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)
-------------------------------------------------------------------------------------------------------
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)
-------------------------------------------------------------------------------------------------------
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)
-------------------------------------------------------------------------------------------------------