2. INTRODUCTION
In mathematics, a Lissajous curve also known as Lissajous
figure or Bowditch curve , is the graph of a system
of parametric equations
It describe complex harmonic motion. This family
of curves was investigated by Nathaniel Bowditch in 1815,
and later in more detail by Jules Antoine Lissajous in 1857
You can credit the name to French physicist Jules Antoine
Lissajous. He originally used sounds at differing
frequencies to vibrate a mirror and trace patterns with a
beam of reflected light.
3. Formation of Lissajous Pattern:
Lissajous patterns are formed when you combine periodic
waves moving back and forth withperiodic waves moving up
and down.
We can generate thispattern by applying signals horizontal
and vertical inputs of an oscilloscope.
In fact, this techniqueis often used to measure frequencies in
the day before frequency meters
4. Method to measure frequency
Thesignal whose frequencyis to bemeasured is given at vertical axis(Y-plate)
The signal whose frequency is given to horizontal plate(X-plate).
Nowthe known and standard frequency is adjusted so Lissajous patterns canbe
obtained on the screenwhich depends onthe ratio of two frequencies.
Two lines are drawn ,one vertical and one horizontal so that they do not pass
through any intersection on Lissajious pattern.
Then the number of intersections of the horizontal and vertical lines with the
lissajous patterns and counted separately.
After finding the tangencies if we have oneknown, we caneasily calculate the
unknown frequency applied to vertical plate.
7. Formula :
Fy/fx =hx/hy
fy: unknown frequency
Fx: known frequency
hy: tangencies at y axis
hx: tangencies at x axis
8. Phase difference measurement:
If the ratio of frequencies is rational number, then a closed
curve will be observed on the CRO.
If two signals have same frequencies and in-phase, diagonal
line to right is produced.
If two sine waves have same frequency and amplitude and
180 degree out of phase, diagonal line to the left will
produce.
If two signals have same frequency and phase-shift 90
degree then circle will obtain.
If two signal have different frequency, then there will be
only a patch of light because of the persistence of
oscilloscope screen.
10. Advantages:
Lissajious figure methods are a little more roboustare a
little to noise than direct oscilloscope methods.this is
because there are no triggering problems due to
random noise fluctuations.
Direct methods are,however,much easier to interpret
when harmonics are present.
The accuracy of oscilloscope methods is comparatively
poor than this method.
The uncertainty of measurement is typically in exceeds
of 1degree
11. Disadvantage:
CRO is not a precision instrument for measuring
frequency of an alternating voltage because the
accuracy depends directly on the accuracy of
calibrated scale of variable frequency source, which is
usually a few percent.
It is used for rough estimate of frequency or when
voltage waveform is so complex that a frequency
counter would not operate reliably.
12. Conclusion :
As our conclusion. We can tell that oscilloscope can
measure:
1. the frequency
2. phase of two signal.
Oscilloscope function is not limited to display
waveform. The oscilloscope will help us to calculate
the frequency & phase his Lissajous figure.
