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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 first linear mathematical model of second-order CP-PLL was suggested by F. Gardner in 1980. [2] A nonlinear model without the VCO overload was suggested by M. van Paemel in 1994 [3] and then refined by N. Kuznetsov et al. in 2019. [4] The closed form mathematical model of CP-PLL taking into account the VCO overload is derived in. [5]
Leeson's equation is an empirical expression that describes an oscillator's phase noise spectrum. Leeson's expression [1] for single-sideband (SSB) phase noise in dBc/Hz (decibels relative to output level per hertz) and augmented for flicker noise: [2]
In signal processing, phase noise is the frequency-domain representation of random fluctuations in the phase of a waveform, corresponding to time-domain deviations from perfect periodicity . Generally speaking, radio-frequency engineers speak of the phase noise of an oscillator, whereas digital-system engineers work with the jitter of a clock.
Thus, noise at f 1 is correlated with f 2 if f 2 = f 1 + kf o, where k is an integer, and not otherwise. However, the phase produced by oscillators that exhibit phase noise is not stable. And while the noise produced by oscillators is correlated across frequency, the correlation is not a set of equally spaced impulses as it is with driven systems.
The overall loop response is controlled by the two individual low-pass filters that precede the third phase detector, while the third low-pass filter serves a trivial role in terms of gain and phase margin. The above figure of a Costas loop is drawn under the "locked" state, where the VCO frequency and the incoming carrier frequency have become ...
A multibit PLL offers fine frequency resolution and fast frequency hopping, together with lower phase noise and lower power consumption. It thus enhances the overall performance envelope of the PLL. The loop bandwidth can be optimized for phase noise performance and/or frequency settling speed; it depends less on the frequency resolution.
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).