November 1957 Popular Electronics
Table of Contents
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This is one of a multi-part series of articles that appeared
in Popular Electronics magazine on using an oscilloscope
(o-scope) to analyze signal waveforms. An introduction to square
waves and how to accurately measure them is covered here. Frequency-compensating
the o-scope probe is always an important step prior to sampling
just about any waveform other than a pure sinewave, because
per Fourier series analysis, every periodic waveform can be
defined by a series of sinewave and various frequencies, phases,
and amplitudes. The author demonstrates with a square wave being
composed of the fundamental frequency and its odd harmonics.
I remember being amazed to learn whilst in engineering school
that mathematically it takes a summation of an infinite number
of odd harmonics (appropriately amplitude-adjusted)
to define a purse square wave (the
Gibbs phenomenon), otherwise, there will always be
a slight overshoot at the rising and falling edges.
Next month's article features
radio frequency (RF) measurements.
This easy testing method helps us uncover a multitude of
By Howard Burgess
Square wave testing can be called the "buckshot" approach.
One shot covers a lot of territory, and can bring down a whole
flock of fast clues. In many kinds of testing, a single frequency
or tone is put into the input of an amplifier or system and
the output waveform is checked for distortion and level. But
when an amplifier is to be checked over a wide band of frequencies,
this method can be long and tedious. It would save considerable
time and provide a better overall test if a number of the desired
frequencies could be checked simultaneously.
That's just what actually happens in cases where we employ
a square wave as a test signal. A quick look at the structure
of a square wave shows why this is so.
What Is In the Wave. The oscilloscope pattern
in Fig. 1 is an example of a sine wave. This is a simple sinusoidal
waveform which we will call F1. The square shown in the broken
line is the desired shape of a "square wave."
In Fig. 2, we still have F1 but the third harmonic F3 (or
F1 times 3) has also been added. This combination provides the
waveform labeled F1+F3, which fills out a little more of the
square-wave box. By adding the fifth harmonic, we get the wave
F1+F3+F5 as shown in Fig. 3.
A low-capacity probe such as this one is needed for square-wave
observation. Finished probe is shown in top photo, circuit and
construction details in the two lower illustrations.
Even a simple square-wave generator used in conjunction with
a 'scope will quickly show up defects in an audio system. Primarily
it serves as a good indication of frequency response.
Using our imagination, we can see what is happening to the
original waveshape. With each harmonic added, the shape comes
closer to that of the dotted line square. If the process of
adding odd harmonics is continued, we finally arrive at a fairly
acceptable square wave by the time about 10 harmonics are thrown
in with the fundamental.
The first four figures illustrate the relationship
between the square wave and its constituent sine waves. Fig.
1 compares the sine wave and square wave. In Fig. 2 is a sine
wave and its third harmonic. In Figure 3 is a sine wave plus
its third and fifth harmonics, which together begin to fill
out the shape of the square wave. Figure 4 shows an ideal square
wave containing a large number of harmonics.
Yet, in many cases, 100 or more harmonics may be needed to
produce the desired waveshape with the filled-out corners, as
shown in Fig. 4. Suppose that a 1000-cps square wave which includes
the 10th odd harmonic is used to test an amplifier. The amplifier
must then be able to respond up to 21,000 cps or better to pass
the waveshape without distortion.
By using a square wave as a test signal, it is not only possible
to test the complete frequency response of an amplifier, but
you can also show up troubles such as phase shift and instability
resulting in oscillations and parasitics.
"Square Deal" Probe. When using a square-wave
generator and oscilloscope in a test setup, keep these items
in mind: (1) the generator must be properly matched to the input
of the amplifier; (2) the amplifier output must be properly
loaded; (3) the oscilloscope must be connected across the output
of the amplifier under test in such a way that the 'scope leads
themselves do not distort the waveshape of the signal. In most
cases, simple leads to the 'scope are not adequate and will
cause serious distortion. A simple probe, easy to make, is almost
circuit for such a probe is shown at left, and the photos will
give a general idea of its construction. The low-capacity shielded
line to the 'scope should be less than two feet long and the
entire probe must be kept well-shielded. The ceramic trimmer
is adjusted by feeding a known square wave from a generator
into the tip of the probe and tuning for the squarest wave possible
on the 'scope. Once adjusted, this type of test lead is also
excellent for use on video circuits. The probe, because of its
method of operation, will normally attenuate the input signal
somewhat, but you can compensate for this.
Connections of the square-wave generator and 'scope are very
much like those suggested for testing with a sine-wave oscillator,
but the interpretation of the pattern is very different.
Which End Is Up? When an amplifier is driven
by a square-wave generator and the oscilloscope connected to
its output displays a pattern like Fig. 4, the amplifier is
probably passing up to the 25th or higher harmonic. However,
if the trace more nearly resembles Fig. 5, the slope to the
right indicates a loss at the lower frequencies while retaining
good high-frequency response.
A slope in the reverse direction, as shown in Fig. 6, indicates
just the opposite: good low-frequency response with a dropping
off at the highs. Figure 7 is a curve indicating that an amplifier
is lacking in both low and mid-range response.
The curve in Fig. 8 bears little resemblance to a square
wave and shows an extreme case of high-frequency attenuation.
When using square waves, it can be said in a generalized interpretation
that the left-hand edge of each half-cycle indicates the high-frequency
conditions existing in the tested amplifier while the right-hand
edge of each half-cycle indicates the low-frequency conditions.
Superimposed ripples on the leading (or high-frequency) edge
as in Fig. 9 indicates the presence of oscillation or "ringing."
Complete books have been written about square-wave testing,
and very limited ground can be covered in a few hundred words.
However, even with the simplest kind of square-wave generator,
such as the one shown, used only for the simple patterns given
here, one can gain much experience and knowledge.
Square-wave patterns indicate conditions within the amplifier
under test. The waveform in Fig. 5 indicates good high-frequency
response but poor lows, while the waveform in Fig. 6 indicates
good low-frequency response but poor highs. Figure 7 illustrates
a case of poor low- and medium-frequency response, and Fig.
8 indicates serious attenuation of high frequencies. The pattern
in Fig. 9 betrays the presence of high-frequency instability
or "ringing" in the system.
Posted March 27, 2012