+ vi(t) t R₁ 0 a B 818 C₁ R₂ C₂ (a) Find the input impedance Z(s) = V₁(s)/I1(s) for the circuit above. Leave it in the form 1 SC Z(s) = R + What are R and C in terms of R₁, R₂, C₁, and C₂? (b) Find the transfer function H(s) = V₂(s)/V₁(s) and write it in the form H(s) = KS+B s + a 1 v₂ (t) What are K, B, and a in terms of R1, R2, C1, and C₂? (c) Choose realizable component values such the transfer function is H(s) = K Hint: Let C₁ C2 = C, pick R₂ to meet the ß constraint, then find the value of R₁ that meets the a constraint. What is your value of K? s+1000 8+100 (d) Find formulas for H(jw) and ZH (jw). (e) Explain the behavior of the circuit at the corner frequencies in terms of the input impedance Z(s) as well as the impedance R₂+1/sC2 of the output branch. What's special about Z(j100) and [R2 + 1/sC2]s=;1000? (f) Make a copy of the table below and complete the entries. Is this a frequency-selective or a frequency- shaping circuit? H(jw)| 20 log10 H(jw)| LH(jw) (deg)

+ vi(t) t R₁ 0 a B 818 C₁ R₂ C₂ (a) Find the input impedance Z(s) = V₁(s)/I1(s) for the circuit above. Leave it in the form 1 SC Z(s) = R + What are R and C in terms of R₁, R₂, C₁, and C₂? (b) Find the transfer function H(s) = V₂(s)/V₁(s) and write it in the form H(s) = KS+B s + a 1 v₂ (t) What are K, B, and a in terms of R1, R2, C1, and C₂? (c) Choose realizable component values such the transfer function is H(s) = K Hint: Let C₁ C2 = C, pick R₂ to meet the ß constraint, then find the value of R₁ that meets the a constraint. What is your value of K? s+1000 8+100 (d) Find formulas for H(jw) and ZH (jw). (e) Explain the behavior of the circuit at the corner frequencies in terms of the input impedance Z(s) as well as the impedance R₂+1/sC2 of the output branch. What's special about Z(j100) and [R2 + 1/sC2]s=;1000? (f) Make a copy of the table below and complete the entries. Is this a frequency-selective or a frequency- shaping circuit? H(jw)| 20 log10 H(jw)| LH(jw) (deg)

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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