Evaluation of multi-level Bang–Bang phase detector with metastability effect using Markov chain

Bang–Bang phase detector (BBPD) as a bistable system has the metastability problem. In addition, BBPD is a non-linear block in the phase locked-loop (PLL) and clock and data recovery (CDR) that makes their analysis complicate. To simplify the analysis of the non-linear BBPD, the linear expression for the gain of multi-level BBPD (ML-BBPD) is derived in this paper by considering the metastability failure. The ML-BBPD gain is developed based on Markov chain to provide more realistic model. Simulation results show that the metastability failure not only attenuates the gain of ML-BBPD for the small input jitter, but also increases the output jitter and consequently the BER of the CDR. It is shown that by increasing the number of sampling clocks the output jitter and BER is reduced. Also, the gain of ML-BBPD is decreased for small values of the input jitter, but for the large values of input jitter ML-BBPD gain is the same for every over sampling ratio.