A New Discrete-Time Model of Fractional-Order PLL

this work presents a new discrete-time fractional-order phase-locked loop (DTFoPLL). The new model is developed by introducing a 1st-order z-transfer function that approximates a dynamic fractional-order discrete-time integrator that depends on its fractional order. Such structure is used to realize both the discrete-time fractional-order filter (DTFoF) and a fractional-order digital controlled-oscillator (FoDCO) of the PLL. The flexibility of the design follows from choosing low-order PLLs (between $\boldsymbol{0.1\leq\alpha\leq 0.2)}$ that provides wider bandwidth and requires lower gains than its integer-order counter parts. The main points of this work are illustrated via numerical simulation.