Comparison between those two methods that calculate the loudspeaker efficiency has very high variation at 2k Hz. Difference of loudspeaker efficiency at 2k Hz is about two decade multiple as a result of accuracy problem of electrical power measurement.
REFERENCES
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Table 1. Acoustic resistance of a screen of area S
Number of wires per inch
Wire diameter
in cm
Acoustic Resistance
N.s/m
530 0.033 5.67/S
50 0.022 5.88/S
100 0.0115 9.10/S
120 0.0092 13.5/S
200 0.0057 24.6/S
Table 2. Experimentally identified lumped-parameters of a microspeaker
Parameters Value Parameters Value
a 6.20 mm Bl 0.54 T.m
f 0 791.9 Hz C AS 1.55e-11 m5/N
R E 7.76 ohm M AS 2598.07 kg/m4
R ES 4.40 ohm R AS 4.52e6 N.s/m5
Q MS 2.86 CMES 0.000131 F
Q ES 5.05 LCES 0.000309 H
Q TS 1.83 R AT 7.07e6 N.s/m5
V AS 0.002213 L R MT 0.01 N.s/m5
C MS 0.001066 mm/N MMD 3.63e-5 kg
M MS 3.79e-5 kg L e 2.62e-5 H
R MS 0.066 N.s/m RE' 61.72 m2
Table3. The dimensions of the diaphragm and voice-coil assembly of the microspeaker
Parameters Value Radius of diaphragm, R 7.8 mm
Thickness of diaphragm, t 0.029 mm Height of inner arc, H 0.5 mm
Height of outer arc, h 0.4 mm Bandwidth of outer arc, d 3 mm
Height of voice-coil, h
vc10 mm
Table 4. The L9(3 )4 orthogonal array of the Taguchi method.
Height of inner arc,
H
Table 5. Four weighting schemes for the cost function.
Weighting Scheme 1 Scheme 2 Scheme 3 Scheme 4
w10.25 0.35 0.25 0.8/3
w20.25 0.15 0.15 0.8/3
w30.25 0.25 0.35 0.8/3
w40.25 0.25 0.25 0.2
Table 6. The values of the cost function in the Taguchi analysis for nine runs and four weighting schemes
Run Scheme 1 Scheme 2 Scheme 3 Scheme 4
1 -0.0610 -0.0052 0.0025 -0.0279 2 -0.0080 0.0242 0.0322 0.0136 3 0.1029 0.1068 0.1119 0.1116 4 0.0634 0.0836 0.0611 0.0657 5 0.1714 0.1835 0.1575 0.1770 6 -0.1731 -0.2035 -0.1541 -0.1712
7 0.2506 0.2792 0.2381 0.26158 -0.0970 -0.1349 -0.0960 -0.1016
9 0.0533 0.0369 0.0430 0.0510
Table 7. The calculated performance parameters of sensitivity analysis and the associated cost function.
Corrugation
f0
(Hz)
f1(Hz)
SPL(dB)
STD0 567.25 20000 84.8 1.88 10 527.45 20000 86.4 1.80 20 507.55 20000 88.7 1.81 30 497.60 20000 90.0 1.85 40 507.55 20000 90.3 1.88 Corrugation Scheme 1 Scheme 2 Scheme 3 Scheme 4
10 0.0324 0.0394 0.0343 0.0346
20 0.0465 0.0570 0.0511 0.0496
30 0.0493 0.0616 0.0554 0.052640 0.0418 0.0523 0.0483 0.0446
Table 8. Resulting obtained using the constrained optimization of vented-box system parameters original optimal difference(%)
Duct radius (mm) 1.785 2.2 23.3
Volume (cc) 3 4.47 49
SPL at 400Hz (dB) 66.13 71.41 8
Duct length (cm) 2.8 3.6 28.6
Table9. Input data of diaphragm geometry
Table10 Output data of SPL response of microspeaker 18 1223.95 86.0795 4.3616 19 567.25 84.8149 1.8754 20 925.45 85.8685 4.2671 21 676.7 86.8331 3.2073 22 1273.7 86.583 4.1729 23 1223.95 87.9437 4.1069 24 1223.95 86.0795 4.3616 25 975.2 86.718 3.4823 26 985.15 86.7977 3.6071 27 1054.8 86.4403 3.0097 28 587.15 88.9168 4.4336 29 597.1 88.9348 4.431 30 1094.6 85.8592 4.425511 31 1323.45 86.23508 4.34173 32 1243.85 87.3613 4.1312
Table11. Normalize the input and output data
Run H h hvc t f0 SPL Std
1 0.166667 0.2 0 0 0.432099 0.546613 0.778648 2 0.166667 0.2 0 0.5 0.469136 0.548179 0.773417 3 0.166667 0.2 0 1 0.518519 0.554017 0.797957 4 0.166667 0.6 0.5 0.5 0.444444 0.513223 0.75463
28 0.75 0 0.25 0.25 0.037037 0.255187 0.994006 29 0.75 0 0.25 0.75 0.049383 0.256052 0.993415 30 0.583333 0.4 0 0.5 0.666667 0.10827 0.992167 31 0.583333 0.8 0 0.5 0.950617 0.126331 0.973112
32 0 0.6 0 1 0.851852 0.180446 0.92523
Table12. difference between target output and actual output
Run f0 SPL Std
1 -0.42613 -0.018788 -0.0076 2 0.234319 0.010479 0.004152 3 -0.18792 -0.004344 -0.001 4 -0.13398 -0.003328 0.000808 5 -0.01474 -0.001436 -0.00206 6 -0.13437 -0.003833 -0.00186 7 -0.15634 -0.002703 -0.0011 8 -0.10618 -0.001918 -0.00137 9 0.291111 0.000678 -0.0011 10 -0.30361 -0.007197 -0.00271 11 -0.35976 -0.005935 -0.00165 12 0.055848 -0.000771 -0.00097 13 -0.00596 -0.002297 -0.00183 14 0.030824 -0.001265 -0.00084 15 0.066737 -0.001034 -0.00165 16 1.128039 0.001893 -0.01476 17 1.745159 0.027755 0.000498 18 5.92718 0.053829 -0.01214 19 0.040372 0.002054 -9.7E-05 20 3.189864 0.04128 -0.01187 21 1.555462 0.022809 -0.00707 22 4.186743 0.037457 -0.01307 23 4.207969 0.064671 -0.00079 24 4.309533 0.057579 -0.00374 25 1.545691 0.023033 -0.00834 26 2.397174 0.021782 -0.00746 27 2.990334 0.032486 -0.00755 28 2.154917 0.029699 0.000122 29 2.568321 0.045554 0.000466 30 0.943214 0.011669 -0.01745 31 -1.74793 0.001198 0.009493 32 -0.09111 -0.010246 -0.00412
Table13. New set of input-output pair
Run H h d t f0 SPL Std
1 0.333333 0.6 0 1 0.851852 0.182296 0.974242 2 0.35 0.4 0.25 0.25 0.432099 0.251184 0.938671 3 0.666667 0.1 0.75 0.75 0 0.413684 0.453734
4 0.509 0.6258 0.9939 1 0.299069 1 0
Table14. difference of new set of microspealer performance
∆f0(Hz) ∆SPL(dB) ∆STD -54.8809 -0.208193 -0.15428 -42.1958 2.056779 -0.12227 -26.9846 -2.621956 1.145778 -16.5807 -8.269137 1.356635
Table 15. Compare results obtained via ANSYS and NNSA
Geometry parameter H h d t
Value(mm) 0.16266 0.20095 3.9566 0.02855
Performance f (Hz) 0 SPL(dB) STD
ANSYS 617 86 4
NNSA 828 117 1.05
difference 211 31 -2.95
Table16、TS parameters of microspeaker with type HYCOM2008C
Parameter Value Parameter Value
a (mm) 10 Bl (T.m) 0.974776
f0 (Hz) 658.33 Cas (m5/N) 4.57815e-011 Re (ohm) 6.17548 Mas (kg/m4) 1276.63 Res (ohm) 8.69629 Ras (N.s/m5) 1.10707e+006
Qms 4.76992 Cmes (F) 0.000132603 Qes 3.38726 Lces (H) 0.000440758 Qts 1.9807 Rat (N.s/m5) 2.66605e+006 Vas (L) 0.00651723 Rmt (N.s/m5) 0.263128 Cms (mm/N) 0.000463863 Mmd (kg) 0.000119545
Mms (kg) 0.000125998 LE (H) 2.88294e-005 Rms (N.s/m) 0.109264 RE1 (m2) 27.5663
(a)
(b)
Figure 1. (a) Electro-mechano-acoustical analogous circuit of loudspeaker. (b) Same circuit with acoustical impedance reflecting to mechanical system.
Figure 2. The mechanical system of loudspeaker. (M is diaphragm and voice coil mass, k is stiffness of suspension, C is damping factor)
1
MS
K = C C = R
MSM
RMS CMS
Figure 3. (a) Detailed Electro-mechano-acoustical analogous circuit of loudspeaker.
(b) Another form of acoustic system.
(a) (b)
Figure 4. (a) An acoustic resistance consisting of a fine mesh screen.
(b) Analogous circuit.
Figure 5. (a) Closed volume of air that acts as acoustic compliance.
(b) Analogous circuit.
Figure 6. (a) Cylindrical tube of air which behaves as acoustic mass.
(b) Analogous circuit.
Figure 7. Analogous circuit for radiation impedance on one side of circuit piston in infinite baffle.
Figure 8. (a) Perforated sheet of thickness t having holes of radius a spaced a distance b. (b) Geometry of the narrow slit.
(a)
(b)
Figure 9 (a) The model of microspeaker diaphragm with top view (b) The dimensions of diaphragm-voice coil assembly
R
H h
d diaphragm
voice-coil hvc
(a)
(b)
Figure10 The finite element model and mesh including diaphragm and voice-coil (a) top view (b) bottom view
diaphragm
voice-coil
(a)
(b)
Figure11. The results of the modal analysis with mode shape (a) the first piston mode (b) the second piston mode
Figure12 mechanical impedance of the diaphragm-voice coil assemblyZ ms
n f2
Input layer Output layer
Hidden layer
x1 x2 xi xI
vji wkj
1 k K
1 j J
Figure13 a frame of EBP x
v m f1 O w
y1 yk yK
y
(a)
(b)
Figure 14. Photos of a mobile phone microspeaker. (a) Front view (b) Rear view
(a)
(b)
Figure 15 the experimental arrangement for (a)measuring voice-coil impedance (b)measuring the on-axis SPL response
ch 2
(a)
(b)
Figure16 Simulated and measured frequency responses of the microspeaker. (a) the voice-coil impedance and (b) on-axis SPL response.
Figure17 Definitions of performance parameters of the SPL response
f0 f1
3dB 3dB
Bandwidth
Hz dB
(a)
(b)
(c)
(d)
Figure18. Simulated voice-coil impedence and the on-axis SPLresponse obtained in the Taguchi analysis. (a)Voice-coil impedance for Runs 1-5. (b) Voice-coil impedance for Runs 6-9. (c) On-axis SPL for Runs 1-5 (d) On-axis SPL for Runs 6-9
(a)
(b)
Figure19. Simulated frequency responses of Run 7 for different number of corrugation. (a)Voice-coil impedance. (b) On-axis SPL response
Figure 20. Schematic diagram of the vented-box loudspeaker system
Figure 21. The overall EMA analogous circuit of vented-box using FEA-lumped hybrid method
(a) Mechanical system
D D D
U =u S p
+
−
RABP
CAB
MABP
Figure 22. The acoustic circuit of vented box system is simplified to parallel second-order oscillator circuit
Figure 23. Compare the SPL response of vented-box system between original design and optimal design.
101 102 103 104 105
Figure 24. Frequency response of optima vented-box design of microspeaker (a)Voice- coil impedance (b) On-axis SPL
Figure 25. The frame of neural network system with 4-NH-MH-3.
0 1000 2000 3000 4000 5000 6000 -0.5
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Time
E
Figure 26. Converge profile of SA algorithm with 4-10-6-3 NN system
(a)
(b)
Figure 27. The efficiency comparison between experiment and simulation (a) experiment of microspeaker sensitivity (b) efficiency of microspeaker derived by four methods
Figure 28. Experimental arrangement for measuring sound power Height of
microphone
Horizontal distance between
microspeaker and semi-sphere center
102 103 104 -100
-50 0 50
Frequency (Hz)
dB
Experiment Simulation
Figure 29. Loudspeaker efficiency comparison between experiment and simulation