CAAD
4.1 * TECHNICAL LIBRARY * (ed. 1995)
MONACOR
INTERNATIONAL & CO.KG, Bremen.
CONTENTS:
Formulas
for crossover calculation.
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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)
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FIRST-ORDER BUTTERWORTH CROSSOVER ( 6
dB/octave):
2-way
6 BW (with examples): (2500 Hz, 8 ohms)
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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)
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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)
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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)
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SECOND-ORDER
BUTTERWORTH CROSSOVER (12 dB/octave):
2-way 12 BW (with examples): (2500 Hz, 8 ohms)
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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)
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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)
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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)
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SECOND-ORDER LINKWITZ-RILEY
CROSSOVER (12 dB/octave):
2-way 12 LR (with examples): (2500 Hz, 8 ohms)
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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)
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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)
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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)
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THIRD-ORDER BUTTERWORTH CROSSOVER (18
dB/octave):
2-way 18 BU (with examples): (2500 Hz, 8 ohms)
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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)
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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)
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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)
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FOURTH-ORDER BUTTERWORTH CROSSOVER (24
dB/octave):
2-way 24 BU (with examples): (2500 Hz, 8 ohms)
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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)
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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)
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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)
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FOURTH-ORDER LINKWITZ-RILEY CROSSOVER (24
dB/octave):
2-way 24 LR (with examples): (2500 Hz, 8 ohms)
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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)
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