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A phase detector characteristic is a function of phase difference describing the output of the phase detector.
Contents
- Analog multiplier phase detector characteristic
- Sine waveforms case
- Square waveforms case
- General waveforms case
- References
For the analysis of Phase detector it is usually considered the models of PD in signal (time) domain and phase-frequency domain. 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
and filter output for phase-frequency domain model
are almost equal:
Sine waveforms case
Consider a simple case of harmonic waveforms
Standard engineering assumption is that the filter removes the upper sideband
Consequently, the PD characteristic in the case of sinusoidal waveforms is
Square waveforms case
Consider high-frequency square-wave signals
General waveforms case
Let us consider general case of piecewise-differentiable waveforms
This class of functions can be expanded in Fourier series. Denote by
the Fourier coefficients of
Obviously, the PD characteristic
Modeling method based on this result is described in