臺灣博碩士論文加值系統

失真是現階段微型揚聲器的最大問題，以往開發揚聲器時只能透過錯誤嘗試法(Trial &; Error Method)來解決失真問題，不僅開發時間冗長且研發成本過高。因此本文建立一套揚聲器之失真分析模型與流程，利用有限元素模擬揚聲器之主要的失真參數，包含磁力轉換因子Bl(x)及振膜剛性Km(x)，並利用 Tytron 250微拉力試驗機及KLIPPEL 量測儀器驗證Bl(x)及Km(x)模擬的準確性，同時將失真參數代入理論分析模型中計算其頻率響應及失真。

本文也探討Bl(x)與Km(x)對於失真的相對關係，且修改磁路及懸吊系統的尺寸，研究其對Bl(x)與Km(x)的影響。對Bl(x) 來說，增加下片高度0.2 mm、磁鐵厚度0.1 mm並減少極片厚度0.1 mm可有效降低失真；對Km(x)來說，彎曲花紋的失真比直線花紋來的好，花紋在長軸比長短軸皆有花紋的失真來的好。將Bl(x)最佳化與Km(x)最佳化代入至失真程式，可發現失真降低約20%，效果顯著。藉由以上分析結果，本文最後提出一套微型揚聲器設計準則，可協助微型揚聲器在開發階段時，能預測其頻率響應及失真，使設計之產品不僅在模擬階段就能獲得改善，亦可減少開發時間及研發成本。

Electrodynamic (moving-coil) transducer such as loudspeaker is subjected to distortion during performance mainly due to nonlinearities. Major nonlinearities are motor and suspension nonlinearities, Bl(x) and Km(x), respectively, which are displacement dependent. Force factor Bl(x) and mechanical suspension stiffness Km(x) nonlinearities are investigated in this thesis for elliptical loudspeaker with various magnetic circuits and track patterns. Analytical modeling and finite element method (FEM) are used to investigate these nonlinearities.
For Bl(x) nonlinearities, the FEM commercial software COMSOL and Klippel measurement system in air and vacuum are performed. To validate the simulation by COMSOL and the measurement by Klippel, Tytron 250 micro tensile testing is employed to obtain force factor-displacement dependence. Sound pressure level (SPL) and total harmonic distortion (THD) measurements and simulations are consequently obtained. In order to reduce THD, simulation has been carried out for under-yoke size variations and it is confirmed by anechoic chamber measurements. Promising results are obtained for increase in size of under-yoke by 0.2 mm. Similar methodology is adopted for polar piece and magnet size variations keeping combined height of polar piece and magnet as a constant. Good results are obtained for decrease in size of polar piece by 0.1 mm and corresponding increase in size of magnet.
For Km(x) nonlinearities the same approach is applied. Klippel measurement yielded discrepancy between air and vacuum measurements. Theoretical modeling of Km(x) is done and Km(x) effect on THD is investigated. Simultaneously, simulations are carried out using the other FEM commercial software ANSYS and corresponding THD is obtained. In order to reduce THD, various track patterns along with no track on diaphragm are explored. Results indicate that curved track pattern possesses lower THD than straight-full track pattern. Similarly, straight-partial track pattern shows lower THD than straight-full track pattern.
It is concluded that the trend of Bl(x) and Km(x) could be used to choose the most appropriate suspension and magnetic circuit for microspeaker. Designing of a microspeaker with desired SPL and THD by using the distortion model developed in this work is emphasized. Last but not least, we have proposed certain design rules based on our findings to reduce the time and cost during product design and development.

第一章 緒論 1
1-1 背景 1
1-3 文獻回顧 2
1-4 文章架構 4
第二章 橢圓平板之應用理論 8
2-1 幾何模型 8
2-2 橢圓形薄膜之模態 8
2-3 COMSOL模擬橢圓微型揚聲器 13
2-4平板揚聲器量測與比對 14
第三章 失真系統建立 23
3-1 失真模型建立 23
3-2磁力轉換因子Bl(x)所造成的失真 25
3-2.1磁力轉換因子Bl(x)非線性 25
3-2.2 Bl(x)之模擬方法 26
3-2.3 Bl(x)模擬驗證 27
3-3 剛性Km(x)模擬及驗證 28
3-3.1 剛性Km(x)非線性 28
3-3.2 Km(x)之模擬方法 28
3-3.3 Km(x)之驗證 29
第四章 橢圓微型揚聲器失真最佳化 43
4-1 Bl(x)與Km(x)的關係。 43
4-1.1 Km(x)曲線呈水平狀態之失真探討 43
4-1.2 Km(x)曲線為非對稱狀態時之失真探討 44
4-1.3 Km(x) 曲線為對稱形態時之失真探討 44
4-1.4 結論 45
4-2 磁力轉換因子Bl(x)設計 46
4-2.1 修改下片高度對頻率響應及失真之探討 46
4-2.2 修改極片與磁鐵相對高度對頻率響應及失真之探討 47
4-3 剛性Km(x)分析 48
4-3.1 橢圓型花紋比較 48
4-3.2 直線形花紋分佈對頻率響應及失真之探討 49
4-3.3 彎曲形花紋分佈對頻率響應及失真之探討 49
4-4 橢圓微型揚聲器最佳化 50
4-4.1 Bl(x)曲線最佳化 50
4-4.2 Km(x)曲線最佳化 51
4-4.3 整體最佳化 52
4-5 實驗與驗證 52
第五章 結論與未來展望 77
5-1 結論 77
5-2 未來研究方向 79
參考文獻 81
附錄A KLIPPEL揚聲器參數量測 85

[1]W.J. Cunningham, Non-Linear Distortion in Dynamic Loudspeakers due to Magnetic Effects, J. Acoust. Soc. Am., vol. 21, no. 3, 1949, pp. 202-207.
[2]A. J. M. Kaizer, "Modeling of the Nonlinear Response of an Electrodynamic Loudspeaker by a Volterra Series Expansion," J. Audio Eng. Soc., vol. 35 pp. 421-433 (1987 June).
[3]W. Klippel, “Dynamic measurement and interpretation of the nonlinear parameters of electrodynamic loudspeakers,” J. Audio Eng. Soc., vol. 38, no. 12, pp. 944–955, Dec. 1990.
[4]W. Klippel, “Distortion Analyzer – a New Tool for Assessing and Improving Electrodynamic Transducers,” presented at the 108th Convention of the Audio Engineering Society, Paris, February 19-22, 2000, preprint 5109.
[5]W. Klippel, Loudspeaker nonlinearities – cause, parameters, symptoms, J Audio Eng Soc 54 (2006), pp. 907–939
[6]I. Aldoshina, A. Voishvillo, V. Mazin. "Loudspeaker Motor Nonlinear Modeling Based on Calculated Magnetic Field Inside the Gap", presented at the 97th Convention of the Audio Engineering Society, J.Audio Eng. Soc., (Abstracts) vol. 42, N 12, 1994, December, p. 1061 _1062, preprint 3895.
[7]Mihelich, Ryan J ” Loudspeaker Nonlinear Parameter Estimation_ An Optimization Method”, AES 111TH CONVENTION, NEW YORK, NY, USA, 2001 SEPTEMBER 21–24
[8]Hwang G, Kim H, Hwang S, Kang B. Analysis of harmonic distortion due to uneven magnetic field in a microspeaker used for mobile phones. IEEE Transag 2002;38:2376-8
[9]B. Merit, G. Lemarquand, V. Lemarquand, Performances and design of ironless loudspeaker motor structures, Applied Acoustics, Volume 71, Issue 6, June 2010, Pages 546-555
[10]Mowry S., “Simplified Simulation Method for Nonlinear Loudspeaker Parameters”, Voice Coil Mag., 9 (2007).
[11]Benoit Merit , Valerie Lemarquand , Guy Lemarquand , Andrzej Dobrucki , “Motor Nonlinearities in Electrodynamic Loudspeakers: Modelling and Measurement”, archives of acoustics 34, 4 (2009) 579-590
[12]G. Y. Hwang, K. T. Kim, S. U. Chung, S. M. Hwang, B. S. Kang, and I. C. Hwang, J. Appl. Phys. 91, 6979 (2002)
[13]R.Lerch, M. Kaltenabcher, H. Landes, M.Rausch, P.-C. Eccardt, “Combination of Finite Element and Boundary Element Methods in Computational Acoustics and Coupled Field Problems of electro-Acoustic Transducer”, Editor: von Estorff, Corn-putational Mechanics Publivation (2000)
[14]R.Lerch, M. Kaltenabcher, H. Landes, M.Rausch, P.-C. Eccardt, ”Numerical Modeling of Electrodynamic Loudspeakers”, COMPEL 18, no. 3, 504-514 (1999)
[15]M. Rausch, R. Lerch, M. Kaltenbacher, H. Landes, Optimization of electro-dynamic loudspeaker-design parameters by using a numerical calculation scheme, Acustica, 85 (3), (1999), pp. 412-419
[16]Mathieu, E. (1868). "Memoire sur Le Mouvement Vibratoire d’une Membrane de forme Elliptique". Journal des Mathematiques Pures et Appliquees: 137–203.
[17]N. W. McLachlan , Theory and application of Mathieu functions , (Oxford Press , UK , 1951)
[18]Shibaoka Y, (1965), “On the transverse vibration of an elliptic plate with clamped edge”, Journal of Physical Society, 11(7), pp 797-803.
[19]Sato K, (1971), “Free Flexural vibrations of an elliptic plate with simply supported edge”, Journal of Acoustical Society America, 52(3), part 2, pp 919-922.
[20]Sato K, (1973), “Free Flexural vibrations of an elliptic plate with free edge”, Journal of Acoustical Society America, 54, pp 547-550.
[21]Sato K, Free Flexural Vibrations of an Elliptical Plate with Edge Restrained Elastically, Bulletin of the JSME, Vol. 19, No. 129 (1976), pp.260-264
[22]Sato, K., Bending of an Elastically Restrained Elliptical Plate under the Combined Action of Lateral Load and In-Plane Force. JSME International Journal Series A, Vol. 49, No. 1 (2006), pp. 130-137.
[23]Sato, K., Free Flexural Vibration of an Elastically Restrained Elliptical plate Subjected to an In-Plane Force, Journal of System Design and Dynamics, Vol. 1 (2007) , No. 1 pp.97-104
[24]A. N. Thiele, “ Loudspeakers in Vented Boxes, Parts I and II,” Proceedings of the IRE, Australia, vol. 22, pp. 487-508, 1961
[25]R. H. Small, “Closed-Box Loudspeaker Systems, Parts I and II,” J Audio Eng. Soc., vol. 20, no. 10, pp. 798-808, Dec. 1972; vol. 21, no. 1, pp. 11-18, Jan./Feb. 1973.
[26]R.H. Small, “Vented-Box Loudspeaker Systems, ” J Audio Eng. Soc., vol. 21, pp. 549-554, Sept. 1973.
[27]郭晟宇, “ 可攜式揚聲器之分析與模擬 ”, 私立逢甲大學機械工程研究所碩士論文, 96年7月。
[28]A. J. M. Kaizer and A. Leeuwestein, “Calculation of the Sound Radiation of a Nonrigid Loudspeaker Diaphragm Using the Finite-Element Method,” J. Audio Eng. Soc., vol. 36, pp. 539 –551 (1988 July/Aug.).
[29]Bai, Mingsain R.; Liu, Ching-Yu; Chen, Rong-Liang, “Optimization of Microspeaker Diaphragm Pattern Using Combined Finite Element-Lumped Parameter Models”, IEEE Transactions on Magnetics, vol. 44, issue 8, pp. 2049-2057
[30]R. M. Aarts, “High-Efficiency Low-Bl Loudspeakers,”J. Audio Eng. Soc., vol. 53, pp. 579–592 (2005 July/Aug.).