Two-way Network Design Formulas

The values are in henries (L), farads (C), ohms (R) and hertz (f). To convert to standard component values:

Multiply L with 1000 to get mH.
Multiply C with 1000000 to get uF.

Symbols used:

Rh = DC Resistance of the tweeter
Rl = DC Resistance of the bass driver
f = Crossover frequency

First-Order Networks

First-order filter consists of two components, an inductor and a capacitor. The filter type damps 6 dB per octave. 
     + -----C1-----+
                   | +
                  Tweeter
                   |
     - ------------+

     + -----L1-----+
                   | +
                  Bass
                   |
     - ------------+

Butterworth

      0.159               Rl
C1 = -------      L1 = --------
       Rh f             6.28 f

Second-Order Networks

Second-order filter consists of four components, two inductors and two capacitors. The filter type damps 12 dB per octave. 
     + -----C1---+------+
                 |      | +
                 L1    Tweeter
                 |      |
     - ----------+------+

     + -----L2---+------+
                 |      | +
                 C2    Bass
                 |      |
     - ----------+------+

Bessel

      0.0912             0.2756 Rh
C1 = --------      L1 = -----------
       Rh f                 f


      0.0912             0.2756 Rl
C2 = --------      L2 = -----------
       Rl f                 f

Butterworth

      0.1125             0.2251 Rh
C1 = --------      L1 = -----------
       Rh f                 f


      0.1125             0.2251 Rl
C2 = --------      L2 = -----------
       Rl f                 f

Chebychev

      0.1592             0.1592 Rh
C1 = --------      L1 = -----------
       Rh f                 f


      0.1592             0.1592 Rl
C2 = --------      L2 = -----------
       Rl f                 f

Linkwitz-Riley

      0.0796             0.3183 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.0796             0.3183 Rl
C2 = --------      L2 = -----------
       Rl f                  f

Third-Order Networks

Third-order filter consists of six components, three inductors and three capacitors. The filter type damps 18 dB per octave. 
     + -----C1---+---C2-----+
                 |          | +
                 L1        Tweeter
                 |          |
     - ----------+----------+

     + -----L2---+---L3-----+
                 |          | +
                 C3        Bass
                 |          |
     - ----------+----------+

Bessel

      0.07911            0.1317 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.3953             0.3294 Rl
C2 = --------      L2 = -----------
       Rh f                  f


      0.1897             0.06592 Rl
C3 = --------      L3 = -----------
       Rl f                  f

Butterworth

      0.1061             0.1194 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.3183             0.2387 Rl
C2 = --------      L2 = -----------
       Rh f                  f


      0.2122             0.0796 Rl
C3 = --------      L3 = -----------
       Rl f                  f

Fourth-Order Networks

Fourth-order filter consists of eight components, four inductors and four capacitors. The filter type damps 24 dB per octave. 
     + -----C1---+---C2---+------+
                 |        |      | +
                 L1       L2    Tweeter
                 |        |      |
     - ----------+--------+------+

     + -----L3---+---L4---+------+
                 |        |      | +
                 C3       C4    Bass
                 |        |      |
     - ----------+--------+------+

Bessel

      0.0702             0.0862 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.0719             0.4983 Rh
C2 = --------      L2 = -----------
       Rh f                  f


      0.2336             0.3583 Rl
C3 = --------      L3 = -----------
       Rl f                  f


      0.0504             0.1463 Rl
C4 = --------      L4 = -----------
       Rl f                  f

Butterworth

      0.1040             0.1009 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.1470             0.4159 Rh
C2 = --------      L2 = -----------
       Rh f                  f


      0.2509             0.2437 Rl
C3 = --------      L3 = -----------
       Rl f                  f


      0.0609             0.1723 Rl
C4 = --------      L4 = -----------
       Rl f                  f

Gaussian

      0.0767             0.1116 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.1491             0.3251 Rh
C2 = --------      L2 = -----------
       Rh f                  f


      0.2235             0.3253 Rl
C3 = --------      L3 = -----------
       Rl f                  f


      0.0768             0.1674 Rl
C4 = --------      L4 = -----------
       Rl f                  f

Legendre

      0.1104             0.1073 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.1246             0.2783 Rh
C2 = --------      L2 = -----------
       Rh f                  f


      0.2365             0.2294 Rl
C3 = --------      L3 = -----------
       Rl f                  f


      0.0910             0.2034 Rl
C4 = --------      L4 = -----------
       Rl f                  f

Linear-Phase

      0.0741             0.1079 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.1524             0.3853 Rh
C2 = --------      L2 = -----------
       Rh f                  f


      0.2255             0.3285 Rl
C3 = --------      L3 = -----------
       Rl f                  f


      0.0632             0.1578 Rl
C4 = --------      L4 = -----------
       Rl f                  f

Linkwitz-Riley

      0.0844             0.1000 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.1688             0.4501 Rh
C2 = --------      L2 = -----------
       Rh f                  f


      0.2533             0.3000 Rl
C3 = --------      L3 = -----------
       Rl f                  f


      0.0563             0.1500 Rl
C4 = --------      L4 = -----------
       Rl f                  f

Sixth-Order Networks

Sixth-order filter consists of twelve components, six inductors and six capacitors. The filter type damps 36 dB per octave. 
     + -----C1---+---C2---+---C3---+------+
                 |        |        |      | +
                 L1       L2       L3    Tweeter
                 |        |        |      |
     - ----------+--------+--------+------+

     + -----L4---+---L5---+---L6---+------+
                 |        |        |      | +
                 C4       C5       C6    Bass
                 |        |        |      |
     - ----------+--------+--------+------+

Linkwitz-Riley

      0.08841            0.08594 Rh
C1 = --------      L1 = -----------
       Rh f                  f


      0.1081             0.1420 Rh
C2 = --------      L2 = -----------
       Rh f                  f


      0.2188             0.6366 Rh
C3 = --------      L3 = -----------
       Rh f                  f


      0.2947             0.2865 Rl
C4 = --------      L4 = -----------
       Rl f                  f


      0.1783             0.2344 Rl
C5 = --------      L5 = -----------
       Rl f                  f


      0.03979            0.1157 Rl
C6 = --------      L6 = -----------
       Rl f                  f

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