Controlled-root formulation for digital phase-locked loops

In a new formulation for digital phase-locked loops, loop-filter constants are determined from loop roots that can each be selectively placed in the s-plane on the basis of a new set of parameters, each with single and direct physical meaning in terms of loop noise band, width root-specific decay rate, or root-specific damping. Loops of first to fourth order are treated in the continuous-update approximation (B _LT→0) and in a discrete-update formulation with arbitrary B _LT. Deficiencies of the continuous-update approximation in large-B _LT applications are avoided in the new discrete-update formulation. A new method for direct, transient-free acquisition with third- and fourth-order loops can improve the versatility and reliability of acquisition with such loops.<>