32 October 2015
base frequency waveform viewed. The operation of the
harmonic switch is demonstrated in Figure 3.
Using the circuit in Figure 2, we can shift the
amplitude, phase, and frequency of the harmonic. There
are some key points to be made here. Harmonics produce
variations in the shape of the base wave. The higher the
amplitude of the harmonic frequency, the greater the
change in the base wave’s shape. The higher the multiple
the harmonic frequency is, the greater the number of
changes that occur to each base wave cycle. These
concepts are demonstrated in Figure 4.
In Figure 5, I took one of the signals in Figure 4 and
(using Microsoft Paint) shifted the position of the traces so
as to recreate the harmonic signal. Below that, I compared
one cycle to another by overlapping the signals.
Let’s look a little more deeply at harmonics. The thing
that is significant about harmonics is that they are stable,
Visualizing the frequency content of a waveform is
challenging. This is most true with live signals with their
constant small changes. If possible, store the trace and
look back at it in a stationary form. Focus in on the
characteristics of the waveform that are stable, keeping in
mind how the base waveform looked. Figure 6 shows the
original base waveform placed on top of the harmonic
signal to highlight the differences. You are looking for
variations in the signal that repeat from cycle to cycle, not
just random changes in the signal. Figure 7 is an illustration
of a square wave with non-harmonic interference. Note
the variation in the change between cycles.
The differentiation between harmonic and non-harmonic interference is important. Harmonics are caused
by non-linear changes in current and voltage. Harmonic
interference is commonly the result of a distortion to the
base signal, such as clipping with a diode. Non-harmonic
interference is from a source unrelated to the base signal.
Next, let’s try to identify specific harmonic
frequencies. The closest we can get to this with our
technique is to identify the harmonic number. The
FIGURE 3. Circuit with harmonic enhancement
FIGURE 4. The effect of harmonics on base signals.
FIGURE 5. Signal graphic manipulation.
FIGURE 6. Square wave with non-harmonic interference
highlighted in red.
FIGURE 7. Square wave with non-harmonic