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A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is fixed relative to the phase of an input signal. Keeping the input and output phase in lockstep also implies keeping the input and output frequencies the same, thus a phase-locked loop can also track an input frequency.
In the 1st edition of his well-known work, Phaselock Techniques, Floyd M. Gardner introduced a lock-in concept: [8] If, for some reason, the frequency difference between input and VCO is less than the loop bandwidth, the loop will lock up almost instantaneously without slipping cycles.
The classical Costas loop will work towards making the phase difference between the carrier and the VCO become a small, ideally zero, value. [ 10 ] [ 11 ] [ 12 ] The small phase difference implies that frequency lock has been achieved.
Following Gardner's results, by analogy with the Egan conjecture on the pull-in range of type 2 APLL, Amr M. Fahim conjectured in his book [8]: 6 that in order to have an infinite pull-in(capture) range, an active filter must be used for the loop filter in CP-PLL (Fahim-Egan's conjecture on the pull-in range of type II CP-PLL).
The receiver generates a clock from an approximate frequency reference, and then phase-aligns the clock to the transitions in the data stream with a phase-locked loop (PLL). This is one method of performing a process commonly known as clock and data recovery (CDR). Other methods include the use of a delay-locked loop and oversampling of the ...
Jitter is a form of phase noise that must be minimised in applications such as radio receivers, transmitters and measuring equipment. When a wider selection of clock frequencies is needed the VCXO output can be passed through digital divider circuits to obtain lower frequencies or be fed to a phase-locked loop (PLL). ICs containing both a VCXO ...
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Floyd M. Gardner introduced "a lock-in range concept" for PLLs and posed the problem on its formalization (known as the Gardner problem on the lock-in range [5] [6]).In the 1st edition of his book he introduced a lock-in frequency concept for the PLL in the following way: [1]: 40 "If, for some reason, the frequency difference between input and VCO is less than the loop bandwidth, the loop will ...