IEEE Circuits and Systems Magazine - Q2 2020 - 19

data representing temperature, which is then processed
by a DSP + DDS block. The output of this block is fed
into a PLL as its input. The frequency tuning hence occurs from the input side of the PLL. In another example
of any-rate clock generator [63], the frequency tuning
is accomplished through a digitally controlled on-chip
oscillator. The digital control is generated from a DSP
processor as shown in Figure 9(d).
Figure 9(e) shows the structure of our TAF-DPS based
solution. It can be viewed as a DCXO since its frequency
control is a digital. The frequency stability of this XO
(or MEMS or LCO) plus TAF-DPS structure is dominated
by the stability of the XO. However, thanks to TAF-DPS's
superior tunability, frequency error on XO can be compensated [53] and frequency variation caused by environment can be counteracted in real time. Table I compares all the aforementioned sources in their suitability
for assisting the task of time synchronization
IV. TAF-DPS Syntonistor for Time Synchronization
A. Definition
t: real time, Newtonian time, unobservable.
k: a natural number, its increase represents
the forward movement of real time t.
t[k]: the value of t at k, unobservable.
R[k]: a golden time reference, observable, e.g. the
UTC.
Tt : = t [k + 1] - t [k] or = R [k + 1] - R [k]

T lc [k]: a common notion of time established within a
network, logical clock, calculated by algorithm.

fi [k]: ith node's clock hardware frequency at k.

T i [k]:
ith node's physical clock at step k, influenced only by fi [k].
T li [k]:
ith node's logical clock at step k, can be adjusted by algorithm.
mi[k]: rate of T li [k] increment at step k, T li [k + 1] =
T li [k] + m i [k]
N: number of ticks between two consecutive
synchronizations in unit of k, also called
one interval, or one round.
M: number of ticks between two syntonization
events, in unit of k.
Accuracy: A parameter quantifying a relationship between two objects of a target and an objectunder-study: the distance between the target and the object-under-study, measured
using certain unit. Accuracy is the degree
of conformity of a measured or calculated
value to its definition.
P recision: A parameter quantifying a relationship among
multiple objects-under-study: the standard
deviation of the distances of all the objects
to the mean value.
Stability: A parameter quantifying the degree of variation over a given time interval of a quantifiable parameter, such as accuracy or precision. Stability doesn't indicate whether the
parameter, such as accuracy, is "good" or
"bad," but only whether it stays the same.
Those definitions establish the base for future discussion. k is a natural number which is independent of time.
Its monotonic increase corresponds to the arrow-of- ardware,
time: the forward movement of real time t. In h

Table I.
Suitability of frequency-tunable sources for assisting time synchronization.
Source

Frequency Tunability

Switch Speed

Circuit Cost

Programmability

Mechanism trim

N/A

None

VCXO

Tuned by voltage, frequency
granularity is limited by
voltage resolution, sub-ppm

~ Hundreds of
clock cycles

High cost, high
power, hard to be
integrated

Difficult to program, unsuitable for being
used in algorithm since response time is
long and precision is not predictable

DCXO

Tuned by digital word,
granularity is limited by
varactor, sub-ppm

~ Hundreds of
clock cycles

Large area,
medium power,
easy to integrate

Easy to program, but unsuitable for
being used in algorithm since hardware
response time is long

MEMS

Tuned by digital word,
granularity is limited by the
PLL circuit, sub-ppm

~ Hundreds of
clock cycles

Medium cost, and
power, hard to be
integrated

Easy to program, unsuitable for being used
in algorithm since hardware response time
is long and precision is not predictable

DSP
Synthesizer

Tuned by voltage,
granularity is limited by
voltage resolution, sub-ppm

~ Hundreds of
clock cycles

Large area, high
power, hard to be
integrated

Difficult to program, unsuitable for
being used in algorithm since hardware
response time is long

TAF-DPS
DCXO

Tuned by digital word,
frequency granularity
sub-ppb

Two clock
cycles

Small area, low
power, easily
integrated on-chip

Easy to program, friendly to be used in
algorithm since hardware responds fast
and precisely

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IEEE Circuits and Systems Magazine - Q2 2020

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