EEE 302 Lecture 23

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EEE 302 Lecture 23 Powered By Docstoc
					       EEE 302
Electrical Networks II
   Dr. Keith E. Holbert
      Summer 2001


          Lecture 23      1
                  Filter Networks
• Filters pass, reject, and attenuate signals at various
  frequencies
• Common types of filters:
   Low-pass: pass low frequencies and reject high frequencies
   High-pass: pass high frequencies and reject low frequencies
   Band-pass: pass some particular range of frequencies, reject
     other frequencies outside that band
   Band-rejection: reject a range of frequencies and pass all
     other frequencies (e.g., a special case is a notch filter)


                            Lecture 23                       2
  Common Filter Bode Plots


Low Pass                          High Pass

    Frequency                  Frequency




                             Band Reject
   Band Pass

    Frequency                  Frequency


                Lecture 23                    3
                 Passive Filters
• Passive filters use R, L, C elements to achieve the
  desired filter
• The half-power frequency is the same as the break
  frequency (or corner frequency) and is located at the
  frequency where the magnitude is 1/2 of its
  maximum value
• The resonance frequency, 0, is also referred to as
  the center frequency
• We will need active filters to achieve a gain greater
  than unity

                         Lecture 23                   4
           Class Examples
• Extension Exercise E12.16
• Extension Exercise E12.17
• Extension Exercise E12.18




                   Lecture 23   5
           First-Order Filter Circuits
          High Pass                          Low Pass


      +      R                           +       R
VS                     Low        VS                         High
      –          C                       –              L
                       Pass                                  Pass


     GR = R / (R + 1/sC)                HR = R / (R + sL)
     GC = (1/sC) / (R + 1/sC)           HL = sL / (R + sL)


                           Lecture 23                          6
         Second-Order Filter Circuits

         Band Pass
                                      Z = R + 1/sC + sL
          R                           HBP = R / Z
              Low    C
VS   +        Pass       Band         HLP = (1/sC) / Z
     –
                         Reject
              High   L
                                      HHP = sL / Z
              Pass
                                      HBR = HLP + HHP


                         Lecture 23                       7
Frequency & Time Domain Connections

• First order circuit break frequency: break = 1/
• Second order circuit characteristic equation
      s2 + 20 s + 02             [  = 1/(2Q) ]
      (j)2 + 2(j) + 1          [  = 1/0 ]
      s2 + BW s + 02
      s2 + R/L s + 1/(LC)           [series RLC]
   Q value also determines damping and pole types
      Q < ½ ( > 1) overdamped, real & unequal roots
      Q = ½ ( = 1) critically damped, real & equal roots
      Q > ½ ( < 1) underdamped, complex conjugate pair

                          Lecture 23                        8
         PSpice Design Example
• Repeat E12.18 using Pspice
  – Plot the resistor voltage in DBs
  – Use goal function “BPBW” to determine the band-pass
    filter bandwidth: BPBW(VDB(#),3))
  – Use goal function “CenterFreq(VDB(#),0?)”
• Bandwidth design
  – Design circuit to achieve a bandwidth of 300 Hz
• Center frequency design
  – Design circuit for a center frequency of 100 Hz

                         Lecture 23                       9

				
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posted:5/12/2013
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