This paper provides an in-depth analysis of the third-order bang-bang clock and data recovery (BBCDR) circuit, which accurately predicts its operating characteristics, namely, the jitter transfer function (JTF), the jitter tolerance (JTOL), and the jitter generation (JGEN). By formulating the time-domain waveforms, we introduce a characterizing method and also derive the closed-form equations and their simplified versions under specific conditions, which are related with the second-order loop filter (LF). Our framework is consistent with the conclusions of the prior works. Also, we discuss through the time-domain behavior, the sinking area of the JTOL and other specific phenomenon appearing in the third-order BBCDR loop. We verify all above prediction by system-level simulations with the MATLAB/simulink model.