LabReport: LISSAJOUS PATTERNS

Aim

Tostudy the Lissajou patterns on the CRO screen.

Introductionand Theory Evaluation

Oscilloscopescan be employed in the measurement and observation of ac waveforms.It can as well be of importance in the observation ofvoltage-versus-voltage pattern by removing the time parameter. Theresult of such an arrangement is referred to as a lissajous pattern.Lissajous figures can also be known as Bowditch curves. Lissajousfigures are obtainable through the intersection of two sine waves theaxis of which are perpendicular to each other. These curves aremostly used in the lab observation and analysis of electric signalsusing the cathode ray oscilloscope. The experiment is purposed toacquaint the student with the use of such patterns and variousmethods through which they may be observed (Fisichelli,1996).

Ifthe sweep generator of the oscilloscope is disconnected and two acwaveforms connected to the vertical amplifier and the horizontalamplifier, a lissajous pattern is observed. Supposing that the inputwaveform characteristics of one waveform are known, then the unknownwaveform parameters can be determine (Fisichelli,1996).

Assumingthat the alternating voltages have similar frequency and are in thesame phase, a lissajou figure would be formed as below. Both thevertical and horizontal intersect forming the lissajou figure and byreducing the voltages the light spot traces back the same path. Henceby adding two voltages with equal frequencies and in phase with eachother would result in a straight line on the screen. The line makesan angle of 45 degrees with both the X and Y axes. If the amplitudeof the voltages differs, the line would make a different angle fromthe 45 degrees (Fisichelli,1996).

Results

Theshapes of the lissajous patterns may differ on a CRO screen ifalternating potentials of different amplitude ratios, frequencyratios and phase differences are fed to the vertical and horizontalplates of the oscilloscope. (Insert the photos here).

*Figure1*

*Figure2*

*Figure3*

*Figure4*

*Figure5*

*Figure6*

*Figure7*

*Figure8*

Analysisand Discussion

Inthe first lissajou figure, the phase angle between the horizontal andvertical plates is 3π/4 and the frequency ratios 1:1. In the case offig 2, the phase angle between the two waveforms is δ=π and has afrequency ratio of 2:3. The third lissajou figure is described by aphase angle of 3π/4 and a frequency ratio of 1:3. The forth lissajoufigure is as a result of the voltage phase difference of π/4 and afrequency ratio of 1:2.

Fig(1) fig(2) fig (3)

Fig(4) fig (5)fig (6)

Fig(7)fig (8)

Forthe pattern in fig (5), the frequency ratio is 3:2 and the phasedifference is π/4. In fig (6) the frequency ratio was found to be2:1 and the phase difference was foud as 2π. For the pattern infigure (7), the frequency ratio was 3:1 and the phase difference is7π/4. The lissajou pattern in fg (7) had a frequency ratio of thetwo waves of 3:2 and a phase difference of 3π/4. The figures in theresult section and the figures in the discussion are namedaccordingly to correspond.

References

Fisichelli,V. R. (1996). Effect of rotational axis and dimensional variations onthe reversals

ofapparent movement in Lissajous figures. *TheAmerican journal of psychology*,669-

675.