CAAD 4.1       * TECHNICAL LIBRARY *       (ed. 1995)

MONACOR INTERNATIONAL & CO.KG, Bremen.

 

CONTENTS:

Formulas for crossover calculation.

  -------------------------------------------------------------------------------------------------------

CROSSOVER CALCULATION:

Symbols used:

 

   fo   : crossover frequency in two-way system                                            (Hz)

   fo1 : crossover frequency between bass and midrange                              (Hz)

   fo2 : crossover frequency between midrange and tweeter                         (Hz)

   fo3 : crossover frequency between tweeter and supertweeter                   (Hz)

 

   Zb    :  impedance of bass unit                                                                    (ohms)

   Zbm :  impedance of bass/midrange unit                                                    (ohms)

   Zm   :  impedance of midrange unit                                                             (ohms)

   Zt     :  impedance of tweeter unit                                                               (ohms)

 

   Zs    :  impedance of supertweeter unit                                                       (ohms)

 

   L   :  calculated coil value, milliHenries                                                    (mH)

   C   :  calculated capacitor value, microFarads                                           (uF)

 

   (L & C with suffixes 1-12 according to actual position in the circuit  as shown on the screen)

  -------------------------------------------------------------------------------------------------------

 

      FIRST-ORDER BUTTERWORTH CROSSOVER ( 6 dB/octave):

 

   2-way  6 BW (with examples):                         (2500 Hz, 8 ohms)

 

  -------------------------------------------------------------------------------------------------------

   L1 = 159.15494*Zbm/fo   = mH                  (BASS/MID, phase normal)   (0.509)

 

   C1 = 159154.94/(Zt*fo)  = uF                     (TWEETER, phase normal)   (7.957)

 

   3-way  6 BW (with examples):                     (500/3000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 159.15494*Zb/fo1   = mH      (BASS, phase normal)                       (2.546)

 

   C1 = 159154.94/(Zm*fo1) = uF      (MIDRANGE)                                   (39.78)

   L2 = 159.15494*Zm/fo2   = mH      (phase normal)                                   (0.424)

 

   C2 = 159154.94/(Zt*fo2) = uF                    (TWEETER, phase normal)   (6.631)

 

   4-way  6 BW (with examples):                (200/2200/9000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 159.15494*Zb/fo1   = mH      (BASS, phase normal)                       (6.366)

 

   C1 = 159154.94/(Zm*fo1) = uF      (MIDRANGE)                                   (99.47)

 

   L2 = 159.15494*Zm/fo2   = mH      (phase normal)                                   (0.578)

 

   C2 = 159154.94/(Zt*fo2) = uF                    (TWEETER)                          (9.042)

   L3 = 159.15494*Zt/fo3   = mH                   (phase normal)                        (0.141)

 

   C3 = 159154.94/(Zs*fo3) = uF       (          SUPERTWT, phase normal)  (2.210)

  -------------------------------------------------------------------------------------------------------

 

SECOND-ORDER BUTTERWORTH CROSSOVER  (12 dB/octave):

 

   2-way 12 BW (with examples):                         (2500 Hz, 8 ohms)

 

  -------------------------------------------------------------------------------------------------------

   L1 = 225.07908*Zbm/fo   = mH      (BASS/MID)                                      (0.720)

   C1 = 112539.54/(Zbm*fo) = uF      (phase normal)                                   (5.627)

 

   L2 = 225.07908*Zt/fo    = mH                    (TWEETER)                          (0.720)

   C2 = 112539.54/(Zt*fo)  = uF                     (phase reversed)                     (5.627)

 

   3-way 12 BW (with examples):                     (500/3000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

 

   L1 = 225.07908*Zb/fo1   = mH      (BASS)                                              (3.601)

   C1 = 112539.54/(Zb*fo1) = uF                   (phase normal)                       (28.13)

 

   C2 = 112539.54/(Zm*fo1) = uF      (MIDRANGE)                                   (28.13)

   L2 = 225.07908*Zm/fo1   = mH      (phase reversed)                                 (3.601)

   L3 = 225.07908*Zm/fo2   = mH                                                                 (0.600)

   C3 = 112539.54/(Zm*fo2) = uF                                                                 (4.689)

 

   C4 = 112539.54/(Zt*fo2) = uF                    (TWEETER)                          (4.689)

   L4 = 225.07908*Zt/fo2   = mH                   (phase normal)                        (0.600)

 

   4-way 12 BW (with examples):                (200/2200/9000 Hz, 8 ohms)

 

  -------------------------------------------------------------------------------------------------------

   L1 = 225.07908*Zb/fo1   = mH      (BASS)                                              (9.003)

   C1 = 112539.54/(Zb*fo1) = uF                   (phase normal)                        (70.33)

 

   C2 = 112539.54/(Zm*fo1) = uF      (MIDRANGE)                                   (70.33)

   L2 = 225.07908*Zm/fo1   = mH      (phase reversed)                                 (9.003)

   L3 = 225.07908*Zm/fo2   = mH                                                                 (0.818)

   C3 = 112539.54/(Zm*fo2) = uF                                                                 (6.394)

 

   C4 = 112539.54/(Zt*fo2) = uF                    (TWEETER)                          (6.394)

 

   L4 = 225.07908*Zt/fo2   = mH                   (phase normal)                       (0.818)

   L5 = 225.07908*Zt/fo3   = mH                                                                  (0.200)

   C5 = 112539.54/(Zt*fo3) = uF                                                                   (1.563)

 

   C6 = 112539.54/(Zs*fo3) = uF                   (SUPERTWEETER)              (1.563)

   L6 = 225.07908*Zs/fo3   = mH                   (phase reversed)                     (0.200)

  -------------------------------------------------------------------------------------------------------

 

     SECOND-ORDER LINKWITZ-RILEY CROSSOVER  (12 dB/octave):

 

   2-way 12 LR (with examples):                         (2500 Hz, 8 ohms)

 

  -------------------------------------------------------------------------------------------------------

   L1 = 318.30988*Zbm/fo   = mH      (BASS/MID)                                      (1.018)

   C1 = 79577.471/(Zbm*fo) = uF      (phase normal)                                   (3.978)

 

   L2 = 318.30988*Zt/fo    = mH                    (TWEETER)                          (1.018)

   C2 = 79577.471/(Zt*fo)  = uF                     (phase reversed)                     (3.978)

 

   3-way 12 LR (with examples):                     (500/3000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

 

   L1 = 318.30988*Zb/fo1   = mH      (BASS)                                              (5.092)

   C1 = 79577.471/(Zb*fo1) = uF                   (phase normal)                       (19.89)

 

   C2 = 79577.471/(Zm*fo1) = uF      (MIDRANGE)                                   (19.89)

   L2 = 318.30988*Zm/fo1   = mH      (phase reversed)                                 (5.092)

   L3 = 318.30988*Zm/fo2   = mH                                                                 (0.848)

   C3 = 79577.471/(Zm*fo2) = uF                                                                 (3.315)

 

   C4 = 79577.471/(Zt*fo2) = uF                    (TWEETER)                          (3.315)

   L4 = 318.30988*Zt/fo2   = mH                   (phase normal)                        (0.848)

 

   4-way 12 LR (with examples):                (200/2200/9000 Hz, 8 ohms)

 

  -------------------------------------------------------------------------------------------------------

   L1 = 318.30988*Zb/fo1   = mH      (BASS)                                              (12.73)

   C1 = 79577.471/(Zb*fo1) = uF                   (phase normal)                       (49.73)

 

   C2 = 79577.471/(Zm*fo1) = uF      (MIDRANGE)                                   (49.73)

   L2 = 318.30988*Zm/fo1   = mH      (phase reversed)                                 (12.73)

   L3 = 318.30988*Zm/fo2   = mH                                                                 (1.157)

   C3 = 79577.471/(Zm*fo2) = uF                                                                 (4.521)

 

   C4 = 79577.471/(Zt*fo2) = uF                    (TWEETER)                          (4.521)

 

   L4 = 318.30988*Zt/fo2   = mH                   (phase normal)                       (1.157)

   L5 = 318.30988*Zt/fo3   = mH                                                                  (0.282)

   C5 = 79577.471/(Zt*fo3) = uF                                                                   (1.105)

 

   C6 = 79577.471/(Zs*fo3) = uF                   (SUPERTWEETER)              (1.105)

   L6 = 318.30988*Zs/fo3   = mH                   (phase reversed)                     (0.282)

  -------------------------------------------------------------------------------------------------------

 

     THIRD-ORDER BUTTERWORTH CROSSOVER (18 dB/octave):

 

   2-way 18 BU (with examples):                         (2500 Hz, 8 ohms)

 

  -------------------------------------------------------------------------------------------------------

   L1 = 238.73241*Zbm/fo   = mH      (BASS/MID)                                      (0.763)

   C1 = 212206.59/(Zbm*fo) = uF      (phase normal)                                   (10.61)

   L2 = 79.577471*Zbm/fo   = mH                                                                 (0.254)

 

   C2 = 106103.29/(Zt*fo)  = uF                     (TWEETER)                          (5.305)

   L3 = 119.36620*Zt/fo    = mH                    (phase normal)                       (0.381)

   C3 = 318309.88/(Zt*fo)  = uF                                                                    (15.91)

 

   3-way 18 BU (with examples):                     (500/3000 Hz, 8 ohms)

 

  -------------------------------------------------------------------------------------------------------

   L1 = 238.73241*Zb/fo1   = mH      (BASS)                                              (0.763)

   C1 = 212206.59/(Zb*fo1) = uF                   (phase normal)                       (10.61)

   L2 = 79.577471*Zb/fo1   = mH                                                                  (0.254)

 

   C2 = 106103.29/(Zm*fo1) = uF      (MIDRANGE)                                   (26.52)

   L3 = 119.36620*Zm/fo1   = mH      (phase reversed)                                 (1.909)

   C3 = 318309.88/(Zm*fo1) = uF                                                                 (79.57)

   L4 = 238.73241*Zm/fo2   = mH                                                                 (0.636)

 

   C4 = 212206.59/(Zm*fo2) = uF                                                                 (8.841)

   L5 = 79.577471*Zm/fo2   = mH                                                                 (0.212)

 

   C5 = 106103.29/(Zt*fo2) = uF                    (TWEETER)                          (4.420)

   L6 = 119.36620*Zt/fo2   = mH                   (phase normal)                       (0.318)

   C6 = 318309.88/(Zt*fo2) = uF                                                                   (13.26)

 

   4-way 18 BU (with examples):                (200/2200/9000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 238.73241*Zb/fo1   = mH      (BASS)                                              (9.549)

 

   C1 = 212206.59/(Zb*fo1) = uF                   (phase normal)                       (132.6)

   L2 = 79.577471*Zb/fo1   = mH                                                                  (3.183)

 

   C2 = 106103.29/(Zm*fo1) = uF      (MIDRANGE)                                   (66.31)

   L3 = 119.36620*Zm/fo1   = mH      (phase reversed)                                 (4.774)

   C3 = 318309.88/(Zm*fo1) = uF                                                                 (198.9)

   L4 = 238.73241*Zm/fo2   = mH                                                                 (0.868)

   C4 = 212206.59/(Zm*fo2) = uF                                                                 (12.05)

   L5 = 79.577471*Zm/fo2   = mH                                                                 (0.289)

 

   C5 = 106103.29/(Zt*fo2) = uF                    (TWEETER)                          (6.028)

 

   L6 = 119.36620*Zt/fo2   = mH                   (phase normal)                        (0.434)

   C6 = 318309.88/(Zt*fo2) = uF                                                                   (18.08)

   L7 = 238.73241*Zt/fo3   = mH                                                                  (0.212)

   C7 = 212206.59/(Zt*fo3) = uF                                                                   (2.947)

   L8 = 79.577471*Zt/fo3   = mH                                                                  (0.070)

 

   C8 = 106103.29/(Zs*fo3) = uF                   (SUPERTWEETER)              (1.473)

   L9 = 119.36620*Zs/fo3   = mH                   (phase normal)                       (0.106)

   C9 = 318309.88/(Zs*fo3) = uF                                                                  (4.420)

  -------------------------------------------------------------------------------------------------------

 

     FOURTH-ORDER BUTTERWORTH CROSSOVER (24 dB/octave):

 

   2-way 24 BU (with examples):                         (2500 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 243.62383*Zbm/fo   = mH      (BASS/MID)                                      (0.779)

   C1 = 251012.97/(Zbm*fo) = uF      (phase normal)                                   (12.55)

   L2 = 172.26806*Zbm/fo   = mH                                                                 (0.551)

   C2 = 60905.959/(Zbm*fo) = uF                                                                 (3.045)

 

   C3 = 103972.97/(Zt*fo)  = uF                     (TWEETER)                          (5.198)

 

   L3 = 100.91298*Zt/fo    = mH                    (phase normal)                       (0.322)

   C4 = 147039.99/(Zt*fo)  = uF                                                                    (7.351)

   L4 = 415.89190*Zt/fo    = mH                                                                   (1.330)

 

   3-way 24 BU (with examples):                     (500/3000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 243.62383*Zb/fo1   = mH      (BASS)                                              (3.897)

   C1 = 251012.97/(Zb*fo1) = uF                   (phase normal)                        (62.75)

   L2 = 172.26806*Zb/fo1   = mH                                                                  (2.756)

 

   C2 = 60905.959/(Zb*fo1) = uF                                                                  (15.22)

 

   C3 = 103972.97/(Zm*fo1) = uF      (MIDRANGE)                                   (25.99)

   L3 = 100.91298*Zm/fo1   = mH      (phase normal)                                   (1.614)

   C4 = 147039.99/(Zm*fo1) = uF                                                                 (36.75)

   L4 = 415.89190*Zm/fo1   = mH                                                                 (6.654)

   L5 = 243.62383*Zm/fo2   = mH                                                                 (0.649)

   C5 = 251012.97/(Zm*fo2) = uF                                                                 (10.45)

   L6 = 172.26806*Zm/fo2   = mH                                                                 (0.459)

   C6 = 60905.959/(Zm*fo2) = uF                                                                 (2.537)

 

   C7 = 103972.97/(Zt*fo2) = uF                    (TWEETER)                          (4.332)

 

   L7 = 100.91298*Zt/fo2   = mH                   (phase normal)                       (0.269)

   C8 = 147039.99/(Zt*fo2) = uF                                                                   (6.126)

   L8 = 415.89190*Zt/fo2   = mH                                                                  (1.109)

 

   4-way 24 BU (with examples):                (200/2200/9000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 243.62383*Zb/fo1   = mH      (BASS)                                              (9.744)

   C1 = 251012.97/(Zb*fo1) = uF                   (phase normal)                       (156.8)

   L2 = 172.26806*Zb/fo1   = mH                                                                  (6.890)

 

   C2 = 60905.959/(Zb*fo1) = uF                                                                  (38.06)

 

   C3 = 103972.97/(Zm*fo1) = uF      (MIDRANGE)                                   (64.98)

   L3 = 100.91298*Zm/fo1   = mH      (phase normal)                                   (4.036)

   C4 = 147039.99/(Zm*fo1) = uF                                                                 (91.89)

   L4 = 415.89190*Zm/fo1   = mH                                                                 (16.63)

   L5 = 243.62383*Zm/fo2   = mH                                                                 (0.885)

   C5 = 251012.97/(Zm*fo2) = uF                                                                 (14.26)

   L6 = 172.26806*Zm/fo2   = mH                                                                 (0.626)

   C6 = 60905.959/(Zm*fo2) = uF                                                                 (3.460)

 

   C7 = 103972.97/(Zt*fo2) = uF                    (TWEETER)                          (5.907)

 

   L7 = 100.91298*Zt/fo2   = mH                   (phase normal)                       (0.366)

   C8 = 147039.99/(Zt*fo2) = uF                                                                   (8.354)

   L8 = 415.89190*Zt/fo2   = mH                                                                  (1.512)

   L9 = 243.62383*Zt/fo3   = mH                                                                  (0.216)

   C9 = 251012.97/(Zt*fo3) = uF                                                                   (3.486)

  L10 = 172.26806*Zt/fo3   = mH                                                                  (0.153)

  C10 = 60905.959/(Zt*fo3) = uF                                                                  (0.845)

 

  C11 = 103972.97/(Zs*fo3) = uF      (SUPERTWEETER)                          (1.444)

  L11 = 100.91298*Zs/fo3   = mH      (phase normal)                                   (0.089)

 

  C12 = 147039.99/(Zs*fo3) = uF                                                                  (2.042)

  L12 = 415.89190*Zs/fo3   = mH                                                                 (0.369)

  -------------------------------------------------------------------------------------------------------

 

     FOURTH-ORDER LINKWITZ-RILEY CROSSOVER (24 dB/octave):

 

   2-way 24 LR (with examples):                         (2500 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 300.10543*Zbm/fo   = mH      (BASS/MID)                                      (0.960)

 

   C1 = 253213.96/(Zbm*fo) = uF      (phase normal)                                   (12.66)

   L2 = 150.05271*Zbm/fo   = mH                                                                 (0.480)

   C2 = 56269.769/(Zbm*fo) = uF                                                                 (2.813)

 

   C3 = 84404.654/(Zt*fo)  = uF                     (TWEETER)                          (4.220)

   L3 = 100.03514*Zt/fo    = mH                    (phase normal)                       (0.320)

   C4 = 168809.30/(Zt*fo)  = uF                                                                    (8.440)

   L4 = 450.15815*Zt/fo    = mH                                                                   (1.440)

 

   3-way 24 LR (with examples):                     (500/3000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

 

   L1 = 300.10543*Zb/fo1   = mH      (BASS)                                              (4.801)

   C1 = 253213.96/(Zb*fo1) = uF                   (phase normal)                       (63.30)

   L2 = 150.05271*Zb/fo1   = mH                                                                  (2.400)

   C2 = 56269.769/(Zb*fo1) = uF                                                                  (14.06)

 

   L3 = 300.10543*Zm/(fo2-fo1)           = mH            (MIDRANGE)            (0.960)

   C3 = 84404.654*(fo2-fo1)/(Zm*fo1*fo2) = uF      (phase normal)            (17.58)

   L4 = 100.03514*Zm*(fo2-fo1)/(fo1*fo2) = mH                                        (1.333)

   C4 = 253213.96/(Zm*(fo2-fo1))         = uF                                                (12.66)

 

   L5 = 150.05271*Zm/(fo2-fo1)           = mH                                               (0.480)

   C5 = 168809.30*(fo2-fo1)/(Zm*fo1*fo2) = uF                                          (35.16)

   L6 = 450.15815*Zm*(fo2-fo1)/(fo1*fo2) = mH                                        (6.002)

   C6 = 56269.769/(Zm*(fo2-fo1))         = uF                                                (2.813)

 

   C7 = 84404.654/(Zt*fo2) = uF                    (TWEETER)                          (3.516)

   L7 = 100.03514*Zt/fo2   = mH                   (phase normal)                        (0.266)

   C8 = 168809.30/(Zt*fo2) = uF                                                                   (7.033)

   L8 = 450.15815*Zt/fo2   = mH                                                                  (1.200)

 

   4-way 24 LR (with examples):                (200/2200/9000 Hz, 8 ohms)

  -------------------------------------------------------------------------------------------------------

   L1 = 300.10543*Zb/fo1   = mH      (BASS)                                              (12.00)

   C1 = 253213.96/(Zb*fo1) = uF                   (phase normal)                       (158.2)

   L2 = 150.05271*Zb/fo1   = mH                                                                  (6.002)

   C2 = 56269.769/(Zb*fo1) = uF                                                                  (35.16)

 

   L3 = 300.10543*Zm/(fo2-fo1)           = mH            (MIDRANGE)            (1.200)

 

   C3 = 84404.654*(fo2-fo1)/(Zm*fo1*fo2) = uF      (phase normal)            (47.95)

   L4 = 100.03514*Zm*(fo2-fo1)/(fo1*fo2) = mH                                        (3.637)

   C4 = 253213.96/(Zm*(fo2-fo1))         = uF                                                (15.82)

   L5 = 150.05271*Zm/(fo2-fo1)           = mH                                               (0.600)

   C5 = 168809.30*(fo2-fo1)/(Zm*fo1*fo2) = uF                                          (95.91)

   L6 = 450.15815*Zm*(fo2-fo1)/(fo1*fo2) = mH                                        (16.36)

   C6 = 56269.769/(Zm*(fo2-fo1))         = uF                                                (3.516)

 

   L7 = 300.10543*Zt/(fo3-fo2)           = mH  (TWEETER)                           (0.353)

 

   C7 = 84404.654*(fo3-fo2)/(Zt*fo2*fo3) = uF        (phase normal)            (3.623)

   L8 = 100.03514*Zt*(fo3-fo2)/(fo2*fo3) = mH                                          (0.274)

   C8 = 253213.96/(Zt*(fo3-fo2))         = uF                                                  (4.654)

   L9 = 150.05271*Zt/(fo3-fo2)           = mH                                                 (0.176)

   C9 = 168809.30*(fo3-fo2)/(Zt*fo2*fo3) = uF                                           (7.246)

  L10 = 450.15815*Zt*(fo3-fo2)/(fo2*fo3) = mH                                         (1.236)

  C10 = 56269.769/(Zt*(fo3-fo2))         = uF                                                 (1.034)

 

  C11 = 84404.654/(Zs*fo3) = uF      (SUPERTWEETER)                          (1.172)

 

  L11 = 100.03514*Zs/fo3   = mH      (phase normal)                                   (0.088)

  C12 = 168809.30/(Zs*fo3) = uF                                                                  (2.344)

  L12 = 450.15815*Zs/fo3   = mH                                                                 (0.400)

  -------------------------------------------------------------------------------------------------------