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May 1939 QST
Most people engaged in circuit design and adjustment in a professional environment own or have access to a spectrum analyzer and/or digital oscilloscope with an FFT function, so measuring the harmonic content of a signal is a fairly simple job. A lot of instruments will display a listing of frequency makeup and the percentage of the whole signal it occupies. Many, though, particularly hobbyists, use simple analog o-scopes where determining harmonic content requires a largely subjective assessment of the displayed waveform. In 1939 when this article appeared in QST magazine, almost nobody, whether amateur or professional, had even an analog spectrum analyzer available, and therefore relied on drawings and a trained eye to discern harmonic content. The original article included two sets of full-size drawings of the distorted waveforms - one for comparing to a 2-inch CRT display and another for a 3-inch CRT. The user could trace the shapes onto a piece of onion paper and overlay it directly on the CRT for comparison.
By George Grammer
A Simple Method of Determining Whether Distortion Exceeds Acceptable Limits
Harmonic distortion is something which cannot wholly be avoided in an audio amplifier, but it must be kept within tolerable limits if the quality of reproduction is to be good. It is of considerable interest, therefore, to know the order of distortion present in an amplifier, but its measurement requires rather expensive equipment. On the other hand, for amateur work it is less important to know the exact amount and type of distortion generated than it is to know whether it lies above or below limits which represent "good," "fair," or "poor" performance.
If one has an oscilloscope with a linear sweep the order of distortion can be found quite readily with the help of the accompanying plots. These drawings, which were prepared by John L. Stiles, W8PLN, give typical cases of the types of harmonic distortion ordinarily encountered in audio equipment. The second-harmonic cases are characteristic of single-ended stages using triode tubes, while the third-harmonic drawings are representative of push-pull amplifiers or Class-B modulators. The sixth case, marked "7% second plus 5% third" is typical of a single-ended pentode amplifier working at rated output.
To utilize the drawings it is necessary to have a rather pure single-frequency signal for reference. This signal can be compared with the sine-wave curve to make sure that it meets the specifications. If no audio-frequency generator is available, the power-line wave-shape usually will be pretty close to a pure sine wave, and in case there is an appreciable discrepancy the harmonics can be filtered out by connecting a fairly good-sized condenser across the source. With the power line as the signal source, a step-down transformer should be used both for insulation and to reduce the voltage to a suitable value. The wave-shape of the source should be checked directly against the oscilloscope, of course, and should not be fed through the speech amplifier until after the purity of the wave has been established.
It is generally more convenient to use a higher frequency than 50 or 60 cycles, since a good many speech amplifiers will not respond well to such low frequencies - nor is it necessary that they should, since speech seldom contains any components below 100 cycles. The simple sine-wave oscillator shown in the Handbook1 will serve nicely for this purpose. It costs very little to make and is a handy gadget for testing purposes.
The two sets of figures shown are suitable for use with 3-inch and 2-inch tubes respectively. They are about as large as is practicable without running too close to the circumference of the cathode-ray tube screen. To use them, lay a sheet of transparent paper or celluloid over the drawing and carefully trace the plots, using as fine a line as possible. The tracing can then be held or fastened to the screen of the tube with the plot appropriately centered. With the signal applied to the oscilloscope, the horizontal and vertical controls should be manipulated until the screen pattern coincides as closely as possible with the tracing. It is not necessary to pay any particular attention to the dotted base-line, since this may or may not correspond to the horizontal sweep line on the screen when there is no vertical input.
The figures show a characteristic difference in form between waves containing even and odd harmonics. When even harmonics are present the lower half-cycle is not the same shape as the upper; in this case one half-cycle is more peaked while the second is broadened. With odd-harmonic distortion, however, the two half-cycles are identical, both being flattened at the peaks. The general rule that the wave is symmetrical in shape with odd-harmonic distortion and asymmetrical with even-harmonic distortion is true in all cases, although the actual shapes shown here are applicable only in the special case of distortion generated by the ordinary tube amplifier. A shift in the phase of the harmonic with respect to the fundamental will change the wave-shape considerably, even though the relative amplitudes are the same. When both even and odd harmonics are present, the resultant wave-shape is naturally a combination of the two effects, and the type of distortion is not easily recognizable.
By trying various of the plots against the pattern on the screen it should be possible to determine quite readily whether the distortion is excessive. If the output wave is not quite a sine wave but fails between the sine and 5 per cent second-harmonic curves, then the distortion is certainly less than 5 per cent, which is good. Distortion between 5 per cent and 10 per cent is tolerable enough, but if it exceeds 10 per cent it would be advisable to look into the speech amplifier. In general, attempt to make the lines coincide as far as possible starting from the center, letting the peaks indicate the order of distortion.
1 "Instruments and Measurements" chapter.
Posted June 3, 2016