Stopwatch and Timer Calibrations - National Institute of Standards ...
Stopwatch and Timer Calibrations - National Institute of Standards ...
Stopwatch and Timer Calibrations - National Institute of Standards ...
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The Time Base Method <br />
7.B.2. Using a Frequency Counter <strong>and</strong> an Acoustic Pickup<br />
If an acoustic pickup <strong>and</strong> amplifier are available, you can measure the frequency<br />
<strong>of</strong> a stopwatch time base directly with a frequency counter. The reading on<br />
the counter display can be used to calculate the frequency <strong>of</strong>fset using this<br />
equation:<br />
f f<br />
f (<strong>of</strong>fset) measured nominal ,<br />
f<br />
nominal<br />
where f measured<br />
is the reading displayed by the frequency counter, <strong>and</strong> f nominal<br />
is<br />
the frequency labeled on the oscillator (the nominal frequency it is supposed to<br />
produce).<br />
If f nominal<br />
is 32 768 Hz <strong>and</strong> f measured<br />
is 32 767.5 Hz, then the frequency <strong>of</strong>fset is<br />
–0.5 / 32 768 or –1.5 10 -5 or –0.0015 %. To get time <strong>of</strong>fset in seconds per day,<br />
multiply the number <strong>of</strong> seconds per day (86400) <strong>and</strong> the frequency <strong>of</strong>fset:<br />
86 400 (–1.5 10 -5 ) = -1.3 s per day ,<br />
which means the stopwatch can be expected to lose 1.3 s per day. You might find<br />
it easier to note that a 1 Hz error in a 32 768 Hz device equates to a time <strong>of</strong>fset <strong>of</strong><br />
about 2.64 s, since 86 400 / 32 768 = 2.64. Therefore, a 2 Hz <strong>of</strong>fset is about 5.3<br />
s / day, a 3 Hz <strong>of</strong>fset is about 7.9 s / day, <strong>and</strong> so on. If the acceptable tolerance is<br />
10 s / day, then you’ll know that 3 Hz is well within tolerance.<br />
These results show that even a low cost eight-digit frequency counter will<br />
provide more measurement resolution than necessary when measuring 32 768<br />
Hz devices. The last digit on an eight-digit counter represents 0.001 Hz (1 mHz),<br />
<strong>and</strong> a 1 mHz frequency <strong>of</strong>fset represents a time <strong>of</strong>fset <strong>of</strong> just 2.6 ms per day. Very<br />
few stopwatches or timers can perform at this level.<br />
7.B.3. Advantages <strong>of</strong> the Time Base Method<br />
The time base method completely eliminates the uncertainty introduced by<br />
human reaction time. The measurement uncertainty can be reduced by at least<br />
two orders <strong>of</strong> magnitude when compared to the direct comparison method, <strong>of</strong>ten<br />
to 1 10 -6 or less. This method is also much faster. The measurement can <strong>of</strong>ten<br />
be performed in a few seconds, as opposed to the several hours <strong>of</strong>ten required for<br />
the direct comparison method.<br />
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