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This paper applies new analytical techniques to evaluate the stability and mean-square error (MSE) convergence of a multi-loop LMS pseudo-random noise canceller which applies to a variety of known mixed-signal circuit calibration techniques. To the authors’ knowledge, it is the first published MSE analysis of any multi-loop LMS system, and, unlike most published MSE analyses of single-loop LMS systems, it does not make any simplifying assumptions. The analysis proves that the noise canceler can be made unconditionally stable by design, and provides guidance on how to choose design parameters to achieve a desired level of noise cancellation. [ABSTRACT FROM AUTHOR]

Clock skew and component mismatches in continuous-time DACs introduce two types of error: static error and dynamic error. Both types of error typically limit the performance of practical, high-resolution, and continuous-time DACs, but most prior calibration techniques primarily reduce only static error. An exception is a recently published mismatch noise cancellation (MNC) technique that adaptively measures and cancels both types of error over the DAC’s first Nyquist band. However, a disadvantage of the technique is that it requires an oversampling ADC that operates at several times the DAC’s Nyquist rate to prevent convergence error that would otherwise be caused by aliasing. This paper presents a sub-sampling version of the MNC technique that avoids this limitation at the expense of a lower calibration convergence rate. As proven in the paper, the subsampling MNC technique allows aliasing to occur, but in such a way that convergence error is avoided. [ABSTRACT FROM AUTHOR]

Inadvertent but inevitable mismatches among nominally identical unit element 1-bit digital-to-analog converters (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 have had limited success in suppressing dynamic mismatch error. This paper presents a digital calibration technique that adaptively measures and cancels both static and dynamic mismatch error over the DAC’s first Nyquist band. The technique is capable of either foreground or background operation, and is relatively insensitive to non-ideal circuit behavior. The paper presents a rigorous mathematical analysis of the technique, and demonstrates the results of the paper with both behavioral and transistor-level circuit simulations. [ABSTRACT FROM PUBLISHER]