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Higher Order Analog Butterworth Filter Designs, a Tutorial

Instructions

  1. Make sure you have Java turned on in your browser.
  2. Enter high and low pass speaker impedances.
  3. Enter desired crossover frequency.
  4. On the second-order crossover calculator you must select type of crossover.
  5. Click on the "calculate" button to get the answers.
  • Impedance is the nominal resistance of the speaker (typically 4 Ohms).
  • Enter frequency in Hertz (not kHz).
  • Capacitor value(s) are given in millionths of a Farad (F).
  • Inductor value(s) are given in thousands of a Henry (mH).
  • For the Zobel circuit, enter inductance in Henries (not mH).
  • Calculators *

    1. First Order Crossover (6db/octave).
    2. Second Order Crossover (12db/octave).
    3. Third Order Crossover (18db/octave).
    4. Fourth Order Crossover (24db/octave).
    5. Zobel Circuit (Impedance Stabilization).
    6. L-pad Circuit (Speaker Attenuation).

    First Order (6db/octave) Two-Way Crossover

    High Pass Impedance: Ohms
    Low Pass Impedance: Ohms
    Frequency Hz

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    6dB Crossover Diagram     C1= F




      L1= mH

    • Phase shift on a first-order crossover is 90 degrees.

     


    Second Order (12db/octave) Two-Way Crossover

    Linkwitz-Riley Butterworth Bessel

    High Pass Impedance: Ohms
    Low Pass Impedance: Ohms
    Frequency Hz

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    12dB Crossover Diagram     C1 = F

      L1 = mH


      C2 = F

      L2 = mH

    • Linkwitz-Riley crossovers match attenuation slopes so that system response is flat at crossover point.
    • Butterworth crossovers yield to a peak at the crossover frequency.
    • Bessel crossovers have a frequency response between Linkwitz-Riley and Butterworth crossovers.
    • The phase shift on a second-order crossover is 180 degrees (reversed polarity).

     


    Third Order (18db/octave) Two-Way Crossover

    High Pass Impedance: Ohms
    Low Pass Impedance: Ohms
    Frequency Hz

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    18dB Crossover Diagram     C1 = F
      C2 = F
      L1 = mH

      L2 = mH
      L3 = mH
      C3 = F

    • Phase shift on a third-order crossover is 270 degrees (-90 degrees).

     


    Fourth order (24dB/octave) Two-Way Crossover

    High Pass Impedance: Ohms
    Low Pass Impedance: Ohms
    Frequency Hz

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    24dB Crossover Diagram     C1 = F
      C2 = F
      L1 = mH
      L2 = mH

      C3 = F
      C4 = F
      L3 = mH
      L4 = mH

    • The phase shift on a fourth-order crossover is 360 degrees = 0 degrees (no phase shift).

     


    Zobel Circuit (Impedance Stabilization)

    DC resistance (Re): Ohms
    Inductive Equivalent (Le): Henries

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    Zobel Circuit Diagram     C1= F


      R1= Ohms

    • Even though speakers are rated at a certain "resistance" (i.e. 4 Ohms), the actual impedance varies with frequency (speakers have inductance). To compensate for the non-linearity of speakers (on mainly subwoofers), Zobel circuits are used.
    • Re is the DC resistance of the woofer (can be measured with an ohmmeter)
    • Le (or Lces) is the electrical inductive equivalent of the driver.

     


    L-pad (Speaker Attenuation)

    Driver Impedance = Ohms
    Desired Attenuation = dB

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    l-pad.gif (1013 bytes)     R1 = Ohms


      R2 = Ohms

    • An L-pad circuit will attenuate a speaker.
    • L-pads keep the load "seen" by the amplifier constant, affecting only the power delivered to the speaker.  The power delivered by the amplifier remains constant.
    • Since L-pads are made from resistors, it does not induce any phase shifts, or affect frequency response.
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