# Oscilloscope Traces: Square WavesNovember 1957 Popular Electronics

 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.

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 March 27, 2012

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