AMERICAN INTERNATIONAL UNIVERSITY–BANGLADESH (AIUB)

Spring 2023-24

INTRODUCTION TO ELECTRIC CIRCUITS LAB

Section:K

Lab Report On:

To be familiar with the operations of an oscilloscope and measuring corresponding AC

quantities from the waveforms obtained from the oscilloscope.

Supervised By:
RETHWAN FAIZ

Name ID
1. MD ASADULLA AL GALIB 23-50029-1
2. MD EKRAMUL HOQUE 23-51057-1

3. TAFSIR RAHAMAN 23-51061-1

4. HABIBUR RAHAMAN SYIMON 23-50644-1

5.Mouj Ferdous 23-51778-2

Date of Submission: 24/12/2024

Title of the Experiment:
To be familiar with the operations of an oscilloscope and measuring corresponding AC quantities
from the waveforms obtained from the oscilloscope.

Abstract:
This experiment aims to familiarize students with the basic operations of an oscilloscope and function generator, as well as to
measure various AC quantities such as peak value, peak-to-peak value, average value, RMS value, time period, frequency, and
phase difference. By connecting the function generator to the oscilloscope, waveforms of different frequencies are observed and
analyzed. Measurements are taken to calculate and validate key AC parameters. This practical exercise provides hands-on
experience with critical laboratory equipment and strengthens the understanding of waveform analysis, contributing to a deeper
grasp of AC circuit fundamentals.

Introduction:
In this experiment, we explore two critical pieces of equipment: the oscilloscope and the function
generator, which are fundamental tools for analyzing and generating electrical signals.
Additionally, the experiment involves measuring and calculating key AC parameters such as peak value,
peak-to-peak value, RMS value, average value, time period, frequency, and phase difference.
1. Function Generator: A function generator is an electronic device used to generate different types
of waveforms, such as sine, square, triangular, and sawtooth, over a wide range of frequencies.
These waveforms are used for testing and analyzing electrical circuits. The frequency and
amplitude of the generated signal can be manually controlled.

Figure - 1: Function Generator [3]

 Frequency: The number of cycles of a waveform per second, expressed in Hertz (Hz).
 Amplitude: The peak voltage level of the generated waveform.

2. Oscilloscope:
An oscilloscope is a measurement instrument used to observe and analyze time-varying
voltage signals. It displays voltage (Y-axis) versus time (X-axis) on a screen, providing a
visual representation of waveforms. Modern oscilloscopes can measure voltage, frequency,
phase difference, and other parameters.

Figure - 2: Oscilloscope [3]

 Peak Value (Vp): The maximum amplitude of a waveform.

 Peak-to-Peak Value (Vp-p): The total voltage difference between the positive and
negative peaks of the waveform. It is given by:
V p-p= 2Vm
 Average Value (Vavg): The average of all instantaneous values over one cycle. For a
sinusoidal waveform, it is given by:
Vavg = 0.636 Vm.
 RMS Value (Vrms): The Root Mean Square value is the equivalent DC value of an AC
waveform that produces the same heating effect in a resistive load. For a sinusoidal
waveform:
V rms = 0.707V

Figure - 3: Characterization of sinusoidal time varying signal [1]

 Time Period (T): The time taken for one complete cycle of a waveform.
 Frequency (f): The number of cycles per second. It is the reciprocal of the time period:
f= 1/T

 Phase Difference: When two waveforms of the same frequency are not in sync, a phase difference
exists between them. The phase difference is given by:
θ = (Phase Shift (divisions) / Time Period (divisions)) × 360°
3.Basic Oscilloscope Controls:
 Vertical Sensitivity: Adjusts the amplitude (volts/division) of the waveform displayed
 Horizontal Sensitivity: Controls the time base (time/division) to adjust the display of the
waveform along the X-axis.
 Intensity and Focus Controls: Adjust the brightness and sharpness of the waveform display

4.Waveform Analysis: The oscilloscope is used to measure various AC parameters, including peak, RMS,
and average values, by analyzing the displayed waveform. The function generator provides a sinusoidal
input signal with a known frequency and amplitude to the oscilloscope.Changes in frequency and
amplitude can be observed by adjusting the function generator.

5.Phase Difference and Leading/Lagging Waves: If two signals are displayed on the oscilloscope, the
time shift between them can be used to determine phase difference. One waveform may lead or lag the
other depending on the position of the waveforms on the screen.

Methodology:
1. Setup of the Equipment:
Connect the output of the function generator to Channel 1 of the oscilloscope using an oscilloscope probe.

Turn on the function generator and set the following initial conditions:

Waveform shape: Sinusoidal

Amplitude: 10V (peak-to-peak)
Frequency: 1 kHz

Turn on the oscilloscope and adjust the following settings:

Vertical sensitivity: Set to an appropriate value (e.g., 2 V/div) for clear waveform display.
Horizontal time base: Set to an appropriate value (e.g., 0.2 ms/div).
Adjust the intensity and focus controls to ensure a sharp and visible waveform.

2. Waveform Observation and Measurements:

Sketch the Waveform:

Observe the sinusoidal waveform displayed on the oscilloscope screen.

Sketch the waveform, labeling the axes and indicating the peak-to-peak amplitude.

•Determine Time Period and Frequency:

Measure the number of horizontal divisions (graticules) for one complete cycle of the waveform.
Use the time base setting to calculate T-(Number of divisions) (Time/division)
Calculate the frequency f.
3. Variation of Frequency and Waveform Analysis:

Increase the Frequency:

Change the frequency of the function generator to 2.5 kHz and observe the changes
on the oscilloscope display.
Sketch the waveform and record the changes in time period and amplitude.

Further Increase the Frequency:

Set the frequency to 10 kHz and observe the waveform.

Sketch the waveform and record the changes in time period and amplitude.

4. Measurement of AC Quantities:
For each frequency (1 kHz, 2.5 kHz, and 10 kHz)

5. Phase Difference Measurement (if applicable)

If two waveforms are displayed simultaneously on the oscilloscope:
Measure the horizontal phase shift (in divisions) between the two waveforms.
Measure the total time period of one waveform in divisions.

6. Record the Observations.

Apparatus:
1. Function Generator.
2. Oscilloscope.
3. Probes and Connecting Wires.

Diagram:

Figure 1: Typical Function Generator and Different Wave Shapes.

 Figure 2: An Oscilloscope. Figure 3: Functional Diagram of Oscilloscope.

Calculation and Result:

Here, We Know,
1
f=
T
1 1
so, f 1= = = 1.001 kHz ≈ 1 kHz
T 1 998.8 µ s
1 1
f 2= = = 2.001 kHz ≈ 2 kHz
T 2 499.7 µ s
1 1
f 3= = = 3.002 kHz ≈ 3 kHz
T 3 333.08 µ s
1 1
f 4= = = 4.001 kHz≈ 4 kHz
T 4 249.92 µ s
1 1
f 5= = = 5.045 kHz ≈ 5 kHz
T 5 198.2 µ s

V avg = 0.636 × V p = 0.636 × 1.27= 810 mV

1

V rms = 0.707 × V p = 0.707 × 1.27= 897.9 mV

1

V avg = 0.636 × V p = 0.636 × 1.30= 827.8 mV

2

V rms = 0.707 × V p = 0.707 × 1.30= 919.1 mV

2

V avg = 0.636 × V p = 0.636 × 1.255= 789.2 mV

3

V rms = 0.707 × V p = 0.707 × 1.255= 887.3 mV

3
V avg = 0.636 × V p = 0.636 × 1.265= 804.5 mV
4

V rms = 0.707 × V p = 0.707 × 1.265= 894.4 mV

4

V avg = 0.636 × V p = 0.636 × 1.27= 810 mV

5

V rms = 0.707 × V p = 0.707 × 1.27= 897.9 mV

5

Simulation:

Figure 4: Time period for 1kHz

 Figure 5: peak value for 1kHz

Figure 6: peak to peak value for 1kHz

Figure 7: Time period for 2kHz

Figure 8: peak value for 2kHz

Figure 9: peak to peak value for 2kHz

Figure 10: Time period for 3kHz

Figure 11: peak value for 3kHz

Figure 12: peak to peak value for 3kHz

Figure 13: Time period for 4kHz

Figure 14: peak value for 4kHz

Figure 15: peak to peak value for 4kHz

Figure 16: Time period for 5kHz

Figure 17: peak value for 5kHz

 Figure 18: peak to peak value for 5kHz

Experimental Procedure and Data:

1. We have connected the output of the function generator directly to the channel 1 of the

oscilloscope. Then we have set the amplitude of the wave 10V peak to peak and the

frequency at 1 kHz. After that the sinusoidal wave shape is being selected.

2. We have sketched the wave shape observed in the oscilloscope. The time period of the

wave and calculate the frequency is to be determined.

3. The frequency to 2 kHz is changed and what happens to the display of the wave is noted.

Then when frequency is increased 5 kHz, it is repeated. The wave shapes for both cases

in

drawn.

4. We have measured the peak value, peak-to-peak value, average value, rms value for all

the

five frequencies. Finally, we have filled the following table with necessary calculations.
Data Table:

Frequency Time Period Vavg (Volts) Vrms (Volts)

VP-P (Volts) VP (Volts)
(KHz) (µs) (mV) (mV)

1 998.8 2.57 1.27 810 897.9

2 499.7 2.61 1.30 827.8 919.1

3 333.08 2.51 1.255 789.2 887.3

4 249.92 2.53 1.265 804.5 894.4

5 198.2 2.57 1.27 810 897.9

Discussion:
In this experiment, we explored the relationship between input signals from a function generator
and output waveforms on an oscilloscope. Despite setting a constant amplitude of 10V, we faced
challenges in controlling the frequency precisely. This led to fluctuations in the peak-to-peak
value of the output waveform.

The main issue was the difficulty in maintaining accurate frequency control on the function
generator. This inconsistency affected the reliability and consistency of the results, making it
challenging to draw meaningful conclusions. To overcome this, calibration of equipment for
precise frequency output and the use of high-quality signal generators were suggested.

In conclusion, overcoming frequency control challenges is crucial for obtaining reliable

experimental results. By implementing calibration and signal processing techniques, these issues
can be mitigated, ensuring more accurate experimentation and data analysis.
Conclusion:
By completing this experiment, we had become familiar with the function generator and
oscilloscope by measuring peak value, peak to peak value, average value, rms value, time period,
frequency, form factor and peak factor and also the use of oscilloscope.

References:
1] P. Horowitz and W. Hill, The Art of Electronics, 3rd ed., Cambridge
University Press,2015.
[2] R. A. Witte, Electronic Test Instruments: Analog and Digital Measurements , 2nd
ed., PrenticeHall,2002.
[3] T. H. Curtis, Introduction to Oscilloscopes: A Practical Guide , 4th ed., Wiley,
2018.
[4] All About Circuits - Oscilloscopes: https://www.allaboutcircuits.com