Noise Analysis and Minimization in Bang-Bang Digital PLLs

In digital bang-bang phase-locked loops (BBPLLs), both the hard nonlinearity of the phase detector and the frequency granularity of the digitally controlled oscillator (DCO) can give rise to undesired tones or peaking in the output spectrum. This work derives the maximum ratio between DCO resolution and jitter, which avoids limit cycles, in the case of dominant DCO noise over reference noise. Moreover, the output jitter is expressed in closed form as a function of the loop parameters and latency, revealing the existence of a minimum and suggesting an optimum design criterion. Finally, an estimation of the BBPLL output spectrum taking into account the quantization noise is provided.