In this paper we investigate the lock time behavior of charge pump phase locked loops (CP-PLLs) which employ voltage controlled oscillators (VCOs) with non-linear frequency tuning characteristics. Since non-linear tuning characteristics leads to variable tuning gain (Kvco), we extend the state space analysis of PLLs to account for tuning gain variations. The frequency behavior is approximated by a polynomial which fits the equally spaced data points of tuning curve best in a least-square sense. We have analytically evaluated the integrals arising from high order terms in polynomial representation and migrated to state space analysis. The method is validated by simulating the lock-time process of a VCO with varying tuning gain and comparing the results with commercial PLL simulation software.
Linear frequency tuning in an LC-resonant system using a C–V response controllable MEMS varactor
