Conclusion

A push-pull electret loudspeaker is a thin, light and flat loudspeaker and it is very suitable to using in space-concerned applications. However, the absence of low frequency response is a defect of the push-pull electret loudspeaker. Therefore, the subwoofer system is adopted to recover the low frequency response. The combination of the push-pull electret loudspeaker and the subwoofer can provide a complete audio system.

The EMA analogous circuit is employed to establish a conventional lumped parameter model of the subwoofer. Via the electrical impedance measurement, the curve fitting and added mass method, the T-S parameters of the subwoofer can be identified. Using the platform, the electrical impedance and the on-axis SPL responses of the subwoofer can be simulated. The response predicted by conventional lumped parameter model is in good agreement with the measurement.

Next, the conventional lumped parameter model is employed to the simulation of vented-box system. The constrained optimization technology was also employed to find the design that can enhance the low frequency response of the vented-box system.

The push-pull electret loudspeaker is also analyzed in this thesis. A fully experimental modeling technique and an optimization procedure have been developed for push-pull electret loudspeakers. The experimental modeling technique relies on not only the electrical impedance measurement but also the membrane velocity measured by using a laser vibrometer. With the aid of a test box, the voltage-force conversion factor and characteristics of motional impedance can be identified from the membrane velocity. The experimentally identified model serves as the simulation platform for optimizing the design parameters of the electret loudspeaker.

The SA algorithm was exploited to find the parameters that yield optimal level-bandwidth performance. Either only the gap distance or the comprehensive search for various parameters can be optimized by using the SA procedure. The results reveal that the optimized design has effectively enhanced the performance of the electret loudspeaker, as compared to the original design.

REFERENCES

[1] H. Olson, Acoustical Engineering (Van Nostrand, New York, 1957. Reprinted by Professional Audio Journals, Philadelphia, PA, 1991).

[2] L. L. Beranek, Acoustics (Acoustical Society of America, Woodbury, NY. 1996).

[3] W. M. Leach, Jr., Introduction to Electroacoustics and Audio Amplifier Design (Kendall-Hunt, Dubuque, IA, 2003).

[4] N. Thiele and R. Small, in AES Loudspeaker Anthologies, Vols. 1–3 (Audio Engineering Society, New York, 1978, 1984, 1996).

[5] A. N. Thiele, “Loudspeakers in Vented-boxes: Part I,” Audio Engineering Society, Vol. 19, No. 5, pp. 382-392 (1971).

[6] A. N. Thiele, “Loudspeakers in Vented-boxes: Part II,” Audio Engineering Society, Vol. 19, No. 6, pp. 471-483 (1971).

[7] R. Small, “Vented-Box Loudspeaker Systems, Part I: Small-Signal Analysis,”

Audio Engineering Society, Vol. 21, No. 5, pp. 363-372 (1973).

[8] R. Small, “Vented-Box Loudspeaker Systems, Part II: Large-Signal Analysis,”

Audio Engineering Society, Vol. 21, No. 6, pp. 438-444 (1973).

[9] R. Small, “Vented-Box Loudspeaker Systems, Part III: Synthesis,” Audio Engineering Society, Vol. 21, No. 7, pp. 549-554 (1973).

[10] R. Small, “Vented-Box Loudspeaker Systems, Part IV: Appendices,” Audio Engineering Society, Vol. 21, No. 8, pp. 635-639 (1973).

[11] M. R. Bai and J., Liao, “Acoustic Analysis and Design of Miniature Loudspeakers for Mobile Phones,” Audio Engineering Society, Vol. 53, No. 11, pp. 1061-1076, 2005.

[12] P. J. Baxandall, “Electrostatic loudspeakers” in Loudspeaker and Headphone Handbook, 3^rd ed. edited by J. Borwick, (Focal Press, Oxford, 2001).

[13] J. Lekkala and M. Paajanen, “EMFi-New electret material for sensors and actuators,” IEEE Tenth International Symposium on Electrets, Athens, Greece, (1999).

[14] M. Paajanen, J. Lekkala and K. Kirjavainen, “Electromechanical film (EMFi)-A new multipurpose electret material,” Sens. Actuators, A 84, 95-102 (2000).

[15] Y. Cao, Z. Xia, Q. Lin, J. S, L. Chen and B. Zhou, “Study of porous dielectrics as electret materials,” IEEE Trans. Dielectr. Electr. Insul. 5(1), 58-62 (1998).

[16] D. M. Chiang, W. L. Liu, J. L. Chen and R. Susuki, “PALS and SPM/EFM investigation of charged nanoporous electret films,” Chem. Phys. Lett. 412, 50-54 (2005).

[17] D. M. Chiang and J. L. Chen, “A novel flexible loudspeaker driven by an electret diaphragm,” AES 121^st Convention, San Francisco, CA (2006).

[18] T. Mellow and L. Kärräinen, “On the sound field of a circular membrane in free space and an infinite baffle,” J. Acoust. Soc. Am. 120(5), 2460-2477 (2006).

[19] T. Mellow and L. Kärräinen, “On the forces in single-ended and push-pull electret transducers,” J. Acoust. Soc. Am. 124(3), 1497-1504 (2008).

[20] M. R. Bai, R. L. Chen and C. J. Wang, “Electroacoustic analysis of an electret loudspeaker using combined finite-element and lumped-parameter models,” J.

Acoust. Soc. Am. 125(6), 3632-3640 (2009).

[21] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller,

“Equations of state calculations by fast computing machines,” J. Chem. Phys. 21, No. 6, 1087-1092 (1953).

[22] A. Das and B. K. Chakrabarti, (Eds.), Quantum Annealing and Related Optimization Methods (Springer, Heidelberg, 2005).

[23] J. De Vicente, J. Lanchares, and R. Hermida, “Placement by thermodynamic simulated annealing,” Phys. Lett. A 317, 415-423 (2003).

[24] Audio Engineering Society Inc., AES Recommended Practice Specification of Loudspeaker Components Used in Professional Audio and Sound Reinforcement, AES2-1984, NY (2003).

[25] M. R. Bai and R. L. Chen, “optimal design of loudspeaker systems based on sequential quadratic programming (SQP),” J. Audio Eng. Soc. 55(1/2), 44-54 (2007).

Table 1. Acoustic resistance of a screen of area S Number

of wires per inch

Wire diameter

in cm

Acoustic Resistance

N.s/m⁵

30 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 subwoofer

Parameters Value Parameters Value

a 6 cm Bl 8.4 T.m

f 0 59.8 Hz CAS 9.89356e-008 m⁵/N

R E 7.4 ohm M_AS 70.3371 kg/m⁴

R ES 85.0716 ohm R _AS 10160.8 N.s/m⁵

QMS 2.62415 CMES 8.13714e-005 F

Q ES 0.245356 LCES 0.0855195 H

Q TS 0.224377 R_AT 7.07e6 N.s/m⁵

VAS 0.0107 L R_MT 15.198 N.s/m⁵

CMS 6.0678e-4 mm/N MMD 0.00160116 kg

MMS 0.0117 kg L e 1.0000e-003 H

RMS 1.7545 N.s/m R_E^' 110 m²

Table 3. Resulting obtained using the constrained optimization of vented-box system parameters Value

Duct radius (m) 0.05

Volume (m^3) 0.088

Duct length (m) 0.23

Table 4. Parameters of the optimized design versus the original non-optimized design.

RM(N*s/m) C_M^' (m/N) MM (kg)

Gap distance(mm) Original (1) 3.465 1.95 10× ⁻⁵ 1.16 10× ⁻² 1.2 Optimal (2) 4.0 1.03 10× ⁻⁴ 1.1 10× ⁻² 0.55

(2)/(1) % 115.44 528.21 94.83 45.83

(a)

(b)

Figure 1. (a) Electro-mechano-acoustical analogous circuit of loudspeaker (b) Same circuit with acoustical impedance reflecting to mechanical system

M

C = R

MS

1

MS

K = C

Figure 2. The mechanical system of loudspeaker (M is diaphragm and voice coil mass, k is stiffness of suspension, C is damping factor)

RMS C_MS

RE LE

RE'

eg BluD

fD=Blic

fD=pDSD

MMD

ic

uD

+

-+

-+

-ZAB ZAF

- p + UD=SDu

(a)

(b)

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

Speaker Cavity

Figure 9. Schematic diagram of vented-box system

Duct

Figure 10. The overall EMA analogous circuit of vented-box using FEA-lumped hybrid method

p 1

+

−

p 2

+

−

U 1 U ₂

Figure 11. T-circuit of transmission line

(a)

(b)

Figure 12. (a) Front view of subwoofer (b)Back view of subwoofer

ch 2

e_g

es

microspeak

signal generator

ch 1 R

analyzer

resisto

(a)

(b)

Figure 13. The experimental arrangement for (a)measuring voice-coil impedance (b)measuring the on-axis SPL response

analyzer

signal generator ch 1

microspeak

baffl

microphone

10⁰ 10¹ 10² 10³ 10⁴ 10⁵

Sound Pressure Level (dB)

Experiment Simulation

(b)

Figure 14. Simulated and measured frequency responses of the subwoofer. (a) the voice-coil impedance and (b) on-axis SPL response

1

MAB

RABP R_AB1 RAB2

CAB

1

CAB

Zb

u1

u2

ZB

Figure 15. The impedance Z_AB of Vented-box

10⁰ 10¹ 10² 10³ 10⁴ 10⁵

Sound Pressure Level (dB)

Vented box Simulation Vented box experiment

(b)

Figure 16. Frequency response of optima vented-box design of subwoofer (a)Voice- coil impedance (b) On-axis SPL

(a)

+ ^e

^spk

-Fixed perforated electrode plate Membrane

Fixed perforated electrode plate

(b)

Figure 17. The push-pull electret loudspeaker. (a) Photo. (b) The configuration of the push-pull electret loudspeaker.

1: φ _u

²

S

_D

:1 C

E

φ

− R

E

L

_E

e

spk

^C

_E

e

in

(a)

Z _mot

i

+

-R

E

L

_E

+

-e spk

e in _{terminals C E}

Reflected to electrical domain

(b)

Figure 18. The electroacoustic analogous circuits of the push-pull electret loudspeaker.

(a) Electrical, mechanical, and acoustics systems. (b) Combined circuit referred to the electrical system.

(a)

Figure 19. The electrical impedance measurement of the push-pull electret

loudspeaker. (a) Experimental arrangement. (b) The electrical impedance versus the motional impedance.

Amplifier Transformer Resistor

e

R

10¹ 10² 10³ 10⁴ 10⁵ 10¹

10² 10³

Output Voltage of Transformer

Frequency (Hz)

Voltage (v)

Loaded, measured Loaded, simulated Unloaded, measured

Figure 20. The comparison of the measured and simulated output voltage responses of the loaded and unloaded transformer.

u

e

in

φ ^C

₂^E

φ C ′

^M

M

M

R

_M

2

R

E

φ L

_E

φ

²

^{− C} _φ

^2E

(a)

u e

in

φ ^C _φ

₂^E

_C

_M

M

M

R

_M

(b)

Figure 21. The electroacoustic analogous circuits of the push-pull electret loudspeaker.

(a) Combined circuit referred to the mechanical system. (b) The weakly coupled approximation.

Amplifier

Figure 22. The membrane velocity measurement of the push-pull electret loudspeaker.

(a) Experimental arrangement. (b) The comparison of the velocity responses of the loudspeaker, with and without the test box.

Push-pull electret

Sound Pressure Level (dB)

Experiment Simulation

(b)

Figure 23. The on-axis SPL measurement of the push-pull electret loudspeaker. (a) Experimental arrangement. (b) The comparison of the measured and the simulated on-axis SPL responses.

Signal generator Microphone

Analyzer

Amplifier

Transformer

10¹ 10² 10³ 10⁴ 10⁵ 0

10 20 30 40 50 60 70 80 90 100

THD Spectrum

Frequency (Hz)

THD (%)

Push-pull configuration Single-ended configuration

Figure 24. The comparison of the measured THD of the electret loudspeaker between the push-pull and the single-ended configurations.

10¹ 10² 10³ 10⁴ 10⁵

Sound Pressure Level (dB)

Experiment, Gap 1.2 mm, Original Simulation, Gap 1.2 mm, Original Simulation, Gap 0.86 mm, Optimal Simulation, Gap 0.19 mm, Critical

(a)

Sound Pressure Level (dB)

Experiment, Original design Simulation, Original design Simulation, Optimal design

(b)

Figure 25. The comparison of the on-axis SPL responses between the original and the optimal designs. (a) Results of optimizing only the gap distance. (b) Results of

optimizing four parameters including the gap distance, the resistance, the mass, and the compliance.

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