Analysis of Frequency-Aid Technique for Fractional-N Digital BB-PLLs in Time-Domain

This brief make an original analysis of the frequency-aid technique using ternary phase detectors (TPDs) for fractional-N digital Bang-Bang (BB) phase-locked loops (PLLs). We prove that the minimum value of the TPD dead-zone to prevent a limit-cycle happening in the BB-PLL, in fact, can be reduced by a factor of 28 when using a novel mathematical expression, for a reference signal with -155 dB noise floor. Furthermore, we show that increasing the gain of the integral path tuning the digitally-controlled oscillator coarse bank does not guarantee a faster locking as typically believed. Finally, this brief proposes closed-form expressions for the TPD dead-zone and the gain of the additional proportional path to minimize the transient time.