BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention generally relates to calibrating a comparator offset of a successive-approximation-register (SAR) analog-to-digital converter (ADC). 
         [0003]    2. Description of Related Art 
         [0004]    Persons of ordinary skill in the art understand terms and basic concepts related to microelectronics that are used in this disclosure, such as “signal,” “sampling,” “circuit node,” “switch,” “comparator,” “finite-state machine,” “analog-to-digital converter (ADC),” and “digital-to-analog converter (DAC).” Terms and basic concepts like these are understood by those of ordinary skill in the art and thus will not be explained in detail here. 
         [0005]    A functional block diagram of a successive-approximation-register (SAR) analog-to-digital converter (ADC)  100  is shown in  FIG. 1A . SAR ADC  100  comprises: a sampling network  110  sampling an input voltage V IN  and outputting a first voltage V 1  in accordance with a sampling signal SAMP; a digital-to-analog converter (DAC)  120  converting an output data D O  into a second voltage V 2 ; a summing circuit  130  receiving the first voltage V 1  and the second voltage V 2  and outputting a summed voltage V X ; a comparator  140  receiving the summed voltage V X  and outputting a binary decision D X  indicating a polarity of the summed voltage V X ; and a SAR controller  150  receiving the binary decision D X  and outputting the sampling signal SAMP and the output data D O . SAR ADC  100  operates in two phases: a sampling phase and a conversion phase. In the sampling phase, the sampling signal SAMP is asserted, and the input voltage V IN  is sampled into the first voltage V 1 . In the conversion phase, the sampling signal SAMP is de-asserted, and the SAR controller  150  conducts a process of successive approximation to adapt the output data D O  to make the second voltage V 2  approximately equal to the first voltage V 1  in accordance with the binary decision D X . The SAR controller  150  increases a value of the output data D O  to raise the second voltage V 2  and thus lower the summed voltage V X  when the binary decision D X  is 1, indicating that the summed voltage V X  is too high and needs to be lowered. Otherwise the SAR controller  150  decreases the value of the output data D O  to lower the second voltage V 2  and thus raise the summed voltage V X . At the end of the process of successive approximation, the summed voltage V X  is approximately zero, the second voltage V 2  is approximately equal to the first voltage V 1 , and a final value of the output data D O  is a digital representation of the input voltage V IN  as a result of the successive approximation. 
         [0006]    Ideal transfer characteristics of comparator  140  is shown in  FIG. 1B . As shown, D X  is 1 when V X  is greater than 0. Otherwise, D X  is 0. A practical comparator, however, might have an offset. Exemplary transfer characteristics of comparator  140  with a 10 mV offset is shown in  FIG. 1C . As shown, D X  is 1 when V X  is greater than 10 mV; otherwise, D X  is 0. In the presence of offset (e.g., 10 mV) of comparator  140 , the summed voltage V X  is approximately equal to the offset voltage (e.g., 10 mV), instead of zero, at the end of the successive approximation. As a result, the second voltage V 2  might not be an accurate approximation to the first voltage V 1 , and the final value of the output data D O  might not be an accurate digital representation of the input voltage V IN . This introduces an error to the analog-to-digital conversion and degrades a performance of SAR ADC  100 . 
         [0007]    Comparator offset can be calibrated by using an “auto-zero” scheme. An “auto-zero” scheme, however, increases complexity of the comparator. 
         [0008]    What is desired is a method for calibrating the comparator offset of SAR ADC without increasing complexity of the comparator. 
       BRIEF SUMMARY OF THE INVENTION 
       [0009]    An object of an exemplary embodiment of the present invention is to calibrate a voltage offset of a comparator of a successive-approximation-register analog-to-digital converter. 
         [0010]    An object of an exemplary embodiment of the present invention is to cancel a voltage offset of a comparator of a successive-approximation-register analog-to-digital converter using an offset-correction digital-to-analog converter in response to an offset-correction code obtained using successive approximation. 
         [0011]    In an exemplary embodiment, a successive-approximation-register analog-to-digital converter comprises: a multiplexed sampling network sampling either an input voltage or a common-mode voltage into a sampled voltage in accordance with a sampling signal, and based on the status of a foreground calibration indicator; a first digital-to-analog converter outputting a conversion voltage in response to a conversion code; a second digital-to-analog converter outputting an offset-correction voltage in response to an offset-correction code; a summing circuit receiving the sampled voltage, the conversion voltage, and the offset-correction voltage and outputting an error voltage; a comparator receiving the error voltage and outputting a binary decision; and a successive-approximation-register finite state machine receiving the binary decision and outputting an output data, the sampling signal, the foreground calibration indicator, the conversion code, and the offset-correction code, wherein: the finite state machine includes a foreground calibration state and a normal operation state. When the finite state machine is in the foreground calibration state, the common-mode voltage is sampled, and the conversion code is set to a common-mode code, and a calibrated value of the offset-correction code is established by successive approximation. In contrast, when the finite state machine is in the normal operation state, the input voltage is sampled, the offset-correction code is set to the calibrated value obtained when the state machine is in the foreground calibration state, and the conversion code is established by successive approximation. In an exemplary embodiment, a resolution of the second digital-to-analog converter is higher than a resolution of the first digital-to-analog converter. 
         [0012]    In an exemplary embodiment, a method comprises: using a first digital-to-analog converter to generate a conversion voltage in response to a conversion code; using a second digital-to-analog converter to generate an offset-correction voltage in response to an offset-correction code; using a summing circuit to generate an error voltage representing a sum of a sampled voltage, the conversion voltage, and the offset-correction voltage; using a comparator to output a binary decision indicating a polarity of the error voltage; and performing a first successive approximation including: setting the conversion code to a common-mode code; setting the offset-correction code to a neutral code; sampling a common-mode voltage into the sampled voltage; iteratively adapting the offset-correction code in accordance with the binary decision using successive approximation; saving a final value of the offset-correction code as a calibrated value; and performing a second successive approximation including: setting the offset-correction code to the neutral code; setting the conversion code to the common-mode code; sampling an input voltage into the sampled voltage; setting the offset-correction code to the calibrated value obtained when performing the first of successive approximation; iteratively adapting the conversion code in accordance with the binary decision using successive approximation; and outputting an output data using a final value of the conversion code. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1A  shows a functional block diagram of a prior art successive-approximation-register (SAR) analog-to-digital converter (ADC). 
           [0014]      FIG. 1B  shows ideal transfer characteristics of a comparator of the SAR ADC of  FIG. 1A . 
           [0015]      FIG. 1C  shows exemplary transfer characteristics of a comparator of the SAR ADC of  FIG. 1A  with 10 mV offset. 
           [0016]      FIG. 2  shows a functional block diagram of a SAR ADC in accordance with an exemplary embodiment of the present invention. 
           [0017]      FIG. 3  shows a flow diagram of an SAR finite state machine for the SAR ADC of  FIG. 2 . 
           [0018]      FIG. 4  shows a schematic diagram of a circuit embodiment for the SAR ADC of  FIG. 2 . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0019]    The present invention relates to calibration of a comparator offset of a successive-approximation-register analog-to-digital converter. While the specification describes several exemplary embodiments of the invention considered favorable modes of practicing the invention, it should be understood that the invention can be implemented in many ways and is not limited to the particular examples described below or to the particular manner in which any features of such examples are implemented. In other instances, well-known details are not shown or described to avoid obscuring aspects of the invention. 
         [0020]    The present invention is disclosed in an “engineering sense,” wherein a first quantity is said to be “equal to” a second quantity if a difference between the first quantity and the second quantity is smaller than a given tolerance. The amount of appropriate tolerance would be understood by one of ordinary skill. For example, 100.2 mV is said to be equal to 100 mV if the given tolerance is 0.5 mV. Likewise, a physical quantity is said to be pre-determined if the physical quantity is established by engineering means so as to be equal to a pre-determined value in the engineering sense. For instance, a voltage is said to be pre-determined if it is generated by an apparatus so that the voltage is equal to a pre-determined value (say, 100 mV). Transfer characteristics of a device are said to be pre-known if an output of the device in response of a given input of the device is pre-determined by engineering means. 
         [0021]    A functional block diagram of a successive-approximation-register (SAR) analog-to-digital converter (ADC)  200  in accordance with an embodiment of the present invention is shown in  FIG. 2 . SAR ADC  200  includes: a multiplexed sampling network  220  receiving an input voltage V IN  and a common-mode voltage V CM  and outputting a sampled voltage V S  in accordance with a sampling signal SMP and based on the status of a foreground calibration indicator FGC. A first DAC (digital-to-analog converter)  230  receives a conversion code D C  and outputs a conversion voltage V C . A second DAC  240  receives an offset-correction code D OC  and outputs an offset-correction voltage V OC . A summing circuit  250  receives the conversion voltage V C , the offset-correction voltage V OC , and the sampled voltage V S  and outputs an error voltage V E . A comparator  260  receives the error voltage V E  and outputs a binary decision D E . An SAR FSM (finite-state machine)  270  receives the binary decision D E  and outputs an output data D OUT , the sampling signal SMP, the foreground calibration indicator FGC, the conversion code D C , and the offset-correction code D OC . The function of the summing circuit  250  can be expressed by the following equation: 
         [0000]        V   E   =V   S   −V   C   −V   OC .   (1)
 
         [0022]    SAR ADC  200  has two states: foreground calibration, and normal operation. When the foreground calibration indicator FGC is asserted, SAR ADC  200  is in the foreground calibration state; otherwise SAR ADC  200  is in the normal operation state. Regardless of the state, SAR ADC  200  performs analog-to-digital conversion in two phases: a sampling phase and a conversion phase. When the sampling signal SMP is asserted, SAR ADC  200  is in the sampling phase. Otherwise SAR ADC  200  is in the conversion phase. In the sampling phase, either V CM  or V IN  is sampled into the sampled voltage V S . In the conversion phase, either D OC  or D C  is iteratively adapted by the SAR FSM  270  in accordance with D E . At the end of the conversion phase, the error voltage V E  will be approximately equal to zero if the comparator  260  is without offset (e.g., see  FIG. 1B , with V X  and D X  being replaced by V E  and D E , respectively). Otherwise the comparator  260  has a nonzero offset voltage (e.g., see  FIG. 1C , with V X  and D X  being replaced by V E  and D E , respectively), and V E  will be approximately equal to the offset voltage of the comparator  260 . Let the offset voltage of the comparator  260  be V OS . The foreground calibration is used to estimate the offset voltage V OS . 
         [0023]    The common-mode voltage V CM  is a pre-determined voltage that serves as a reference for calibrating SAR ADC  200  in the foreground calibration state. Transfer characteristics of DAC  230  are pre-determined such that V C  is equal to V CM  when D C  is set to a determined common-mode code D CM . Transfer characteristics of DAC  240  are also pre-determined such that V OC  is equal to 0V when D OC  is set to a neutral code D OC0 . In the foreground calibration state, during the sampling phase, D C  is set to D CM , D OC  is set to D OC0 , and V CM  is sampled into V S . In the foreground calibration state, during the conversion phase, D OC  is iteratively adapted by SAR FSM  270  in accordance with D E  as follows. SAR FSM  270  increases D OC  to raise V OC  and thus lower V E  when D E  is 1. Otherwise SAR FSM  270  decreases D OC  to lower V OC  and thus raise V E . At the end of the conversion phase after the successive approximation, V E  is approximately equal to the offset voltage V OS  of comparator  260  (due to the successive approximation), and therefore V OC  is approximately equal to −V OS , per Equation (1) along with using the conditions that V S =V CM  (due to the sampling), and V E =V OS  (due to the successive approximation). Let the final value of D OC  at the end of the conversion phase of the foreground calibration state be D OCC , which is a calibrated value for D OC  that makes V OC  approximately equal to −V OS . After the calibrated value D OCC  is obtained, SAR ADC  200  can enter the normal operation state, wherein the foreground calibration indicator FGC is de-asserted. In the normal operation state, D OC  is set to the neutral value D OC0 , D C  is set to the common-mode code D CM , and the input voltage V IN  is sampled into the sampled voltage V S  during the sampling phase. During the conversion phase, D OC  is set to the calibrated value D OCC , and a successive approximation process is conducted by the SAR FSM  270  to iteratively adapt the conversion code D C  in accordance with the binary decision D E  as follows. SAR FSM  270  increases D C  to raise V C  and thus lower V E  when D E  is 1, and otherwise decreases D C  to lower V C  and thus raise V E . At the end of the conversion phase, V E  is approximately equal to the offset voltage V OS  of comparator  260  as a result of the successive approximation, and thus the conversion voltage V C  is approximately equal to the input voltage V IN , per Equation (1) along with the conditions that V S =V IN  (due to the sampling) and V OC =−V OS  (due to D OC  being set to calibrated value D OCC ). Therefore, the conversion code D C  can accurately represent the input voltage V IN . 
         [0024]    In an exemplary embodiment, SAR FSM  270  works in accordance with an algorithm illustrated by a flow diagram  300  shown in  FIG. 3 . Upon start up (step  305 ), SAR FSM  270  enters the foreground calibration state comprising the following steps: assert the foreground calibration indicator FGC (step  310 ); set the conversion code D C  to the common-mode code D CM  and the offset-correction code D OC  to the neutral code D OC0  (step  315 ); assert the sampling signal SMP (step  320 ); de-assert the sampling signal SMP (step  325 ); iteratively adapt the offset-correction code D OC  in accordance with the binary decision D E  (step  330 ); save the final value of the offset-correction code D OC  as a calibrated value D OCC  (step  335 ); and de-assert the foreground calibration indicator FGC (step  340 ). Then, SAR FSM  270  enters the normal operation state comprising the following steps: set the conversion code D C  to the common-mode code D CM  and the offset-correction code D OC  to the neutral code D OC0  (step  342 ); assert the sampling signal SMP (step  345 ); de-assert the sampling signal SMP (step  350 ); set the offset-correction code D OC  to the calibrated value D OCC  (step  352 ); iteratively adapt the conversion code D C  in accordance with the binary decision D E  (step  355 ); update the output data D OUT  using a final value of the conversion code D C  (step  360 ); and loop back to step  342 . In step  330 , a plurality of iterations are taken, wherein in each iteration, D OC  is increased when D E  is 1, and decreased otherwise. Likewise, in step  355 , a plurality of iterations are taken, wherein in each iteration, D C  is increased when D E  is 1, and decreased otherwise. 
         [0025]    Comparator  260  of  FIG. 2  can be embodied by conventionally known comparator circuit at the discretion of circuit designer. 
         [0026]    Note that  FIG. 2  illustrates a functional block diagram that describes functions that embody SAR ADC in accordance with an example of the present invention. A function can be fulfilled in various means using various circuit embodiments at the discretion of circuit designer. A schematic diagram of a circuit  400  that can fulfill a combination of the functions of multiplexed sampling network  220 , DAC  230 , DAC  240 , and summing circuit  250  of  FIG. 2  is depicted in  FIG. 4 . The function of multiplexed network  220  of  FIG. 2  is fulfilled by sub-circuit  410  of  FIG. 4 . The function of DAC  230  of  FIG. 2  is fulfilled by sub-circuit  470  of  FIG. 4 ; the function of DAC  240  of  FIG. 2  is fulfilled by sub-circuit  480  of  FIG. 4 , and the function of summing circuit  250  of  FIG. 2  is implied and fulfilled by using a common node N X  for sub-circuit  410 , sub-circuit  470 , and sub-circuit  480  of  FIG. 4 . Sub-circuit  410  comprises two switches  411  and  412  for sampling V CM  and V IN , respectively, to the common node N X . By using AND gate  413 , switch  411  is turned on to sample the common-mode voltage V CM  to the common node N X  when both the sampling signal SMP and the foreground calibration indicator FGC are asserted, and turned off otherwise. By using AND gate  414  and inverter  415 , switch  412  is turned on to sample the input voltage V IN  to the common node N X  when both the sampling signal SMP and the logical inversion of the foreground calibration indicator FGC are asserted, and turned off otherwise. The function of the multiplexed sampling network  220  of  FIG. 2  is thus fulfilled by sub-circuit  410 , and the sampled voltage V S  of  FIG. 2  is implied and stored at the common output node N X  at the end of the sampling. In this exemplary embodiment, which is by way of example but not limitation, the conversion code D C  is a 9-bit code denoted as D C [8:0], and the offset-correction code D OC  is a 5-bit code denoted as D OC [4:0]. Sub-circuit  470  comprises nine capacitors C 0 , C 1 , C 2 , . . . , C 8 , and nine switches  430 ,  431 ,  432 , . . . ,  438  controlled by the nine bits of the conversion code D C [8:0], respectively. Each of the nine capacitors couples the common node N X  to either a first reference voltage V R1  or a second reference voltage V R0  via a respective switch controlled by a respective bit of the control code D C . For instance, capacitor C 0  couples the common node N X  to the first reference voltage V R1  if D C [0] is 1, or to the second reference voltage V R0  if D C [0] is 0, via switch  430 . As a result, the conversion voltage V C  is generated as a linear combination of the first reference voltage V R1  and the second reference voltage V R0  in accordance with the conversion code D C [8:0], and superimposed onto the common output node N X . Sub-circuit  470  thus fulfills the function of DAC  230 . Likewise, sub-circuit  480  comprises five capacitors C′ 0 , C′ 1 , C′ 2 , . . . , C′ 4 , and five switches  440 ,  441 ,  442 , . . . ,  444  controlled by the five bits of the offset-correction code D OC [4:0], respectively. Each of the five capacitors couples the common node N X  to either the first reference voltage V R1  or the second reference voltage V R0  via a respective switch controlled by a respective bit of the offset correction code D OC [4:0]. For instance, capacitor C′ 0  couples the common node N X  to the first reference voltage V R1  if D OC [0] is 1, or to the second reference voltage V R0  if D OC [0] is 0, via switch  440 . As a result, the offset-correction voltage V OC  is generated as a voltage of a linear combination of the first reference voltage V R1  and the second reference voltage V R0  in accordance with the offset-correction code D OC [4:0], and superimposed on the common node N X . Sub-circuit  480  thus fulfills the function of DAC  240 . By way of example but not limitation: C 0 =4 fF; C 1 =8 fF; C 2 =16 fF; C 3 =32 fF; C 4 =64 fF; C 5 =128 fF; C 6 =256 fF; C 7 =512 fF; C 8 =1024 fF; C′ 0 =2 fF; C′ 1 =4 fF; C′ 2 =8 fF; C′ 3 =16 fF; C′ 4 =32 fF; D OC0 =5′b1,0000; D CM =9′b1,0000,0000; V CM =0; V R1 =−0.5V; and V R0 =0.5V. Note that in this exemplary embodiment, the resolution of DAC  240  is higher than DAC  230  due to using smaller capacitors (C′ 0  is smaller than C 0 ; C′ 1  is smaller than C 1 ; C′ 2  is smaller than C 2 ; and so on). Using this arrangement, the offset voltage V OS  of comparator  260  can be calibrated to be smaller than a least-significant bit of DAC  230 . 
         [0027]    Referring to  FIG. 2 , in the normal operation state, the offset-correction code D OC  is set to the calibrated value D OCC  in the conversion phase. If the offset voltage V OS  of comparator  260  stays unchanged, then the offset voltage V OS  of comparator  260  can be effectively corrected by DAC  240 . However, if the offset voltage V OS  of comparator  260  changes over time, then the offset voltage V OS  of comparator  260  may not be effectively corrected by DAC  240 . In this case, a background calibration is needed. The background calibration is based on statistics of the output data D OUT . In an embodiment, the common-mode voltage V CM  is equal to a statistical mean of the input voltage V IN . If the offset voltage V OS  of comparator  260  is effectively corrected by DAC  240 , then a statistical mean of the output data D OUT  will be equal to the common-mode code D CM . If the statistical mean of the output data D OUT  is greater than the common-mode code D CM , it indicates the calibrated value D OCC  is too low and needs to be increased. Otherwise, it indicates the calibrated value D OCC  is too high and needs to be decreased. 
         [0028]    Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention. Accordingly, the invention should not be limited by the exemplary embodiments, but is described by the appended claims and equivalents thereof.
A circuit and method compensates for comparator offset in a successive approximation register analog-to-digital converter. The circuit includes a multiplexed sampler to sample either a common mode voltage or an input signal. The sampled signal is added to a conversion voltage and an offset correction voltage and input to a comparator. The comparator determines a polarity of deviation of the sum of the sampled signal, conversion voltage and off-set correction voltage. Based on the polarity, the offset correction voltage and the conversion voltage are alternately subjected to a successive approximation process to compensate for the offset of the sum from the sampled input signal or sampled common voltage signal.