On the dynamics of regenerative frequency dividers

A comprehensive analytical study of regenerative frequency dividers (RFD) is presented. The study includes two fundamental modes of operation in RFDs, namely locked (or stable) and quasi-locked modes, and the study also covers the transition from free-running oscillation to quasi-locked, and ultimately to locked operation mode. Differential equations characterizing the RFD behavior for both operation modes as well as the transition between the two are derived. An RFD circuit for Bluetooth applications was designed and fabricated in a 65-nm CMOS process with a supply voltage of 1.2 V. Measurement results of the RFD prototype verify the accuracy of the proposed analytical models.