The Gardner Problem and Cycle Slipping Bifurcation for Type-2 Phase-Locked Loops
Abstract
In the present work, a second-order type-2 phase-locked loop (PLL) with a piecewise-linear phase detector characteristic is analyzed. An exact solution to the Gardner problem on the lock-in range is obtained for the considered model. The solution is based on a study of cycle slipping bifurcation, which improves the well-known engineering estimates.
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