the method of finding phase, frequency relation ship of two waveforms using Lissajous figures

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The method of finding phase, frequency relation ship of two waveforms using Lissajous figure.:

 Measurement of the Phase:

When sinusoidal voltages simultaneously applied to vertical and horizontal plates,
 the pattern, appearing on the CRT is called as Lissajous pattern in this method
 the standard known frequency is applied to X-plate or horizontal plate.

 The resulting pattern appeared on the screen depends on phase relationship
 between the two frequencies.

Equal voltages of same frequency but of different phase angles- cause
 the pattern to vary from a straight diagonal line to ellipses of 
different eccentricities. The sine of the phase angle between the voltages is given
 by equation,

Sinφ = y1 /y2 = x1/x2

As shown in figure  the gains of horizontal or vertical amplifiers are 
adjusted so that ellipse fits exactly into a square marked by lines on the screen.

 

Measurement of the Frequency :

Lissajous pattern also helps to measure frequency. The signal whose

 frequency is to be measured is given I F-plates or vertical plates and

 the signal whose frequency is given to X-plates or horizontal plates.

 Now the know frequency or standard frequency is adjusted so Lissajous patterns can be obtained on the screen which depends on the ratio of two frequencies.

 In the given figure (2),

Let, fv - Unknown frequency signal applied to vertical plates. fh - Known frequency signal applied to horizontal plates.

Two lines are drawn, one vertical and one horizontal so that they do not pass through any

intersection o Lissajous pattern. Then the number of intersections of the horizontal and vertical lines with the Lissajous patterns and counted separately.

So after finding the tangencies if we know we can easily calculate the unknown frequency applied to vertical plate.

All electronic circuits in the oscilloscope like attenuators, time base generators, amplifiers cause some amount of time delay while transmitting signal voltage to deflection plates.

We also know that horizontal signal is initiated or triggered by some portion of output

signal applied to vertical plates of CRT. So the delay line is used to delay the signal for

some time in the vertical section of CRT.

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