Fall22_ECE210_report4-3

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University of Illinois, Urbana Champaign *

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210

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Electrical Engineering

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Apr 3, 2024

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ECE210 Laboratory Lab Report #4 Fall 2022 Net ID: Student Name: Lab Section: 2 Laboratory exercise 2.1 Fourier Transform Your scope is capable of displaying the Fourier transform of its input signal. We have already used this feature in Lab 3 in “observing” the Fourier coe ﬃ cients of periodic signal inputs. In this section we will learn how to examine non-periodic inputs in the frequency domain. 1. No circuit is used for this part of the laboratory. Connect the “W” pin (signal generator output) to the “1” pin (Channel 1 input) and connect both grounds. 2. To generate the “non-periodic” square wave from Signal Generator in Scopy, you will play the recorded square wave signal from .wav files made by TAs. • Download the complimentary files from ECE 210 webpage and unzip it. • In the Signal Generator module, select “Bu ff er” and click “Load file”, then select the .wav file named “square.wav” from the complimentary files. • Set the Amplitude to 1 V , SamplingRate to 5 Mhz, and 0 for O ff set and Phase. The setting should be similar to Figure 3. • Click “Run” to start generating the signal. • Go to the Oscilloscope module, set the Time Base as 500 μ s and click “Single”. Zoom in the signal by selecting a smaller region in the display panel, you should see some clear “rectangles” that periodically repeat but with large intervals, similar to Figure 4. Figure 3 – Bu ff er panel for loading the recorded square wave Page 3 of 7

Figure 4 – Select the rectangle waveform and zoom in • Next, measure the rectangle width ⌧ choosing an adequate time scale (zoom in): ⌧ = ( / 2) 3. Go to the Spectrum Analyzer module and adjust the Sweep settings to the following: • Frequency Start at 1 kHz, Stop at 50 kHz • Resolution BW at 97.66 Hz • Units of dBV as shown in Figure 5. Figure 5 – Settings for Sweep panel in Spec- trum Analyzer Page 4 of 7 252.114 ms

4. Sketch only the frequency spectrum | F ( ! ) | (in dB) of the Spectrum Analyzer and compare with theory (Hint: look back to Problem 4 in the Prelab). Span : Center : Scale : ( / 2) Write down the Fourier transform pair: ( / 2) Compare the obtained spectrum with the theoretical expectation: ( / 2) 5. Now, let’s examine the Sinc function. Load the file with name “sinc.wav” from the complimentary files in the Signal Generator module under “Bu ff er” tap. Use the same setting as used for the rectangular signal. Go to the Oscilloscope and focus on one Sinc function after zooming in, estimate the time di ff erence ( Δ T ) between the immediate zero-crossing surrounding the main lobe of the sinc function and calculate the corresponding value of W (Be aware of the DC o ff set of the signal, the “zero” to the sinc function is not exactly at zero). Δ T = ( / 2) W = rad s ( / 1) W = Hz ( / 1) 6. Go to the Spectrum Analyzer module and adjust the Sweep settings as shown in Figure 5. Then compare with theory. Span : Center : Scale : ( / 2) Write down the Fourier transform pair: ( / 2) Compare the obtained spectrum with the theoretical expectation: ( / 2) 2.2 AM Signal in Frequency Domain Amplitude Modulation (AM) is a communications scheme that allows many di ff erent message signals to be trans- mitted in adjacent band-pass channels. Before the message signal is multiplied by the high-frequency sinusoidal carrier, a DC component is added so that the voltage of the message signal is always positive. This makes it easy to recover the message signal from the envelope of the carrier. In Lab 1, you synthesized an AM signal with the function generator and then displayed it on the oscilloscope in the time domain. Let’s see how the AM signal looks in the frequency domain. The two recorded AM signals use some single frequency sinusoid as message signal and 13 kHz sinusoidal carrier. (Hint: Use the modulation property to interpret what you will see on Oscilloscope module): 1. No circuit is used for this part of the laboratory. Connect the “W” pin (signal generator output) to the “1” pin (Channel 1 input) and connect both grounds. 2. In the Signal Generator module, load the .wav file named “Sine_modulation.wav”,set the Amplitude to 1 V , SamplingRate to 1 Mhz, and 0 for O ff set and Phase. 3. Go to the Spectrum Analyzer module and adjust the Sweep settings as in Figure 5. Page 5 of 7 hmm ° -22 × 10-3 since / 0.22 × 210-3-1 w ) this matches the theoretical expectation as the output is a sine function 49kHz 25.5kHz 20 71.376ms 88.029 × 103 14010 hhhfmmm.mn#Taxiosxrect.;g..* , this matches what we enpected since the output looks like a rect function

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4. Sketch both, the time domain AM signal and its frequency spectrum and explain what you see in terms of the modulation property of the Fourier transform. (Hint: What is the frequency spectrum of the message signal (co-sinusoid of 880 Hz) plus a DC component in base band, i.e. before modulation?) Span : Center : Scale : V/div : t/div : ( / 2) Explain the shape of the frequency spectrum. ( / 4) 5. Then, in the Signal Generator module, load the .wav file named “Square_modulation.wav.” Set the Amplitude to 1 V , SamplingRate to 1 Mhz, and 0 for O ff set and Phase.. Sketch the AM signal in time domain and its frequency spectrum and explain what you see. (Hint: Remember the Fourier analysis of the square wave performed in Lab #3.) Span : Center : Scale : V/div : t/div : ( / 2) Explain the shape of the frequency spectrum. ( / 4) 2.3 AM Radio Receiver The most popular AM communications receiver is the superheterodyne receiver, which was developed for greater sensitivity and selectivity. A block diagram for the superheterodyne receiver is shown in Figure 6. The antenna, RF amplifier, and frequency mixer all rely on electrical components not covered in the textbook, but their e ff ects on the incoming signal should be familiar. You built the remaining components of the circuit in Labs 1 through 3. In this section, you will combine all of the components to tune in a simulated AM radio broadcast and follow the signal from after the RF module to the loudspeaker. Figure 6 – Superheterodyne AM receiver. 1. The test signal is recorded after the RF module (TP 1.) Assuming the signal is from WILL 580 (580 kHz) station. What are the theoretical frequencies you should use for the Local Oscillator, so that Page 6 of 7 frenulum www.nm The frequency spectrum has domain 3 peaks out at which the middle is the tallest Only dokken MMM these peaks are heirs MMM transmitted 49kHz 25.5kHz 20 IV 500ms The freeway spectrum has peaks at tremens MMMMM domain equal intervals A small section is taller than the other peaks tin wullthm .MN domain 49.9kHz 25.5 20 1. OV 500ms

the AM station shifts in frequency from its carrier frequency to the intermediate frequency (13 kHz) ? ( / 2) 2. Power the op-amps by enabling the DC supplies with 5 V. 3. In the Signal Generator module, load the file named “TP1_recorded_x.wav”, where x can be 1,2,3,4 (There are four audio files, choose any of them). Then set the Amplitude to 330 mV and click “Run.” 4. Connect your “2” pin (Channel 2) to TP 2 and connect your “1” pin (Channel 1) to “w” pin (Signal generator), and observe the spectrum in the Spectrum analyzer module. Sketch both spectrum of Channel 1 and Channel 2. Span : Center : Scale : ( / 2) Which part of the spectrum gets attenuated ? Explain your reason . ( / 4) 5. Connect your “2” pin (Channel 2) to TP 3 and move your “1” pin (Channel 1) to TP1, go to the Oscilloscope module and observe the signal in the time domain. • Click “Single” to have a snapshot of the signal in the time domain. • Zoom in to a proper region where you can clearly see the oscillation of Channel 1. Compare the signal from Channel 1 to Channel 2, what does the envelope detector accomplish in the time domain ? ( / 2) . 6. Now, let’s examine the frequency domain. Go to the Spectrum analyzer module, use the same sweep setting as given in Figure 5 and click Run. Sketch both the spectrum of Channel 1 and of Channel 2. Span : Center : Scale : ( / 2) What are the di ff erences that you notice ? ( / 2) Compare the spectrum from Channel 1 to the one from Channel 2. What does the envelope detector accomplish in the frequency domain ? ( / 2) 7. (Demo required) Connect the loudspeaker to TP 3, your speaker should start playing something if everything connected correctly. What do you hear from the speaker ? Does your circuit accomplish the job of demodulation ? . ( / 4) Page 7 of 7 580 -13 - 567kHz 5801-13 = 593kHz The parts with a high frequency that are outside the range aam%fh@Thhh of the frequency of the local channel 1 oscillator 49kHz 25.5112 20 it carries the treavencies of the input . channel L has higher trcahencies than channel 2 channels wMÑhwmmmmnMm Channel 't the envelope detector makes sure that channel L carries channel 2 49kHz 25.5kHz 20 The speaker plays the music which means the circuit demodulated the signal