Page 355 - The Mechatronics Handbook

FIGURE 17.10 Phase plots of four noise types.

17.3 Time and Frequency Standards

All time and frequency standards are based on a periodic event that repeats at a constant rate. The device
that produces this event is called a resonator. In the simple case of a pendulum clock, the pendulum is the
resonator. Of course, a resonator needs an energy source before it can move back and forth. Taken
together, the energy source and resonator form an oscillator. The oscillator runs at a rate called the
resonance frequency. For example, a clock’s pendulum can be set to swing back and forth at a rate of
once per second. Counting one complete swing of the pendulum produces a time interval of 1 s. Counting
the total number of swings creates a time scale that establishes longer time intervals, such as minutes,
hours, and days. The device that does the counting and displays or records the results is called a clock.
Table 17.3 shows how the frequency uncertainty of a clock’s resonator corresponds to the timing uncer-
tainty of a clock.
Throughout history, clock designers have searched for more stable resonators, and the evolution of
time and frequency standards is summarized in Table 17.4. The uncertainties listed for modern standards
represent current (year 2001) devices, and not the original prototypes. Note that the performance of
time and frequency standards has improved by 13 orders of magnitude in the past 700 years, and by
about nine orders of magnitude in the past 100 years.
The stability of time and frequency standards is closely related to their quality factor, or Q. The Q of
an oscillator is its resonance frequency divided by its resonance width. The resonance frequency is the
natural frequency of the oscillator. The resonance width is the range of possible frequencies where the
oscillator will oscillate. A high-Q resonator will not oscillate at all unless it is near its resonance frequency.
Obviously, a high resonance frequency and a narrow resonance width are both advantages when seeking
a high Q. Generally speaking, the higher the Q, the more stable the oscillator, since a high Q means that
an oscillator will stay close to its natural resonance frequency.
This section begins by discussing quartz oscillators, which achieve the highest Q of any mechanical-
type device. It then discusses oscillators with much higher Q factors, based on the atomic resonance of
rubidium and cesium. Atomic oscillators use the quantized energy levels in atoms and molecules as the
source of their resonance. The laws of quantum mechanics dictate that the energies of a bound system,
such as an atom, have certain discrete values. An electromagnetic field at a particular frequency can boost
an atom from one energy level to a higher one. Or, an atom at a high energy level can drop to a lower
level by emitting energy. The resonance frequency (f ) of an atomic oscillator is the difference between

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