In case of a monolithic phase-locked loop, the equation of free running frequency of the voltage controlled oscillator is

Phase-locked loop (PLL):

• A phase-locked loop is a control system that generates an output signal whose phase is related to the phase of an input signal.
• The circuit can track an input frequency or it can generate a frequency that is a multiple of the input frequency.
• The basic elements of a PLL circuit are phase comparator/detector, a loop filter, voltage-controlled oscillator (VCO).

The figure shows a schematic of a phase-locked loop:

The center frequency of the PLL is determined by the free-running frequency of the VCO, which is given by:

\({f_{OUT}} = \frac{{1.2}}{{4{R_1}{C_1}}}Hz\)

R1 and C1 = External resistors and Capacitors

The VCO free-running frequency fout is adjusted externally with R1 and C1 to be at the center of the input frequency range.

The lock range fL and capture of PLL is given by:

\({f_L} = \; \pm \frac{{8{f_{OUT}}}}{V}Hz\)  

fOUT = Free-running frequency of VCO (Hz)

v = (+v) – (-v) volts