that communicates with the input of the second amplifier and an opposite end that communicates with the output of the second amplifier. A third amplifier has an input, an output and a third transconductance. A fourth amplifier has an input that communicates with the output of the third amplifier, an output and a fourth transconductance. A third resistance has one end that communicates with the input of the third amplifier. A fourth resistance has one end that communicates with the input of the fourth amplifier and an opposite end that communicates with the output of the fourth amplifier. A fifth amplifier has an input that communicates with the output of the second amplifier, an output and a fifth transconductance. A sixth amplifier has an input that communicates with the output of the fifth amplifier, an output and a sixth transconductance. A seventh amplifier has an input that communicates with the output of the fourth amplifier, an output and a seventh transconductance. An eighth amplifier has an input that communicates with the output of the seventh amplifier, an output and a eighth transconductance. An opposite end of the first resistance communicates with the output of the eighth amplifier. An opposite end of the third resistance communicates with the output of the sixth amplifier. 
   In other features, the first and third transconductances are greater than the second and fourth transconductances, respectively. The second and fourth transconductances are greater than the fifth and sixth and the seventh and eighth transconductances, respectively. The second and fourth transconductances are approximately equal to one-fourth of the first and third transconductances, respectively. The fifth and sixth transconductances and the seventh and eighth transconductances are approximately equal to one-twelfth of the first and second transconductances, respectively. 
   In still other features, a first capacitance has one end that communicates with the one end of the first resistance and an opposite end that communicates with the opposite end of the first resistance. A second capacitance has one end that communicates with the one end of the third resistance and an opposite end that communicates with the opposite end of the third resistance. A fifth resistance that has one end that communicates with the input of the sixth amplifier and an opposite end that communicates with the output of the sixth amplifier. A sixth resistance that has one end that communicates with the input of the eighth amplifier and an opposite end that communicates with the output of the eighth amplifier. 
   Further areas of applicability of the present invention will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein: 
       FIG. 1  is an electrical schematic of a transimpedance amplifier circuit according to the prior art; 
       FIG. 2  is a graph illustrating output impedance as a function of frequency for the amplifier circuit of  FIG. 1 ; 
       FIG. 3  is an electrical schematic of a transistor with parasitic capacitances according to the prior art; 
       FIG. 4  is a graph illustrating input impedance as a function of frequency for the amplifier of  FIG. 1 ; 
       FIG. 5  is an electrical schematic illustrating the output resistance of the transistor of  FIG. 3 ; 
       FIG. 6  is the amplifier circuit of  FIG. 1  in an open loop response configuration; 
       FIG. 7  illustrates the open loop response of the circuit shown in  FIG. 6 ; 
       FIG. 8  is an electrical schematic of an amplifier circuit according to one embodiment of the present invention; 
       FIG. 9  is an electrical schematic of a differential circuit implementation of the circuit of  FIG. 8 ; 
       FIG. 10  is a graph illustrating input impedance as a function of frequency for the differential circuit of  FIG. 9 ; 
       FIG. 11  illustrates the open loop response of the differential circuit of  FIG. 9 ; 
       FIG. 12  is an electrical schematic of an amplifier circuit according to another embodiment of the present invention; 
       FIG. 13  is a graph illustrating the output impedance as a function of frequency for the differential circuit of  FIG. 9 ; 
       FIG. 14  is an electrical schematic of an amplifier circuit including additional amplifier stages according to yet another embodiment of the present invention; 
       FIG. 15  illustrates the open loop response of the circuit of  FIG. 14 ; 
       FIG. 16  is an electrical schematic of a differential circuit implementation using the circuit of  FIG. 14 ; 
       FIG. 17  is a functional block diagram of the multiple amplifier circuit according to the present invention that is implemented in a read head of a disk drive system; and 
       FIG. 18  is a functional block diagram of the multiple amplifier circuit according to the present invention that is implemented in a low noise amplifier (LNA) of a wireless device. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   The following description of the preferred embodiment(s) is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. For purposes of clarity, the same reference numbers will be used in the drawings to identify similar elements. 
   An amplifier circuit according to one embodiment of the present invention is illustrated in  FIG. 8  and is designated by reference number  100 . The circuit  100  includes a first amplifier  102  having a transconductance g m1  and a second amplifier  104  having a transconductance g m2 . The first and second amplifiers  102 ,  104  are connected in series. Specifically, an output  108  of the first amplifier  102  is coupled to an input  110  of the second amplifier  104 . 
   An output  112  of the second amplifier  104  is coupled to an input  114  of the first amplifier  102  through a feedback circuit  116 . The feedback circuit  116  includes a feedback resistance R f  and an inverter  106 . In one implementation, the inverter  106  has a gain equal to −1, although other gain values can be used. A resistance R 2  is coupled in parallel with the second amplifier  104 . Also shown in  FIG. 8  are parasitic capacitances C 1 , C 2 , and C 3 . An input current source I in    126  is coupled to the input terminal  114  of the first amplifier  102 . A load resistance R L  is coupled to the output terminal  112  of the second amplifier  104 . In this implementation, g m1  is preferably greater than g m2 . The amplifiers  102 ,  104  can be inverting CMOS amplifiers (although other transistor types may be used), and the parasitic capacitances C 1  and C 2  are preferably much larger than the parasitic capacitance C 3 . 
   Referring now to  FIG. 9 , a differential circuit  200  corresponding to the circuit  100  shown in  FIG. 8  is illustrated. The differential circuit  200  includes a first set of amplifiers  202 ,  204  connected in series and having transconductances g m1  and g m2 , respectively. A second set of amplifiers  206 ,  208  are connected in series and have transconductances g m1  and g m2 , respectively. An output  210  of the first set of amplifiers is coupled to an input  212  of the second set of amplifiers through a feedback resistance R f . An output  214  of the second set of amplifiers is coupled to an input  216  of the first set of amplifiers through a feedback resistance R f . Negative feedback is achieved by feeding the output  210  from the first set of amplifiers to the input  212  of the second set of amplifiers  206 ,  208 , and vice versa. 
   The effective transconductance g m-eff  of the differential circuit  200  of  FIG. 9  is given by the following equation: 
             g     m   -   eff       =             g   m     ⁢     R   2         R   L             g   m2     ⁢     R   L       +   1       ≈       g   m2     ·     g   m1     ·       R   2     .               
Therefore, the overall transconductance for the differential circuit  200  is greater than the amplifier circuit that is shown in  FIG. 1 . Even if amplifiers  202 ,  206  have the same transconductance g m  as the amplifier of  FIG. 1 , the overall transconductance g m-eff  is the product of this transconductance multiplied by g m2  and R 2  for the circuit of  FIG. 9 .
 
   The input impedance for the differential circuit of  FIG. 9  is as follows: 
             R   in     =         1     g   m_eff       ⁢     (     1   +     Rf     R   L         )       ⇒         1       g   m2     ⁢     g   m1     ⁢     R   2         ⁢     (     1   +     Rf     1   /     g   m           )       ≈       1       g   m2     ⁢     g   m1     ⁢     R   2         +       R   f     ⁢     g   m1     ⁢     R   2                   
Note that, in this embodiment, R L  is not shunted because the parasitic capacitance C 3  is relatively low. Therefore, the differential circuit  200  is capable of higher frequency operation than the amplifier circuit of  FIG. 1 .
 
   Referring now to  FIG. 10 , the input impedance is shown as a function of frequency. The input impedance is relatively flat or constant to a higher frequency 
           (       i   .   e   .     ,     1       R   L     ⁢     C   3           )         
as compared to the input impedance for the circuit of  FIG. 1 . Moreover, in the differential circuit of  FIG. 9 , the value of the feedback resistance R f  can be increased as desired for increased gain because this resistance R f  is not limited by the output impedance as in  FIG. 1 .
 
   Relative to the amplifier circuit of  FIG. 1 , the output impedance of the amplifier circuits shown in  FIGS. 8 and 9  is also increased because the second amplifier  104  has a low transconductance g m2  and a high output impedance. Thus, the overall output impedance is not limited by the second amplifier  104 , and is merely limited by the load impedance R L . The noise of the amplifier circuits  100 ,  200  is similar to the amplifier circuit of  FIG. 1  because the noise of the first amplifier  102  dominates the overall noise for the circuit, and the noise generated by the second amplifier  104  is divided by g m1 . 
   Referring now to  FIG. 11 , the open loop response of the differential circuit of  FIG. 9  is illustrated using the open loop response technique described above. As shown therein, at DC, the capacitor C 1  is effectively an open circuit and the input impedance is high, so the DC gain of the open loop response is equal to g m1 ·R 2 . There is a dominant pole at 
           1       R   f     ⁢     C   1             
and the crossover frequency is
 
   
     
       
         
           
             ( 
             
               
                 
                   g 
                   m1 
                 
                 · 
                 
                   R 
                   2 
                 
               
               
                 
                   R 
                   f 
                 
                 ⁢ 
                 
                   C 
                   1 
                 
               
             
             ) 
           
           . 
         
       
     
   
   As compared to the amplifier circuit of  FIG. 1 , the crossover frequency is determined by the resistance R 2  rather than the load impedance R L . Therefore, the resistance R 2  can be increased to increase bandwidth. Further, the crossover frequency is a function of one capacitor C 1  not two. Thus, given the same transconductance g m1  as the circuit of  FIG. 1 , the bandwidth of the differential circuit  200  will be greater. However, there are two nondominant poles at 
               g   m1       C   2       ⁢           ⁢   and   ⁢           ⁢         g   m2       C   3       .           
These poles set an upper limit on the differential circuit&#39;s bandwidth.
 
   Referring now to  FIG. 12 , to mitigate this problem, a capacitor C z  can be coupled in parallel across the feedback resistance R f  in the differential mode, as shown in the half-circuit illustrated in  FIG. 12 . The capacitor C 2  adds a zero at a frequency of 
           1       R   f     ⁢     C   z             
as shown in  FIG. 1 .
 
   Referring now to  FIG. 13 , the transconductance g m1  is noise dependent and is typically set to a level corresponding to minimal noise. Therefore, the transconductance g m1  cannot be further increased to further enhance the bandwidth of the differential circuit  200 . The feedback resistance R f  is set by the input impedance R in , so those two variables are generally fixed. As the resistance R 2  is increased to increase bandwidth, at some point the output impedance is affected. This is illustrated in  FIG. 13 , where it can be seen that the output impedance R o  of the differential circuit  200  is relatively constant or flat up to a frequency of approximately 
   
     
       
         
           
             1 
             
               
                 R 
                 2 
               
               ⁢ 
               
                 C 
                 2 
               
             
           
           . 
         
       
     
   
   Moreover, and with further reference to  FIG. 11 , at a frequency of 
               g   m2     =       R   2       C   2         ,         
R o  increases. Therefore, by increasing the resistance R 2 , one of the nondominant poles moves down in frequency, which limits bandwidth. For all of these reasons, the resistance R 2  generally cannot be increased without restraint.
 
   Referring now to  FIG. 14 , another embodiment of an amplifier circuit is shown that mitigates the problems described above by increasing the transconductance g m2  of the second amplifier  104 , adding amplifiers  150 ,  152 , and reducing the resistance R 2 . In the embodiment of  FIG. 14 , the transconductance of the amplifier  104  is approximately one-quarter of the amplifier  102 . The transconductance of amplifiers  150 ,  152  are approximately one-twelfth of amplifier  102 . As used herein, the term approximately means within +/−0.25% of the designated value. 
   Referring now to  FIGS. 15 and 16 , the open loop response of the circuit of  FIG. 14  is illustrated using the open loop response technique. Note that three nondominant poles occur at very high frequencies due to fact that the parasitic capacitances C 3 , C 4 , and C 5  have a relatively low value. The lowest nondominant pole also occurs at a relatively high frequency since the resistance R 2  has a relatively low value. As for the crossover frequency, note that the transconductance g m1  is fixed for noise purposes, the feedback resistance R f  is fixed by the input impedance R in , capacitor C 1  is fixed, and the resistance R 2  is set low for bandwidth purposes. However, transconductances g m3  and g m4  can be adjusted to further increase bandwidth. Thus, the circuit of  FIG. 14  provides even greater flexibility in achieving a high gain, high bandwidth amplifier with other desirable circuit characteristics. In  FIG. 16 , a differential embodiment of the circuit of  FIG. 14  is illustrated. Note that the parasitic capacitances have been omitted in  FIG. 16 . 
   Referring now to  FIGS. 17 and 18 , several exemplary implementations of the multiple amplifier circuit  200  are shown. The multiple amplifier circuit  200  may be any of the multiple amplifier circuits shown in  FIGS. 8-16 . In  FIG. 17 , the multiple amplifier circuit  200  according to the present invention is implemented in a read head  202  of a disk drive system  204 . In  FIG. 18 , the multiple amplifier circuit  200  is implemented in a low noise amplifier (LNA)  210  of a wireless device  212 . For example, the wireless device  212  may be compliant with Bluetooth networks, cellular networks, and/or Ethernet networks such as 802.11a, 802.11b, 802.11n, 802.11g, 802.16 and/or other present and future wireless standards. 
   Skilled artisans will appreciate that there are a wide variety of other applications for the multiple amplifier circuit according to the present invention. As can be appreciated, the resistance and capacitances can be implemented in a wide variety of ways including but not limited to discrete elements such as resistors and capacitors, nonlinear variable resistors and capacitors, and/or transistor-based resistances and capacitances. Still other variations are contemplated. 
   Those skilled in the art can now appreciate from the foregoing description that the broad teachings of the present invention can be implemented in a variety of forms. For example, the present invention can be applied to a wide variety of applications including, for example, CMOS readers. Therefore, while this invention has been described in connection with particular examples thereof, the true scope of the invention should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the drawings, specification, and the following claims.