A phase lock loop (PLL) includes: a binary phase detector configured to generate a first and second polarity signals that respectively indicating whether an incoming data stream is leading a feedback signal, or whether the feedback signal is leading the incoming data stream, wherein a difference between the first and second polarity signals does not represent an amount of phase difference between the incoming data stream and the feedback signal; a digital filter configured to: generate filtered first polarity signal on a first path and a second path that are different; and generate filtered second polarity signal on a third path and a fourth path that are different; a charge pump coupled to the digital filter and configured to: integrate the filtered first polarity signal and the filtered second polarity signal; and an oscillator configured to generate the synthesized clock signal serving as the feedback signal.