Abstract:
Circuits and methods for converting a signal from analog to digital. A random number generator provides a random number to a memory. The memory is preconfigured to include codes of predetermined digital to analog (DAC) configurations that provide the maximum amount of DAC gradient suppression. At least one Flash reference generation DAC (FRGD) has an input coupled to the memory unit and an output providing a reference voltage level for its respective Flash comparator. The Flash comparators compare the analog input signal to their respective reference voltage and provide a digital output signal based on the comparison.

Description:
PRIORITY INFORMATION 
     The present application claims priority of provisional patent application No. 61/556,440 filed Nov. 7, 2011, the contents of which are incorporated herein in their entirety. 
     TECHNICAL FIELD 
     The disclosure generally relates to improving signal precision in view of component mismatches inherent in electronic circuitry. More particularly, the disclosure relates to systems and methods for normalizing the effects of component mismatches by randomizing interconnections among circuit components in DACs, thereby improving ADC linearity. 
     DESCRIPTION OF RELATED ART  
     Although real world signals are analog, it is often desirable to convert them to the digital domain using analog-to-digital converters (ADCs). Circuit designers are motivated to perform this conversion because of the efficient methods currently available for the transmission, storage and manipulation of digital signals. A digital representation of an audio signal, for example, allows a CD player to achieve virtually error free storage using optical discs. The need for complicated signal processing may also necessitate analog-to-digital conversion because such signal processing may only be feasible in the digital domain using either digital computers or special purpose digital signal processors. 
     One popular type of ADC includes the Flash or parallel ADC. This type of converter uses a linear voltage ladder with a comparator at each hierarchy of the ladder to compare the input voltage to successive reference voltages. Each comparator represents one LSB (least significant bit) of the ADCs digital output. If the input voltage common to all comparators is larger that the reference voltage for a given comparator, then the output of the comparator is true and all comparators connected to lower reference voltages are also true. The total number of comparators with true outputs represents the digital value of the analog input. These reference ladders may be constructed of a plurality of resistors. Other implementations may use capacitive voltage division. 
     High resolution Flash ADCs are not practical because of the need for 2 N −1 comparators, where N is the resolution (i.e., number of bits) in the ADC. Sub-ranging and pipeline ADCs use two or more Flash ADCs to convert the analog signal in subsequent steps. This method may require substantially fewer comparators in comparison to a Flash ADC. However, this method may require additional precision hardware, which results in additional cost and circuit complexity. 
     For example, in a two-step, sub-ranging, N-bit ADC, the analog input signal is first digitized by a first K-bit Flash ADC, where K is the resolution (i.e., number of bits) in the first Flash ADC. The digital output of the first Flash ADC is then input to a K-bit DAC (reference DAC). The output of the DAC is then subtracted from the original analog input, resulting in a residue voltage. The residue voltage is the difference between the original analog input voltage and the estimate of the first K bit Flash ADC. The residue, which is a small portion of the original analog input, is then amplified and applied to the input of the second Flash ADC of (N−K) bits. The results of the two Flash ADCs are combined to yield the full N bit representation of the original analog input. 
     In the two-step, sub-ranging N-bit ADC example above, the linearity of the first K-bit Flash ADC generally has to be as accurate as the over-all N-bit ADC. Additionally, the offset of the residue amplifier generally has to have an offset that is substantially less than 1 LSB of the over-all ADC. Both of these requirements can be relaxed if the second Flash ADC has additional voltage range such that it can accommodate the expected errors. This additional range is often referred to as error correction range. For example if the residue amplifier is expected to have a maximum output offset of +/−200 mV (e.g., due to process variation) then the second Flash ADC typically has an additional 200 mV of range at the top and bottom of it&#39;s input voltage range. 
     In pipeline and sub-ranging analog to digital converters the linearity depends on the linearity of the reference DAC and the gain and linearity of the residue amplifier. The linearity of a DAC largely depends of the matching of the elements (e.g., switches and capacitors) within the DAC. For example, a 3-bit DAC may include 7 identical unit capacitors. Each capacitor has two terminals, a top plate and a bottom plate. All top plates are connected together and form the DAC output. Each bottom plate is connected to a switch that can switch between ground and a reference voltage. The digital input to the DAC controls the bottom plate switches. In this example, the linearity of the DAC depends on how closely each capacitor matches the other capacitors. Additionally, in sub-ranging ADCs the gain and linearity of the residue amplifier may also impact the linearity of the over-all ADC. Trimming and auto calibration can be used to improve matching, but these methods may not be enough to completely remove adverse effects of component mismatch. 
     Another approach that has been used to reduce linearity errors caused by mismatch errors is to shuffle the reference DAC elements (sometimes referred to as dynamic element matching (DEM)). For example, the electrical connection path between each Flash comparator and each reference DAC element is randomized. Accordingly, for a given ADC input voltage the number of DAC elements that are turned on in the reference DAC is always the same—but it is a randomly selected group of elements. By randomly selecting a given number of elements (or shuffling), mismatch errors appear as white noise instead of linearity errors. One drawback with component shuffling is that it requires additional hardware. This additional hardware typically results in slower operation as compared to non-shuffled circuitry. 
       FIG. 1  illustrates a pipeline stage with DAC element shuffling. In circuit  100  each digital output of the Flash ADC comparators  102  are coupled to a switch matrix  104 . The outputs of the switch matrix  104  can be coupled to any one of the reference DAC capacitor elements  108 . The time delay through the switch matrix  104  can be significant and thus contributes to slower system operation. 
     Circuit  100  of  FIG. 1  shuffles DAC elements by shuffling the connection between the Flash comparator  102  output lines and the reference DAC switches  106 . A similar result could be achieved by shuffling the connection between the Flash reference ladder  102  and the Flash comparator  110  reference inputs, as illustrated in  FIG. 2 . 
     In circuit  200  of  FIG. 2 , the reference voltages for the Flash are generated with a resistor ladder  202 . A switch matrix  104  coupled between the reference resistor ladder  202  and the Flash comparators  110 , allows any reference voltage to be provided to any Flash comparator  110 . That is because the outputs of the switch matrix  104  can be coupled to any one of the Flash comparators  110 . Although circuit  200  relieves the speed issue for the DAC, it introduces another complex switching matrix for the Flash converter. Accordingly, circuit  200  also results in slower operation. 
     There are numerous topologies for switch matrices but each has drawbacks. Topologies that provide simplified control typically suffer from high connection path resistance. Topologies that reduce connection path resistance generally require a high number of control lines. These drawbacks become more severe as the number of inputs and outputs increase. Indeed, it is often desirable for the first Flash converter in a sub-ranging ADC to have 4 or more bits of resolution, thereby requiring a switch matrix with at least 15 inputs and 15 outputs. For such a matrix, a simplified control topology may have 4 series switches with high capacitance intermediate nodes. The low resistance path topology requires 225 control lines and has high parasitic capacitance on both the input and output nodes. 
     In addition to speed problems, the shuffle methods proposed to date only address element match problems in the reference DAC. In this regard, other element match problems, such as residue amplifier gain error, which cause linearity errors of the same magnitude as the reference DAC matching, are not addressed. 
     Accordingly, in view of the foregoing, it would be desirable to provide systems and methods that overcome these and other drawbacks of the prior art. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects and advantages of the present invention will be apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout, and in which: 
         FIG. 1  illustrates a pipeline stage with DAC element shuffling with the switch matrix coupled between the Flash and the reference DAC. 
         FIG. 2  illustrates a pipeline stage with the switch matrix coupled between the resistive ladder and the Flash comparators. 
         FIG. 3  is a schematic diagram of a DAC in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Illustrative embodiments are now described. Other embodiments may be used in addition or instead. Details that may be apparent or unnecessary may be omitted to save space or for a more effective presentation. Some embodiments may be practiced with additional components or steps and/or without all of the components or steps that are described. 
       FIG. 3  shows a schematic diagram of one stage of a pipeline analog to digital converter (ADC) in accordance with an exemplary embodiment of the present invention. As illustrated, circuit  300  includes a pseudo random number generator  302 , a digital address circuit  304 , a dither DAC  306 , a memory unit (e.g., ROM)  308 , Flash reference generation DACs (FRGDs)  310 , resistors  314 , common resistor for dither  312 , Flash comparators  110 , a reference DAC  108 , and DAC switches  106 . 
     The pseudo random number generator  302  generates a sequence of numbers that approximates the properties of random numbers. These random numbers are provided to digital address unit  304 . The digital address unit  304  takes the random number and converts it to a memory address. For example, instead of providing the digital address based on the pseudo random number generator directly to the FLASH reference generation DACs (FRGD)  310 , the random addresses are provided to a memory (e.g., ROM)  308 . 
     To understand the benefit in using a memory in connection with FRGDs, it is instructive to discuss some contributors of DAC linearity errors and the resultant effect on ADC distortion errors. For example, in a capacitive DAC (CDAC) each capacitor element may have different capacitance due to process variation. These variations include random individual unit variations and systematic errors (or gradient errors). Gradient errors typically vary linearly or quadradically across the DAC element array, resulting in a gradient of DAC element values. Gradient errors are often larger in magnitude than random errors and thus may be more problematic. Additionally, because gradient errors are systematic, they may result in systematic DAC errors. As to random errors, they typically result in DAC errors that appear more random and are more noise like in nature. For example, if a DAC is used to generate a single tone sine wave, gradient type errors result in large error tones that may include second or third order harmonic distortion. 
     In one embodiment, the digital addresses produced by the pseudo random number generator  302  select an ordered set of codes stored in the ROM  308 . These ordered sets of codes are then provided as inputs to the Flash reference generation DACs (FRGD)  310 . The Flash reference generation DACs  310  provide a threshold voltage for each of the Flash comparators  110  in the Flash ADC. As a result, for a fixed input voltage (VIN) to the pipeline stage ADC  300  each ordered set of codes selected from the memory unit selects a different combination of the Reference DAC elements  108 , while the total number of Reference DAC elements  108  switched to Vref or ground remains constant. 
     Some combinations of Reference DAC elements suppress systematic DAC errors due to gradient type errors better than others. In one embodiment, random combinations of ordered sets are tested for their ability to suppress typical process gradient errors through computer modeling. Over a course of many tests, (which may take months,) the best combinations (i.e., combinations that suppress gradient type errors) may be determined and programmed into the memory  308 . For example, the ROM  308  may be programmed with 32 ordered sets of codes. These 32 ordered sets of codes may be the ordered sets of codes that result in the maximum amount of gradient error suppression (e.g., as determined by prior tests). 
     The integrity of an ADC may be tested by applying a pure sinusoidal input signal and then collecting a large number of digital output samples. In one example, the collection of samples are processed with a Fast Fourier Transform (FFT) to provide frequency domain results. Ideally, when the ADC has no errors, the resultant FFT should show only one tone, namely the original input signal. However, if the ADC has errors, other spurious tones will be present. For a sub-ranging ADC, typical DAC element gradient errors in the reference DAC have 2 nd  and 3 rd  order distortion tones. 
     By randomizing the selection of DAC element combinations used at each sample, the impact of distortion is decreased. In this regard, the randomization spreads the errors in the spectrum to appear as random noise. For example, by using DEM, the random sequence causes the DAC element gradient errors to appear as white noise rather than spurious tones. Without randomization, DAC element gradient errors result in spurious tones in an FFT spectrum. Through randomization, the detrimental energy is spread over the entire spectrum, resulting in a slightly elevated noise floor, which is generally preferred. Accordingly, DEM increases DAC linearity at the expense of slightly increasing the noise floor. In many applications, the tradeoff between better linearity at the expense of a slightly elevated noise floor is favorable. 
     In the example of  FIG. 3 , a 3-bit Flash ADC  310  drives a 3-bit Reference DAC  108 . Current output reference generation DAC (FRGD)  310  generates the Flash ADC reference voltages across output resistors  314  for each of the Flash comparators  110 . For example, a finite number of ordered sets of words for the FRGDs are stored in ROM  308 . The ROM is addressed by a pseudo random number generator  302 . Using a pseudo random number generator  302  helps ensure that no tones are produced in the ADC output while cycling through a finite number of FRGD words. 
     In one aspect, performance of the ADC is further improved by using dither. In one embodiment, the pseudo random number generator  302  (via the digital address unit  304 ) also drives a current output dither DAC  306 . The dither DAC  306  output current I OUTD  is fed into a resistor  312  that is common to all FRGD output resistors  314 , thereby providing a dither signal to all comparators in the Flash ADC. A dither signal is a small amount of random noise (or pseudo random noise) that, when added to a periodic deterministic input, causes the quantization error of an ADC to behave like white noise. As mentioned earlier, DEM only randomizes the errors associated with the DAC elements. In one embodiment, errors associated with the residue amplifier or the second ADC (not shown) are not improved. For example, these other errors (e.g., errors from the residue amplifier or the second ADC) are due to the second or later step of the sub-ranging ADC. The error due to the second step is cyclic with respect to the input voltage and has 2 N  cycles, where N is the number of bits in the first Flash ADC. By adding a dither signal to the first Flash ADC input the effective threshold of the comparators in the first Flash ADC is randomized. As result, the cyclical errors due to the second and later ADC steps are also randomized. This results in improved linearity at the expense of slightly elevated noise. In this regard, dither is similar in effect to the pseudo random number generator  302  in that it trades off distortion with a slightly elevated noise floor. However, dithering can be configured to operate at a finer scale. 
     In one embodiment, the Flash reference generation output DACs  310  (that may be low resolution current DACs) are driven into a respective resistor  314  to generate the reference voltages for each of the comparators  110 . In one embodiment, each resistor  314  is directly connected to it&#39;s associated Flash comparator  110 , thereby eliminating the parasitic resistance and capacitance associated with a switch matrix. Accordingly, the speed problem associated with the switch matrix of the prior art circuits is eliminated. Additionally, in one embodiment, another current output DAC  306  may be driven into a resistor  312  common to all reference generation DACs to provide a dither signal. This dither signal randomizes errors not associated with the reference DAC  108 . 
     For example, a dither signal added to a Flash ADC input can be described as adding noise or offset to the ADC. As long as the error correction range of the second and later stages have enough error correction range to accommodate the added signal, the introduced dither signal does not significantly change the ADC result. In one embodiment, the dither amplitude is equal to the LSB size of the first Flash ADC. For such dither amplitude an additional correction range (e.g., equal to the nominal input range of the second step ADC) may be used. Additional correction range of this magnitude is difficult to implement due to the limited available voltage range in fine line processes. In one embodiment, the large error correction range is avoided by subtracting the dither voltage injected to the first pipeline Flash from the reference DAC  108 . Put differently, the small amount of white noise added through dithering is subtracted at the output of the DAC  108 . 
     Accordingly, circuit  300  provides reference DAC  108  shuffling and dithering that randomizes linearity errors due to component mismatch. The residual reference DAC  108  errors, as well as other ADC  300  errors, are substantially reduced. 
     Although preferred embodiments of the present invention have been disclosed with various circuits connected to other circuits, persons skilled in the art will appreciate that it may not be necessary for such connections to be direct and additional circuits may be interconnected between the shown connected circuits without departing from the spirit of the invention as shown. Moreover, although the invention has been illustrated herein in the context of analog-to-digital and digital-to-analog converters, it will be understood that it is applicable to any circuit in which determining component ratios or component measurement is desired. 
     Furthermore, although the invention has been illustrated using capacitors, it will be understood that other types of components such as inductors and resistors may be used if desired. Further still, although the embodiments herein have been described in the context of voltage signals, it will be understood that it is contemplated that in other embodiments these voltages signals may be replaced with current signals, charge signals, or other electrical energy signals (with the appropriate components) without departing from the spirit and scope of the present invention. Persons skilled in the art also will appreciate that the present invention can be practiced by other than the specifically described embodiments.