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Spectral Shaping of Circuit Errors in DigitaltoAnalog Converters
, 1997
"... Recently, various multibit noiseshaping digitaltoanalog converters (DAC's) have been proposed that use digital signal processing techniques to cause the DAC noise arising from analog component mismatches to be spectrally shaped. Such DAC's have the potential to significantly increase the present p ..."
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Cited by 43 (19 self)
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Recently, various multibit noiseshaping digitaltoanalog converters (DAC's) have been proposed that use digital signal processing techniques to cause the DAC noise arising from analog component mismatches to be spectrally shaped. Such DAC's have the potential to significantly increase the present precision limits of 16 data converters by eliminating the need for onebit quantization in deltasigma modulators. This paper extends the practicality of the noiseshaping DAC approach by presenting a general noiseshaping DAC architecture along with two specialcase configurations that achieve first and secondorder noiseshaping, respectively. The secondorder DAC configuration, in particular, is the least complex of those currently known to the author. Additionally, the paper provides a rigorous explanation of the apparent paradox of how the DAC noise can be spectrally shaped even though the sources of the DAC noisethe errors introduced by the analog circuitryare not known to the ...
Simplified Logic for FirstOrder and SecondOrder MismatchShaping DigitaltoAnalog Converters
 AND GALTON: NECESSARY AND SUFFICIENT CONDITIONS FOR MISMATCH SHAPING 759
, 2001
"... Mismatchshaping digitaltoanalog converters (DACs) have become widely used in highperformance deltasigma data converters because they facilitate deltasigma modulators with multibit quantization. Relative to singlebit quantization, multibit quantization significantly relaxes the analog circuit ..."
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Cited by 8 (5 self)
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Mismatchshaping digitaltoanalog converters (DACs) have become widely used in highperformance deltasigma data converters because they facilitate deltasigma modulators with multibit quantization. Relative to singlebit quantization, multibit quantization significantly relaxes the analog circuit performance necessary to achieve a given level of data converter precision, but significant digital logic is required to perform the mismatch shaping. In modern very large scale integration processes optimized for digital circuitry, this tends to be a good tradeoff in terms of both area and power consumption. It is nonetheless desirable to minimize the digital complexity as much as possible. Moreover, in deltasigma analogtodigital converters the mismatchshaping logic is in the feedback path of the deltasigma modulator, so it is essential to maintain a sufficiently small propagation delay through the mismatchshaping logic. This paper presents and analyzes several variations of the switching blocks within a treestructured mismatchshaping DAC that result in the most hardwareefficient firstorder and secondorder mismatch shaping DAC implementations yet known to the authors. The variations presented allow designers to tradeoff complexity for propagationdelay reduction so as to tailor designs to specific applications.
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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Cited by 7 (4 self)
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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 study of dynamic element matching techniques for threelevel unit elements
 IEEE Trans. Circuits Syst. II
, 2000
"... Abstract—Highly linear 3level unit elements are available in any fully differential circuit. This is because each unit element in such a circuit can be either positively selected, negatively selected, or not selected. This paper presents a study of dynamic element techniques for such elements. It i ..."
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Cited by 5 (4 self)
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Abstract—Highly linear 3level unit elements are available in any fully differential circuit. This is because each unit element in such a circuit can be either positively selected, negatively selected, or not selected. This paper presents a study of dynamic element techniques for such elements. It is shown how traditional dynamic elementmatching techniques for 2level unit elements such as the data directed swapper, the vector selector, and the tree structure can be adapted toward linear 3level elements. In all these cases, the amount of hardware is reduced significantly by using 3level elements. Also several efficient “data weighted averaging”like implementations are presented. Then the effect of the nonlinearity of the 3level unit element is analyzed. It is shown that this gives an additional error contribution that may limit the performance. Therefore, several efficient techniques to shape this effect as well are introduced. Index Terms—Analogtodigital, digitaltoanalog, dynamic elementmatching, spectral shaping.
An approach to tackle quantization noise folding in doublesampling 61 modulation A/D converters
 IEEE Trans. Circuits Syst. II
, 2003
"... Abstract—61modulation is a proven method to realize high and very highresolution analogtodigital converters. A particularly efficient way to implement such a modulator uses doublesampling where the circuit operates during both clock phases of the masterclock. Hence, the sampling frequency is ..."
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Cited by 5 (4 self)
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Abstract—61modulation is a proven method to realize high and very highresolution analogtodigital converters. A particularly efficient way to implement such a modulator uses doublesampling where the circuit operates during both clock phases of the masterclock. Hence, the sampling frequency is twice the masterclock frequency. Unfortunately, path mismatch between both sampling branches causes a part of the quantization noise to fold from the Nyquist frequency back in the signal band. Therefore, the performance is severely degraded. In this paper, we show that the problem is reduced but not eliminated by employing multibit quantization. Next, we present an indepth solution for the problem. The approach consists of modifying the quantization noise transfer function of the overall modulator to have one or several zeros at the Nyquist frequency. This way the effect of noise folding can nearly be eliminated. It is shown that this can be implemented by a simple modification of one of the integrators of the overall modulator circuit. Finally, several design examples of singlebit and multibit modulators are discussed. Index Terms—Analogtodigital conversion, doublesampling, spectral shaping.
DeltaSigma Data Conversion in Wireless Transceivers
, 2002
"... Highperformance analogtodigital converters, digitaltoanalog converters, and fractional frequency synthesizers based on deltasigma (16) modulationcollectively referred to as data convertershave contributed significantly to the high level of integration seen in recent commercial wirel ..."
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Cited by 4 (2 self)
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Highperformance analogtodigital converters, digitaltoanalog converters, and fractional frequency synthesizers based on deltasigma (16) modulationcollectively referred to as data convertershave contributed significantly to the high level of integration seen in recent commercial wireless handset transceivers. This paper presents a tutorial on data converters and their uses and implications with respect to wireless transceiver architectures.
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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Cited by 2 (2 self)
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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 Power Optimized ContinuousTime 16 ADC for Audio Applications
"... Abstract—We present design considerations for lowpower continuoustime 16 modulators. Circuit design details and measurement results for a 15 bit audio modulator are given. The converter, designed in a 0.18 m CMOS technology, achieves a dynamic range of 93.5 dB in a 24 kHz bandwidth and dissipates ..."
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Abstract—We present design considerations for lowpower continuoustime 16 modulators. Circuit design details and measurement results for a 15 bit audio modulator are given. The converter, designed in a 0.18 m CMOS technology, achieves a dynamic range of 93.5 dB in a 24 kHz bandwidth and dissipates 90 Wfroma 1.8 V supply. It features a thirdorder activeRC loop filter, a very lowpower 4bit flash quantizer, and an efficient excessdelay compensation scheme to reduce power dissipation. Index Terms—Analogtodigital converter (ADC), continuous time, data converter, jitter, oversampling, sigmadelta modulation.
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.