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Phase detector characteristic
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Phase detector characteristic : ウィキペディア英語版
Phase detector characteristic
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.〔A. J. Viterbi,
Principles of Coherent Communication, McGraw-Hill, New York,
1966〕
In this case for constructing of an adequate nonlinear mathematical model of PD in phase-frequency domain it is necessary to find the characteristic of phase detector.
The inputs of PD are high-frequency signals and the output contains a low-frequency error correction signal, corresponding to a phase difference of input signals. For the suppression of high-frequency component of the output of PD (if such component exists) a low-pass filter is applied. The
characteristic of PD is the dependence of the signal at the
output of PD (in the phase-frequency domain) on the difference of phases
at the input of PD.
This characteristic of PD depends on the realization of PD and the types of waveforms of signals. Consideration of PD characteristic allows to apply averaging methods for high frequency oscillations and to pass from analysis and simulation of non autonomous models of phase synchronization systems in time domain to analysis and simulation of autonomous dynamical models in phase-frequency domain
.〔

== Analog multiplier phase detector characteristic ==
Consider a classical phase detector implemented with analog multiplier and low-pass filter.
Here f^1(\theta^1(t)) and f^2(\theta^2(t)) denote high-frequency signals, piecewise differentiable functions f^1(\theta), f^2(\theta) represent waveforms of input signals, \theta^(t) denote phases, and g(t) and denotes the output of the filter.
If f^(\theta) and \theta^(t) satisfy the high frequency conditions (see ) then phase detector characteristic \phi(\theta) is calculated in such a way that time-domain model filter output
:
g(t) = \int\limits_0^t f^1(\theta^1(t))f^2(\theta^2(t))dt

and filter output for phase-frequency domain model
:
G(t) = \int\limits_0^t \varphi(\theta^1(t) - \theta^2(t))dt

are almost equal:
:g(t) - G(t) \approx 0
:

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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