Convergence behavior of the first-order time-delay digital tanlock loop

Abstract

Convergence behavior of the previously proposed time-delay digital tanlock loop (TDTL) is analyzed. The approach is built on the actual number of steps required for the convergence of the phase error to its steady-state value. Unlike the first-order conventional digital tanlock loop (CDTL), the Lipschitz bound of TDTL is not a tight limit for the actual convergence time, especially for higher values of the absolute difference between the initial and the steady-state phase errors. For a frequency step input, the first-order TDTL locks faster than CDTL under suitable arrangement of the loop parameters.