Behavioural analysis of charge-pump PLL's

This paper presents a method for the numerical analysis of charge-pump Phase-Locked Loops in the time domain, using behavioural modelling of non-linear elements. The time domain is divided into intervals according to zero crossing of input and VCO signals. Inside each time interval, all signals in the network can be expressed with a set of functions made of complex polynomials and complex exponentials. A direct solution can be found, without requiring iterative procedures to converge. A computer program implementing the proposed analysis method has been written and applied to second- and third order PLL's.