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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]
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.
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 outputs of these low-pass filters are inputs to another phase detector, the output of which passes through a noise-reduction filter before being used to control the voltage-controlled oscillator.
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).
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 long list of noise measures have been defined to measure noise in signal processing: in absolute terms, relative to some standard noise level, or relative to the desired signal level. They include: Dynamic range, often defined by inherent noise level; Signal-to-noise ratio (SNR), ratio of noise power to signal power