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Problem 5: The asymptotic Bodé plots of dB magnitude and phase are given. a) What are the DC gains | Hyr (0)|dB and Hyr (0)| ? b) d) | Hyr (0) |dB = 40 dB 20log | Hyr (0)| = 40 ⇒ log | Hyr (0)|=2 ⇒ | Hyr (0)| = 100 due to a unit step input? Find the steady-state output yss (Hyr (0) = 100 since ZHyr (0) = 0°) c) Frequency Yss=lim s Hyr - Hyr (0) = 100 1 S s→0 Find the steady-state output yss due to the input r(t) of the input: w = 1 rad/s Hyr | Hyr (1) |dB = 20 dB = 20 log | Hyr (1)| → |Hyr(1)|= 10, Yss = 3| Hyr (1)| cos (t + ZH(j1)) Write the transfer function Hyr based on the Bodé plot 100 (0.5 s + 1) (10s +1) (0.1 s + 1)² = = 3 cos (t). also correct: Hyr ZHyr (1) = -40° 30 cos (t-40°) 500 (s+2) (s+0.1) (s+10)²

Problem 5: The asymptotic Bodé plots of dB magnitude and phase are given. a) What are the DC gains | Hyr (0)|dB and Hyr (0)| ? b) d) | Hyr (0) |dB = 40 dB 20log | Hyr (0)| = 40 ⇒ log | Hyr (0)|=2 ⇒ | Hyr (0)| = 100 due to a unit step input? Find the steady-state output yss (Hyr (0) = 100 since ZHyr (0) = 0°) c) Frequency Yss=lim s Hyr - Hyr (0) = 100 1 S s→0 Find the steady-state output yss due to the input r(t) of the input: w = 1 rad/s Hyr | Hyr (1) |dB = 20 dB = 20 log | Hyr (1)| → |Hyr(1)|= 10, Yss = 3| Hyr (1)| cos (t + ZH(j1)) Write the transfer function Hyr based on the Bodé plot 100 (0.5 s + 1) (10s +1) (0.1 s + 1)² = = 3 cos (t). also correct: Hyr ZHyr (1) = -40° 30 cos (t-40°) 500 (s+2) (s+0.1) (s+10)²

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Problem 5: The asymptotic Bodé plots of dB magnitude and phase are given. a) What are the DC gains | Hyr (0)|dB and Hyr (0)| ? b) d) | Hyr (0) |dB = 40 dB 20log | Hyr (0)| = 40 ⇒ log | Hyr (0)|=2 ⇒ | Hyr (0)| = 100 due to a unit step input? Find the steady-state output yss (Hyr (0) = 100 since ZHyr (0) = 0°) c) Frequency Yss=lim s Hyr - Hyr (0) = 100 1 S s→0 Find the steady-state output yss due to the input r(t) of the input: w = 1 rad/s Hyr | Hyr (1) |dB = 20 dB = 20 log | Hyr (1)| → |Hyr(1)|= 10, Yss = 3| Hyr (1)| cos (t + ZH(j1)) Write the transfer function Hyr based on the Bodé plot 100 (0.5 s + 1) (10s +1) (0.1 s + 1)² = = 3 cos (t). also correct: Hyr ZHyr (1) = -40° 30 cos (t-40°) 500 (s+2) (s+0.1) (s+10)²
Transcribed Image Text:Problem 5: The asymptotic Bodé plots of dB magnitude and phase are given. a) What are the DC gains | Hyr (0)|dB and Hyr (0)| ? b) d) | Hyr (0) |dB = 40 dB 20log | Hyr (0)| = 40 ⇒ log | Hyr (0)|=2 ⇒ | Hyr (0)| = 100 due to a unit step input? Find the steady-state output yss (Hyr (0) = 100 since ZHyr (0) = 0°) c) Frequency Yss=lim s Hyr - Hyr (0) = 100 1 S s→0 Find the steady-state output yss due to the input r(t) of the input: w = 1 rad/s Hyr | Hyr (1) |dB = 20 dB = 20 log | Hyr (1)| → |Hyr(1)|= 10, Yss = 3| Hyr (1)| cos (t + ZH(j1)) Write the transfer function Hyr based on the Bodé plot 100 (0.5 s + 1) (10s +1) (0.1 s + 1)² = = 3 cos (t). also correct: Hyr ZHyr (1) = -40° 30 cos (t-40°) 500 (s+2) (s+0.1) (s+10)²
50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 -70 10-3 10 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 dB -100 -110 -120 -130 -140 -150 -160 -170 -180 -190 10-3 Hyr (jw) dB 10-2 ZHyr (jw) 10-2 10-1 10-1 100 10⁰ 10¹ 10¹ 102 10² rad/s 103 rad/s 103
Transcribed Image Text:50 40 30 20 10 0 -10 -20 -30 -40 -50 -60 -70 10-3 10 0 -10 -20 -30 -40 -50 -60 -70 -80 -90 dB -100 -110 -120 -130 -140 -150 -160 -170 -180 -190 10-3 Hyr (jw) dB 10-2 ZHyr (jw) 10-2 10-1 10-1 100 10⁰ 10¹ 10¹ 102 10² rad/s 103 rad/s 103
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