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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]
Since the maximum output frequency is limited to /, the output phase noise at close-in offsets is always at least 6 dB below the reference clock phase noise. [ 6 ] At offsets far removed from the carrier, the phase-noise floor of a DDS is determined by the power sum of the DAC quantization noise floor and the reference clock phase noise floor.
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).
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.
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 ...
The phase detector needs to compute the phase difference of its two input signals. Let α be the phase of the first input and β be the phase of the second. The actual input signals to the phase detector, however, are not α and β, but rather sinusoids such as sin(α) and cos(β). In general, computing the phase difference would involve ...
A PLL multibit or multibit PLL is a phase-locked loop (PLL) which achieves improved performance compared to a unibit PLL by using more bits. Unibit PLLs use only the most significant bit (MSB) of each counter's output bus to measure the phase , while multibit PLLs use more bits. [ 1 ]