Analog circuits that use on-chip digital-to-analog converters for calibration use DSP based algorithms for optimizing and calibrating the system parameters. However, the performance of traditional online-gradient descent based optimization and calibration algorithms suffer from artifacts due to quantization noise which adversely affects the real-time and precise convergence to the desired parameters. This thesis proposes and analyzes a novel class of on-line learning algorithms that can noise-shape the effect of quantization noise during the adaptation procedure and in the process achieve faster spectral convergence compared to the conventional quantized gradient-descent approach. We extend the proposed framework to higher-order noise-shaping and derive criteria for achieving optimal system performance. The thesis also explores the application of stochastic perturbative gradient descent techniques to the proposed noise-shaping online learning framework where we show the performance of the stochastic algorithm can be improved in the spectral domain. The thesis applies the proposed optimization method for online calibration of subthreshold analog circuits where artifacts like mismatch and non-linearity are more pronounced. We also show that even with non-monotonic calibration DACs, the proposed algorithm is still able to find an optimal system solution without getting trapped into local minima. Using measured results obtained from prototype fabricated in a 0.5μm CMOS process, we demonstrate the robustness of the proposed algorithm for the task of: (a) compensating and tracking of offset parameters; and (b) calibration of the center frequency of a sub-threshold gm-C biquad filter.
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