Lissajous Had a Figure for It
sci-fi movies were famous for displaying Lissajous patterns on oscilloscopes
in hopes of portraying a futuristic look. The first time I hooked
up signals to the x and y axes of a scope and played around with
the frequencies and amplitudes, I was mesmerized by the patterns
and the fact that it was me creating them. Of course that was 30-something
years ago when I was first getting into electronics and electricity,
but even today it's a cool thing to do. In a typical, male-dominated,
Chauvinistic manner, this article from the March 1957 edition of
Popular Electronics delves into the subject of Lissajous patterns.
The author dares to compares men's attraction to curvaceous o-scope
figures to a similar attraction to curvaceous women. Can you imagine
the hateful feedback the editor of a current magazine would receive
if something like this slipped past the proofreading crew? Of course,
it's still OK to denigrate men in any way deemed necessary to spice
up an article, but don't dare kid around with women! The NOW crowd
will screech a banshee's fit and demand a public apology - and,
of course, a large donation to the NOW fund.
March 1957 Popular Electronics
Wax nostalgic about and learn from the history of early electronics. See articles
published October 1954 - April 1985. All copyrights are hereby acknowledged.
See all articles
Lissajous Had a Figure for It
By Howard Burgess
Century-old light pattern now
serves as electronic yardstick
are traditionally attracted by figures with curves. A certain
Frenchman named Lissajous, who lived around 1855, was no exception.
He became an exception when he found that he could control these
"figures with curves" in a dark room. He discovered that light reflected
from two flat, rapidly rotating mirrors formed simple wave patterns
when projected upon a screen.
This discovery set in motion
a chain of developments culminating in the modern oscilloscope.
Lissajous patterns on the oscilloscope screen measure sound frequencies
or the rotary speed of a motor, tell whether a transmitter is multiplying
frequency properly, check phase shift and distortion in hi-fi equipment,
calibrate audio signal generators, and do many other jobs.
The light source for Lissajous' mirror-generated patterns was
a simple candle. In place of a candle, the modern oscilloscope contains
an electron gun in the narrow neck of the tube. This gun shoots
about 6,000,000,000 electrons per second in a concentrated high-velocity
beam toward the face of the tube. When the impact of this beam strikes
the chemically coated face of the tube, it converts its energy into
light, forming a small luminous dot.
Basic Traces. In its travel toward the tube screen,
the electron beam must pass between two separate pairs of deflection
plates capable of bending the path of travel. These correspond in
their action to Lissajous' mirrors. An electrical signal or voltage
applied to one set of the plates bends the beam up or down; a signal
applied to the other set of plates bends the beam to the left or
right, depending on the polarity of the signal. As the beam bends,
the dot of light moves across the screen. Because it rapidly retraces
its path and because the chemical used on the screen continues to
glow for an instant after the dot has moved, the eye has the illusion
of seeing a continuous and steady bright line rather than a fast-moving
Fig. 1. Lissajous patterns representing phase relationships
between two 60-cycle currents.
If different signals are placed simultaneously on
each set of deflection plates, the beam makes a track like a Sunday
driver. If the two signals have a fixed periodic relationship to
each other, the pattern may seem like the "doodlings" of a lace
designer, but to the experienced operator it will be a source of
valuable information. These are still known as Lissajous figures.
Figure 1 is an example of the result obtained by putting
a low value of line voltage on each set of deflection plates.
In 1(A), the voltage on both sets of plates
is in phase, that is, both are rising and falling at the same time
and in the same direction. The result is a straight line. In 1(B),
the rise and fall on one set of plates is lagging behind the rise
and fall of the voltage on the other set, resulting in a curve.
The trace and retrace curves together form an ellipse. The more
one signal lags behind the other, the fatter grows the ellipse,
until it turns into a perfectly round circle when the lag equals
a quarter cycle. When one voltage lags behind the other in phase
by 180°, a straight line results.
Closely related are the curves of Fig. 2. These represent simple
tests for overloading in an audio amplifier. Most well-designed
amplifiers, when fed increasing amounts of input signal, show little
increase in distortion until a specific point is reached. Beyond
this point, the distortion increases very rapidly. Any amplifier
can be checked for this type of distortion with a simple setup as
audio signal source is used to drive both the amplifier under test
and the horizontal plates of the oscilloscope. The output of the
amplifier under test is used to drive the vertical plates of the
'scope. If there is no phase lag present in the amplifier, the pattern
will be a straight line as in Fig. 2(A) and will increase in length
as the input to the amplifier is increased. When the overload point
is reached, the pattern will take on the appearance of 2(B). At
this point distortion increases rapidly. Figures 2(C) and 2(D) indicate
that phase shift is present in the system. In many cases it will
be found that the amount of phase shift varies with a change of
Perhaps the most widely employed Lissajous patterns are those for
frequency comparison. If separate signals of the same frequency
are on the vertical and horizontal inputs to the 'scope, a circle
or ellipse (depending on their phase relation) will be formed, as
in Fig. 3(A). For each cycle, the spot will make one trip sideways
and one trip up and down. For frequency comparison, a perfect shape
is not important.
Fig. 2. Setup and test patterns for checking
amplifier overload as described in the text.
Fig. 3. The number of loops measures frequency
by comparison with a known standard.
If the frequency on the horizontal input is left unchanged and the
frequency input to the vertical input is exactly doubled, the result
will be a pattern like that in Fig. 3(B). In this case, the beam
must make two trips up and down for each one across and back. If
the frequency on the vertical deflection plates is made three times
that on the horizontal plates, the pattern will be that of 3(C)
because it must make three swings vertically for each one it travels
"... the number is more important than the shape in frequency
Fig. 4. For measuring the speed of a small motor, a self-generating
type photocell is mounted on the white insulator (top), catching
flashlight reflection from revolving shaft. This signal is then
compared by the 'scope to audio generator frequency. Block diagram
below shows setup for this test.
Reversing the situation and reducing the frequency
of the signal on the vertical plate to one-half of that on horizontal
will give the pattern of Fig. 3(D). The spot now has time to make
two trips across while traveling vertically once.
a usable pattern, the two frequencies being compared do not have
to be exact multiples of one another. In Fig. 3(E), by counting
the loops (or peaks), it is found that two horizontal excursions
were made for each three that were made vertically. The frequency
on the horizontal plates is then two-thirds of that on the vertical.
Using this sort of frequency comparison, a home-built
or commercial audio generator can be calibrated at a large number
of points by using only the 60-cycle line current as a standard
or one of the audio tones broadcast by the National Bureau of Standards
on Station WWV. The table below shows a few of the cardinal points
that can be calibrated by using 60 cycles as a standard. If the
600-cycle tone from WWV is used, all figures are multiplied by 10.
This same method serves the "ham" in checking the multiplying
stages in short-wave transmitters. A signal picked up from the input
of the stage to be checked is compared with a signal taken from
the output of the same stage. The number of loops in the pattern
indicates the number of times the stage is multiplying the frequency.
Almost all of the common makes of oscilloscopes will operate in
this manner up to 30 megacycles if the signal is applied directly
to the deflection plates.
A few examples of calibrating audio frequencies
(listed in "vertical" column) against the 60·cycle standard
obtainable from the a.c. power line.
Mechanical Tests. The value of an oscilloscope is not limited
to those interested in sound or electronics. For the hobbyist who
would like to know the speed of small motors, perhaps one too weak
to drive a mechanical tachometer, the scheme in Fig. 4 (page 65)
is the answer.
The shaft has been given a light coat
of dull black paint or ink and a white spot of paint is dabbed on
one side. When a flashlight or some other source of light (operated
on direct current) is directed on the shaft, the light reflected
from the white dot as the shaft revolves induces a voltage in a
photocell. This signal, which consists of one pulse for each revolution
of the motor, is placed on one set of 'scope plates. If a signal
from a calibrated signal source is placed on the other set of plates
and adjusted until a single loop pattern is formed, the revolutions
per second of the motor tested can be read from the oscillator.
Almost any type of rotating machinery can be checked
with this method by using the proper variation. The speed of a model
airplane engine can be checked by shining the light through the
rotating propeller to the photocell. Of course, the result must
be divided by two, because the double blade of the propeller is
generating two pulses for each revolution.
variation of this same method is the use of a microphone to pick
up sounds. The sustained note of a musical instrument can be picked
up and the resulting impulses used to energize one set of 'scope
plates. If the second set of deflection plates is fed from a calibrated
audio signal source, the frequency of tone picked up by the microphone
can be determined with precision.
In using the Lissajous
form of oscilloscope display, several things should be remembered.
The general shape of the pattern is not important for frequency
comparison. Ignore odd ripples and bumps. The number of line-crossings
or loops is what counts.
1996 - 2018
BSEE - KB3UON
RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling
2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas
and reference material while performing my work as an RF system and circuit design engineer.
The Internet was still largely an unknown entity at the time and not much was available
in the form of WYSIWYG
All trademarks, copyrights, patents, and other rights of ownership to images and text
used on the RF Cafe website are hereby acknowledged.
My Hobby Website: AirplanesAndRockets.com