Comprehensive Stability‐Criterion Analysis for Generic Type‐II All‐Digital Phase‐Locked Loops

ABSTRACT A linear time‐variant analysis method for the type‐II all‐digital phase‐locked loop (ADPLL) is proposed to provide a precise frequency response analysis in this paper. From this analysis, a universal stability criterion for ADPLL is established, and the relationship between the maximum phase margin and loop bandwidth is revealed. The analysis indicates that one half of the reference frequency is the zero‐PM upper limit of the unit‐gain bandwidth, whereas practical ADPLL designs with a positive PM must operate below this limit. The proposed theory is verified through extensive simulations and can provide an important guide for the design and optimization of various ADPLL schemes.