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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.
A VCO is also an integral part of a phase-locked loop. VCOs are used in synthesizers to generate a waveform whose pitch can be adjusted by a voltage determined by a musical keyboard or other input. A voltage-to-frequency converter (VFC) is a special type of VCO designed to be very linear in frequency control over a wide range of input control ...
Here is a normalized phase shift and + is a ratio of the VCO frequency + to the reference frequency . Finally, the discrete-time model of second order CP-PLL without the VCO overload [ 4 ] [ 6 ]
Costas loop working in the locked state. 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 loop may not lock within one beat note, but the VCO frequency will be slowly tuned toward the reference frequency (acquisition process). This effect is also called a transient stability. The pull-in range is used to name such frequency deviations that make the acquisition process possible (see, for example, explanations in Gardner (1966 , p.
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 a traditional phase locked loop (PLL), the frequency divider in the feedback path acts to multiply the phase noise of the reference oscillator and, within the PLL loop bandwidth, impresses this excess noise onto the VCO output.
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 ...
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