Abstract:
A system and method are disclosed for correcting for output distortion of an analog to digital converter, comprising: estimating the output distortion, providing an estimated distortion, and combining an output of the analog to digital converter with the estimated distortion to compensate for the output distortion. The compensating module for correcting output distortion of an analog to digital converter comprises a calibration module configured to estimate the output distortion and a combiner configured to combine an output of the analog to digital converter with the estimated distortion to compensate the output distortion.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of Ser. No. 11/031,609 filed Jan. 05, 2005, now U.S. Pat. No. 7,002,495, which is a continuation of U.S. patent application Ser. No. 10/641,332 now U.S. Pat. No. 6,885,323 entitled ANALOG TO DIGITAL CONVERTER filed Aug. 14, 2003 which is incorporated herein by reference for all purposes, which claims priority to U.S. Provisional Patent Application No. 60/483,493 entitled ANALOG-TO-DIGITAL CONVERTER filed Jun. 27, 2003, and claims priority to U.S. Provisional Patent Application No. 60/486,053 entitled ANALOG-TO-DIGITAL CONVERTER filed Jul. 10, 2003, which are incorporated herein by reference for all purposes. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to analog to digital converters (ADCs). More specifically, distortion correcting analog to digital converters (DCADCs) and methods for correcting distortion are disclosed. 
     BACKGROUND OF THE INVENTION 
     An analog to digital converter (ADC) is a device used to map continuous time signals to sampled time digital values. It is widely used in electronic systems. 
     An ideal ADC does not have any errors in its output. A sinusoidal input signal sampled by an ideal ADC does not have any harmonics in the frequency domain. In practice, however, ADCs are not ideal. Mismatches and nonlinearity of ADC elements introduces errors that distort the output of the ADC. The sampled sinusoidal signal has harmonics in the frequency domain, and the signal fidelity is degraded. 
     The quality of ADCs may be improved by trimming the ADCs to achieve desired transfer characteristics.  FIG. 1  is a block diagram illustrating a system used to improve the quality of ADCs. A digitized sinusoidal reference signal is sent to a 16-bit digital to analog converter (DAC)  102 . The DAC has good transfer characteristics and low noise. Its output is sent to a 16-bit ADC  104  that is under test. The ADC samples the output of the DAC, and sends its output to a filter  106  that performs a Fast Fourier Transform (FFT). If the output of the FFT is determined to have significant harmonic distortion, certain components of the ADC are trimmed. The trimming process usually changes the resistance or capacitance of the ADC, which may in turn reduce the harmonic distortion of the ADC. 
     There are several issues associated with the trimming technique. It takes time to test and trim the ADC, which increases the production cost. The design of trimming circuits also increases the complexity of the ADC. Furthermore, trimming the circuitry to adjust the transfer characteristics of the ADC for one frequency may adversely affect the transfer characteristics of the ADC for other frequencies. It would be desirable to have a technique that could correct the distortions in the ADC, without increasing the complexity of the circuitry or the production cost. It would also be useful if the technique could correct the distortions over the operating spectrum of the ADC. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention will be readily understood by the following detailed description in conjunction with the accompanying drawings, wherein like reference numerals designate like structural elements, and in which: 
         FIG. 1  is a block diagram illustrating a system used to improve the quality of ADCs. 
         FIG. 2A  is a block diagram illustrating the operations of an analog to digital converter according to one embodiment. 
         FIG. 2B  is a diagram illustrating a distortion correcting analog to digital converter according to one embodiment of the present invention. 
         FIG. 3  is a block diagram illustrating an analog to digital converter model with distortion, according to one embodiment of the present invention. 
         FIG. 4A  is a block diagram illustrating a DCADC in training mode, according to one embodiment of the present invention. 
         FIG. 4B  is a block diagram illustrating the steady state operation of the ADC embodiment show in  FIG. 4A . 
         FIG. 5  is a block diagram illustrating a DCADC embodiment trained using a noise signal source. 
         FIG. 6  is a block diagram illustrating another distortion correcting analog to digital converter embodiment trained using a low noise digital to analog converter. 
         FIG. 7  is a block diagram illustrating another distortion correcting analog to digital converter embodiment trained using a noisy digital to analog converter. 
         FIG. 8  is a block diagram illustrating the steady state configuration of a distortion correcting analog to digital converter, according to one embodiment of the present invention. 
         FIG. 9A  is a block diagram illustrating the details of a digital signal processor used in a distortion correcting analog to digital converter, according to one embodiment of the present invention. 
         FIG. 9B  illustrates the details of linear filter  900  shown in  FIG. 9A . 
         FIG. 10  is a block diagram illustrating a multi-stage distortion correcting analog to digital receiver, according to an embodiment of the present invention. 
         FIG. 11  is a block diagram illustrating a receiver circuit that includes a distortion correcting analog to digital converter, according to one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The invention can be implemented in numerous ways, including as a process, an apparatus, a system, a composition of matter, a computer readable medium such as a computer readable storage medium or a computer network wherein program instructions are sent over optical or electronic communication links. In this specification, these implementations, or any other form that the invention may take, are referred to as techniques. In general, the order of the steps of disclosed processes may be altered within the scope of the invention. 
     A detailed description of one or more embodiments of the invention is provided below along with accompanying figures that illustrate the principles of the invention. The invention is described in connection with such embodiments, but the invention is not limited to any embodiment. The scope of the invention is limited only by the claims and the invention encompasses numerous alternatives, modifications and equivalents. Numerous specific details are set forth in the following description in order to provide a thorough understanding of the invention. These details are provided for the purpose of example and invention may be practiced according to the claims without some or all of these specific details. For the purpose of clarity, technical material that is known in the technical fields related to the invention has not been described in detail so that the invention is not unnecessarily obscured. 
     An improved technique for correcting distortion in the output of an analog to digital converter is disclosed. In some embodiments, a distortion correcting analog to digital converter (DCADC) employs a calibration module that is trained to compensate the distortion in the output of a conventional ADC. In some embodiments, the calibration module models the interference effects of the most significant bits (MSBs) on the least significant bits (LSBs). The calibration module may be trained using a random noise generator, a custom digital to analog converter (DAC) or a noisy DAC. In some embodiments, the calibration module includes a nonlinear digital signal processor (DSP) that is comprised of linear filters and nonlinear elements. The DCADC may include several ADC stages and several calibration modules. The DCADC can be used to correct distortions in the overall circuit in some embodiments. The techniques described are applicable to various types of ADC architectures, including pipelining, folding, and sigma delta. 
       FIG. 2A  is a block diagram illustrating the operations of an analog to digital converter according to one embodiment. ADC  200  has N bits of outputs, where N is an integer. Each quantized output bit of the ADC is denoted as m j , where j∈{0,1, . . . ,N−1} and m j ∈{0,1}. The input to ADC  200  is analog signal  204 , which can be represented as the following:
   x=m   N−1 2 N−1   +m   N−2 2 N−2    . . . +m   1 2 1   +m   0 2 0   +u   (Equation 1), 
where u is the value of the signal that is below the finest ADC quantization level. The output of an ideal ADC can be expressed as:
   y   i   =m   N−1 2 N−1   +m   N−2 2 N−2    . . . +m   1 2 1   +m   0 2 0   (Equation 2). 
     In practice, the ADC output has some distortion. Its output may be viewed as a combination of two components: an ideal output component  206  and a distortion component  208 . The two components are combined to give the actual output  210 . As used herein, combining refers to subtraction, summation, or any other appropriate operation performed on two or more signals. 
       FIG. 2B  is a diagram illustrating a distortion correcting analog to digital converter according to one embodiment of the present invention. The DCADC includes an ADC  250  that includes a digitizing circuit that converts an analog signal to digital, and a calibration module  254 . The components of the DCADC may be implemented as a single integrated circuit, separate discrete components or any other appropriate scheme. The output of ADC  250  includes and ideal output component  260  and a distorted output component  262 . A calibration module  254  is used to generate a signal that models the distorted output component. Combiner  266  subtracts the output of the calibration module from the output of the ADC, outputting signal  268  that is approximately the ideal output. 
     The distorted output component can be modeled as the following:
 
 y=m   N−1   k   N−1 2 N−1   +m   N−2   k   N−2 2 N−2    . . . +m   1   k   1 2 1   +m   0   k   0 2 0   (Equation 3),
 
where k j  is a constant that is equal to 1 ideally, but may deviate from 1 by some quantization offset when distortion is present. For example, if k N−1 =1.001 and if m N−1 =1, then the contribution of the term m N−1 k N−1 2 N−1  to the quantization is 2 N−1 +0.001·2 N−1 , where 2 N−1  is the desired output bit and 0.001·2 N−1  is the distortion; if m N−1 =0, then the term does not contribute to the distortion error. Similar analysis is applicable to any m j .
 
     Other equations may also be used to model more complex forms of distortion. In some embodiments, the output also includes a component u representing distortion that is a function of cross terms of the bits, such as the following:
 
 u=m   N−1   q   N−1   m   N−2   q   N−2 2 N−2   +m   N−2   q   N−2   m   N−3   q   N−3 2 N−3   (Equation 4).
 
     For the same quantization error offsets in the most-significant bits (MSBs) and least-significant bits (LSBs), higher order bits make a greater contribution to the distortion than the lower order bits. Returning to Equation 3, in an ADC where N=8, k 1  and k N−1  are both 0.001, the corresponding contributions to distortion are 0.001·2 1  for bit  1  and 0.001·2 7  for bit  7 . Thus, in practice, most of the ADCs output distortion comes from the quantization offsets of its higher order bits. Furthermore, the contributions of the higher order bits are geometrically more significant than the contributions of the lower order bits. Thus, DCADCs can achieve good performance without having to correct the errors associated with the lower order bits. 
       FIG. 3  is a block diagram illustrating an analog to digital converter model with distortion, according to one embodiment of the present invention. Signal  300  is the analog input to an N-bit ADC, denoted as X n . The ideal output of the ADC is divided into two components, signals  302  and  304 . Component  302  includes k of the most significant bits. Component  304  includes (N−k) of the least significant bits. Combiner  305  combines signals  302  and  304 , outputting an ideal ADC signal  306 . To approximate the effects of distortion, only the most significant bits are operated on by distortion model  312 . The output of the distortion model, signal  308 , is the distortion component. Ideal output  306  and distortion component  308  are combined to produce the actual output, signal  310 . 
     The actual output of an ADC can be expressed as the following in some embodiments:
 
 w=m   N−1 2 N−1   +m   N−2 2 N−2    . . . +m   1 2 1   +m   0 2 0   +f ( m   N−1   ,m   N−2   ,m   N−3   ,m   N−4 )  (Equation 5),
 
where f(m N−1 , m N−2 ,m N−3 ,m N−4 ) is the transfer function of the distortion model. In some embodiments, it is a nonlinear function of the higher order bits. Note that the distortion resulting from the lower order bits is neglected and that the number of higher order bits selected for the nonlinear function depends on implementation and may vary for other embodiments. Alternatively, w may be expressed as:
 
 w=y+f ( m   j )  (Equation 6),
 
where y is the ideal ADC output and f(m j ) is a nonlinear function of the output bits. The quantization error, ε, can be expressed as a difference between the actual output and the input:
 
ε= w−x=f ( m   N−1   ,m   N−2   ,m   N−3   ,m   N−4 )− u   (Equation 7).
 
     In some embodiments, the DCADC includes a calibration module trained to model the nonlinear distortion component f(m N−1 ,m N−2 ,m N−3 ,m N−4 ) of the ADC. The output of the ADC can be corrected by subtracting the nonlinear distortion component from its actual output.  FIG. 4A  is a block diagram illustrating a DCADC in training mode, according to one embodiment of the present invention. In this embodiment, the calibration module includes a digital signal processor (DSP)  422 . Signal  400  is an analog input signal to ADC  420 . The output of the ADC includes an ideal output signal  404  and a distortion component  406 . Signals  404  and  406  are combined to form the ADCs actual output  408 . Signal  408  is sent to DSP  422  that outputs an estimated distortion signal  414 . DSP  422  adapts to improve its estimated distortion by minimizing the difference between the estimated distortion and the output distortion. 
     Signal  402  is an ideal digitized version of signal  400  used to train the calibration module. Signal  402  is virtually free from distortion. It is subtracted from signal  408 , to form a distortion signal  412 . The difference between the distortion signal and the simulated distortion signal, signal  418 , is the error adaptation signal. Signal  418  is fed back to the DSP so that the DSP may adapt itself to minimize the error adaptation signal and better model the distortion. Details of the DSP and its adaptation techniques will be discussed later. 
       FIG. 4B  is a block diagram illustrating the steady state operation of the ADC embodiment shown in  FIG. 4A . In steady state, the adaptation path of the DSP is disconnected. The DSP uses the configuration it obtained during the training process to model the distortion and output a distortion signal  460 . The distortion signal is subtracted from the output of the ADC, signal  456 . The resulting signal  458  is error-corrected and has substantially less distortion than signal  456 . 
     In practice, however, an ideal training signal may not be available. Several approaches that do not require an ideal training signal are discussed. These approaches take advantage of the principle that uncorrelated analog input signal leads to uncorrelated quantized output bits for an ideal ADC. The following example illustrates the principle. 
     Assuming that the overall distortion is relatively small, the amount of distortion may be represented in terms of the LSBs. Let the nonlinear distortion be the following:
 
 f ( m   N−1   ,m   N−2   ,m   N−3   ,m   N−4 )= m   N−1 2 1   +m   N−2 2 0   (Equation 8).
 
The actual output of the DSP can be expressed as the following:
 
 w=m   N−1 2 N−1   +m   N−2 2 N−2  . . . +( m   1   +m   N−1 )2 1 +( m   0   +m   N−2 )2 0   (Equation 9).
 
Bits N−1 and  1  are correlated since they both have a common component m N−1 ; bits N−2 and  0  are also correlated since they both have a common component m N−2 . In this example, the calibration module is trained to output a simulated distortion signal (m N−1 ) 2   1 +(m N−2 ) 2   0  that is subtracted from w. The resulting signal is a corrected output that is approximately equal to the ideal ADC output.
 
     To properly train the calibration module, the training input signal of the ADC is preferably random, uniformly distributed and uncorrelated.  FIG. 5  is a block diagram illustrating a DCADC embodiment trained using a noise signal source. Uniform noise signal source  500  provides an analog signal  516  that is random and uncorrelated. The uniform noise signal source may be implemented using a thermal noise source or any other appropriate elements. Signal  516  is sent to ADC  502 . If ADC  502  were ideal, its output would be random uncorrelated bits. In practice, however, the ADC is not ideal and its output bits are not completely uncorrelated. In this embodiment, the output of ADC  502 , w, is the same as the w shown in Equation 8. Output signal  506  of the ADC includes two MSBs, and can be expressed as the following:
 
 y   MSB   =m   N−1 2 N−1   +m   N−2 2 N−2   (Equation 10).
 
Output signal  510  of the ADC includes two LSBs as well as the distortion components associated with the MSBs. It can be expressed as:
 
 y   LSBE =( m   1 2 1   +m   0 2 0 ) +( m   N−1 2 1   +m   N−2 2 0 )  (Equation 11).
 
     DSP  504  models the distortion of the ADC associated with the MSBs. Its output signal  508  is subtracted from signal  510 . The resulting adaptation signal  512  is approximately the LSBs without the distortion. In other words, the bits in signal  512  are approximately random; any correlation in the signal is mainly due to the difference between the DSP&#39;s model and the actual distortion function. Signal  512  is fed back to the DSP for adapting its operations to filter out any interference between the MSBs and the LSBs. In some embodiments where the correlation is nonlinear, the DSP is a nonlinear filter. Details of a nonlinear DSP will be discussed in  FIGS. 9A and 9B . 
       FIG. 6  is a block diagram illustrating another distortion correcting analog to digital converter embodiment trained using a low noise digital to analog converter. ADC  602  has N bits of linearity. DAC  600  is a low noise K-bit DAC, where K is preferably less than N. DAC  600  preferably has better than N bits of linearity. The DAC provides an input signal  614  to the ADC. In this embodiment, the output of ADC  602 , w, is the same as what was shown in Equation 8. Output signal  606  of the ADC includes two MSBs, and can be expressed as Equation 9. 
     Since DAC  600  has fewer bits than ADC  602 , the LSBs of the ADC would be zero if the ADC were ideal. When distortion is present, the LSBs include components from the MSBs. Output signal  610  of the ADC can be expressed as the following:
 
 y   LSBE   =m   N−1 2 1   +m   N−2 2 0   (Equation 12).
 
     DSP  604  converges to provide an output  608  that cancels signal  610 . The resulting adaptation signal  612  is fed back to the DSP for adjusting its output to more closely match signal  610 . Using a low noise DAC to provide training signals allows the DSP to more quickly converge. 
       FIG. 7  is a block diagram illustrating another distortion correcting analog to digital converter embodiment trained using a noisy digital to analog converter. The circuitry is similar to that of  FIG. 6 , although DAC  700  may be a non-ideal, noisy K-bit DAC, where K is preferably less than N. Different types of non-ideal DACs may be used, for example, a dynamic element matching (DEM) DAC. Output signal  706  of ADC  702  includes two MSBs, and can be expressed as Equation 9. Output signal  710  of the ADC includes MSB components and noise. It can be expressed as:
   y   LSBE   =m   N−1 2 1   +m   N−2 2 0   +u   (Equation 13). 
     DSP  704  converges to provide an output  708  that cancels signal  710 . The resulting adaptation signal  712  is fed back to the DSP for adjusting its output to more closely match signal  710 . A DSP trained with a noisy DAC converges more slowly than a DSP trained with a low noise DAC, but tends to be more cost effective since noisy DACs are generally cheaper than low noise DACs. 
     It should be noted that the training signals used in  FIGS. 5-7  usually cover the full frequency spectrum of the ADC, thereby achieving distortion correction for the operating frequencies of the ADC. 
       FIG. 8  is a block diagram illustrating the steady state configuration of a distortion correcting analog to digital converter, according to one embodiment of the present invention. The DCADC ends its training period and enters steady state operation once its calibration module has converged. During steady state operation, the adaptation feedback path of the DSP is disconnected. Analog input signal  800  is sent to an ADC  802  to be converted to digital. Output signal  806  of the ADC includes the MSBs, and output signal  810  of the ADC includes the LSBs with distortion. Signal  806  is sent to DSP  804 , which utilizes the coefficients it acquired during the training period to duplicate the distortion and generate an output signal  808 . Signal  808  is subtracted from signal  810 , resulting in signal  812  that is approximately the ideal lower order output bits of the ADC. This configuration is applicable generally to the steady state operation of DCADCs, including the ones shown in  FIGS. 5-7 . 
     The distortion of the ADC is often nonlinear. Compensating for nonlinear effects of the ADC is a difficult task using traditional techniques. In U.S. patent application Ser. No. 10/372,638 by Batruni, filed Feb. 21, 2003 entitled: “NONLINEAR FILTER” which is herein incorporated by reference for all purposes and U.S. patent application Ser. No. 10/418,944 by Batruni filed Apr. 18, 2003 entitled: “NONLINEAR INVERSION” which is herein incorporated by reference for a 1  purposes, Batruni described improved techniques for building nonlinear filters using linear elements, and for adapting such nonlinear filters to achieve desired transfer characteristics. These techniques greatly reduce the complexity associated with the compensation of nonlinear effects, and may be applied to the design and configuration of the DCADCs.  FIGS. 9A-9B  illustrate some of the techniques. 
       FIG. 9A  is a block diagram illustrating the details of a digital signal processor used in a distortion correcting analog to digital converter, according to one embodiment of the present invention. An input vector X is sent to a bank of linear feed forward filters ( 900 ,  902 ,  904  and  906 ). The filter outputs are combined with several coefficients (b 0 , β 1 , β 2  and β 3 ) and then processed by a bank of nonlinear processors. In this embodiment, the nonlinear processors are implemented as absolute value operators ( 908 ,  910  and  912 ). The results from the absolute value operations are multiplied with coefficients C 1 , C 2  and C 3 , and combined to form an output signal  914 . The transfer characteristics of the DSP can be expressed as the following:
   Y=ax+b+c   1 |α 1   x+β   1   |+c   2 |α 2   x+β   2   |+c   2 |α 2   x+β   2   |+c   3 |α 3   x+β   3 |  (Equation 14). 
     During training, the DSP adapts its transfer function by adjusting its coefficients, using techniques such as the least mean squared (LMS) algorithm and the back-propagation property of derivatives to better model the distortion component of signal  916 . 
       FIG. 9B  illustrates the details of linear filter  900  shown in  FIG. 9A . The input vector X is scaled by a factor a 0  using a multiplier  950 . The input is also sent to a plurality of delay stages ( 952 - 964 ). The delayed signals are scaled by factors of a 1 -a 7 , respectively. The scaled signals are combined by a combiner  966 . 
       FIG. 10  is a block diagram illustrating a multi-stage distortion correcting analog to digital receiver, according to an embodiment of the present invention. The input is a noise source  1000 . Four k-bit ADCs ADC  1  are used to generate the outputs of an ADC that has 4 k bits. In this embodiment, k is 5. Several DSPs are coupled to the ADC stages to cancel the interference effect of the higher order bits on the lower order bits. Once the effects of the higher order bits are removed from the lower order bits, the resulting bits then undergo the same process of removing their effects from the bits of yet a lower order. ADC 1  generates the highest order bits, A, expressed as m 19 2 19 +m 18 2 18 +m 17 2 17 +m 16 2 16 +m 15 2 15 . The highest order bits are sent to DSP 1  that is trained to remove the interference effect of the highest order bits from the lower order bits generated by ADC  1004 . The resulting distortion corrected signal  1002  is expressed as n 14 2 14 +n 13 2 13 +n 12 2 12 +n 11 2 11 +n 10 2 10 . 
     The output of ADC  1  is also sent to DSP 2  and DSP 3  for removing the interference effects from the lower order bits generated by ADC 3  and ADC 4 , respectively, to obtain signals  1004  and  1006 . The distortion corrected signal  1002  is also sent to DSP 4  and DSP 5  to further remove any interference effects it may have on the lower order bits generated by the DSPs. Similarly, signal  1008  is sent to DSP 6 , which is trained to remove any interference present in signal  1010 . The distortion corrected output signals  1008  and  1012  are expressed as n 9 2 9 +n 8 2 8 +n 7 2 7 +n 6 2 6 +n 5 2 5  and n 4 2 4 +n 3 2 3 +n 2 2 2 +n 1 2 1 +n 0 2 0 , respectively. 
     It should be noted that the number of bits in the ADC stages, the number of stages and the number of DSPs used are implementation dependent. The same general architecture can be modified to use different numbers of ADC stages and DSPs. 
     The calibration module in a DCADC may also be used to correct distortion in the overall circuit that includes the DCADC. A receiver circuit example is discussed for the purposes of illustration, although it should be noted that the DCADC can also be used for correcting distortion in transmitter circuits or any other appropriate circuits. 
       FIG. 11  is a block diagram illustrating a receiver circuit that includes a distortion correcting analog to digital converter, according to one embodiment of the present invention. The receiver circuit includes an automatic gain control (AGC)  1104 , a buffer  1102 , and a DCADC  1100 . There are several signal sources available for training the circuit, including a DEM DAC  1108 , a custom low noise DAC  1110 , and a random noise generator  1112 . Switch  1106  selects one of the signal sources during the training process. The calibration module in DCADC  1100  adapts to correct not only the distortion in the ADC itself, but also the distortion introduced by the AGC and the buffer. Once training is completed, switch  1106  connects to interface  1114  and the circuit operates in its steady state mode, where distortion in the overall circuit is corrected by the calibration module of the DCADC. 
     An improved technique for correcting an output distortion has been disclosed. Several embodiments that employ calibration modules to compensate the distortion have been discussed. The technique provides low distortion output over a wide spectrum without significantly increasing the production cost of the ADC. 
     Although the foregoing invention has been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications may be practiced within the scope of the appended claims. It should be noted that there are many alternative ways of implementing both the process and apparatus of the present invention. Accordingly, the present embodiments are to be considered as illustrative and not restrictive, and the invention is not to be limited to the details given herein, but may be modified within the scope and equivalents of the appended claims.