harmonic number is the multiple of the base frequency
that the harmonic frequency equals. For example, if the
base frequency was 1,000 Hz, the third harmonic would
be 3,000 Hz.
This technique is not good for harmonics alone. It can
also be used to identify near-harmonic interference. This is
in many cases as accurate as necessary, for example,
when selecting a filter. Make note of the number of
changes that occur within a waveform cycle and the
shifting position of the changes. This is easiest when
you’re able to observe several cycles at once.
To help visualize this, I simulated a square wave
harmonic on a sine wave base frequency. This caused the
harmonic to produce a definitive red pulse on the base
sine wave. In Figure 9, I generated a sine wave with a
square wave set at the fifth harmonic. The number of the
harmonic corresponds with the number of times the
change occurs in a cycle. In this case, the change that
occurred was five red pulses that appeared in each full
cycle of the sine wave.
When I went to school, I was taught that a square
wave consisted of a fundamental frequency and all its odd
harmonics. If we virtually reverse-engineer a square wave
and reassemble it from its harmonics, we will see that this
is not entirely true. As shown in Figure 10, when
attempting to add a fundamental frequency and its odd
harmonics, nothing approximating a square wave results
because the harmonic formula is incorrect.
In a square wave, the level of each harmonic should
equal the base amplitude divided by the harmonic
number. Observe how Figure 11 more closely
approximates a square wave.
Both triangle and square waves contain the same
harmonics; it is only the harmonic mix that is different.
Triangle waves contain less energy in their harmonics, and
as a result more closely resemble a sine wave (as
illustrated in Figure 12). It is often not the frequency of a
harmonic that matters, but the energy contained in the
harmonics that could possibly result in interference. The
magnitude of the change to a sine wave is an indication of
the energy contained in the harmonics. By noting the
differences between a signal and a sine wave, one can
start to gauge the energy in the harmonics.
In a square wave, the amplitude of the harmonics is
determined by dividing the amplitude of the base
frequency by the harmonic number. In a triangle wave, the
amplitude of the harmonics is determined by dividing the
FIGURE 8. Interpreting non-harmonic interference.
FIGURE 11. Waveform with harmonic levels adjusted
to approximate a square wave.
FIGURE 9. Sine wave with a square wave at the
FIGURE 10. Signal produced by equal level odd
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