Explain measurement of phase and frequency using Lissajous pattern. Write the formula for each one.

Explain measurement of phase and frequency using Lissajous pattern. Write the formula for each one.
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1 Answer

Answer :

Phase measurement of Lissajous pattern:

The phase measurement can be done by using Lissajous figures.

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

Depending on the phase shift between the two signals, the shape of the Lissajous pattern will go on changing.

The phase shift is given by,

Ө = sin-1 (A/B)

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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-

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Frequency measured using Lissajous pattern: 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).

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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. 

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