Abstract:
A bit-and-one-half analog to digital converter comprising a multiplying analog to digital converter (MDAC) operating in cooperation with a comparator which generates a two-bit digital output signal by comparison of an output of the MDAC against a pair of thresholds, wherein the thresholds are stretched outwardly from symmetrical thresholds centered at +/−¼ of the comparison range.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to multi-stage pipelined analog to digital converters in which each stage includes a bit-and-one-half analog to digital sub-converter, and particularly relates to reductions in differential non-linearities for such an analog to digital converter. 
     2. Background of the Invention 
     Multi-stage pipelined analog to digital converters (ADC) provide efficient high speed conversion of analog signals to digital equivalents A representative multi-stage pipelined ADC  10  is shown in FIG.  1 . As seen there, ADC  10  includes multiple stages such as stages  11 ,  12  and  13  each providing one or more bits of digital data to a digital correction circuit  15 , which resolves the digital outputs from each stage into an overall digital output  16  that corresponds to an analog input  17 . Each stage is a switched capacitor circuit operating in response to clock signals such as Φ 1  and Φ 2  and comparing an analog voltage input to thresholds based on reference signals Vrefp and Vrefn so as to produce the digital outputs as well as a residual analog signal. The residual analog signal is provided as input to the subsequent stage. 
     FIG. 2 is a generalized block diagram of each stage. As seen in FIG. 2, each stage applies its input analog voltage to a multiplying digital to analog converter (MDAC)  19  so as to generate its residual output analog voltage. This output voltage is provided to comparator  18  which generates the digital output. MDAC  19  uses this digital output, together with clock signal Φ 1  and Φ 2  and reference voltages Vrefp and Vrefn, to generate the residual output analog voltage. 
     FIG. 3A illustrates a typical MDAC  19 . As seen there, during sample phase Φ 1 , an input voltage signal is sampled and stored on capacitors C 1  and C 2 . During amplification phase Φ 2 , capacitor C 1  is placed in the feedback leg of amplifier  21 , and a voltage is applied to capacitor C 2  in accordance with whether the digital output from comparator  18  is a digital  1  or a digital  0 . As a consequence of this arrangement, so long as capacitors C 1  and C 2  are exactly equal, the output from MDAC  19  is a correctly multiplied residual voltage in dependence on the digital data generated at a stage, as shown in FIG.  3 B. 
     Most often, however, capacitors C 1  and C 2  are not equal, resulting in a non-ideal slope for the digital converter, as shown in FIG.  3 C. The non-ideal slope results in missing codes or wide codes. In FIG. 3C, it is assumed that C 1  is slightly smaller than C 2 . Thus, the drop from voltage Va to Vb is slightly less than one digital bit, resulting in wide codes as shown in FIG.  3 D. Of course, if C 2 &gt;C 1 , then Va−Vb&gt;one digital bit, resulting in unillustrated missing codes. 
     One solution to capacitor mismatch has been proposed by Yu, et al., “A 2.5-V, 12-b, 5-Msample/s Pipelined CMOS ADC”, IEEE Journal of Solid State Circuits, Vol. 31, No. 12, p. 1854 (Dec. 1996). Yu, et al. proposed a commutated feedback-capacitor switching technique in which the role of the feedback capacitor is switched in dependence on the digital data. With the Yu, et al. technique, differential non-linearity is reduced, as seen in FIG. 3E, since the voltage drop Va−Vb is very nearly equal to one digital bit. Thus, wide codes and missing codes are avoided, and differential non-linearity is reduced as shown in FIG.  3 F. 
     Another difficulty encountered with the multi-stage pipelined ADC shown in FIG. 1 is the problem caused by an undesired offset in comparator  18 . As shown in FIG. 4A, with an undesired or uncompensated offset in comparator  18 , missing codes are encountered because of a shift in the transfer function of MDAC  19 . One solution proposed for this difficulty is the provision of multiple bits from each stage as already described. The bits are generated by comparison with thresholds which are +/−¼ of the comparison range centered symmetrically around zero. With multiple bits for each stage, a transfer function such as in FIG. 4B is obtained, in which two bits of digital output are obtained for each stage, and the digital outputs of all stages are resolved by correction circuitry  15  so as to result in the overall ADC output. The arrangement shown in FIG. 4D is often referred to as a “bit-and-one-half converter”. 
     Combining the techniques of bit-and-one-half converters with the Yu, et al. technique of commutated feedback-capacitor switching is expected to yield a highly efficient pipelined ADC with good differential non-linearity. However, one source of differential non-linearity remains, as follows. 
     Specifically, commutated feedback-capacitor switching works in single-bit MDACs because the voltage drop from the voltage Va to Vb is approximately equal to one bit. However, in bit-and-a-half MDACs, when capacitive mismatch is present, the voltage drop from Va to Vb is not equal to one bit as seen in FIG. 5A, resulting in differential non-linearity shown in FIG.  5 B. Thus, commutated feedback-capacitor switching in bit-and-a-half MDACs only reduces differential non-linearity by about 50%, primarily because of unequal threshold spacing between the 00 and 01 decision point and between the 01 and 11 decision point. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to reduce differential non-linearity in bit-and-one-half analog to digital converter by threshold-stretching the threshold at which each stage of the bit-and-one-half converter operates. 
     In more detail, FIG. 6A is a graph showing input versus output for one stage of a multi-stage bit-and-one-half ADC. As seen there, the threshold for conversion has been shifted outwardly relative to the threshold shown in the conventional arrangement of FIG.  5 A. As a result, the voltage drop from Va to Vb is much closer to the desired one bit at which commutated feedback-capacitive switching operates most ideally, yielding an overall transfer curve shown in FIG. 6B in which differential non-linearity, though still present, is reduced relative to the conventional arrangement shown in FIG.  5 B. 
     Thus, in one aspect the invention is a bit-and-one-half conversion stage for a multi-stage pipelined ADC in which conversion thresholds are stretched outwardly relatively to corresponding thresholds in conventional conversion stages. Shifting outwardly too much completely destroys the effectiveness of bit-and-one-half conversion such that when the thresholds are shifted completely to the edge of positive and negative reference voltages divided by two (i.e., Vrefn/2 and Vrefp/2), the benefits of bit-and-one-half conversion are eliminated. An intermediate shift is therefore preferable; the inventor herein has determined that for a 1% mismatch in capacitance, a preferred shift is a shift outwardly of approximately 0.125 (normalized to +1 and −1 reference voltages) from conventional threshold locations of +/−¼. 
     Also, with reference to FIG. 6A, by shifting the positive threshold to the right by approximately Vrefp/8, and by shifting the negative threshold to the left by approximately Vrefn/8, a desired drop in residue can be achieved. The entire residue is preferably located inside the window (e.g., the box) shown in FIG.  6 A. However, when using the entire capability of error correction logic to compensate for capacitor mismatch, op-amp and comparator offset (plus charge injection) may cause differential non-linearity noise. 
     The shift in threshold can be obtained by a variety of techniques, including simple resistive ladders, internal generation of reference voltages, or converter-wide reliance on globally-generated thresholds. 
     In another aspect, the invention is a multistage pipelined ADC using the aforementioned bit-and-one-half converter with outwardly stretched conversion thresholds. 
     This brief summary has been provided so that the nature of the invention may be understood quickly. A more complete understanding of the invention can be obtained by reference to the following detailed description of the preferred embodiment thereof in connection with the attached drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1 and 2 are functional block diagrams showing a conventional multi-stage pipelined ADC. 
     FIGS. 3A through 3F are views for explaining differential non-linearity caused by a multiplying digital to analog converter in individual stages. 
     FIGS. 4A and 4B are views for explaining a conventional bit-and-one-half converter stage for a multi-stage ADC. 
     FIGS. 5A and 5B are views for explaining differential non-linearity in a conventional bit-and-one-half converter stage. 
     FIGS. 6A and 6B are views for explaining reduced differential non-linearity in a bit-and-one-half converter according to the invention. 
     FIG. 7 is a detailed diagram showing a bit-and-one-half converter according to the invention in which thresholds have been shifted outwardly. 
     FIG. 8 is a graph showing the effectiveness of the present invention in reducing differential non-linearity. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     As shown in FIG. 7, each stage of a multistage bit-and-one-half ADC includes a switched capacitor MDAC  100  operating in cooperation with a stretched-threshold comparator  120 . The MDAC  100  includes a pair of capacitors C 1  and C 2  which operate in a sampling phase Φ 1  and an amplification phase Φ 2 , with the role of the feedback capacitor being switched in accordance with the digital output data from comparator  120 . Thus, as shown in FIG. 7, capacitors C 1  and C 2  charge to an input voltage during sampling phase Φ 1 . Then, during amplifying phase Φ 2 , one of capacitors C 1  and C 2  is placed in the feedback loop for amplifier  101 , and the other is fed a bias voltage. The selection of which capacitor is in the feedback loop and which is fed a bias voltage depends on the digital output of comparator  120 . Thus, if the digital output indicates operation in center section corresponding to digital output  01 , then capacitor C 1  is in the feedback loop to amplifier  101 , whereas capacitor C 2  is fed a bias voltage. Conversely, if the digital output from comparator  120  signifies operation in the outermost regions corresponding to digital output 00 or 10, then capacitor C 2  is in the feedback loop and capacitor C 1  is fed the bias voltage. 
     The bias voltage fed to the selected capacitor depends on the digital output from comparator  120 . As illustrated in FIG. 7, if the digital output signifies operation in left-most region corresponding to digital output 00, then the selected capacitor is biased by a voltage corresponding to Vrefn. If the digital output signifies operation in center-most region corresponding to digital output 01, then the selected capacitor is biased by a voltage of zero. If the digital output signifies operation in right-most region corresponding to digital output 10, then the selected capacitor is biased by a voltage corresponding to Vrefp. 
     The output of MDAC  100  is provided to comparator  120  which consists of two comparators COMP 1  and COMP 2 . Thresholds for the comparators are set at thresholds stretched relatively to conventional bit-and-one-half converters. As shown in FIG. 7, the threshold for comparator COMP 1  is set at one-quarter from the lower-most range Vrefp and Vrefn, whereas the threshold for comparator COMP 2  is set at one-quarter from the uppermost range of Vrefn and Vrefp. Thus, operation in the central section corresponds to one-half of the overall range from Vrefp to Vrefn, thereby resulting in thresholds stretched relative to the thresholds of conventional bit-and-one-half converters. 
     Although FIG. 7 illustrates thresholds set by virtue of a resistive ladder, other techniques for setting thresholds may be utilized. In particular, thresholds may be set buy globally-generated thresholds for use by all stages of the multi-stage ADC, and thresholds may also be set by voltage generation circuitry specifically tailored to produce desired thresholds. 
     The amount of shift depends on the anticipated capacitive mismatch between capacitors C 1  and C 2 , and further depends on the desired amount of reduction in differential non-linearity. FIG. 8 shows differential non-linearity as a function of comparator offset, and compares differential non-linearity for various shifts with that for conventional circuitry. A first line  141  shows differential non-linearity that results when commutative feedback-capacitor switching is not used, and line  142  shows differential non-linearity when commutative feedback-capacitor switching is utilized, both for capacitive mismatches of 1.2%. As shown at line  143 , additional reduction in differential non-linearity can be obtained in accordance with the invention by stretching thresholds outwardly from their nominal value (i.e., +/−¼ of the comparator range centered symmetrically around zero) by about +/−0.125. An additional decrease in differential non-linearity can be obtained by further stretching of threshold by about +/−0.175. As shown in the graph of  144 , however, a point of diminishing returns occurs since other errors begin to affect operation and can affect operation catastrophically. The inventor herein has found that with an anticipated capacitive mismatch of 1%, good reduction in differential non-linearity can be obtained when both thresholds are stretched outwardly from their nominal values (which are +/−¼ of the comparator range centered symmetrically around zero) by an amount equal to 0.125 of the normalized range. 
     The invention has been described with respect to particular illustrative embodiments. It is to be understood that the invention is not limited to the above-described embodiments and that various changes and modifications may be made by those of ordinary skill in the art without departing from the spirit and scope of the invention.