Higher Order Analog Butterworth Filter Designs, a Tutorial
Instructions
 Make sure you have Java turned on in your browser.
 Enter high and low pass speaker impedances.
 Enter desired crossover frequency.
 On the secondorder crossover calculator you must
select type of crossover.
 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 *
 First Order Crossover
(6db/octave).
 Second Order Crossover
(12db/octave).
 Third Order Crossover
(18db/octave).
 Fourth Order Crossover
(24db/octave).
 Zobel Circuit (Impedance
Stabilization).
 Lpad Circuit (Speaker
Attenuation).
First Order (6db/octave) TwoWay
Crossover
 Phase shift on a firstorder crossover is 90
degrees.

Second Order (12db/octave) TwoWay
Crossover
 LinkwitzRiley 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 LinkwitzRiley and Butterworth crossovers.
 The phase shift on a secondorder crossover
is 180 degrees (reversed polarity).

Third Order (18db/octave) TwoWay
Crossover
 Phase shift on a thirdorder crossover is
270 degrees (90 degrees).

Fourth order (24dB/octave) TwoWay
Crossover
 The phase shift on a fourthorder crossover
is 360 degrees = 0 degrees (no phase shift).

Zobel Circuit (Impedance
Stabilization)
 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 nonlinearity 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.

Lpad (Speaker Attenuation)
 An Lpad circuit will attenuate a
speaker.
 Lpads 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 Lpads are made from resistors, it
does not induce any phase shifts, or affect frequency response.

