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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 (µF).
  • 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= µF




  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 = µF

  L1 = mH


  C2 = µF

  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 = µF
  C2 = µF
  L1 = mH

  L2 = mH
  L3 = mH
  C3 = µF

  • 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 = µF
  C2 = µF
  L1 = mH
  L2 = mH

  C3 = µF
  C4 = µF
  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= µF


  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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