Crystal oscillators jitter measurements and its estimation of phase noise

It is shown that common method of jitter variance estimating by integrating phase fluctuations spectrum is not correct for sampling oscilloscope jitter measurements have been performed with synchronization to the measured signal. It is obtained that oscillators phase noise transformation depends on the sampling oscilloscope implementation and has many options have not been investigated deep enough. The inconsistence between the phase noise transformation and measurement results interpretation lead to errors in the measurements and specifications of crystal oscillators and other high stability sources, decrease the accuracy and stability of GPS, radar-systems, telemetry systems, etc. It is shown below that jitter variance should be estimated by integrating the spectrum of the frequency fluctuations, but not the spectrum of the phase fluctuations. It is obtained that jitter characterizes the high frequency part of the phase noise spectrum. The results obtained open the way of the phase noise evaluation from jitter measurements at frequency range up to 50 GHz and higher. The new relations between jitter measurements and phase noise are established for different types of oscilloscope synchronization measurements (transition jitter, period jitter, half-period jitter, etc.). It is obtained that famous way calculations jitter thorough Allan variance characterizes the circle-to-circle jitter. The methodology for jitter specification and characterization is discussed.