This document provides instructions for an experiment to determine unknown signal frequencies using a Lissajous polar on an oscilloscope. Students will input a known 1 kHz horizontal signal and unknown vertical signal into an oscilloscope put in X-Y mode. By counting the number of intersections of the signals, the frequency ratio can be calculated using TH/TV = FV/FH. Different frequency ratios create different Lissajous patterns like circles or ellipses. Students then measure unknown frequencies for different ratios and compare to calculated values. A report is to be written explaining the theory, technique, and comparing measurement results.

1. EEEC6430312
Measurements and Instrumentation
Faculty of Engineering and Computer Technology
Laboratory Manual
Lecturer: Ravandran Muttiah BEng (Hons) MSc MIET
Year/Semester: Year 2 / Semester 1
Academic Session: 2020/2021
The information in this documentis important and should be noted by all students undertaking the
Bachelor of Engineering (Honours) in Electrical and Electronic Engineering
Approved by Coordinator: Endorsed By Dean:
------------------------------------------ __________________

2. AIMST University Faculty of Engineering and Computer Technology
BEng (Hons) in Electrical and Electronic Engineering Measurements and Instrumentation 1
Experiment 1 - Frequency Determination Using The Lissajous Polar
Objective
This experiment will serve as an introduction to the Lissajous polar to gain hands on
experience in using oscilloscope and calibration methods. Where the oscilloscope can be
used to determine the frequency of a signal by using the Lissajous polar. The Lissajous
polar can be obtained by using a 2-trace oscilloscope. Further to gain practical skills to
set TIME/CM knob to its x-y mode, CH1 to produce a vertical shift and CH2 to produce
a horizontal shift.
Materials and Apparatus
(1) Oscilloscope
(2) Function Generator
Procedure
Obtain the horizontal input to a signal of a known frequency, 𝐹H = 1 KHz, from a
function generator. Obtain the vertical input to a signal of an unknown frequency, 𝐹V is
the frequency that we would like to determine. The magnitude of both signals should be
approximately the same. Figure 1 shows some Lissajous polar at different frequency
ratios. If the number of horizontal contact is 𝑇H and the number of vertical contact is 𝑇V,
then the unknown frequency 𝐹V can be calculated using the following formula,
𝐹V
𝐹H
=
𝑇H
𝑇V
If both signals are of the same frequency, the polar shown on the screen can be a straight
line, a circle or a varying ellipse. The polar depends on the phase shift between the two
signals. To get a stable and constant polar, the frequency of the unknown signal may need
to be adjusted slowly.

3. AIMST University Faculty of Engineering and Computer Technology
BEng (Hons) in Electrical and Electronic Engineering Measurements and Instrumentation 2
𝑇H
𝑇V
Lissajous Polars
1
1
1
2
1
3
1
4
Figure 1

4. AIMST University Faculty of Engineering and Computer Technology
BEng (Hons) in Electrical and Electronic Engineering Measurements and Instrumentation 3
Determine the Lissajous polar according to the ratio stated in Table 1 and calculate 𝐹V.
Compare the calculated 𝐹V with 𝐹V determined from the oscilloscope (not in the x-y
mode).
Table 1
𝑇H 𝑇V Polar 𝐹V (calculated) 𝐹V (measured)
1 3
2 3
3 1
4 2
Report
Write a laboratory report on this experiment.
(1) Explain in detail about the theory and its experimental techniques of Lissajous
polar.
(2) Discuss the results that obtained by comparing both the measured and calculated
values.