May 1941 Radio-Craft
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio-Craft,
published 1929 - 1953. All copyrights are hereby acknowledged.
As with so many topics, the basics
of topics like harmonic distortion (and other forms of distortion) in an amplifier
circuit has not changed much - if at all - over the decades. Test equipment and
circuits being measured get more advanced, but, especially if you are new to the
concept, articles like this one on audio-frequency distortion from a 1941 edition
of Radio-Craft magazine are as useful today as it was when it was written.
When studying, in particular, harmonic distortion, having a knowledge of the Fourier
series for common waveforms like
square waves, and even a
shaped wave is especially enlightening since it explains a lot of waveform shapes
where harmonics are present.
Measuring Distortion in Audio-Frequency Amplifiers
Fig. 1 - Simple amplifier stage with meters for detecting distortion.
In the following article (reproduced from "The Aerovox Research Worker" by courtesy
of the publishers) the elements of qualitative analyses of A.F.-amplifier frequency
distortion, as commonly applied by sound technicians, are mentioned. The more precise
methods of making quantitative analyses an then described. at length.
The simplest qualitative test for distortion in a class A audio-frequency amplifier
stage may be made, as shown in Fig. 1, by applying a signal voltage of proper
level to the input and inspecting the circuit for one or all of the following abnormal
(a) Presence of D.C. grid current.
(b) Fluctuation of the D.C. plate current,
(c) Fluctuation of the D.C. cathode voltage, if the circuit employs cathode resistor
Each of these indications generally occurs in a positive direction, and each
will disappear upon removal of the signal. It must be borne in mind, however, that
this method is purely rudimentary in nature and serves only to detect the presence
of distortion. One or two of the indications may be absent, depending upon the main
cause of the trouble.
Qualitative Tests for Distortion
The 3 simple indications are well known and frequently used by Servicemen and
P.A. .testers who have no equipment suitable for making quantitative distortion
measurements, but must, in the course of routine testing, localize distortion without
reference to the actual per cent harmonic energy present.
Fig. 2 - Signal plate current.
Audio-frequency amplifier may be checked for distortion.
Fig. 4 - Pronounced third harmonic content.
The cathode circuit effects noted above are due to fluctuations in the voltage
drop across the cathode resistor, occasioned by variations in the D.C. component
of plate current. The current indicated by the plate-circuit milliammeter is the
average value of the fluctuating "signal" plate current, is identical with the D.C.
component, and is the current that produces the cathode resistor drop.
These facts may be better comprehended when it is remembered that the fluctuating
signal plate current (Fig. 2) is an alternating current, corresponding to the
signal, superimposed upon a direct current. It will be evident from the fundamental
relations of this combination that the average value of plate current, as indicated
by the plate-circuit milliammeter, will be constant in the company of the alternating
component under distortionless operating conditions.
Figure 2 is a graphical representation of signal plate current. Here, Imax.
is the maximum value reached by the fluctuating plate current; Io the
zero-signal value; Imin. the minimum value. From these values, it may
be shown that the per cent 2nd-harmonic content (often the most troublesome distortion
factor) is equal to:
Quantitative methods of checking distortion are harmonic analyses, and are concerned
with measurement of the actual amount of energy present in each separate harmonic
of the signal frequency (or in the total harmonic content) and establishment of
percentages with respect to the fundamental frequency. The most representative methods
employed in wave analysis and the apparatus necessary thereto will be described
The cathode-ray oscilloscope is notably useful in the observation of wave shapes.
When the horizontal plates of the ray tube are energized by a sawtooth-wave sweep-oscillator-amplifier
circuit to furnish the linear time base, and a signal voltage which it is desired
to observe is applied to the vertical plates through a substantially flat-response
amplifier, the cathode-ray trace will be an exact reproduction of the waveform of
the applied signal voltage.
An audio-frequency amplifier may be checked for distortion with the oscilloscope
in the manner illustrated in Fig. 3. At A is an audio oscillator possessing
an output voltage waveform of known purity, B is the amplifier under test, and C
is an oscilloscope having horizontal and vertical amplifiers with substantially
flat frequency responses. The units are connected in the order shown.
It is the purpose of the oscillator to supply a signal of as pure waveform as
practicable to the amplifier, and that of the oscilloscope to reproduce the wave-shape
of the signal after it has passed through the amplifier. In order that as little
distortion as possible be introduced by the instruments themselves, the oscillator
used for such a test must be of exceptionally high quality and the amplifiers in
the oscilloscope must possess an excellent frequency characteristic. Likewise, the
oscilloscope sweep circuit must be uncompromisingly linear in its characteristic.
If the amplifier had no distortion at all, the signal it delivered to the oscilloscope
would be an exact reproduction of, the input signal waveform. This is never encountered
in practice, however, the most efficient amplifier arrangement being beset with
the distortion characteristics of its tubes and other components.
For observations, a perfect sine wave (or, better still, a tracing of a single
cycle from the test oscillator) might be inscribed on the transparent viewing screen
of the oscilloscope, and signals from the amplifier matched to this pattern to discover
variations from the original shape due to amplifier distortion. In making such a
test, it would of course be necessary to adjust both oscilloscope amplifier gain
controls in such manner that the maximum amplitude and width of the signal trace
coincided with those dimensions of the inscribed pattern.
With the low percentages encountered with most well-designed amplifying equipment,
it will be difficult to estimate the percentage of harmonic content from the reproduced
wave-shape, in the oscilloscopic method, unless the operator makes use of the transparent
screens furnished by some oscilloscope manufacturers for the purpose. These screens
carry printed patterns of single cycles corresponding to the shapes obtained (variations
from true sinusoidal) with various low percentages of distortion. Severe cases would
result in images similar to Fig. 4 which is an exaggerated representation of
pronounced 3rd-harmonic content.
Fig. 5 - Wien bridge circuit.
Fig. 6 - Bridge harmonic totalizer.
Fig. 7 - Arrangement employed in the distortion and noise meters
found in broadcast stations.
Certain bridge circuits, notably the Wien bridge (see Fig. 5) can be used
for the identification of frequencies in the audio-frequency spectrum. If an alternating
voltage is delivered to the bridge circuit, the latter may be adjusted for a null
at that particular signal frequency. The null point would not hold for the same
voltage of another frequency. Thus, the adjustable element of the bridge might be
calibrated to read directly in cycles/second.
The Wien bridge in its most useful form for this purpose would have its constants
so chosen. that the ratio arm, R2 is twice the ohms value of R1
the condensers C1 and C2 are equal in capacity, and the 2
simultaneously-adjustable resistance legs, R3 and R4 are at
all positions equal. Under these conditions, the frequency of the impressed voltage
at null would be equal to:
Frequency is in cycles/second,
R is the resistance of R3 or R4 in ohms,
C is the capacity of C1 or C2 in farads.
Since the bridge may be balanced for only one frequency at a time, it would appear
that any residual voltage indicated by the vacuum-tube voltmeter, M, at null would
be due to some other frequency or frequencies (such as harmonics of the fundamental).
And this harmonic voltage would be due to the total of harmonic voltages present.
As such, the bridge might be connected, as shown in Fig. 5, to the output circuit
of an audio-frequency amplifier which is passing a signal from a high-quality audio
While the device might be used as shown as such a harmonic totalizer, the percentage
total harmonic content with respect to the readings of the meter before and after
null would not be reliable, nor would its error be uniform for all frequencies.
These facts are due to the peculiar nature of the bridge to attenuate various harmonics
Another popular type of bridge harmonic totalizer (due to *U.T.C.) is shown in
Fig. 6. Here, 3 legs of the bridge, R2, R3 and R4,
contain pure resistance, while the 4th leg contains the shielded parallel resonant
circuit, L-C, which is resonant at the test frequency. The transformer, T, like
the one shown in the bridge previously described, must have an excellent frequency
At resonant frequency of L-C, the inductive reactance of the tuned circuit equals
the capacitive reactance, the former is canceled by the latter, and the bridge balances
as if all 4 legs were pure resistance. Any voltage applied by the circuit to the
vacuum-tube voltmeter is then due to harmonics of the test frequency (and it is
assumed that these harmonics have been delivered to the bridge by the amplifier
In operation, the double-pole, double-throw switch, S, is thrown to position
2 and the bridge balanced with the assistance of the vacuum-tube voltmeter, M, as
a null indicator. The reading at null (due to harmonics) is recorded. The switch
is then thrown into position 1 and R5 is adjusted until the meter gives
the same reading (as before at null). The following calculation may be performed
to determine the percent of total harmonics from this operation:
A dial indicator attached to the potentiometer R5 may be calibrated
directly in these percentages.
A very efficient method of measuring total harmonic content in the signal delivered
by an audio-frequency amplifier makes use of the arrangement employed in the distortion
and noise meters found in broadcast stations. (See Fig. 7.)
In this arrangement, the signal from a high-quality sine-wave audio test oscillator
is fed into the amplifier under test. The amplifier output is connected to a high-pass
filter which removes the test frequency but leaves all of its harmonics.
The actual voltage due to the harmonics is then measured by means of an attenuator
and vacuum-tube output voltmeter. This measurement is one of total harmonic distortion,
but it is entirely possible to arrange additional flat-response amplification with
various high-pass filters to remove the various harmonics singly along with the
The wave analyzer, a highly-developed and refined form of heterodyne vacuum-tube
voltmeter, provides the most advanced, accurate, and complete means of measuring
amplifier distortion by determining the various harmonic voltage magnitudes. The
instrument is tunable to the fundamental and any of a series of its harmonics separately,
so that waveforms of considerable complexity may be investigated. At the same time,
measurements of hum and noise amplitude are made available. In effect it is a highly
selective electronic voltmeter.
Fig. 8 - Input multiplier, amplifier, and pad functional block
The representative wave analyzer (General Radio) receives the signal to be inspected
through an input channel embracing an input multiplier, amplifier, and pad (see
the functional block diagram of Fig. 8). The frequencies accepted by the input
channel lie in the range 20 to 16,000 cycles/second - the entire common audio-frequency
spectrum. A local heterodyne oscillator stage supplies heterodyning voltage of such
frequency variation that throughout the signal input range, an intermediate frequency
of 50 kc. may be produced. The dial controlling this oscillator is graduated in
the frequencies admitted by the input channel.
The fixed-frequency 50 kc. I.F. channel is extremely sharp, containing 3 quartz
crystals and is preceded by a balanced modulator, the output of which contains the
upper and lower sidebands obtained from the heterodyning process. The carrier is
suppressed. The superselective I.F. channel is followed by a 50 kc. amplifier and
the indicating instrument.
In operation, the wave analyzer is tuned to the .fundamental test frequency and
then to the successive harmonics to an extent determined by the amount of frequency
tuning range between the fundamental and the 16-kc. limit of the dial. The harmonic
amplitudes are indicated directly by the meter.
*United Transformer Corp.
Posted October 3, 2023
(updated from original
post on 11/4/2015)