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Áà*ÁÓÓÃÃCharacterization of slave clock phase stabilityÄÄƒ
Ð€Ð1.ÁHÁThe slave clock model is described by the following equation:
À)À = t
ÁHÁx(t) = yÃÃbiasÄÄÃÃ.tÄÄ + ÃÃDÄÄ ÃÃ.ÄÄtÃÃ2ÄÄ + eÃÃpmÄÄ(t) + eÃÃfmÄÄ(À)À)dÀ)À
2
À)À = 0
where,
Ð8ÐÂHHÂÂX ÂÁ€HÁÁ€ÁÁHÁx(t)ÁøÁ is the phase©time output relative to the reference input
(dimensions of time)ÆÆ
ÐpÐÂHHÂÂX ÂÁ€HÁÁ€ÁÁHÁyÃÃbiasÄÄÁøÁ is a residual fractional frequency offset which can arise from Á@Qp&AÁ
ƒ disruption events on the reference input
(dimensionless)ÆÆ
Ð°ÐÁHÁDÂà Â is the linear frequency drift component when the clock is in
holdover condition (dimension 1/time)ÆÆ
ÐXÐÁHÁeÃÃpmÄÄ(t) is a white noise phase modulation (PM) component associated with
ÂHHÂÂX Â the short©term instability of the clock (dimension
time)ÆÆ
Ð` Ð
ÐÐÐÁHÁeÃÃfmÄÄ(t) is a white noise fractional frequency modulation (FM) component
ÂHHÂÂX Â associated with the disruption process of the
reference (dimensionless)ÆÆ
Ð` Ð
ÐÐÐÁHÁThe clock model is best understood by considering the three categories
of clock operation:
ÁHÁ©Á Áideal operation;
ÁHÁ©Á Ástressed operation;
ÁHÁ©Á Áholdover operation.
1.1ÁHÁÃÃIdeal operationÄÄ
ÁHÁFor short observation intervals outside the tracking bandwidth of the
PLL, the stability of the output timing signal is determined by the short term
stability of the local synchronizer time base. In the absence of reference
disruptions, the stability of the output timing signal behaves asymptotically as a white
noise PM process as the observation period is increased to be within the
tracking bandwidth of the PLL. The output of the clock can be viewed as a superposition
of the high frequency noise of the local oscillator riding on the low frequency
portion of the input reference signal. In phase locked operation the high
frequency noise must be bounded, and is uncorrelated (white) for large observation
periods relative to the bandwidth of the phase locked loop.
ÁHÁUnder ideal conditions, the only non©zero parameter of the model is the
white noise PM component.
1.2ÁHÁÃÃStressed operationÄÄ
ÁHÁIn the presence of interruptions, the stability of the output timing
signal behaves as a white noise FM process as the observation period is increased
to be within the tracking bandwidth of the PLL. The presence of white noise FM
can be justified based on the simple fact that in general, network clocks extract
time interval, rather than absolute time from the time reference. An
interruption is by nature a short period during which the reference time interval is not
available. When reference is restored there is some ambiguity regarding the
actual time difference between the local clock and the reference. Depending on the
sophistication of the clock phase build©out there can be various levels of
residual phase error which occur for each interruption. There is a random component
which is independent from one interruption event to the next which results in a
random walk in phase, i.e. a white noise FM noise source.
ÁHÁIn addition to the white noise FM component, interruption events can
actually result in a frequency offset between the clock and its reference. This
frequency offset (yÃÃbiasÄÄ) results from a bias in the phase build©out when reference
is restored. This is a critical point. The implications of this effect are that
in actual network environments there is some accumulation of frequency offset
through a chain of clocks. Thus, clocks controlled by the same primary reference
clock are actually operating plesiochronously to some degree.
ÁHÁTo summarize, under stress conditions the non©zero parameters of the
clock model are the white noise FM component (eÃÃfmÄÄ) and the frequency offset
component (yÃÃbiasÄÄ). The stressed category of operation reflects a realistic
characterization of what "normal" operation of a clock is.
1.3ÁHÁÃÃHoldover operationÄÄ
ÁHÁIn holdover, the key components of the clock model are the frequency
drift (D) and the initial frequency offset (yÃÃbiasÄÄ). The drift term accounts for the
significant ageing associated with quartz oscillators. The initial frequency
offset is associated with the intrinsic setability of the local oscillator
frequency.
2.ÁHÁÃÃRelationship of slave clock model to TIE performanceÄÄ
ÁHÁIt is useful to consider the relationship between the clock model and
the Time Interval Error (TIE) that would be expected. It is proposed that the two
sample Allan variance be used to describe the stochastic portion of the clock
model. The following equations apply for the three categories of operation:
ÃÃIdealÄÄ
ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ
À%ÀÃÃTIEÄÄ = ÀÀ 3 À%ÀÃÃ2ÄÄÃÃ,ÄÄ (À)À = t) ÃÃ.ÄÄt
ÃÃStressedÄÄ
ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ
À%ÀÃÃTIEÄÄ = ÀÀ À%ÀÃÃ2ÄÄÃÃbiasÄÄ + À%ÀÃÃ2ÄÄÃÃ,ÄÄ (À)À = t) ÃÃ.ÄÄt
ÃÃHoldoverÄÄ
ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ
À%ÀÃÃTIEÄÄ = ÃÃDÄÄ ÃÃ.ÄÄtÃÃ2ÄÄ + ÀÀ À%ÀÃÃ2ÄÄÃÃbiasÄÄ + À%ÀÃÃ2ÄÄÃÃ,ÄÄ (À)À = t) ÃÃ.ÄÄt
2
where,
ÐðÐÂHHÂÂX ÂÁ€HÁÁ€ÁÁHÁÀ%ÀÃÃTIEÄÄÁøÁis the standard deviation of the relative time interval error ofÔ
.,Ôthe clock output compared to the reference over the observation time t.ÆÆ
ÂHHÂÂX ÂÁ€HÁÁ€ÁÁHÁÀ%À,(À)À)ÁøÁis the two sample standard deviation describing the random
frequency fluctuation of the clock, andÆÆ
ÂHHÂÂX ÂÁ€HÁÁ€ÁÁHÁÀ%ÀÃÃbiasÄÄÁøÁdescribes the two sample standard deviation of the frequency bias.ÆÆ
3.ÁHÁÃÃGuidelines concerning the measurement of jitter and wanderÄÄ
ÁHÁVerification of compliance with jitter and wander specifications requires
standardized measurement methodologies to eliminate ambiguities in the measurements
and in the interpretation and comparison of measurement results. Guidance concerning
the measurement of jitter and wander is contained in Supplement No. 35.