Multibit digital-to-analog converters (DACs) are often constructed by combining several 1-bit 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 mismatch-shaping DACs and have been used widely as enabling components in state-of-the-art data converters. Several different mismatch-shaping 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 mismatch-shaping DAC and applies the conditions to evaluate the DAC noise generated by several of the previously published mismatch-shaping DACs and qualitatively compare their behavior.

Abstract—A major problem in oversampling digital-to-analog 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.

Abstract—Many applications employ digital-to-analog 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 signal-to-noise ratio (SNR) and hence the obtainable accuracy of the DAC. Mismatch-shaping DACs exploit built-in redundancy to suppress the DAC noise in the input signal’s frequency band. Although mismatch-shaping 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 mismatch-shaping DAC: the dithered first-order low-pass tree-structured DAC. This design ensures that its DAC noise has a spectral null at dc (i.e., zero frequency) by generating digital, dc-free 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 signal-band DAC noise power that can be used to predict worst case performance in practical circuits. Index Terms—Analog-to-digital, data converters, dc-free sequences, delta–sigma (16), digital-to-analog, dynamic element matching, mismatch shaping, multibit, sigma–delta, spectral shaping. I.

(DEM) methods are extensively used in multi-bit Sigma-Delta Modulators (SDM) to reduce the effects of element mismatches. To date, only first and second-order mismatch-shaping DEM techniques have been reported in the literature. In this paper, a higher-order mismatch-shaping DEM method is reported, which is an extension of the known vector-feedback mismatch-shaping technique. Example simulation results are presented for thirdorder and fourth-order mismatch-shaping DEMs. I.

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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.