Measurement of unknown frequency by Lissajous pattern wave CRO.

Experiment No.: 08

Aim of the Experiment: –

Measurement of unknown frequency by Lissajous pattern wave CRO.

Apparatus Required: –

Sl. No.	Name	Specification	Quantity
1	CRO		1 no.
2	Function Generator		2 nos.
3	Connecting probes		As per required

Circuit Diagram: –

Theory: –

When Sinusoidal voltages are simultaneously applied to horizontal and vertical plates, then a pattern of closed figure is obtained which is known as Lissajous figure or pattern.

Two sinusoidal inputs are applied to the oscilloscope in X-Y mode and the relationship between the signals is obtained as a Lissajous figure. To generate a Lissajous pattern two different signals are applied to the vertical and horizontal inputs of the CRO. Earlier this technique used to measure frequencies before the frequency meter were discover. A signal generally sine wave of unknown frequency was applied to horizontal input and a frequency whose value is known applied to the vertical input of CRO. The pattern observed was depend on the ratio of the two frequencies applied to the vertical and horizontal inputs.

as per figures 8.1:

It can be shown that the ratio of the two frequencies is:

f_y/f_x= (number of times tangent touches top or bottom)/(number of times tangent touches either side)

= (number of horizontal tangencies)/(number of vertical tangencies)

where,

f_y= Frequency of signal applied to vertical or Y-plates.

f_x= Frequency of signal applied to horizontal or X-plates.

Thus, if one of the frequency is known and the other is unknown by looking at the Lissajous pattern we can find out the unknown frequency.

Procedures: –

1. Two function generators were used, the first generator as the standard frequency source where as frequency from the second function generator is consider as unknown.
2. Set the frequency of generator one to 1kHz, vary the frequency of second function generator until a stable Lissajous pattern is displayed to the screen of CRO.
3. Trace the pattern record the number of horizontal and vertical tangents and frequency of second function generator.
4. Repeat the procedure for 4-5 unknown frequencies it will give different Lissajous pattern.

Observation Table: –

Sl. No.	Lissajous pattern	Vertical tangent points	Horizontal tangent points	Unknown frequency
1
2
3
4
5
6

Phase Measurement:

1. Connect an R-C series circuit with an AC supply.
2. Give the voltage outputs from resistance and capacitance to the two channels in the oscilloscope.
3. By looking at the Lissajous pattern find out the phase.
4. From fig. 3, The phase shift can be found out by, Sinɸ= (Y₁/Y₂) = (X₁/X₂).
5. Check the phase angle by solving mathematically.

Conclusion: –

To be written by student.