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In addition to the definition on the
previous page, equivalent definitions of Q are shown above. Q is the frequency divided by the bandwidth
of resonance, and it also determines the rate at which a signal decays after
the vibration excitation stops - the higher the Q, the narrower the bandwidth
and the longer it takes for the excitation to decay. Q is proportional to the time it takes for
the signal to decay to 1/e of the amplitude of vibration prior to the
cessation of excitation. This
relationship is used in one method (sometimes referred to as the “logarithmic
decrement” method) of measuring Q.
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The relationship between Q and decay time
is also relevant to oscillator startup time.
When an oscillator is turned on, it takes a finite amount of time for
the oscillation to build up. The
oscillator’s startup time depends on the loaded Q of the resonator in the
sustaining circuit, and the loop gain of the circuit.
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H. Hellwig,
"Frequency Standards and Clocks: A Tutorial Introduction," NBS
Technical Note 616, 1977, Time and Frequency Division, NIST, Boulder, CO
80303.
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