3552c LAB1

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Electrical Engineering

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Apr 3, 2024

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Experiment 1: Spectrum Analysis EEL 3552C: Signal Analysis and Analogue Communication Professor Ismail Alkhouri Joshua Barshay 1/28/23

1.0 Objective: The objective of this experiment is to analyze the spectrum of a simple signal. 2.0 Equipment: This experiment uses an oscilloscope to analyzed the signal created by a function generator. A USB flash drive was also listed in the equipment for this experiment, but since the lab manual was released two hours before the lab, 23 minutes before the lecture portion for this lab, and after I was in transit to the lecture section for this class a USB flash drive was unable to be used. 3.0 Pre-Lab: For question “a” the amplitude of a value in dBV can be given by the equation dBV = 20log ( Vi Vr ) where (in this case) Vr is a reference value of 1V RMS. The amplitude given in this problem is in peak-to-peak so to plug it into the dBV equation it must be converted to RMS voltage first. To convert from peak-to-peak to RMS the value must be multiplied by 1 over 2 raised to the three halves power. Once these steps are performed the value is found to be -3.01 dBV. For question “b” these steps were reversed. The value of -10dBV was divided by 20 and then used as the power of ten giving approximately .316. Finally this value was multiplied by two and root two to find an amplitude value of .894 V. 4.0 Experiment: For this experiment no actual circuit was used as the function generator was directly connected to the input of the oscilloscope using a BNC-to-BNC cable. After this the oscilloscope was configured to maximum sample rate and the function generator was configured to a 4kHz sine wave with a 2Vpp amplitude. After scaling the oscilloscope the following input was displayed.

After the time domain waveform was confirmed, the oscilloscope’s FFT (fast Fourier transform) function was performed to view the signal in the frequency domain. The FFT’s parameters were configured to a frequency range of 8kHz with a center frequency of 4kHz and an output in dBV. The following frequency domain graph was created. After obtaining this graph in the frequency domain the cursors were used to measure when the maximum amplitude occurred in the frequency spectrum and the value of that amplitude. It was measure to be approximately -3.68dBV at 4kHz. This is slightly greater than the calculated value of -3.01dBV in preparation. This is probably due to some noise generated naturally by the function generator and oscilloscope and is also likely to be partially due to imprecise measurements as the cursors themselves have a certain level of inaccuracy and can be hard to obtain a fully precise reading with. The function generator was then set to 2kHz instead of 4 and the following frequency domain graph was obtained.

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The frequency spectrum did initially display and accurately show some of the frequency spectrum but since the center frequency for this new spectrum was 2kHz and the FFT function of the oscilloscope was currently set to 4kHz the spectrum was shifted and compressed by quite a bit. To fix this the upper bound of the frequency spectrum was changed to 4kHz and the center frequency was changed to 2kHz resulting in the above graph. After doing so the graph represents the signal accurately without removing any information. After this the function generator was changed to 1kHz and the following graph was generated. The time base of the oscilloscope had to be expanded from 200ms to 500ms to allow for a stop frequency of 2kHz in the FFT mode of the oscilloscope. The waveform does confirm that the input is 1kHz as the peak value lies at 1kHz, however, there is lots of noise in the frequency spectrum and the frequencies much greater than of less than the peak value lose much of their resolution. This means that while it was possible to configure the oscilloscope to properly view a waveform at 1kHz with 1kHz as the center frequency it seems that the oscilloscope is slightly too imprecise to fully properly show the frequency spectrum at a lower frequency value. Finally the input of the function generator was adjusted until the input on the oscilloscope had an amplitude of -10dBV. The following graph was obtained (the frequency of the generator was still 1kHz).

As can be seen on the graph the “measure” function of the oscilloscope was used to find the peak-to-peak value of the input that was used which was found to be approximately .884V. This is very close to the value of .894V that was calculated in preparation so the results can be said to agree with the value calculated in preparation. 5.0 Conclusion The objective of this experiment was to view a frequency spectrum using the oscilloscope and function generator. This was done successfully for three differing input frequencies. This also helped teach how to properly adjust and use the FFT function of the oscilloscope. It also taught how to adjust the time base of the oscilloscope to properly configure the FFT function of the oscilloscope. There were some slight discrepancies in the output measured in certain sections of the experiment. This could probably be remedied with slightly more accurate function generators or oscilloscopes as well as more time to ensure that the value measured with the cursors is completely accurate. This could also probably be helped by zooming in very closely on the maximum value and finding the amplitude while zoomed in. Similarly the discrepancy in the peak-to-peak reading that the oscilloscope generated is probably due to some noise from the internals which is probably unreconcilable. However, despite these small inaccuracies the experiment can be viewed as a success as the frequency spectrum was able to be properly viewed and the experiment succeeded in teaching how to access and use the FFT function of the oscilloscope.