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Define a phase-locked loop (PLL) circuit and its function.

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A phase-locked loop (PLL) is an electronic control system that is widely used in various applications to synchronize the phase of an output signal with the phase of an input signal. It is commonly used in communication systems, clock generation, frequency synthesis, and other applications where precise timing and synchronization are essential.

The basic components of a PLL circuit include:

Phase Detector (PD): Also known as a phase comparator or phase/frequency detector, this component compares the phase of the input signal (reference signal) and the feedback signal (output signal). The phase detector produces an output voltage proportional to the phase difference between the two signals.

Voltage-Controlled Oscillator (VCO): The VCO generates the output signal with a frequency that can be adjusted by a control voltage. The control voltage is provided by the phase detector and is used to keep the output frequency in sync with the input frequency.

Low-Pass Filter (LPF): The low-pass filter smooths and filters the output voltage from the phase detector, providing a stable and continuous control voltage for the VCO. This filter eliminates high-frequency noise and unwanted variations from the control signal.

The function of a PLL is as follows:

Capture: Initially, when the PLL is powered on or started, the output frequency of the VCO might not match the input frequency (reference signal). The phase detector detects the phase difference between the input and output signals.

Control: The phase detector's output is filtered by the low-pass filter to generate a DC control voltage. This control voltage is proportional to the phase difference between the input and output signals.

Adjustment: The control voltage is fed into the VCO, causing the VCO's output frequency to change. The VCO's frequency will either increase or decrease, depending on the phase relationship between the input and output signals.

Lock: As the VCO's frequency changes, it starts to align with the input frequency, reducing the phase difference between the two signals. When the phase difference reaches zero, meaning the output is in sync with the input, the VCO's frequency stabilizes, and the PLL is said to be "locked."

Once locked, the output signal from the VCO remains synchronized with the input signal, maintaining a fixed phase and frequency relationship. The PLL's ability to lock onto and track an input signal's frequency and phase makes it an essential tool in various applications that require precise timing and synchronization.
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