Page 350 - The Mechatronics Handbook

FIGURE 17.3 Measurement using a frequency counter.

FIGURE 17.4 Phase comparison using an oscilloscope.

Frequency offset can be measured in either the frequency domain or time domain. A simple frequency
domain measurement involves directly counting and displaying the frequency output of the DUT with
a frequency counter. The reference for this measurement is either the counter’s internal time base oscillator,
or an external time base (Fig. 17.3). The counter’s resolution, or the number of digits it can display, limits
its ability to measure frequency offset. For example, a 9-digit frequency counter can detect a frequency
-8
offset no smaller than 0.1 Hz at 10 MHz (1 × 10 ). The frequency offset is determined as
f measured – f nominal
(
f offset) = --------------------------------------
f nominal
where f measured is the reading from the frequency counter, and f nominal is the frequency labeled on the
oscillator’s nameplate, or specified output frequency.
Frequency offset measurements in the time domain involve a phase comparison between the DUT and
the reference. A simple phase comparison can be made with an oscilloscope (Fig. 17.4). The oscilloscope
will display two sine waves (Fig. 17.5). The top sine wave represents a signal from the DUT, and the
bottom sine wave represents a signal from the reference. If the two frequencies were exactly the same,
their phase relationship would not change and both would appear to be stationary on the oscilloscope
display. Since the two frequencies are not exactly the same, the reference appears to be stationary and
the DUT signal moves. By measuring the rate of motion of the DUT signal we can determine its frequency
offset. Vertical lines have been drawn through the points where each sine wave passes through zero. The
bottom of the figure shows bars whose width represents the phase difference between the signals. In this
case the phase difference is increasing, indicating that the DUT is lower in frequency than the reference.
Measuring high accuracy signals with an oscilloscope is impractical, since the phase relationship
between signals changes very slowly and the resolution of the oscilloscope display is limited. More precise
phase comparisons can be made with a TIC, using a setup similar to Fig. 17.2. If the two input signals
have the same frequency, the time interval will not change. If the two signals have different frequencies,

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