Detectors 177
Detectors 177 : Particle Detectors: (4.21) Phase Detector Characteristic: (1) Analog multiplier Phase Detector Characteristic: Consider a classical phase detector implemented with analog miltiplier and low-pass filter. Here and denote high-frequency signals, piecewise differentiable functions, represent waveforms of input signals, denote phases, and denotes the output of the filter. If and satisfy the high frequency conditions (see ) then phase detector characteristic is calculated in such a way that time-domain model filter output. are almost equal: Phase detector in phase-frequency domain. (1. 1) Sine waveforms case: Consider a simple case of harmonic waveforms and integration filter. Standard engineering assumption is that the filter removes the upper sideband from the input but leaves the lower sideband without change. Consequently, the PD characteristic in the case of sinusoidal waveforms is. (1. 2) Square waveforms case: Consider high-frequency square-wave signals and. For this signals it was found that similar thing takes place. The characteristic for the case of square waveforms is. (1. 3) 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 and. Then the phase detector characteristic is Obviously, the PD characteristic is periodic, continuous, and bounded on
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