CAAD 4.1       * TECHNISCHE BIBLIOTHEEK *       (ed. 1995)

MONACOR INTERNATIONAL & CO.KG, Bremen.

 

INHOUD:

Formules voor filterberekeningen.

 

FILTERBEREKENING:

Gebruikte symbolen:

 

   fo   :            kantelfrequentie in een twee-weg systeem                                   (Hz)

   fo1 :            kantelfrequentie tussen bas en middentoner                            (Hz)

   fo2 :            kantelfrequentie tussen middentoner en tweeter                   (Hz)

   fo3 :            kantelfrequentie tussen tweeter en supertweeter               (Hz)

 

   Zb    :  impedantie van de basluidspreker                                                (Ohm)

   Zbm :  impedantie van de bas/middentoonluidspreker                (Ohm)

   Zm   :  impedantie van de middentoner                                        (Ohm)

   Zt     :  impedantie van de tweeter                                                       (Ohm)

 

   Zs    :  impedantie van de supertweeter                                       (Ohm)

 

   L   :  berekende waarde van de spoel, milliHenries                (mH)

   C   :  berekende waarde van de condensator, microFarads            (uF)

 

 

(L & C met aanduidingen van 1 tot 12 afhankelijk van de plaats in het schema)

 

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Eerste orde BUTTERWORTH-filter ( 6 dB/octaaf):

 

   2-weg  6 BW (met voorbeelden):                         (2500 Hz, 8 Ohm)

 

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

 

   L1 = 159.15494*Zbm/fo   = mH             (BAS/MID, normale fase)    (0.509)

 

   C1 = 159154.94/(Zt*fo)  = uF            (TWEETER, normale fase)    (7.957)

 

   3-way  6 BW (met voorbeelden):                     (500/3000 Hz, 8 Ohm)

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

   L1 = 159.15494*Zb/fo1   = mH            (BAS, normale fase)              (2.546)

 

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

   L2 = 159.15494*Zm/fo2   = mH            (normale fase)                                    (0.424)

 

   C2 = 159154.94/(Zt*fo2) = uF            (TWEETER, normale fase)    (6.631)

 

   4-way  6 BW (met voorbeelden):                (200/2200/9000 Hz, 8 Ohm)

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

   L1 = 159.15494*Zb/fo1   = mH            (BAS, normale fase)              (6.366)

 

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

   L2 = 159.15494*Zm/fo2   = mH            (normale fase)                                    (0.578)

 

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

 

   L3 = 159.15494*Zt/fo3   = mH            (normale fase)                                    (0.141)

 

   C3 = 159154.94/(Zs*fo3) = uF            (SUPERTWT, normale fase)            (2.210)

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

 

2-way 12 BW (met voorbeelden):                         (2500 Hz, 8 Ohm)

 

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

 

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

   C1 = 112539.54/(Zbm*fo) = uF            (normale fase)                                    (5.627)

 

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

   C2 = 112539.54/(Zt*fo)  = uF            (omgekeerde fase)                  (5.627)

 

 

3-way 12 BW (met voorbeelden):           (500/3000 Hz, 8 Ohm)

 

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

 

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

   C1 = 112539.54/(Zb*fo1) = uF            (normale fase)                                    (28.13)

 

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

   L2 = 225.07908*Zm/fo1   = mH            (omgekeerde fase)                  (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            (normale fase)                                    (0.600)

 

 

4-way 12 BW (met voorbeelden):           (200/2200/9000 Hz, 8 Ohm)

 

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

 

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

   C1 = 112539.54/(Zb*fo1) = uF            (normale fase)                                    (70.33)

 

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

   L2 = 225.07908*Zm/fo1   = mH            (omgekeerde fase)                  (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            (normale fase)                                    (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            (omgekeerde fase)                  (0.200)

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

 

 

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

 

2-way 12 LR (met voorbeelden):                         (2500 Hz, 8 Ohm)

 

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

 

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

   C1 = 79577.471/(Zbm*fo) = uF            (normale fase)                                    (3.978)

 

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

   C2 = 79577.471/(Zt*fo)  = uF            (omgekeerde fase)                  (3.978)

 

 

3-way 12 LR (met voorbeelden):                     (500/3000 Hz, 8 Ohm)

 

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

 

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

   C1 = 79577.471/(Zb*fo1) = uF            (normale fase)                                    (19.89)

 

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

   L2 = 318.30988*Zm/fo1   = mH            (omgekeerde fase)                  (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            (normale fase)                                    (0.848)

 

 

4-way 12 LR (met voorbeelden):                (200/2200/9000 Hz, 8 Ohm)

 

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

 

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

   C1 = 79577.471/(Zb*fo1) = uF            (normale fase)                                    (49.73)

 

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

   L2 = 318.30988*Zm/fo1   = mH            (omgekeerde fase)                  (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            (normale fase)                                    (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            (omgekeerde fase)                  (0.282)

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

 

 

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

 

2-way 18 BU (met voorbeelden):                         (2500 Hz, 8 Ohm)

 

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

 

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

   C1 = 212206.59/(Zbm*fo) = uF            (normale fase)                                    (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            (normale fase)                                    (0.381)

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

 

 

3-way 18 BU (met voorbeelden):                     (500/3000 Hz, 8 Ohm)

 

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

 

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

   C1 = 212206.59/(Zb*fo1) = uF            (normale fase)                                    (10.61)

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

 

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

   L3 = 119.36620*Zm/fo1   = mH            (omgekeerde fase)                  (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            (normale fase)                                    (0.318)

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

 

 

4-way 18 BU (met voorbeelden):                (200/2200/9000 Hz, 8 Ohm)

 

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

 

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

   C1 = 212206.59/(Zb*fo1) = uF            (normale fase)                                    (132.6)

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

 

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

   L3 = 119.36620*Zm/fo1   = mH            (omgekeerde fase)                  (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            (normale fase)                                    (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            (normale fase)                                    (0.106)

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

 

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

 

 

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

 

2-way 24 BU (met voorbeelden):                         (2500 Hz, 8 Ohm)

 

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

 

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

   C1 = 251012.97/(Zbm*fo) = uF            (normale fase)                                    (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            (normale fase)                                    (0.322)

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

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

 

 

3-way 24 BU (met voorbeelden):                     (500/3000 Hz, 8 Ohm)

 

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

 

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

   C1 = 251012.97/(Zb*fo1) = uF            (normale fase)                                    (62.75)

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

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

 

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

   L3 = 100.91298*Zm/fo1   = mH            (normale fase)                                    (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            (normale fase)                                    (0.269)

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

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

 

 

4-way 24 BU (met voorbeelden):                (200/2200/9000 Hz, 8 Ohm)

 

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

 

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

   C1 = 251012.97/(Zb*fo1) = uF            (normale fase)                                    (156.8)

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

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

 

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

   L3 = 100.91298*Zm/fo1   = mH            (normale fase)                                    (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            (normale fase)                                    (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            (normale fase)                                    (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/octaaf):

 

2-way 24 LR (met voorbeelden):                         (2500 Hz, 8 Ohm)

 

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

 

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

   C1 = 253213.96/(Zbm*fo) = uF            (normale fase)                                    (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            (normale fase)                                    (0.320)

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

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

 

 

3-way 24 LR (met voorbeelden):                     (500/3000 Hz, 8 Ohm)

 

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

 

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

   C1 = 253213.96/(Zb*fo1) = uF                   (normale fase)                                    (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            (MIDDENTONER)            (0.960)

   C3 = 84404.654*(fo2-fo1)/(Zm*fo1*fo2) = uF            (normale fase)                        (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                   (normale fase)                                    (0.266)

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

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

 

4-way 24 LR (met voorbeelden):                (200/2200/9000 Hz, 8 Ohm)

 

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

 

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

   C1 = 253213.96/(Zb*fo1) = uF                   (normale fase)                                    (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            (MIDDENTONER)            (1.200)

   C3 = 84404.654*(fo2-fo1)/(Zm*fo1*fo2) = uF            (normale fase)                        (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            (normale fase)                        (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            (normale fase)                                                (0.088)

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

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

 

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