PDF Version - The American Watchmakers-Clockmakers Institute

horological time bases
by Jean-Felix Perotto, CSEM, Neuchâtel, Switzerland
device possessing a natural oscillating frequency or
resonance frequency, and presenting a high quality
factor. The accuracy of the time base is obtained
by adjusting the natural frequency of the resonator
or by modifying its environment, for example
the counter.
Introduction
Since the dawn of humanity, mankind has used
the Earth’s natural rotation cycles, on its axis and
around the Sun, to rhythm his daily activities. The
invention of the sundial in the 3rd century BC enabled
the diurnal fraction of the day to be segmented
into finer divisions. Then, in the 13th century,
rudimentary pendulum clocks activated by weights
appeared. Featuring neither dials nor hands, they
simply rang the hours. In 1658, the Dutch mathematician
Huygens constructed the first real clock.
It had a pendulum, was equipped with a dial, possessed
a single hour hand, and its accuracy was
approximately one hour per day. But the adventure
had finally begun.
First used for maritime navigation, then later to
regulate human activities, to synchronize trains and
more recently for the Internet network and the GPS
satellite navigation system to function, it became
necessary to invent timekeeping instruments of
increasing stability. At the heart of every clock and
watch is stored a fundamental element, the time
base. The present article retraces a brief history of
this time base.
What is a time base
Fundamentally, a time base is a device which produces
a frequency that is as stable as possible. A
timekeeper—clock or watch—is therefore nothing
other than a time base associated with a counter
and a device to display the state of this counter.
An oscillator is invariably found at the heart of a
time base; however, not all oscillators are necessarily
suitable. To be stable, the oscillator must
be based on a resonator; that is to say, a physical
The resonator is a passive element. It only becomes
an oscillator and constitutes a time base when associated
with a driving system. Time base stability
largely depends on the resonator and ultimately,
the clock or the watch it equips. However, at this
point, it might be useful to briefly recall a few notions
relative to resonators.
A bit of physics to help us understand
A resonator, more specifically harmonic, is a device
whose state is defined by a second-order linear differential
equation with constant coefficients:
(1)
where represents the dissipative losses and w 0
the natural pulsation of the resonator, or resonance
frequency. When the losses are weak, the solution
of this equation is a sinusoidal function of time
weighted by an exponential damping term:
(2)
Therefore, a harmonic resonator of non-zero initial
conditions produces damped sinusoidal frequency
oscillations.
However, as can be observed
in a resonator with a chronometric vocation, the
damping factor plays a key role.
The fundamental parameter qualifying any resonator
is its quality factor or Q-factor. It is a dimensionless
number that can be interpreted in two different
ways despite being very closely linked. Firstly,
Q can be considered as the ratio between the
internal energy W of the resonator and the dissipated
energy rW, due to the Joule-loss during an
oscillation cycle:
(3)
Consequently, a resonator with a high quality factor
requires less energy to drive than an identical
resonator with a low quality factor. Another slightly
more abstract interpretation of the Q-factor,
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