Methods for Setting Time Intervals for the Measuring Phase Locking Systems

The work studies the behavior of phase-locked loops (PLL) incorporated into measuring devices with controlled accuracy, constructed for communication systems. Qualitative and analytical evaluation of PLL behavior was made based on the analysis when the system's input was exposed to a phase jump of a reference signal. A description of the system of differential equations was made, showing the time variation of the difference of reference frequency and adjusted generator frequency in the ring with idealized delay line, in the PLL models with delay caused by low-pass filters. The performance of PLL system is investigated. A differential equation was derived that describes the behavior of a non-autonomous PLL when a pulse signal is applied to it, provided that the corresponding voltage is applied to the input of its control element. In the general case, this equation is a nonlinear differential equation of arbitrary order. The order of the equation is determined by the selection of a low-pass filter. Choice of phase detector characteristic type determines whether a given equation is linear. If a sawtooth phase detector is used, the equation is linear. If the characteristic of the phase detector is sinusoidal, cosine or trigonometric, the equations become nonlinear