Ex Term Is 6
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Extremis 6.8 TQWP Alignment By Casey Brown Mathcad Worksheet By Martin J. King
Driver Thiele / Small Parameters : Focal 8V 4412 Average Driver in Final TL Enclosure fd
30 . Hz
V ad
33.2 . liter
Adjustments
Re
7.02 . Ω
Q ed
.383
Re
Q md
2.54
Q ed
.13 . mH
L vc
9.0 .
Bl Sd
newton
Q td
amp
140 . cm
2
Power
Q td
10 . watt
n_open
1
Q ed
Q md
R add
Q ed . R e . R e
R add
1
.332
(Input Power, Applied Voltage Referenced to 8 ohm Driver)
Transmission Line Definition n_closed
1
Re
1 16
(0 lb/ft3 < D < 1 lb/ft3 ) (n_closed > 1) (n_open > 1)
Geometry Definition Closed End of Transmission Line Section Length Lc Lc
0 1
Sc
2.52 . in
Sc
Section Length
Lo Lo Lo Lo
0 1 2 3 4
Initial Area
.5049 . in
Open End of Transmission Line
Lo
(Driver ---> Closed End)
0, 0 1, 0
Final Area
13.66 . in . 11 . in
Sc
13.80 . in . 12 . in
Sc
0, 1 1, 1
Stuffing Density
13.80 . in . 12 . in D c 14.50 . in . 12 . in D c
0 1
.33 . lb . ft
3
.33 . lb . ft
3
(Driver ---> Open End) Initial Area
.5049 . in
So
3.04 . in
So
.5049 . in
So
.5049 . in
So
7.06 . in
So
0, 0 1, 0 2, 0 3, 0 4, 0
Final Area
13.66 . in . 11 . in
So
13.52 . in . 12 . in
So
12.68 . in . 12 . in
So
11.54 . in . 12 . in
So
12.40 . in . 12 . in
So
0, 1 1, 1 2, 1 3, 1 4, 1
Stuffing Density
13.52 . in . 12 . in D o 12.68 . in . 12 . in D o 11.54 . in . 12 . in D o 12.40 . in . 12 . in D o 10.44 . in . 12 . in D o Do
0 1 2 3 4 5
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
1
Lo Lo Lo Lo Lo Lo
4
5
6 7 8 9
7.06 . in
So
.5049 . in
So
.5049 . in
So
3.03 . in
So
.5049 . in
So
.5049 . in
Lo Lo Lo Lo Lo Lo Lo
10 11 12 13 14
15
16
So 14.17 . in
So
4.025 . in
So
5.4044 . in
So
3.1416 . in
So
14.5154 . in
So
1.0385 . in
So
1.0276 . in
So
10 , 0 11 , 0 12 , 0 13 , 0 14 , 0 15 , 0
16 , 0
4, 0 5, 0
6, 0
7, 0 8, 0 9, 0
12.40 . in . 12 . in
So
10.44 . in . 12 . in
So
10.30 . in . 11 . in
So
10.16 . in . 12 . in
So
9.32 . in . 12 . in
So
8.18 . in . 12 . in
9.04 . in . 12 . in
So
5.13 . in . 12 . in
So
5.13 . in . 12 . in
So
4.00 . in . 12 . in
So
4.00 . in . 12 . in
So
.75 . in . 12 . in
So
1.5 . in . 12 . in
So
So
10 , 1 11 , 1 12 , 1 13 , 1
4, 1 5, 1
6, 1
7, 1 8, 1 9, 1
10.44 . in . 12 . in D o 10.30 in . 11 . in D
9.32 . in . 12 . in D o 8.18 . in . 12 . in D o 9.04 . in . 12 . in D o
5.13 . in . 12 . in D o 4.00 . in . 12 . in D o 4.00 . in . 12 . in D o
10 11 12 13
i= 0
i
r= 0
Sc 2
r, 1 .
n_open S or, 0 r= 0
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
0 . lb . ft
3
1.5 in . 12 . in D o 15
0 . lb . ft
3
3.75 . in . 14 . in D o
0 . lb . ft
3
16 , 1
So 2
3
15 , 1
16
i
L c .D c r r
9
.33 . lb . ft
3
Total Amount of Stuffing n_closed S cr , 0
8
3
0 . lb . ft
L o = 63.012 in i= 0
7
.33 . lb . ft
.75 . in . 12 . in D o 14
n_open Lc
6
3
14 , 1
Total Length of the Transmission Line n_closed
o5
10.16 . in . 12 . in D o
5.13 . in . 12 . in D o
4
.33 . lb . ft
r, 1 .
L o .D o r r
= 0.860 lb
Area / Sd
4.009
Transmission Line Profile
5
Area r 2 .S d
3 1
Area r 2 .S d
1 3
4.009 5
0
10
0.000
20
30
40 Length
r
50
60
70 63.012
in Length (in)
Far Field Transmission Line System and Infinite Baffle Sound Pressure Level Responses 180 135 90 45
deg arg p
0 r
45
deg
90 135 180
10
100
3 1 . 10
1 r . dω . Hz 110 105 100 SPL (dB)
Phase (deg)
arg p o r
SPL o r SPL r
95 90 85 80 75 70 65 60
10
100 1 r . dω . Hz Frequency (Hz)
3 1 . 10
90
Phase (deg)
arg Z o r
45
deg 0
arg Z r deg
45
90
10
100
1 . 10
3
1 r . dω . Hz 100
Impedance (ohms)
80 Zo Z r
r
60 40 20 0
10
100
1 . 10
1 r . dω . Hz Frequency (Hz)
Woofer RMS Displacement
6
6
RMS Deflection (mm)
5 xd r
4
mm x
3 r 2
mm
1 0
0
10
100
20
1 r . dω . Hz Frequency (Hz)
1 . 10 1000
3
3
Terminus Air Velocity (should be < 10 m/sec / 342 m/sec = 0.03) Terminus Air Velocity / Speed of Sound
0.03 0.03
Velocity Ratio
0.025 v term r
0.02
c
0.015 0.01 0.005 0 0
10
3
1 . 10
100
10
1 r . dω . Hz Frequency (Hz)
1000
SoundAngle Pressure in TimePressure Domain Phase of System
2000 2000 360 1500 315
Phase (deg)
270 1000 p summed p anglen 225 q 500 Pa 180 deg 1350 90 500 1000
45 1000 0 0 10 0
0.01
0.02
0.03
0.04
0.05 100 n . dt 1 . dω . Hz qTime (sec)
0.06
0.07
0.08
0.09
0.1 3 1 . 10 0.1
System Group Delay
0.05 0.04 φ
0.03 q
sec
0.02 0.01 0 0.01
10
100 1 q . dω . Hz Frequency (Hz)
1 . 10
3
Sound Pressure in Time Domain
2000 2000 1500 p summed 1000 n 500 Pa 0 500 1000 1000
0
0.01
0.02
0.03
0.04
0.05
0.06
n . dt
0
0.07
0.08
0.09
0.1 0.1
Time (sec)
Woofer and Terminus Far Field Sound Pressure Level Responses 180 135 90 45
deg
0
arg p L r
45
deg
90 135 180
10
100
3 1 . 10
1 r . dω . Hz
SPL (dB)
Phase (deg)
arg p d r
110 105 100 95 SPL d r 90 SPL L r
85 80 75 70 65 60
10
100 1 r . dω . Hz Frequency (Hz)
1 . 10
3
Driver Thiele / Small Parameters : Focal 8V 4412 Average Driver in Final TL Enclosure fd
30 . Hz
V ad
33.2 . liter
Adjustments
Re
7.02 . Ω
Q ed
.383
Re
Q md
2.54
Q ed
.13 . mH
L vc
9.0 .
Bl Sd
newton
Q td
amp
140 . cm
2
Power
Q td
10 . watt
n_open
1
Q ed
Q md
R add
Q ed . R e . R e
R add
1
.332
(Input Power, Applied Voltage Referenced to 8 ohm Driver)
Transmission Line Definition n_closed
1
Re
1 16
(0 lb/ft3 < D < 1 lb/ft3 ) (n_closed > 1) (n_open > 1)
Geometry Definition Closed End of Transmission Line Section Length Lc Lc
0 1
Sc
2.52 . in
Sc
Section Length
Lo Lo Lo Lo
0 1 2 3 4
Initial Area
.5049 . in
Open End of Transmission Line
Lo
(Driver ---> Closed End)
0, 0 1, 0
Final Area
13.66 . in . 11 . in
Sc
13.80 . in . 12 . in
Sc
0, 1 1, 1
Stuffing Density
13.80 . in . 12 . in D c 14.50 . in . 12 . in D c
0 1
.33 . lb . ft
3
.33 . lb . ft
3
(Driver ---> Open End) Initial Area
.5049 . in
So
3.04 . in
So
.5049 . in
So
.5049 . in
So
7.06 . in
So
0, 0 1, 0 2, 0 3, 0 4, 0
Final Area
13.66 . in . 11 . in
So
13.52 . in . 12 . in
So
12.68 . in . 12 . in
So
11.54 . in . 12 . in
So
12.40 . in . 12 . in
So
0, 1 1, 1 2, 1 3, 1 4, 1
Stuffing Density
13.52 . in . 12 . in D o 12.68 . in . 12 . in D o 11.54 . in . 12 . in D o 12.40 . in . 12 . in D o 10.44 . in . 12 . in D o Do
0 1 2 3 4 5
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
1
Lo Lo Lo Lo Lo Lo
4
5
6 7 8 9
7.06 . in
So
.5049 . in
So
.5049 . in
So
3.03 . in
So
.5049 . in
So
.5049 . in
Lo Lo Lo Lo Lo Lo Lo
10 11 12 13 14
15
16
So 14.17 . in
So
4.025 . in
So
5.4044 . in
So
3.1416 . in
So
14.5154 . in
So
1.0385 . in
So
1.0276 . in
So
10 , 0 11 , 0 12 , 0 13 , 0 14 , 0 15 , 0
16 , 0
4, 0 5, 0
6, 0
7, 0 8, 0 9, 0
12.40 . in . 12 . in
So
10.44 . in . 12 . in
So
10.30 . in . 11 . in
So
10.16 . in . 12 . in
So
9.32 . in . 12 . in
So
8.18 . in . 12 . in
9.04 . in . 12 . in
So
5.13 . in . 12 . in
So
5.13 . in . 12 . in
So
4.00 . in . 12 . in
So
4.00 . in . 12 . in
So
.75 . in . 12 . in
So
1.5 . in . 12 . in
So
So
10 , 1 11 , 1 12 , 1 13 , 1
4, 1 5, 1
6, 1
7, 1 8, 1 9, 1
10.44 . in . 12 . in D o 10.30 in . 11 . in D
9.32 . in . 12 . in D o 8.18 . in . 12 . in D o 9.04 . in . 12 . in D o
5.13 . in . 12 . in D o 4.00 . in . 12 . in D o 4.00 . in . 12 . in D o
10 11 12 13
i= 0
i
r= 0
Sc 2
r, 1 .
n_open S or, 0 r= 0
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
.33 . lb . ft
3
0 . lb . ft
3
1.5 in . 12 . in D o 15
0 . lb . ft
3
3.75 . in . 14 . in D o
0 . lb . ft
3
16 , 1
So 2
3
15 , 1
16
i
L c .D c r r
9
.33 . lb . ft
3
Total Amount of Stuffing n_closed S cr , 0
8
3
0 . lb . ft
L o = 63.012 in i= 0
7
.33 . lb . ft
.75 . in . 12 . in D o 14
n_open Lc
6
3
14 , 1
Total Length of the Transmission Line n_closed
o5
10.16 . in . 12 . in D o
5.13 . in . 12 . in D o
4
.33 . lb . ft
r, 1 .
L o .D o r r
= 0.860 lb
Area / Sd
4.009
Transmission Line Profile
5
Area r 2 .S d
3 1
Area r 2 .S d
1 3
4.009 5
0
10
0.000
20
30
40 Length
r
50
60
70 63.012
in Length (in)
Far Field Transmission Line System and Infinite Baffle Sound Pressure Level Responses 180 135 90 45
deg arg p
0 r
45
deg
90 135 180
10
100
3 1 . 10
1 r . dω . Hz 110 105 100 SPL (dB)
Phase (deg)
arg p o r
SPL o r SPL r
95 90 85 80 75 70 65 60
10
100 1 r . dω . Hz Frequency (Hz)
3 1 . 10
90
Phase (deg)
arg Z o r
45
deg 0
arg Z r deg
45
90
10
100
1 . 10
3
1 r . dω . Hz 100
Impedance (ohms)
80 Zo Z r
r
60 40 20 0
10
100
1 . 10
1 r . dω . Hz Frequency (Hz)
Woofer RMS Displacement
6
6
RMS Deflection (mm)
5 xd r
4
mm x
3 r 2
mm
1 0
0
10
100
20
1 r . dω . Hz Frequency (Hz)
1 . 10 1000
3
3
Terminus Air Velocity (should be < 10 m/sec / 342 m/sec = 0.03) Terminus Air Velocity / Speed of Sound
0.03 0.03
Velocity Ratio
0.025 v term r
0.02
c
0.015 0.01 0.005 0 0
10
3
1 . 10
100
10
1 r . dω . Hz Frequency (Hz)
1000
SoundAngle Pressure in TimePressure Domain Phase of System
2000 2000 360 1500 315
Phase (deg)
270 1000 p summed p anglen 225 q 500 Pa 180 deg 1350 90 500 1000
45 1000 0 0 10 0
0.01
0.02
0.03
0.04
0.05 100 n . dt 1 . dω . Hz qTime (sec)
0.06
0.07
0.08
0.09
0.1 3 1 . 10 0.1
System Group Delay
0.05 0.04 φ
0.03 q
sec
0.02 0.01 0 0.01
10
100 1 q . dω . Hz Frequency (Hz)
1 . 10
3
Sound Pressure in Time Domain
2000 2000 1500 p summed 1000 n 500 Pa 0 500 1000 1000
0
0.01
0.02
0.03
0.04
0.05
0.06
n . dt
0
0.07
0.08
0.09
0.1 0.1
Time (sec)
Woofer and Terminus Far Field Sound Pressure Level Responses 180 135 90 45
deg
0
arg p L r
45
deg
90 135 180
10
100
3 1 . 10
1 r . dω . Hz
SPL (dB)
Phase (deg)
arg p d r
110 105 100 95 SPL d r 90 SPL L r
85 80 75 70 65 60
10
100 1 r . dω . Hz Frequency (Hz)
1 . 10
3
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