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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.
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).
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 ...
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 ...
A phase detector or phase comparator is a frequency mixer, analog multiplier or logic circuit that generates a signal which represents the difference in phase between two signal inputs. The phase detector is an essential element of the phase-locked loop (PLL).
In the classical implementation of a Costas loop, [4] a local voltage-controlled oscillator (VCO) provides quadrature outputs, one to each of two phase detectors, e.g., product detectors. The same phase of the input signal is also applied to both phase detectors, and the output of each phase detector is passed through a low-pass filter. The ...
One example is the genetic algorithm for optimizing coefficients of a PID controller [2] or discrete-time optimal control. [ 3 ] Control design as regression problem of the first kind: MLC approximates a general nonlinear mapping from sensor signals to actuation commands, if the sensor signals and the optimal actuation command are known for ...
In the classic books on phase-locked loops, [1] [2] published in 1966, such concepts as hold-in, pull-in, lock-in, and other frequency ranges for which PLL can achieve lock, were introduced. They are widely used nowadays (see, e.g. contemporary engineering literature [ 3 ] [ 4 ] and other publications).