Phase-locked Loop

A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input "reference" signal. It is an electronic circuit consisting of a variable frequency oscillator and a phase detector. This circuit compares the phase of the input signal with the phase of the signal derived from its output oscillator and adjusts the frequency of its oscillator to keep the phases matched. The signal from the phase detector is used to control the oscillator in a feedback loop.

Frequency is the time derivative of phase. Keeping the input and output phase in lock step implies keeping the input and output frequencies in lock step. Consequently, a phase-locked loop can track an input frequency, or it can generate a frequency that is a multiple of the input frequency. The former property is used for demodulation, and the latter property is used for indirect frequency synthesis.

Phase-locked loops are widely employed in radio, telecommunications, computers and other electronic applications. They can be used to recover a signal from a noisy communication channel, generate stable frequencies at a multiple of an input frequency (frequency synthesis), or distribute clock timing pulses in digital logic designs such as microprocessors. Since a single integrated circuit can provide a complete phase-locked-loop building block, the technique is widely used in modern electronic devices, with output frequencies from a fraction of a hertz up to many gigahertz.

Read more about Phase-locked Loop:  History, Structure and Function, Applications, Phase-locked Loop Block Diagram

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Phase-locked Loop - Modeling - Linearized Phase Domain Model
... Phase locked loops can also be analyzed as control systems by applying the Laplace transform ... The loop response can be written as Where is the output phase in radians is the input phase in radians is the phase detector gain in volts per radian is the VCO gain in radians ... The loop transfer function in this case is The loop response becomes This is the form of a classic harmonic oscillator ...