CNET304 Lab 3 Signal Analysis in Time and Frequency Domains

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Centennial College *

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Electrical Engineering

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Apr 3, 2024

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Lab 3: Signal Analysis in Time and Frequency Domains Lab 3: Signal Analysis in Time and Frequency Domains Prepared by: Dr. Sattar Hussain, @ Centennial College, 2022 Name Student ID Signature* Loken Khadka 301290074 Umanga Bhandari 301320893 U. B Smaran Subedi 301303504 S.S *By signing above, you attest that you have contributed to this submission and confirm that all work you have contributed to this submission is your work. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, 1 School of Engineering Technology and Applied Science (SETAS) Information and Computing Engineering Technology (ICET) Section No. 011 Group No. Due Date Mark Obtained (out of 25)

Lab 3: Signal Analysis in Time and Frequency Domains Learning Objectives Upon completion of this lab students will reliably demonstrate the ability to:  Set up an oscilloscope and visualize signals for various adjustment  Gain an understanding of signal representation in time domain  Generate signals using the oscilloscope Gen function  Adjust the frequency and amplitude of various signals and understand their characteristics  Be familiar with signal analysis in the frequency domain  Be familiar with signal harmonics and spectral components of various waveforms  Relate frequency domain analysis of different waveforms to their Fourier Series expressions Equipment Required R&S RTB2002B Digital oscilloscope Overview Transmitted message is often an audio signal such as music or voice. These signals have quite variables characteristics. The time-domain analysis is often used to study the signal’s characteristics where waveform, amplitude, period, and phase of a signal are the main concern. In the laboratory, time-domain observation and measurements of a signal are done using a menu-driven digital oscilloscope. To study phenomena associated with amplitude or frequency modulation, we will substitute simpler signals with controllable parameters. The spectral analysis gives information about a signal by decomposing it into sine waves of different frequencies. Spectrum analyzer is the instrument used for studying signals in the frequency domain. If a perfect sinusoidal signal (i.e. no distortion) is injected into the input of a spectrum analyzer, one vertical line would be seen at the precise frequency (f o ) of the signal. However, signal generators provide real signals which are not perfect. There is always some distortion, which causes much smaller lines to appear at the multiples of the fundamental frequency. A non-sinusoidal signal, such as a triangle wave or square wave, also produce more than one line. 2

Lab 3: Signal Analysis in Time and Frequency Domains Prelab Assignment 1. [ 1 mark ] Calculate given power ratios rounded to 3 significant figures and then express them in dB: 123W/456mW = 269.736  24.309dB 0.00123W/456mW = 0.0269  25.7dB 888pW/66nW = 0.01345  18.71dB [ 1 mark ] Convert the given power gain from dB to power ratios: 33dB  1995.262W -12dB  0.063W -40dB  0.0001W 269.736………………………… ..… → ……24.309dB… 269.736………………………… ..… → ……24.309dB… 269.736………………………… ..… → ……24.309dB… Procedure Notes: 3

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Lab 3: Signal Analysis in Time and Frequency Domains a. All screenshots must show the time stamp at the right-bottom corner. b. Note: You are required to print your name and your lab partner name on every single screenshot submitted within this lab using the Annotation tools of the RTB2004B Oscilloscope. c. Throughout this lab, student groups will be assigned different numerical values for some of the analyzed parameters. The lab instructions use the letter x to refer to a certain parameter value. Whenever you see an x, replace this x with the group number. 1. To start, click the [Preset] key to reset the instrument to the scope mode and to default state. 2. Click the [ Gen ] key on the front panel to open the " Function Generator " menu, where you can create various waveforms. 3. Using the Function Generator menu, generate the following signal: 4. Click the [ CH1 ] key and set the oscilloscope Vertical, Horizontal, and Trigger controls as follow: Click Vertical>>Channel 1 and set the following Coupling DC Bandwidth Full Vertical Scale 250 mV Offset 0 Position 0 Click Trigger and set the following 4 Parameter Value Output 1 Function Sine Frequency 1x0.0 kHz Amplitude 1 Vpp Offset 0 V Noise 0 v

Lab 3: Signal Analysis in Time and Frequency Domains Trigger Mode Auto Trigger Type Edge Source C1 Slope Rising Trigger Level 0 V Click Horizontal and set the following Reference Point Middle Time Scale 5 µs Horizontal position 0 5. Use the Annotation tool to print your name and partner name on the top of the Oscilloscope display 6. [2 Marks] Sketch or print and paste the generated signal (Oscilloscope screen) below. 5

Lab 3: Signal Analysis in Time and Frequency Domains 7. Click [ FFT ] key and adjust the FFT screen as follow: Start Frequency 0 Hz Stop Frequency 2 MHz Span 2 MHz RBW 20 kHz Source C1 FFT Window Flat Top Vertical Scale dBm 8. The time domain and frequency domain of an 8-kHz signal is shown below. Use 6

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Lab 3: Signal Analysis in Time and Frequency Domains the up/down arrows to resize the Time-domain (waveform) window and the frequency domain (spectrum) window. 9. Click the [ Cursor ] key and choose V-Marker for Type and Spectrum for Source. Use the Next Peak/Prev. Peak to select a peak in the spectrum. Two vertical cursors will appear. You can use any one of them. Observe the readings on the bottom of the oscilloscope screen. 7

Lab 3: Signal Analysis in Time and Frequency Domains 10. [ 2 marks Sketch or print and paste below the FFT display (the signal spectrum). 8

Lab 3: Signal Analysis in Time and Frequency Domains 11. [ 3 marks ] Based on your observations of the signal spectrum, complete the following table. Note: sinusoidal signals have only the fundamental frequency. Simply, write (-) whenever the answer is not applicable. Harmonic 1 st (Fundamental Frequency) 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 9

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Lab 3: Signal Analysis in Time and Frequency Domains Frequency (kHz) 175.54 - - - - - - - - Amplitude (dB) 3.72 - - - - - - - - 12. Change the waveform to Square (rectangle) wave and repeat steps 4-11. Click FFT to go back and forth between Waveform (time-domain) and FFT (spectrum) display. 13. [4 Marks] Sketch or print and paste the time-domain (waveform) and the frequency domain (FFT) of the generated signal below: 10

Lab 3: Signal Analysis in Time and Frequency Domains 11 Squ ar e Wave Waveform Square Wave FFT (Spectrum)

Lab 3: Signal Analysis in Time and Frequency Domains 14. [ 3 marks ] Based on your observations of the signal spectrum, complete the following table. Write (-) whenever the answer is not applicable. Harmonic 1 st (Fundamental Frequency) 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th Frequency (KHz) 181.9 538.06 903.12 - Amplitude (dB) 6.02 -3.5 -7.94 - 15. [ 4 marks ] Generate a Pulse wave with a Duty Cycle 20% and repeat steps 4-11. Puls 12 Pulse (20% Duty Cycle) Waveform

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Lab 3: Signal Analysis in Time and Frequency Domains 13

Lab 3: Signal Analysis in Time and Frequency Domains Resolution Bandwidth (RBW) 1. Generate a sinusoidal waveform. Set the amplitude to 1 Vpp . Set the frequency to 400.00 kHz . 2. On the FFT display, set the Span to 1 MHz , Strat frequency to 0Hz , End frequency to 1 MHz , and RBW to the minimum value ( 59.1 Hz ). Click the [ Cursor ] key and choose Horizontal for Type and Spectrum for Source. Two horizontal cursors will appear. Locate one of them at the spectrum peak and the other one at the top of the noise floor (see the screenshot below for a case with RBW=15 kHz). Record the signal power in dBm and the noise floor in dBm in the table below. 14

Lab 3: Signal Analysis in Time and Frequency Domains 3. [4 marks] Change the RBW to 1 kHz then to 20 kHz and repeat step 2. Post-Lab Discussion [ 4 marks ] 1. Discuss the bandwidth requirement of the sinusoidal, rectangle, and the pulse waveforms. The bandwidth requirements of sinusoidal, rectangle (square), and pulse waveforms differ based on their inherent characteristics. A sinusoidal waveform, being a pure tone, has a bandwidth equal to its frequency. In contrast, a rectangle wave, with its sharp edges, introduces harmonics, resulting in a broader bandwidth compared to a sinusoidal waveform. The bandwidth of a rectangle wave depends on the rise and fall times, inversely proportional to the duration of each pulse. Pulse waveforms, particularly those with narrow duty cycles, exhibit wider bandwidths as more frequency components are needed to represent the abrupt transitions. Overall, the bandwidth consideration reflects the complexity and harmonic content of each waveform. 2. Discuss the effect of the RBW on the accuracy of spectrum measurement. The Resolution Bandwidth (RBW) in spectrum analysis determines frequency resolution. Smaller RBW values (e.g., 59.1 Hz) offer precise frequency differentiation but extend measurement times. Increasing RBW (e.g., to 1 kHz or 20 kHz) sacrifices resolution for a smoother spectrum appearance, impacting the ability to resolve closely spaced frequencies. This trade-off involves obtaining detailed frequency information versus optimizing measurement efficiency. RBW also influences Signal-to-Noise Ratio (SNR). A smaller RBW enhances SNR by isolating signal and noise components accurately, while larger RBW may average noise over a broader frequency range, affecting perceived SNR. Balancing frequency resolution and measurement time is crucial, aligning with analysis requirements. The choice of RBW is a strategic decision, considering signal nature and analysis goals. 15 Horizantal Cursors Frequency RBW=59.1 Hz RBW=1 kHz RBW=20 kHz Signal Power (dBm) -52 -49.28 -27.78 Noise Power (dBm) -114.5 -101.62 -84.46 Signal to Noise Ratio, SNR (dB) 62.5 52.34 55.68

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