Lab 1 ECET 303 - Carson Hunter

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Purdue University, Fort Wayne *

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303

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Electrical Engineering

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Feb 20, 2024

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Purdue University Fort Wayne – School of Polytechnic Communication I – ECET 303 Experiment: Spectrum Analyzer and Fourier Series Lab 1 Objective: In analog and digital communication systems, the function of the systems is analyzed in time and frequency domain. To validate the function of the parts of the systems in test and troubleshooting operation, most of the times an oscilloscope is enough. We can also estimate the fundamental frequency of periodic signals such as Sinusoid, Pulse and Triangular waveforms using oscilloscope. To find out the frequency elements of signals accurately, oscilloscope is not enough. In this lab we are going to use spectrum analyzer to study the spectrum of a given signal. In this lab, first we will get familiar with spectrum analyzer. Then, we will investigate the Fourier series of periodic signals such as Pulse and Triangular waveforms. We will see that besides complex mathematical calculations, we can also use lab instruments to find the Fourier series coefficients of a periodic waveform. Spectrum Analyzer: Spectrum analyzer is a measurement instrument that gives a visual presentation of the frequency elements of the spectrum of a signal. The horizontal axis of the spectrum analyzer is the frequency and the vertical axis is the amplitude of the frequency element. Fourier Series Theorem: Every periodic waveform with frequency f 0 can be decomposed to the weighted sum of unlimited number of Sine and Cosine each with frequency that is a multiple integer of f 0 (that is called fundamental frequency). The weights of Sine and Cosine are the Fourier series coefficients. Tektronix TDS 1002: Tektronix TDS 1002 digital oscilloscope can be used as spectrum analyzer (Figure 1). In this lab we will become familiar with the features of this lab instrument.

Figure 1: Tektronix TDS 1002 oscilloscope Part 1: Spectrum Analyzer Lab Procedure: 1. Turn on your function generator and set it to make a Sinusoid at 1 kHz with 0.1 Vp-p amplitude. 2. Turn on your TDS 1002 oscilloscope (or any other similar one) and connect the main output of your function generator to the channel 1 (CH 1) of the oscilloscope. If you do not see a proper signal, adjust the VOLTS/DIV and SEC/DIV nobs. You can also press on Auto Set button on the top right corner of the front panel (the black button). Auto Set Acquire Cursor Cursor 1 Cursor 2 MATH MENU 3. If you observe noise on the amplitude of the Sinusoid, press the Acquire button, then on the right side of the LCD, press on Average button and to select the number of averaging, press the Averages button. By increasing the number of averaging from 4 to 128, the effect of the random noise will be reduced, but the speed of the instruments will drop.

4. To work with TDS oscilloscope as spectrum analyzer, press on MATH MENU. Press on the top button on the right side of LCD panel to select FFT as the operation of the instrument. Make sure the CH1 is selected as the Source. On LCD screen you should see a sharp peak and a lot of randomly varying noise. What you observe is the spectrum of a single tone or single Sinusoidal signal. 5. To find out the frequency of the tone press on Cursor button. Then on the right side of the panel, on the type option select Frequency and on the Source option, select CH 1 . Two vertical dashed lines will appear upon selection on Frequency as type. We can use POSITION nobs to find out the frequency of the single tone. On the right side of the LCD panel we can see the frequency at which each cursor is located. Delta is the frequency spacing between the two cursors. 6. Change the frequency of the Sinusoid from 1 kHz to 10 kHz and draw your observation in the following. The frequency of the signal changes from 1KHz to 10KHz and the red line shifts on the oscilloscope.

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Part 2: Fourier Series Lab Procedure: 1. Without changing the function generator’s waveform and its frequency, adjust the amplitude to 1 Vp-p and then add a meaningful DC offset to it. Then observe the spectrum of the modified waveform by switching to frequency domain. Explain why the spectrum of Sinusoid changed. Draw the result in a scaled frame. Changing the offset changes, the magnitude of signal allowing it to reach higher power change. 2. Square Waveform: On function generator, change the Sinusoidal to Square waveform and reduce the DC offset to zero. Without changing the frequency from 10 kHz, look at the spectrum analyzer and sketch your observation. Describe why do you have more than one peak. What does each peak show? The square wave acts like a switch and is turning on and off. Repeatedly. Each peak show the frequency of each time the signal repeats within the square waveform. 3. If you have changed from Cursor mode, press or on Cursor button. On the right side of the LCD press on the type button to change from Frequency to Magnitude . Upon changing to Magnitude , you will observe two horizontal dashed lines . Turn the two POSITION nobs and put one at the top on the first peak and one at the top of the second peak. Read the Delta that is the ratio of the magnitude of these two peaks in dB. How do you connect your observation with Fourier series coefficients of Square waveform?\

When the waveform continues the magnitude of the wave form decreases by a certain amount depicted in the equation for square wave. Hint: Use page 82 of the text book, then calculate the following value: D ( dB )= 20 ×Log 10 A 1 A 3 4. Now move the cursor of the top of the second vertical peak to the third vertical peak. Read the value of Delta. Try to find the value of delta from the Fourier series of Square waveform. Hint: Use page 82 of the book and the above formula. The dB delta is 4 this is shown by the equation of it being 1/3 of the original magnitude. 5. Triangular Waveform: On function generator, change the Pulse to Triangular waveform and keep the DC offset at zero level. Without changing the frequency from 10 kHz, look at the spectrum analyzer and sketch your observation. Describe why you have more than one peak. What does each peak show? The square wave acts like a switch and is turning on and off. Repeatedly. Each peak represent the frequency of at each iteration to the waveform. 6. If you have changed from Cursor mode, press or on Cursor button. On the right side of the LCD press on the type button to change from Frequency to Magnitude . Read the

Delta that is the ratio of the magnitude of these two peaks in dB. How do you connect your observation with Fourier series coefficients of Triangular waveform? Hint: Use page 82 of the text book, then calculate the following value: D ( dB )= 20 ×Log 10 A 1 A 5 The magnitude of the first one is the original voltage while the 5 th one is 1/5 of the original magnitude. 16.2 dB delta Mag1=20.2 dB Mag2=4.0 dB 7. Now move the cursor of the top of the second vertical peak to the third vertical peak. Read the value of Delta. Try to find the value of delta from the Fourier series of Triangular waveform. Hint: Use page 82 of the book and the above formula. The magnitude of the first one is the original voltage while the 9 th one is 1/9 of the original magnitude. 8. Compare the result of parts 4 with 7 and 5 with 8. Describe your conclusion about the relative amplitude of the harmonics of Pulse versus Triangular waveform. The magnitudes is what changes the frequencies stay the same. Same thing with differences between part 5 and 8. The magnitude is what changes instead of it being 1/3 on the second one its 1/5 on the second peak. It can be seen in the equation of the square and triangular waveforms. Conclusion: In this lab we observed the spectrums created by a function generator using an oscilloscope. We observed that changing the frequency, amplitude and DC offset will change the spectrum by shifting the location of the peak or increasing the magnitude of the peak. Changing the shape of the waveform (square or triangle) will make the spectrum have more than one peak with decreasing magnitudes.

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