Page 356 - The Mechatronics Handbook

Table 17.3 Relationship of Frequency Uncertainty to Time Uncertainty
Frequency Uncertainty Measurement Period Time Uncertainty
±1.00 × 10 -3 1 s ± 1 ms
±1.00 × 10 -6 1 s ± 1 µs
±1.00 × 10 -9 1 s ± 1 ns
±2.78 × 10 -7 1 h ± 1 ms
±2.78 × 10 -10 1 h ± 1 µs
±2.78 × 10 -13 1 h ± 1 ns
±1.16 × 10 -8 1 day ± 1 ms
±1.16 × 10 -11 1 day ± 1 µs
±1.16 × 10 -14 1 day ± 1 ns

TABLE 17.4 The Evolution of Time and Frequency Standards
Timing Frequency
Standard Resonator Date of Origin Uncertainty (24 h) Uncertainty (24 h)
Sundial Apparent motion of 3500 B.C. NA NA
the sun
-2
Verge escapement Verge and foliet 14th century 15 min 1 × 10
mechanism
-4
Pendulum Pendulum 1656 10 s 1 × 10
-6
Harrison Spring and balance 1759 350 ms 4 × 10
chronometer (H4) wheel
-7
Shortt pendulum Two pendulums, 1921 10 ms 1 × 10
slave and master
-10
Quartz crystal Quartz crystal 1927 10 µs 1 × 10
87 -12
Rubidium gas cell Rb resonance 1958 100 ns 1 × 10
(6,834,682,608 Hz)
133 -14
Cesium beam Cs resonance 1952 1 ns 1 × 10
(9,192,631,770 Hz)
-14
Hydrogen maser Hydrogen resonance 1960 1 ns 1 × 10
(1,420,405,752 Hz)
133 -15
Cesium fountain Cs resonance 1991 100 ps 1 × 10
(9,192,631,770 Hz)
the two energy levels divided by Planck’s constant (h):
E 2 – E 1
f = ----------------
h

The principle underlying the atomic oscillator is that since all atoms of a specific element are identical,
they should produce exactly the same frequency when they absorb or release energy. In theory, the atom
is a perfect ‘‘pendulum’’ whose oscillations are counted to measure time interval. The discussion of atomic
oscillators is limited to devices that are commercially available, and excludes the primary and experimental
standards found in laboratories such as NIST. Table 17.5 provides a summary [1,4,8].

Quartz Oscillators

Quartz crystal oscillators are by far the most common time and frequency standards. An estimated two
9
billion (2 × 10 ) quartz oscillators are manufactured annually. Most are small devices built for wrist-
watches, clocks, and electronic circuits. However, they are also found inside test and measurement
equipment, such as counters, signal generators, and oscilloscopes; and interestingly enough, inside every
atomic oscillator.

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