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Engineering

Brookhaven College

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I need an answer for question 1 and 2

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EE3301 , Fall 2021 Department of Electrical & Computer Engineering, University of Texas -Dallas Name: Last 4 digits of SID: Instructions: • • • Please write your name and last 4 digits of your student ID. This exam is designed for 24Hrs. Please fill out the following table before turning your papers. Unfair Difficult Contents of the course so far: How do you rate this exam? What grade do you expect: A( ), B( ), C( ), D( ), F( ) Best of Luck Dr. Babak Fahimi Fair Easy EE3301 , Fall 2021 Department of Electrical & Computer Engineering, University of Texas -Dallas Problem 1 (40 points): We need to filter an incoming voltage signal, vin, using an active high pass filter. The specifications are: • We have access to ideal operational amplifiers. • All ideal op-amps have a 5pF parasitic capacitance between any the inverting input and the output. • A roll-off of 40dB/decade is needed. • A cut-off frequency, fc, of 50MHz is required. • |𝐻(𝜔 → ∞)| = 100[𝑉⁄𝑉 ] (a) Draw the bode plot of the magnitude of the desired transfer function. (b) Draw a circuit that can accomplish this. Clearly label vin and vout and keep all components symbolic. Explicitly draw the 5pF parasitic capacitance between the inverting input and the output of the amplifier. EE3301 , Fall 2021 Department of Electrical & Computer Engineering, University of Texas -Dallas (c ) Provide the component values for the above circuit. EE3301 , Fall 2021 Department of Electrical & Computer Engineering, University of Texas -Dallas Problem 2 (30 points): A quartz piezoelectric crystal exhibit s a strong resonance, which is why it is used as a time or frequency standards in clocks, tuners, etc. a) A quartz crystal is used in the following filter. Determine the transfer function of 𝑉 (𝑗𝜔) this filter. That is to find, 𝐻(𝑠) = 𝑉𝑜(𝑗𝜔),. Express your result as a ratio of 𝐼 polynomials in s. EE3301 , Fall 2021 Department of Electrical & Computer Engineering, University of Texas -Dallas b) For a specific set of components, the transfer function is given by: 𝐻(𝑠) = 2.5 × 103 𝑠 𝑠 2 + 5 × 103 𝑠 + 0.25 × 1014 Sketch the frequency response of the magnitude and phase of 𝐻(𝑗𝜔). Determine and label the resonant frequency, the magnitude and phase of the transfer function at that frequency, and the bandwidth (3dB bandwidth) of the filter. EE3301 , Fall 2021 Department of Electrical & Computer Engineering, University of Texas -Dallas Problem 3 (30 points) The circuit below is a boost converter that is used for charging of an ultra-capacitore. The capacitor voltage at t=0 is zero. The switch has been closed for a very long time and opens at t=0. Subsequently, the switch closes at t=1[sec], opens at t=2[sec] and remains open. Assuming 𝑅1 = 10Ω, L=1H, R2=5Ω, C=0.02F, and 𝑣𝑖𝑛 (𝑡) = 20𝑢(𝑡 + 10)[𝑉], compute: (a) 𝑖𝐿 (0− ) (b) 𝑉𝐶 (𝑠) and 𝑣𝐶 (𝑡) for 0 < 𝑡 < 1, specify 𝑣𝐶 (1− ). EE3301 , Fall 2021 Department of Electrical & Computer Engineering, University of Texas -Dallas (c) Is it necessary to know 𝑖𝐿 (1− ) to compute 𝑖𝐿 (2− )? Explain your answer. (d) What is the value of 𝑣𝐶 (2− )? (e) Compute 𝑉𝐶 (𝑠) and 𝑣𝐶 (𝑡) for 2 ≤ 𝑡.
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