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Lissajous Patterns of CRO or Cathode Ray Oscilloscope

Published on 24/2/2012 and last updated on 7/8/2018
Cathode Ray Oscilloscope (CRO) is very important electronic device. CRO is very useful to analyze the voltage wave form of different signals. The main part of CRO is CRT (Cathode Ray Tube). A simple CRT is shown in figure below- cathode ray oscilloscope

When both pairs of the deflection plates (horizontal deflection plates and vertical deflection plates) of CRO (Cathode Ray Oscilloscope) are connected to two sinusoidal voltages, the patterns appear at CRO screen are called the Lissajous pattern. Shape of these Lissajous pattern changes with changes of phase difference between signal and ration of frequencies applied to the deflection plates (traces) of CRO. Which makes these Lissajous patterns very useful to analysis the signals applied to deflection plated of CRO. These lissajous patterns have two Applications to analysis the signals. To calculate the phase difference between two sinusoidal signals having same frequency. To determine the ratio frequencies of sinusoidal signals applied to the vertical and horizontal deflecting plates.

Calculation of the phase difference between two Sinusoidal Signals having same frequency

When two sinusoidal signals of same frequency and magnitude are applied two both pairs of deflecting plates of CRO, the Lissajous pattern changes with change of phase difference between signals applied to the CRO. For different value of phase differences, the shape of Lissajous patterns is shown in figure below,

SL No.Phase angle difference ‘ø’Lissajous Pattern appeared at CRO Screen
10o & 360o
230o or 330o
345o or 315o
460o or 300o
590o or 270o
6120o or 240o
7150o or 210o
8180o
There are two cases to determine the phase difference ø between two signals applied to the horizontal and vertical plates,
Case - I: When, 0 < ø < 90o or 270o < ø < 360o : - As we studied above it clear that when the angle is in the range of 0 < ø < 90o or 270o < ø < 360o, the Lissajous pattern is of the shape of Ellipse having major axis passing through origin from first quadrant to third quadrant: Let’s consider an example for 0 < ø < 90o or 270o < ø < 360o, as shown in figure below, Lissajous Patterns of CRO In this condition the phase difference will be, Another possibility of phase difference, From Above given Lissajous pattern Another Possibility of Phase Difference,
Case - II: When 90o < ø < 180o or 180o < ø < 270o Lissajous Patterns of CRO As we studied above it Clear that when the angle is in the range of 0o < ø < 90o or 270o < ø < 360o, the Lissajous Pattern is of the shape of Ellipse having major axis passing through origin from second quadrant to fourth quadrant: Let’s consider an example for When, 90o < ø < 180o or 180o < ø < 270o, as shown in figure below, In this condition the phase difference will be, Another possibility of phase difference, From Above given Lissajous pattern Another Possibility of Phase Difference, To determine the ratio of frequencies of signal applied to the vertical and horizontal deflecting plates: To determine the ratio of frequencies of signal by using the Lissajous pattern, simply draw arbitrary horizontal and vertical line on lissajous pattern intersecting the Lissajous pattern. Now count the number of horizontal and vertical tangencies by Lissajous pattern with these horizontal and vertical line. Then the ratio of frequencies of signals applied to deflection plates, Or, Let consider some example to clear the concept in details:

Examples Lissajous Pattern
Sl No.Lissajous PatternRatio of Frequencies fy/fx
1 fy/fx = 4/2 = 2
2 fy/fx = 3/1 = 3
3 fy/fx = 6/4 = 3/2
4 fy/fx = 6/8 = 3/4
5fy/fx = 4/3

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Lissajous Patterns of CRO or Cathode Ray Oscilloscope
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