lab 3 report (draft)
TRANSCRIPT
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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 hard- copy?
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