| Multi-bit digital-to-analog converters (DACs) are often constructed by combining several 1-bit DACs in parallel. In such a DAC, mismatches among the 1-bit DACs cause its output to be a nonlinear function of its input. This error is modeled as an additive noise source called the DAC noise . The DAC noise limits the attainable resolution of the multi-bit DAC and, if not addressed, prohibits its use in high-performance applications. Mismatch-shaping DACs mitigate this problem by suppressing the DAC noise power in the data signal's frequency band so that most of it can be removed by frequency-selective filters. These DACs facilitate multi-bit delta-sigma (ΔΣ) modulation and have thus become widely used in high-performance ΔΣ data converters.; However, the theoretical analyses of mismatch-shaping DACs have been limited. For most architectures, the analysis is limited to proving that the DAC noise power spectral density (PSD) is zero at some frequency. Typically, this analysis pertains only to the specific architecture and does not provide a reasonable estimate of the signal-band power of the DAC noise. Consequently, engineers usually rely on simulations to predict their DACs performance, which can be misleading.; This dissertation provides a unifying theory for mismatch-shaping DACs and furthers the development and analysis of an architecture called the tree-structured DAC. The unifying theory, which is given in Chapter 1, is in the form of necessary and sufficient conditions for a multi-bit DAC to be a mismatch-shaping DAC. These conditions are used to analyze and compare several well-known mismatch-shaping DACs. Chapter 2 presents different implementations of the tree-structured DAC that give rise to performance and complexity trade-offs. One such implementation, the dithered first-order low-pass tree-structured DAC, is analyzed in Chapter 3. In this chapter, expressions for the DAC noise PSD and signal-band power are derived and used to obtain an achievable power bound for the DAC noise. In Chapter 4, the DAC noise PSD expression from Chapter 3 is used to develop the theoretical DAC noise PSD for the tree-structured DAC in a ΔΣ modulator application. |
