HW6-Frequency_Response

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Feb 20, 2024

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1. Award: 7.14 points 7.14 points Consider the circuit shown. References References Section Break Section Break Di ﬃ culty: Easy Learning Objective: Understand what transfer functions are and how to determine them. Identify the correct transfer function of the circuit shown in the fi gure. H ( s ) = V o V i  H ( ) = R - RLC + R + j L 2  H ( ) = R - LC + R + j L 2  H ( ) = R LC - R - j L 2 R

2. Award: 7.14 points 7.14 points References References Multiple Multiple Choice Choice Di ﬃ culty: Easy Learning Objective: Understand what transfer functions are and how to determine them. Identify the correct transfer function of the circuit shown in the fi gure. References References  H ( ) = R RLC - R - j L 2 H ( s ) = V o V i  H ( ) = - LC + j RC 2 1 - LC + j RC 2  H ( ) = LC - j RC 2 1 - LC + j RC 2  H ( ) = RC - j RC 2 1 - RLC + j RC 2  H ( ) = - RC + j RC 2 1 - RLC + j RC 2

3. Award: 7.14 points 7.14 points Multiple Multiple Choice Choice Di ﬃ culty: Easy Learning Objective: Understand what transfer functions are and how to determine them. Given NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. References References Section Break Section Break Di ﬃ culty: Medium Learning Objective: Understand Bode plots, and know why we use them and how to determine them. Identify the gain H dB . H dB = 20log 10 |3| – 20log 10 | j ω | – 20log 10 |1 +2 j ω /5 + ( j ω /5) 2 | H dB = 20log 10 |1 + j ω | – 20log 10 | j ω | – 20log 10 |1 +2 j ω /5 + ( j ω /5) 2 | H dB = 20log 10 |3| + 20log 10 |1 + j ω | – 20log 10 | j ω | – 20log 10 |1 +2 j ω /5 + ( j ω /5) 2 | H dB = 20log 10 |3| + 20log 10 |1 + j ω | – 20log 10 |1 +2 j ω /5 + ( j ω /5) 2 | References References Multiple Multiple Choice Choice Di ﬃ culty: Medium Learning Objective: Understand Bode plots, and know why we use them and how to determine them. H ( ) = 75 ( j + 1 ) j ( - + 10 j + 25 ) 2    

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4. Award: 7.14 points 7.14 points 5. Award: 7.14 points 7.14 points Identify the phase . References References Multiple Multiple Choice Choice Di ﬃ culty: Medium Learning Objective: Understand Bode plots, and know why we use them and how to determine them. A circuit consisting of a coil with inductance 20 mH and resistance 30 Ω is connected in series with a capacitor and a generator with an rms voltage of 120 V. References References Section Break Section Break Di ﬃ culty: Medium Learning Objective: Understand series and parallel resonance, why they are important, and how to fi nd them.  = - + ( ) - (2 /5) 90 o tan - 1 tan - 1  = ( ) - ( ) tan - 1 tan - 1 2 /5 1 - /25 2  = - + ( ) - ( ) 90 o tan - 1 tan - 1 2 1 - /5 2  = - + ( ) - ( ) 90 o tan - 1 tan - 1 2 /5 1 - /25 2

6. Award: 7.14 points 7.14 points 7. Award: 7.14 points 7.14 points Find the value of the capacitance that will cause the circuit to be in resonance at 15 kHz. The value of the capacitance that will cause the circuit to be in resonance at 15 kHz is nF. References Numeric Response Difficulty: Medium Learning Objective: Understand series and parallel resonance, why they are important, and how to find them. Find the current through the coil at resonance. The current through the coil at resonance is A rms. References Numeric Response Difficulty: Medium Learning Objective: Understand series and parallel resonance, why they are important, and how to find them. Find the Q of the circuit. The Q of the circuit is .

8. Award: 7.14 points 7.14 points References Numeric Response Difficulty: Medium Learning Objective: Understand series and parallel resonance, why they are important, and how to find them. Identify the correct expression for the resonant frequency of the circuit shown in the fi gure. References References  = 0 1 RC - L 2 C 2  = 0 1 RC + L 2 C 2  = 0 1 LC - R 2 C 2  = 0 1 LC + R 2 C 2

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9. Award: 7.14 points 7.14 points Multiple Multiple Choice Choice Di ﬃ culty: Medium Learning Objective: Understand series and parallel resonance, why they are important, and how to fi nd them. In the "tank" circuit, R = 70 Ω . Find the resonant frequency. The value of the resonant frequency is krad/s. References Numeric Response Difficulty: Medium Learning Objective: Understand series and parallel resonance, why they are important, and how to find them. In the circuit given below, R = 0.25 Ω and L = 10 H. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

10. Award: 7.14 points 7.14 points References References Section Break Section Break Di ﬃ culty: Medium Learning Objective: Understand passive fi lters. Identify the transfer function V o / V s for the given circuit. References References  H ( ) = 0.06 j 0.50 - 2.50 + j 2  H ( ) = 0.25 0.25 - 2.50 + 0.50 j 2  H ( ) = 0.06 j + 0.25 0.25 - 2.50 + 0.50 j 2  H ( ) = 0.25 0.25 - 2.50 + j 10.00 2

11. Award: 7.14 points 7.14 points 12. Award: 7.14 points 7.14 points Multiple Multiple Choice Choice Di ﬃ culty: Medium Learning Objective: Understand passive fi lters. The given circuit is a highpass fi lter. True False References References True / False True / False Di ﬃ culty: Medium Learning Objective: Understand passive fi lters. Identify the transfer function for the active fi lter in the circuit given below.    H ( ) = 1 1 + j RC j RC

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13. Award: 7.14 points 7.14 points 14. Award: 7.18 points 7.18 points References References Multiple Multiple Choice Choice Di ﬃ culty: Medium Learning Objective: Understand active fi lters. Design an active first-order highpass filter with Use a 1- μ F capacitor. The value of R f is M Ω . The value of R i is k Ω . References Numeric Response Difficulty: Medium Learning Objective: Understand active filters. Design an active lowpass filter with a DC gain of –0.25 and a corner frequency of 750 Hz. Assume  H ( ) = j RC 1 + j RC  H ( ) = j 1 + j R  H ( ) = j 1 + j RC H ( s ) = - and s = j 100 s s + 10

that R f = 10 k Ω . The value of R i is k Ω . The value of C is nF. References Numeric Response Difficulty: Medium Learning Objective: Understand active filters.