Performance analysis of fractional-order digital phase-locked loops

A new type of fractional-order digital phase-locked loops (FoDPLLs) is proposed. They comprise a fractional-order digital controlled oscillator (FoDCO) and a new form of fractional-order filters (FoF). The FoDPLLs are obtained by discretizing the continuous fractional differential operators using a closed-form solution. These operators generate biquadratic rational z-transfer functions, which yield robust and stable 4^th-order FoDPLLs. This represents a significant order reduction over other discretization methods. The proposed operators reduce the design of the FoDPLLs to selecting only four parameters; the loop gain, the filter time constant, and the orders of both the FoF and the FoDCO. The performances of the analog and digital phase-locked loops are thoroughly investigated and illustrated via several numerical examples.