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Necessary and Sufficient Conditions for Mismatch Shaping in a General Class of Multibit Dacs
, 2002
"... Multibit digitaltoanalog converters (DACs) are often constructed by combining several 1bit DACs of equal or different weights in parallel. In such DACs, component mismatches give rise to signal dependent error that can be viewed as additive DAC noise. In some cases these DACs use dynamic element ..."
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Multibit digitaltoanalog converters (DACs) are often constructed by combining several 1bit DACs of equal or different weights in parallel. In such DACs, component mismatches give rise to signal dependent error that can be viewed as additive DAC noise. In some cases these DACs use dynamic element matching techniques to decorrelate the DAC mismatch noise from the input sequence and suppress its power in certain frequency bands. Such DACs are referred to as mismatchshaping DACs and have been used widely as enabling components in stateoftheart data converters. Several different mismatchshaping DAC topologies have been presented, but theoretical analyses have been scarce and no general unifying theory has been presented in the previously published literature. This paper presents such a unifying theory in the form of necessary and sufficient conditions for a multibit DAC to be a mismatchshaping DAC and applies the conditions to evaluate the DAC noise generated by several of the previously published mismatchshaping DACs and qualitatively compare their behavior.
A tight signalband power bound on mismatch noise in a mismatch shaping digitaltoanalog converter
 IEEE Trans. Inf. Theory
, 2004
"... Abstract—Many applications employ digitaltoanalog converters (DACs) to obtain the advantages of digital processing (e.g., low power and physical size, resilience to noise, etc.) to generate signals, such as voltages, that are analog in nature. Given the appropriate numerical representation of its ..."
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Abstract—Many applications employ digitaltoanalog converters (DACs) to obtain the advantages of digital processing (e.g., low power and physical size, resilience to noise, etc.) to generate signals, such as voltages, that are analog in nature. Given the appropriate numerical representation of its input, the DAC ideally behaves as a linear gain element. However, as a result of inevitable component mismatches, the output of a multibit DAC (i.e., a DAC designed to output more than two analog levels) is a nonlinear function of its input. The resulting distortion, called DAC noise, limits the overall signaltonoise ratio (SNR) and hence the obtainable accuracy of the DAC. Mismatchshaping DACs exploit builtin redundancy to suppress the DAC noise in the input signal’s frequency band. Although mismatchshaping DACs are widely used in commercial products, little theory regarding the structure of their DAC noise has been published to date. Consequently, designers have been forced to rely upon simulations to estimate DAC noise power and behavior, which can be misleading because the DAC noise depends on the DAC input. This paper addresses this problem. It presents an analysis of the DAC noise power spectral density (PSD) in a commonly used mismatchshaping DAC: the dithered firstorder lowpass treestructured DAC. This design ensures that its DAC noise has a spectral null at dc (i.e., zero frequency) by generating digital, dcfree sequences using the same techniques that have been developed for line codes. An expression is derived for the DAC noise PSD that depends on the statistics of these sequences and is used to show various properties of the DAC noise. Specifically, an attainable bound is derived for the signalband DAC noise power that can be used to predict worst case performance in practical circuits. Index Terms—Analogtodigital, data converters, dcfree sequences, delta–sigma (16), digitaltoanalog, dynamic element matching, mismatch shaping, multibit, sigma–delta, spectral shaping. I.
A digital requantizer with shaped requantization noise that remains well behaved after nonlinear distortion
 IEEE Trans. Signal Process
, 2007
"... Abstract—A major problem in oversampling digitaltoanalog converters and fractional frequency synthesizers, which are ubiquitous in modern communication systems, is that the noise they introduce contains spurious tones. The spurious tones are the result of digitally generated, quantized signals pa ..."
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Abstract—A major problem in oversampling digitaltoanalog converters and fractional frequency synthesizers, which are ubiquitous in modern communication systems, is that the noise they introduce contains spurious tones. The spurious tones are the result of digitally generated, quantized signals passing through nonlinear analog components. This paper presents a new method of digital requantization called Successive Requantization, special cases of which avoids the spurious tone generation problem. Sufficient conditions are derived that ensure certain statistical properties of the quantization noise, including the absence of spurious tones after nonlinear distortion. A practical example is presented and shown to satisfy these conditions. Index Terms—Dither techniques, nonlinearities, quantization. I.
TreeStructured DEM DACs with Arbitrary Numbers of Levels
"... Abstract—Unityweighted treestructured dynamic element matching (DEM) DACs are widely used in deltasigma (16) data converters to ensure that mismatches among nominally identical analog components give rise to shaped noise instead of nonlinear distortion. Treestructured DEM DACs offer an advantage ..."
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Abstract—Unityweighted treestructured dynamic element matching (DEM) DACs are widely used in deltasigma (16) data converters to ensure that mismatches among nominally identical analog components give rise to shaped noise instead of nonlinear distortion. Treestructured DEM DACs offer an advantage over other published DEM DACs in that the shaped noise from component mismatches can be made free of spurious tones. However, previously published unityweighted treestructured DEM DACs have the disadvantage that they require a poweroftwo number of nominally identical 1bit DACs. When applied to a 16 data converter with a nonpoweroftwo number of quantization steps, this requires the DEM DAC to have a larger input range than needed by the 16 data converter which wastes power and circuit area. This paper presents a generalized treestructured DEM encoder applicable to DEM DACs with any number of 1bit DACs, thereby avoiding this limitation. Index Terms—Digitaltoanalog conversion, dynamic element matching (DEM), encoder. I.
LSB Dithering in MASH Delta–Sigma D/A Converters
"... Abstract—Theoretical sufficient conditions are presented that ensure that the quantization noise from every constituent digital delta–sigma (16) modulator in a multistage digital 16 modulator is asymptotically white and uncorrelated with the input. The conditions also determine if spectral shape can ..."
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Abstract—Theoretical sufficient conditions are presented that ensure that the quantization noise from every constituent digital delta–sigma (16) modulator in a multistage digital 16 modulator is asymptotically white and uncorrelated with the input. The conditions also determine if spectral shape can be imparted to the dither’s contribution to the power spectral density of the multistage digital 16 modulator’s output. A large class of popular multistage digital 16 modulators that satisfy the conditions are identified and tabulated for easy reference. Index Terms—Delta–sigma (16) modulation, dither techniques, MASH, quantization. I.
Why DynamicElementMatching DACs Work
"... Abstract—This jumpstart tutorial brief explains the principle that underlies all of the published mismatchscrambling and mismatchshaping dynamicelementmatching (DEM) digitaltoanalog converters (DACs). It explains the apparent paradox of how an alldigital algorithm can cause analog component m ..."
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Abstract—This jumpstart tutorial brief explains the principle that underlies all of the published mismatchscrambling and mismatchshaping dynamicelementmatching (DEM) digitaltoanalog converters (DACs). It explains the apparent paradox of how an alldigital algorithm can cause analog component mismatches to introduce spectrally shaped noise instead of nonlinear distortion, even though the algorithm has no knowledge of the actual mismatches. The concept is first explained in the context of a discretetime threelevel DEM DAC. The results are then generalized to an arbitrary number of levels, to segmented DEM DACs, and to continuoustime DEM DACs. Index Terms—Digitaltoanalog converter (DAC), dynamic element matching (DEM), mismatch scrambling, mismatch shaping. I.
A HigherOrder MismatchShaping Method for Multi Bit SigmaDelta Modulators
"... (DEM) methods are extensively used in multibit SigmaDelta Modulators (SDM) to reduce the effects of element mismatches. To date, only first and secondorder mismatchshaping DEM techniques have been reported in the literature. In this paper, a higherorder mismatchshaping DEM method is reported, ..."
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(DEM) methods are extensively used in multibit SigmaDelta Modulators (SDM) to reduce the effects of element mismatches. To date, only first and secondorder mismatchshaping DEM techniques have been reported in the literature. In this paper, a higherorder mismatchshaping DEM method is reported, which is an extension of the known vectorfeedback mismatchshaping technique. Example simulation results are presented for thirdorder and fourthorder mismatchshaping DEMs. I.