Define Lissajous pattern. Explain how Lissajous pattern is useful for frequency and phase measurement.

Define Lissajous pattern. Explain how Lissajous pattern is useful for frequency and phase measurement.
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1 Answer

Answer :

Lissajous Pattern : The CRO is set to operate in the X- Y mode, when two sine waves of the same frequency are applied to the CRO (One vertical and one horizontal deflection plates) then the display obtained on the screen of a CRO is called Lissajous pattern.

Phase measurement :

The phase shift is given by,

Ө = sin-1 (A/B)

A. The Lissajous pattern will be an ellipse if the sine waves of equal frequency but phase shift between 00 and 900 are applied to the two channels of CRO. The Lissajous pattern will be as shown below 

image

B. For the phase difference above 900 and less than 1800 , the ellipse appears as Shown

image

C. Different Lissajous figure for phase difference 00 , 450 , 900 , 1350 , 1800 , 2250 , 2700 ,3150 , 3600 are shown below respectively

image

Frequency measurement : Lissajous pattern can be used for measurement of unknown frequency. Initially switch ON the CRO on X-Y mode. The unknown frequency signal is applied to the vertical deflection plates of the CRO (Channel Y) and standard known variable frequency signal is applied to the horizontal deflection plates (channel X). The frequency of the standard source is adjusted now, until a circular or elliptical pattern appears on the CRT screen. When such a pattern is observed on the screen, it indicates that the two frequencies are equal. Practically, it is not possible to adjust the standard frequency exactly equal to unknown frequency. Hence the standard frequency is adjusted to be a multiple or sub- multiple of the unknown frequency. The Lissajous pattern appears stationary Consider two sine waves are applied to Y plate and X plate of the CRO. The frequency applied to Y plate is twice that applied to the X plates. The Lissajous pattern

obtains is shown in figure.

The figure ratio is given by,

fy = number of horizontal tangents

fx number of vertical tangents

Some examples are given below,

1. Lissajous pattern for ratio 3:1 

image 

2. Lissajous pattern for ratio 3:2

image  

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