# How a Phase-Locked Loop Works

The phase-locked loop (PLL) is a device with many interesting applications, including frequency synthesis, FM demodulation, and television sweep circuits. Its operation seems nearly miraculous, but feedback makes the job easy, and it is an excellent example of feedback in action. Phase-locked loops, despite their importance and interest, are usually not treated in a university electronics course, though they are very much electronics and help the understanding greatly.

We will consider the fundamental phase-locked loop here. Once its operation is understood, all the applications will follow easily. We generally think of the circuit as accepting an input at some frequency and providing an output at the same frequency that is not a copy of the input, but the output of an independent oscillator whose frequency is controlled by feedback. The output of the oscillator is compared to the input, and if the frequencies are different, the frequency of the oscillator is altered to reduce the difference.

This is what it looks like, but it is better to consider the controlled quantity to be the phase of the signals. A signal of frequency f Hz changes phase by 2πf radians per second. In general, the phase in radians is 2π times the integral of the frequency with respect to time. The phase-locked loop compares the phases of the input signal and the oscillator signal, and adjusts the oscillator to reduce the phase difference. A signal flow diagram of a phase-locked loop is shown below.

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