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November 1957 Popular Electronics
 Table of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
Popular Electronics,
published October 1954 - April 1985. All copyrights are hereby acknowledged.
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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 pure 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.
Oscilloscope Traces
 Square Waves
This easy testing method helps us uncover a multitude of electronic "sins"
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 (below) 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 a necessity.
 
The 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 October 18, 2022
(updated from original post on
8/27/2012)
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