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Although digital phase-locked loops (PLLs) offer several advantages over their analog counterparts, they suffer from a major disadvantage that is rarely mentioned in published articles. The disadvantage, known as spectral breathing, is caused by component mismatches among the frequency control elements within a PLL's digitally controlled oscillator (DCO). The mismatches introduce DCO frequency modulation nonlinearity which fluctuates and, therefore, causes erratic variations in the PLL's measured phase noise spectrum as the DCO's free-running frequency drifts. The phenomenon is called spectral breathing because the measured phase noise spectrum tends to slowly swell and contract over time as if taking breaths of air. During these breaths, the PLL's phase noise often becomes severely degraded. This article presents an experimental demonstration of the spectral breathing phenomenon and its solution in a digital fractional-N PLL. The demonstrated solution is a multi-rate dynamic element matching technique and a mismatch-noise cancellation technique that together eliminate spectral breathing. 

The linearity of high-resolution current-steering digital-to-analog converters (DACs) is often limited by inter-symbol interference (ISI). While dynamic element matching (DEM) can be applied to convert a portion of the ISI to uncorrelated noise instead of nonlinear distortion, DEM alone fails to prevent ISI from at least introducing strong second-order nonlinear distortion. This paper addresses this problem by proposing, analyzing, and experimentally demonstrating a low-cost add-on technique, called ISI scrambling, that, in conjunction with DEM, causes a DAC’s ISI to be free of nonlinear distortion. The ISI scrambling technique is demonstrated in a 1-GS/s, 14-bit DEM DAC implemented in 90 nm CMOS technology. The DAC’s measured linearity is in line with the state of the art and its measured output power spectra closely match those predicted by the paper’s theoretical results. 

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.