Bang-bang phase detector studies were carried out in this thesis. Based on the comparison of linear and non-linear phase detectors, a hybrid phase detector was proposed. It possesses the characteristics of two-XOR phase detectors and improved bang-bang phase detectors. PLLs with the proposed hybrid phase detector possess low timing jitter in lock states and a fast locking process. The effectiveness of the proposed hybrid phase detector was quantified by comparing the performance of three PLLs with identical loop components but different phase detectors. A new bang-bang phase detector with regenerative DFFs was also proposed. The regenerative bang-bang phase detector ensures a fast acquisition of incoming clocks. The effectiveness of the regenerative phase detector was assessed in a 2GHz PLL. A 1X bang-bang phase detector was proposed also. Compared to a 2X bang-bang phase detector, PLLs with a 1X bang-bang phase detector offer faster locking. A DFF frequency detector and a charge-pump frequency detector were also proposed. Both effectively detect the frequency difference.