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 something like making
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 are as useful today as it was when it was written.
Measuring Distortion in Audio-Frequency Amplifiers
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
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 abnor-mal
(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 bias
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.
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
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
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 presently.
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
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.
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
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
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 unequally.
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 characteristic.
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 under measurement).
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 fundamental.
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.
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 November 4, 2015