Initial value problems for ODEs in problem solving environments
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Design of Analog CMOS Integrated Circuits
Design of Analog CMOS Integrated Circuits
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In this paper a new structure for a fast locking charge pump phase locked loop (CPPLL) is introduced which overcomes the trade-off between the settling time and overshoot of the system. This fast locking PLL uses an auxiliary bang---bang frequency comparator (BBFC) as a lock-aid. An additional charge pump current controlled by the output of the BBFC is injected into the main loop filter capacitor to accelerate the locking process. An analytical approach to extract the differential equation governing on the system's dynamics is used to evaluate the performance of this fast locking PLL. A heuristic method that results in an approximate solution for the extracted differential equation is also proposed. The correctness of the presented differential equation and its closed-form solutions are verified by comparing the obtained closed-form solutions and simulation results. Using the obtained closed-form solutions, we predict the behavior of the system and design a fast BBFC-CPPLL which meets the system's requirements. Correctness of the differential equation and its closed-form solutions are verified by comparing the obtained closed-form solutions and simulation results.