Analysis of Mueller–Muller Clock and Data Recovery Circuits with a Linearized Model

With the development of high-speed analog-to-digital converter (ADC)-based wireline receivers, the Mueller–Muller clock and data recovery (MM-CDR) circuit has garnered increasing attention. But in the design stage, evaluating the loop performance of MM-CDR circuits in ADC-based wireline receivers is challenging due to the absence of a linearized model for a Mueller–Muller phase detector (MMPD). In this paper, a linearized model of the MMPD is proposed by analyzing the output probability of the MMPD in different transition patterns with random jitter injection, and the model is combined with an entire MM-CDR system to analyze the performance of the MM-CDR loop. Analysis of the linearized model and corresponding simulations indicate that when the reference voltage level in the MMPD is set equal to the amplitude of the average crossing voltage at the intersection of 011 and 110 patterns, the MMPD can obtain the maximum gain, which is determined by jitter, and the jitter transfer function and jitter tolerance can achieve optimum performance.