Phase-locked loops (PLL) is a phase and/or frequency tracking system, widely used in communication and control systems. The sinusoidal multiplicative type PLL still remains a recurrent model, due the fact that its derivation is originated from the maximum likelihood approach. In this note, it is showed as a generalized product, called q-product, which can be used to implement the phase detector and improve some important parameters of the PLL system, as the block linearity and pull-in characteristics. Numerical examples are presented in order to illustrate the proposal.
Non-linear behaviour of charge-pump phase-locked loops
