Research Papers

Lumped Element Multimode Modeling of Balanced-Armature Receiver Using Modal Analysis

[+] Author and Article Information
Wei Sun

Institute of Acoustics,
Tongji University,
1239 Siping Road,
Shanghai 200092, China
e-mail: sfwei01@163.com

Wenxiang Hu

Institute of Acoustics,
Tongji University,
1239 Siping Road,
Shanghai 200092, China
e-mail: wxhu@tongji.edu.cn

1Corresponding authors.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 6, 2016; final manuscript received August 16, 2016; published online September 30, 2016. Assoc. Editor: Miao Yu.

J. Vib. Acoust 138(6), 061017 (Sep 30, 2016) (8 pages) Paper No: VIB-16-1165; doi: 10.1115/1.4034535 History: Received April 06, 2016; Revised August 16, 2016

For the lack of higher-order modes, lumped element (LE) models currently used may be insufficient to predict the system of balanced-armature receiver (BAR). We develop an LE multimode model for BAR in the frequency domain based on the techniques of mode decomposition, truncation, and selection. The validation is made by comparing with both the corresponding combined finite element (FE)–LE model and the full FE model. Numerical results prove that the developed model is not only as effective as the combined FE–LE model but also much more efficient. Additionally, an in-depth investigation performed discloses the inherent deficiency of the traditional LE model.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Hunt, F. V. , 1954, Electroacoustics: The Analysis of Transduction, and Its Historical Background, Acoustical Society of America, New York, pp. 213–235.
Madsen, H. S. , 1971, “ Small Balanced Armature Receiver for Electronic Telephone Sets,” J. Audio Eng. Soc., 19(3), pp. 209–212.
Kampinga, W. R. , 2010, “ Viscothermal Acoustics Using Finite Elements: Analysis Tools for Engineers,” Ph.D. thesis, University of Twente, Enschede, The Netherlands.
Jensen, J. , Agerkvist, F. T. , and Harte, J. M. , 2011, “ Nonlinear Time-Domain Modeling of Balanced-Armature Receivers,” J. Audio Eng. Soc., 59(3), pp. 91–101.
Kim, N. , and Allen, J. B. , 2013, “ Two-Port Network Analysis and Modeling of a Balanced Armature Receiver,” Hear. Res., 301(1), pp. 156–167. [CrossRef] [PubMed]
Tsai, Y. T. , and Huang, J. H. , 2013, “ A Study of Nonlinear Harmonic Distortion in a Balanced Armature Actuator With Asymmetrical Magnetic Flux,” Sens. Actuators, A, 203(6), pp. 324–334. [CrossRef]
Jensen, J. , 2014, “ Nonlinear Distortion Mechanisms and Efficiency of Miniature Balanced-Armature Loudspeakers,” Ph.D. thesis, Technical University of Denmark, Kgs. Lyngby, Denmark.
Bai, M. R. , Liu, C. Y. , and Chen, R. L. , 2008, “ Optimization of Microspeaker Diaphragm Pattern Using Combined Finite Element-Lumped Parameter Models,” IEEE Trans. Magn., 44(8), pp. 2049–2057. [CrossRef]
Nguyen, C. H. , and Pietrzko, S. J. , 2007, “ Vibroacoustic FE Analysis of an Adaptive Plate With PZT Actuator/Sensor Pairs Connected to a Multiple-Mode, Electric Shunt System,” Finite Elem. Anal. Des., 43(15), pp. 1120–1134. [CrossRef]
Sun, W. , and Hu, W. X. , 2014, “ Integrated Finite-Element and Lumped-Element Modeling of Balanced-Armature Receiver,” 21st International Congress on Sound and Vibration, Beijing, China, July 13–17, pp. 2119–2126.
Tilmans, H. A. C. , 1998, “ Equivalent Circuit Representation of Electromechanical Transducers: II. Distributed-Parameter Systems,” J. Micromech. Microeng., 7(4), pp. 285–309. [CrossRef]
Klippel, W. , and Schlechter, J. , 2009, “ Distributed Mechanical Parameters of Loudspeakers. Part 1: Measurements,” J. Audio Eng. Soc., 57(7), pp. 500–511.
He, J. M. , and Fu, Z. F. , 2001, Modal Analysis, Butterworth-Heinemann, London, pp. 94–129.
Moore, R. E. , and Cloud, M. J. , 2007, Computational Functional Analysis, 2nd ed., Woodhead Publishing, Philadelphia, PA, pp. 24–27.
Xie, N. G. , and Song, P. Y. , 2002, “ An Annotation of Modal Superposition Method of Linear Oscillation System,” Hydro-Sci. Eng., 22(1), pp. 52–55 (in Chinese).
Hatch, M. R. , 2001, Vibration Simulation Using MATLAB and ANSYS, Chapman & Hall/CRC, Boca Raton, FL, pp. 412–414.
Hefferon, J. , 2011, Linear Algebra, Virginia Commonwealth University, Richmond, VA, pp. 249–252.
Yu, R. F. , Zhou, X. Y. , and Yuan, M. Q. , 2012, “ Dynamic Response Analysis of Generally Damped Linear System With Repeated Eigenvalues,” Struct. Eng. Mech., 42(4), pp. 449–469. [CrossRef]
Beranek, L. L. , and Mellow, T. J. , 2012, Acoustics: Sound Fields and Transducers, Elsevier-Academic Press, Waltham, MA, p. 14.


Grahic Jump Location
Fig. 1

Geometry of the concerned simplified BAR: (a) mechanical domain and (b) acoustic domain

Grahic Jump Location
Fig. 2

Energy norms of the system: (a) contour plot of ENc/E12 over the interested frequency range as function of both the truncated modal number and frequency, and (b) ENc/E12 as a function of the truncated modal number

Grahic Jump Location
Fig. 3

DC gains of the system for the first six modes

Grahic Jump Location
Fig. 4

Displacement FR of the mechanical system at MP with the four selected modes (sum(M1, M2, M4, M5) is the superposed result of the four selected modes, sum(M1:M12) is the superposed result of all the concerned 12 modes, FE is the result from the full FE model, and M1, M2, M4, and M5 are, respectively, the modal components of the selected four modes): (a) FRs of the modal components and (b) FR validation by referring to the model including all the concerned 12 modes and the full FE model

Grahic Jump Location
Fig. 5

Equivalent circuit of LE multimode model for BAR

Grahic Jump Location
Fig. 6

FRs of the system (FE, LE-4modes, and LE represent the full FE model, the LE multimode model, and the LE model, respectively): (a) velocity at MP and (b) SPL in the 2 cc coupler

Grahic Jump Location
Fig. 7

FRs of the system (MechaFE-AcoLE represents the combined FE–LE model): (a) velocity at MP and (b) SPL in the 2 cc coupler

Grahic Jump Location
Fig. 8

Computation time comparison between the involved four models

Grahic Jump Location
Fig. 9

Volume velocities for the four componential modes and the whole system: q1, q2, q4, and q5 are, respectively, the volume velocities induced by the membrane for the first, second, fourth, and fifth modes of the mechanical system; qtot is the superposed results of the whole system

Grahic Jump Location
Fig. 11

Volume velocities for the two decisive modes of the mechanical system: (a) amplitudes of the volume velocities and (b) phases of the volume velocities

Grahic Jump Location
Fig. 10

First two modes of mechanical system of simplified BAR: (a) fundamental mode (first mode) and (b) second mode



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In