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Inadvertent but inevitable mismatches among nominally identical unit element 1-bit DACs within a multi-bit Nyquist-rate DAC cause both static and dynamic error in the DAC’s continuous-time output waveform. Prior calibration techniques are able to suppress static mismatch error, but they have had limited success in suppressing dynamic mismatch error.This first chapter of the dissertation presents a mismatch noise cancellation (MNC) technique that adaptively measures and cancels both static and dynamic mismatch error over the DAC’s first Nyquist band. The proposed digital calibration technique is capable of either foreground or background operation and is relatively insensitive to non-ideal circuit behavior. The chapter presents a rigorous mean convergence analysis of the technique and demonstrates the results of the paper with both behavioral and transistor-level circuit simulations. The second chapter of the dissertation presents an integrated circuit DAC which implements the MNC technique of chapter one together with other circuit-level improvement techniques. With MNC enabled, this DAC demonstrates state-of-the-art performance.This third chapter of the dissertation presents an improved version of MNC that addresses a practical concern. The original MNC technique requires an oversampling ADC clocked at a much higher clock rate than that of the DAC to measure the DAC’s mismatch error, while the new technique presented in this chapter overcomes this limitation. This fourth chapter of the dissertation presents a comprehensive mean-square convergence analysis of MNC proposed in chapter one, it proved that the noise impact on each coefficient in MNC, characterized by a steady-state mean square error metric, is bounded and can be arbitrarily reduced under certain practical conditions. It also established an analytical lower bound of DAC signal-to-noise-ratio (SNR) contributed by noise present in the system during calibration. The results of this paper provide guidance into the design of MNC.