QUESTION:
What exactly is TDEV? How is it related to jitter and wander?
ANSWER:
The question regarding TDEV is actually quite a complex one and, to do it full justice, would require much more time and space than a normal quick response. However, I will try to provide just the crux of the matter as I see it and leave the details out.
The principal message that TDEV provides is related to the stability of a clock (or oscillator). TDEV is actually not one number but, rather, a "function" of the observation interval T (we usually use the Greek letter "tau" for the interval). Thus TDEV(T) is a measure of how much the phase (in time units) of a clock could change over an interval of duration T assuming that any systemmatic (i.e. constant) frequency offset has been removed. It is also, indirectly, a measure of how much the short-term (or "instantaneous") frequency could change over an observation interval of T.
One can view a clock waveform as being (almost) periodic, the deviation from periodicity being "clock noise". For example, a prototypical periodic function is the sinusoid and we could write a clock waveform as sin(g(t)) (in siunsoidal form). If g(t) is a perfect straight line, then the waveform would be "perfect", the "frequency" of the waveform would be constant and proportional to the slope of the line (a factor of two-pi comes into play to relate frequency in Hz to frequency in radians-per-second). Clock noise is equivalent to the deviation of g(t) from a perfect straight line and is, generally speaking, a random component. Jitter and wander are both manifestations of this clock noise. The distinction between jitter and wander is artificial, the more rapid fluctuations considered to be "jitter" and the less rapid fluctuations considered to be "wander" (10 Hz is the crossover between rapid and slow).
If g(t) was indeed a straight line, then [g(t+T)-g(t)] would be equal to [g(t+2T)-g(t+T)]. Any difference would be due to clock noise (jitter and/or wander). TVAR(T) is a measure of the power (i.e. variance) of this difference. TDEV(T) is the square-root of TVAR(T) (i.e. the standard deviation, or "root-mean-square", aka rms).
One simple interpretation of TDEV(T) can be contrived in the following manner. Suppose the clock was used to measure an event of duration T and this is done many times. One source of error would be the frequency offset, which would introduce an (fixed, i.e. constant) error every time the measurement is made. The clock noise would introduce an (random) error each time the measurement is made. TDEV(T) is the standard deviation of this random component.
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