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EECS+314+W13+Homework+_6+_Solutions_ - EECS 314 Winter 2013...

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EECS 314 Winter 2013 HW #6 Student’s name _______________________________ Discussion section # _____ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2013 Alexander Ganago Page 1 of 4 Last printed 3/8/2013 9:59:00 PM File: 2013 W 314 HW 6 p1_parts1+2 Problem 1 (100 points) Build a square wave as a sum of its sinusoidal components; determine the Rise/Fall Time of the partial sums Before starting to solve this problem, make sure that you have reviewed the very end of recording of Lecture #10 (February 18, 2013) and read the following: 1. Lab 5 pages 3 – 12, and 25 – 29 in your Lab book 2. Appendix pages A1-10 and A1-11 in your Lab book 3. “Example for 2013 W 314 HW 6 p1” on CTools in HW 6 folder Instructors in Discussion sections and office hours will assume that every student is already familiar with the materials listed above. In this Problem you will start building the square wave at 20 kHz and 12 Vppk (50% duty cycle) as a sum of its sinusoidal components – the fundamental and harmonics up to the 9 th , and determine the Rise Time of the waveforms obtained as the partial sums. Part 1 (20 points) The sinusoidal components of the square wave For square wave with the parameters listed above, calculate the frequency and peak amplitude of its fundamental and harmonic sinusoidal components up to the 9 th . Write your results (with the units of measure) in the table below. The fundamental 3 rd harmonic 5 th harmonic 7 th harmonic 9 th harmonic Frequency 20 kHz 60 kHz 100 kHz 140 kHz 180 kHz Peak amplitude 7.64 V 2.55 V 1.53 V 1.09 V 0.85 V Show your work for the 5 th harmonic. peak amplitude = peak-to-peak amplitude 2 and thus amplitude 𝐴 = 6 V Amplitude of n th harmonic is given as 𝐴 𝑛 = 4𝐴 𝜋𝑛 and so 𝐴 5 = 24 5𝜋 V (continued on the next page)
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EECS 314 Winter 2013 HW #6 Problem 1 Student’s name _______________________________ Discussion section # _____ © 2013 Alexander Ganago Page 2 of 4 Last printed 3/8/2013 9:59:00 PM File: 2013 W 314 HW 6 p1_parts1+2 Using your numerical results for the 5 th harmonic, write the equation in the form , where time t is in µ s and voltage in volts: Note that 100 kHz 1 µ s = 0.1 The 5 th harmonic waveform is 𝑉 5 ( 𝑡 ) = 24 5𝜋 sin(0.2 ∙ 𝜋𝑡 ) V = (1.53 V) sin(0.2 ∙ 𝜋𝑡 ) Problem 1 Part 2 (40 points) Plots of the fundamental and partial sums Use MATLAB to make a computer-generated plot to show the following four waveforms ( 1,000 points per period of the square wave ): 1. The fundamental alone 2. The fundamental plus the 3 rd harmonic 3. The fundamental plus the harmonics up to the 5 th 4. The fundamental plus the harmonics up to the 9 th Do not delete your files until you finish the last part of this Problem! On your plot: Label the horizontal axis in microseconds and the vertical axis in volts Show two periods of the fundamental Clearly indicate which curve shows what (hand-written, OK) Make sure that the peak-to-peak amplitude of the fundamental is between ½ and ¾ of the height of the plot
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