手机音腔及出音孔的设计计算
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Optimal Sound Matching Solution through Helmholtz resonator theory
Optimal Sound Matching Solution through Helmholtz resonator theory
Basic principle
1. Basic theory
Original test result
SS1534P-008 GRAPH in BAFFLE X:900.00Hz 110 Y:98.92dB ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
100 dB 90
80
CASE Back Volume
L Speaker
a : Air Hole V:Front Volume
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result by back volume changed
① Basic Structure ② Air Hole quantity variation ③ Case thickness variation ④ Front Volume variation ⑤ Back Volume variation
Hand Set Matching Solution with Helmholtz resonator
f=
C a 2π VL
Therefore any shapes of resonator is not affecting Resonant Frequency. If the volume & neck’s length is same, the resonator has same resonant frequency even in different shape.
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Case thickness changed
③ Case thickness variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume : 2.42cc 2.5mm
Basic structure
① Basic structure a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume : 2.42cc
CASE Back Volume Speaker L a : Air Hole V:Front Volume
CASE Back Volume
L Speaker
a : Air Hole V:Front Volume
C a 344m/ s 3.77×10−6 m2 f= = 2π VL 2π (1.2×10−6 m3 )(0.0025m)
=2,745Hz
Optimal Sound Matching Solution through Helmholtz resonator theory
Air hole variation
② Air Hole quantity variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume: 2.42cc Φ1.55mm X 2 ea
CASE Back Volume
Helmholtz Resonator was invented for sound analysis by H. VON Helmholtz(1821~1894) Its applications are various from bell, violin, guitar and bass speaker cabinet. It features shorter neck and volume bottle than wave as shown below. Specific frequency depends on air volume in neck(weight) and volume in the bottle(spring) So specific frequency is calculated as below. a V L C : Neck’s area (㎡) ㎡ : Resonator volume (㎥) ㎥ : Neck’s length (m) m : Sound velocity (344m/s)
V:Front Volume
a : Hole total area (m2) L : Case thickness (m) V : Front volume (m3) C : 344 m/s (RT 20℃) ℃
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result by case thickness variation
X:2.6000kHz 110
Y:102.29dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
2,745Hz
2,600Hz
100 dB 90
Optimal Sound Matching Solution through Helmholtz resonator theory
Example
Ex.1) What’s the resonant frequency in case of a bottle with outer dia. 9.8cm, neck length10cm, neck outer dia. 3cm?
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result by front volume variation
X:3.9000kHz 110
源自文库
Y:105.25dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
4,269Hz
3,900Hz
100 dB 90
L Speaker
a : Air Hole V:Front Volume
C a 344m/ s 3.77×10 m f= = 2π VL 2π (1.2×10−6 m3 )(0.00155m)
2
−6
=2,465Hz
Hand Set Matching Solution with Helmholtz resonator
CASE Back Volume
L Speaker
a : Air Hole V:Front Volume
C a 344m/ s 3.77×10−6 m2 f= = 2π VL 2π (0.8×10−6 m3 )(0.00155m)
=4,269Hz
Optimal Sound Matching Solution through Helmholtz resonator theory
Optimal Sound Matching Solution through Helmholtz resonator theory
Application
2. Application
(1) Inside structure of handset
CASE L
Back Volume
Speaker
a : Air Hole
4 3 4 V = πr = (3.14)(0.049m)3 = 4.93×10−4 m3 3 3 2 2 −4 2 a = πr = 3.14(0.015m) = 7.07×10 m C a 344m/ s 7.07×10−4 m2 f= = −4 3 2π VL 2(3.14) (4.93×10 m )(0.1m) = 207Hz
Basic principle
(2) Example model: SS1534P-008 - SIZE : Φ15mm X 3.4 H - Fo : 850 Hz - Ze : 8 ohm
(3) Test conditions * Input power :0.1W at 5cm
Optimal Sound Matching Solution through Helmholtz resonator theory
80
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Front volume variation
④ Front Volume variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc 0.8cc C : 344 m/s (RT 20℃) ℃ Back volume: 2.42cc
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Test condition
(4) TEST according to some variations
C a 344m/ s 7.54×10 m f= = 2π VL 2π (1.2×10−6 m3 )(0.00155m)
2
−6
=3,486Hz
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result
X:3.0000kHz 110
Y:104.23dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
3,486Hz
3,000Hz
100 dB 90
80
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
X:1.3000kHz 110
Y:96.65dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
100 dB 90
80
Loss of low sound
70
60 100 Mode: TSR 200 500 1k 2k Hz
80
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Back volume variation
⑤ Back Volume variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume: 2.42cc 1.5cc
Test result of air hole changed
X:2.4000kHz 110
Y:101.47dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
2,465Hz
2,400Hz
100 dB 90
80
70
Optimal Sound Matching Solution through Helmholtz resonator theory
Basic principle
1. Basic theory
Original test result
SS1534P-008 GRAPH in BAFFLE X:900.00Hz 110 Y:98.92dB ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
100 dB 90
80
CASE Back Volume
L Speaker
a : Air Hole V:Front Volume
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result by back volume changed
① Basic Structure ② Air Hole quantity variation ③ Case thickness variation ④ Front Volume variation ⑤ Back Volume variation
Hand Set Matching Solution with Helmholtz resonator
f=
C a 2π VL
Therefore any shapes of resonator is not affecting Resonant Frequency. If the volume & neck’s length is same, the resonator has same resonant frequency even in different shape.
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Case thickness changed
③ Case thickness variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume : 2.42cc 2.5mm
Basic structure
① Basic structure a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume : 2.42cc
CASE Back Volume Speaker L a : Air Hole V:Front Volume
CASE Back Volume
L Speaker
a : Air Hole V:Front Volume
C a 344m/ s 3.77×10−6 m2 f= = 2π VL 2π (1.2×10−6 m3 )(0.0025m)
=2,745Hz
Optimal Sound Matching Solution through Helmholtz resonator theory
Air hole variation
② Air Hole quantity variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume: 2.42cc Φ1.55mm X 2 ea
CASE Back Volume
Helmholtz Resonator was invented for sound analysis by H. VON Helmholtz(1821~1894) Its applications are various from bell, violin, guitar and bass speaker cabinet. It features shorter neck and volume bottle than wave as shown below. Specific frequency depends on air volume in neck(weight) and volume in the bottle(spring) So specific frequency is calculated as below. a V L C : Neck’s area (㎡) ㎡ : Resonator volume (㎥) ㎥ : Neck’s length (m) m : Sound velocity (344m/s)
V:Front Volume
a : Hole total area (m2) L : Case thickness (m) V : Front volume (m3) C : 344 m/s (RT 20℃) ℃
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result by case thickness variation
X:2.6000kHz 110
Y:102.29dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
2,745Hz
2,600Hz
100 dB 90
Optimal Sound Matching Solution through Helmholtz resonator theory
Example
Ex.1) What’s the resonant frequency in case of a bottle with outer dia. 9.8cm, neck length10cm, neck outer dia. 3cm?
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result by front volume variation
X:3.9000kHz 110
源自文库
Y:105.25dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
4,269Hz
3,900Hz
100 dB 90
L Speaker
a : Air Hole V:Front Volume
C a 344m/ s 3.77×10 m f= = 2π VL 2π (1.2×10−6 m3 )(0.00155m)
2
−6
=2,465Hz
Hand Set Matching Solution with Helmholtz resonator
CASE Back Volume
L Speaker
a : Air Hole V:Front Volume
C a 344m/ s 3.77×10−6 m2 f= = 2π VL 2π (0.8×10−6 m3 )(0.00155m)
=4,269Hz
Optimal Sound Matching Solution through Helmholtz resonator theory
Optimal Sound Matching Solution through Helmholtz resonator theory
Application
2. Application
(1) Inside structure of handset
CASE L
Back Volume
Speaker
a : Air Hole
4 3 4 V = πr = (3.14)(0.049m)3 = 4.93×10−4 m3 3 3 2 2 −4 2 a = πr = 3.14(0.015m) = 7.07×10 m C a 344m/ s 7.07×10−4 m2 f= = −4 3 2π VL 2(3.14) (4.93×10 m )(0.1m) = 207Hz
Basic principle
(2) Example model: SS1534P-008 - SIZE : Φ15mm X 3.4 H - Fo : 850 Hz - Ze : 8 ohm
(3) Test conditions * Input power :0.1W at 5cm
Optimal Sound Matching Solution through Helmholtz resonator theory
80
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Front volume variation
④ Front Volume variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc 0.8cc C : 344 m/s (RT 20℃) ℃ Back volume: 2.42cc
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Test condition
(4) TEST according to some variations
C a 344m/ s 7.54×10 m f= = 2π VL 2π (1.2×10−6 m3 )(0.00155m)
2
−6
=3,486Hz
Optimal Sound Matching Solution through Helmholtz resonator theory
Test result
X:3.0000kHz 110
Y:104.23dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
3,486Hz
3,000Hz
100 dB 90
80
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
X:1.3000kHz 110
Y:96.65dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
100 dB 90
80
Loss of low sound
70
60 100 Mode: TSR 200 500 1k 2k Hz
80
70
60 100 Mode: TSR 200 500 1k 2k Hz
B
5k
K
10k
Optimal Sound Matching Solution through Helmholtz resonator theory
Back volume variation
⑤ Back Volume variation a : Φ1.55mm X 4 ea L : 1.55mm V : 1.2cc C : 344 m/s (RT 20℃) ℃ Back volume: 2.42cc 1.5cc
Test result of air hole changed
X:2.4000kHz 110
Y:101.47dB
ZA:Live Curve TSR fund. Pa/V
A: Frequency Response, Magn dB re 20.00
2,465Hz
2,400Hz
100 dB 90
80
70