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The closed form mathematical model of CP-PLL taking into account the VCO overload is derived in. [5] These mathematical models of CP-PLL allow to get analytical estimations of the hold-in range (a maximum range of the input signal period such that there exists a locked state at which the VCO is not overloaded) and the pull-in range (a maximum ...
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A phase frequency detector (PFD) is an asynchronous circuit originally made of four flip-flops (i.e., the phase-frequency detectors found in both the RCA CD4046 and the motorola MC4344 ICs introduced in the 1970s). The logic determines which of the two signals has a zero-crossing earlier or more often.
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 ...
A phase detector characteristic is a function of phase difference describing the output of the phase detector. For the analysis of Phase detector it is usually considered the models of PD in signal (time) domain and phase-frequency domain. [ 1 ]
The phase detector's comparison is made between the outputs of the two oscillators after frequency division by different divisors. Then by altering the frequency-division divisor(s) under computer control, a variety of actual (undivided) VCO output frequencies can be generated. The PLL technique dominates most radio VFO designs today.
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 ...
To measure the current resonance frequency, a phase-locked loop (PLL) (5) is used. Its voltage-controlled oscillator (VCO) produces the excitation signal (6) for the cantilever. The detected frequency shift ∆f is passed to another feedback loop (7) that keeps the frequency shift constant by changing the distance between the tip and the ...