Question

I have a question regarding Lissajous figures in a CRO:

When we get a Lissajous figure by the input of two channels X and Y as two different waves. What does the X-axis and Y-axis represent in that wave? In other words what is the equation for the x-axis and the y-axis? Like in a sine or cosine wave, what does x-axis and y-axis represent?
Also, if there is phase difference of pi/2 between two waves, say sine and cosine: how do i know which wave is ahead or how do i know which wave has started first?
Please help me out. I really need to clear my concepts regarding this doubt.

Answer 1

Let us take the phase difference between the two signals to be quarter of a wave (pi/2) and the amplitudes of both the signals to be the same. So, if the x-axis has a time-varying input signal given by x = Acos(wt), the y-axis will be a time-varying signal input given as: y = Asin(wt)

These above inputs x(t) and y(t) are parametric equations of a circle of radius A and so this will be the pattern appearing on the CRO. Likewise, any input fed to these perpendicular axes wil give the parametric equations in time for a function (eg: circle) and these functions give out the appropriate Lissajous pattern on the CRO screen. Another example can be two signals with amplitudes not equal to each other. This will trace out an ellipse.

Regarding your 2nd question: In principle, it is possible to determine which signal has ahead of the other by fixing one signal and putting a phase retarder on the other signal. However, for all practical purposes, it is not possible to determine which signal is ahead of the other because the frequencies are very high. Also, note that it is the phase difference which matters for a given Lissajous figure, not the phase itself.