Lab 3 Report (Draft)

8/10/2019 Lab 3 Report (Draft)

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4.3.2 Problem 2 : FFT of square wave

In this part of the lab we use the function generator to generate a square

wave having 1 ms period, 2 Vpp amplitude and no offset.

This is the hardcopy of the signal in time domain:

We were asked to obtain the FFT spectrum of this signal, measure thefrequency and the amplitude of the fundamental frequency and the first

four harmonics.

Firstly, this is the FFT spectrum of the signal:


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Furthermore, here are the hardcopies where we measure the magnitude

and frequency of the fundamental frequency and the first four

harmonics:

Fundamental frequency at 960 Hz and first harmonic at 2.960 KHz


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Second harmonic at 4.96 Khz, third harmonic at 6.96 KHz and fourth

harmonic at 8.96 KHz

Fundamental frequency at -990 mdB and first harmonic at -10.6 dB


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Second harmonic at -15.4 dB and third harmonic at -17.4 dB.

Fourth harmonic at -21 dB

Next we were asked to obtain the FFT spectrum for 20% duty cycles. We

were asked to determine the frequency and amplitude of the

fundamental frequency and the first four harmonics.

Firstly, here is the signal in time domain:


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Here are the hardcopies that weve taken of the FFT spectrum with the

corresponding measurements.

Fundamental frequency at 1 KHz and first harmonic at 2 KHz and second

harmonic at 3 KHz.


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Third harmonic at 4 KHz and fourth harmonic at 5 KHz.

Fundamental frequency at -5.79 dB and first harmonic at -8.59 dB.


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Second harmonic at -10.6 dB and third harmonic at -17 dB.

Fourth harmonic at -45 dB.


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Evaluation:

1. For frequency domain measurements, the frequency scale needs

to be expanded in order to accurately measure the frequency

components. This could be done with the time base (sec/div)control. What is the effect of doing this on the measured

bandwidth? Information can be found in reference [6] and [7].

In the oscilloscope, when we change the time base (sec/div) control, we

change the sample interval. The sample interval is related to the sample

rate or frequency by this formula:

fs = record time/time interval = record time/ d.timebase

In order to represent the signal accurately, the sample frequency should

be at least twice the highest frequency. Therefore, the bandwidth and

the time base control is inversely proportional to the bandwidth. The

higher the time base, the lower the bandwidth displayed.

2. Use the hardcopies taken to discuss the effect of changing the duty

cycle on the FFT results.

Here is the frequency spectrum of the same signal, the second one being

at 20 % duty cycle:


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As we can see from the comparison of the two graphs, in the 20% duty

cycle some of the frequencies dont have an amplitude, as they tend tohave in the original signal. This is because in the 20% duty cycle, the

signal is active only in 20% of the time.

3. What is the effect of the DC offset in problem 4.3.2.3 if you look at

the hardcopy?

Unfortunately the hard copies we posses do not clearly visualize the 0

Hz frequency, but the effect of the offset is that we have another

component in the FFT spectrum which would represent the DC offset of

the signal at 0 Hz frequency.


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4.3.4 Problem 4 : Measure the Fourier Transform

of a sound sample

In this part of the experiment, we downloaded a sample sound file fromCampusnet (Sound_Sample.wav). By using a media player on our laptop,

set it to repeat playing and by connecting the audio out from the laptop

to the oscilloscope we took a look at the signal. We made sure that the

amplitude of the signal was from 1Vppto 2Vpp. This was done by

adjusting the volume.

We took a hardcopy of the signal in both time and frequency domains.

Here is in time domain:

Here is the signal in frequency domain with the appropriate

measurements:


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The fundamental frequency at 500 Hz and first harmonic at 980 Hz.

Second harmonic at 2 kHz and third harmonic at 3.6 kHz.


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1. What are the frequencies used to create this sound

wave?

As seen by our measurements, the frequencies used to create this sound

wave are:

500 Hz

980 Hz

2 kHz

3.6 kHz

2. Compare the measured spectra with calculated spectra.

Explain the differences if necessary.

This is the FFT spectrum we got from our calculations in MATLAB for

the same sound file:

As mentioned in the pre-lab the frequencies are 500 Hz, 1000 Hz, 2000

Hz and 3600 Hz. We can see that only one of the frequencies slightly

differs by just 20 Hz. But this could be due to the cursor placement in

the oscilloscope. So we can say that there is no actual difference

between the calculated results and measured results in this experiment.


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References:

1.

TDS220 manual.

2.

TDS200-Series Extension Modules manual.3. Lab Manual

4.

Wikipedia

5.

Matlab Documentation

Documents

Lab 3 Report (Draft)