title: Frequency Selective Surfaces: Theory and Design
author: Ben A. Munk
description: "well-organized and worth readingThe analysis anddesign concepts, as well as physical insight, presented in thisbook would provide the reader a great benefit." (<i>IEEE Circuits&amp; Devices Magazine</i>, Jan/Feb 2005)
zlib_text: 14
  Introduction to Frequency-Selective
  Circuits
  Assessment Problems
  AP 14.1 fc = 8 kHz,
  ωc = 2πfc = 16π krad/s
  ωc =
  1
  RC ;
  R = 10 kΩ;
  ·. .
  C =
  1
  ωcR =
  1
  (16π × 103)(104) = 1.99 nF
  AP 14.2 [a] ωc = 2πfc = 2π(2000) = 4π krad/s
  L = R
  ωc
  = 5000
  4000π = 0.40 H
  [b] H(jω) =
  ωc
  ωc + jω =
  4000π
  4000π + jω
  When ω = 2πf = 2π(50,000) = 100,000π rad/s
  H(j100,000π) =
  4000π
  4000π + j100,000π =
  1
  1 + j25 = 0.04/− 87.71◦
  ·. .
  |H(j100,000π)| = 0.04
  [c] ·. .
  θ(100,000π) = −87.71◦
  AP 14.3 ωc = R
  L =
  5000
  3.5 × 10−3 = 1.43 Mrad/s
  14–1
  
  14–2
  CHAPTER 14. Introduction to Frequency-Selective Circuits
  AP 14.4 [a] ωc =
  1
  RC = 106
  R = 106
  100 = 10 krad/s
  [b] ωc = 106
  5000 = 200 rad/s
  [c] ωc =
  106
  3 × 104 = 33.33 rad/s
  AP 14.5 Let Z represent the parallel combination of (1/sC) and RL. Then
  Z =
  RL
  (RLCs + 1)
  Thus
  H(s) =
  Z
  R + Z =
  RL
  R(RLCs + 1) + RL
  =
  (1/RC)
  s + R+RL
  RL
  �
  1
  RC
  � =
  (1/RC)
  s + 1
  K
  �
  1
  RC
  �
  where
  K =
  RL
  R + RL
  AP 14.6 ω2
  o =
  1
  LC
  so
  L =
  1
  ω2
  oC =
  1
  (24π × 103)2(0.1 × 10−6) = 1.76 mH
  Q = ωo
  β =
  ωo
  R/L
  