Fractional Calculus based analysis of Phase Locked Loop

Analysis of Phase Locked Loop in Fractional domain is the main objective of the paper. Initially basics of Fractional Calculus and Phase Locked Loop is revisited. A fractional order Phase Locked Loop(FOPLL) is obtained by replacing conventional Low Pass filter and Voltage Controlled Oscillator with their fractional order counterparts. Calculations such as error phase, output phase, steady state errors, stability conditions are carried out. From the results it is observed that phase offset is independent of the fractional order. It has been observed that lower fractional order PLL's will produce higher bandwidth as compared to their integer counterparts. It has also been observed that the Locking range and Capture range can be improved by using lower values of fractional orders.