Electroacoustic analysis, design, and implementation of a small balanced armature speaker

Comparison of Multi-Physical Coupling Analysis of a Balanced Armature Receiver between the Lumped Parameter Method and the Finite Element/Boundary Element Method

The balanced armature receiver (BAR) is a product based on multiphysics that enables coupling between the electromagnetic, mechanical, and acoustic domains. The three domains were modeled using the lumped parameter method (LPM) that takes advantage of an equivalent circuit. In addition, the combined finite element method (FEM) and boundary element method (BEM) was also applied to analyze the BAR. Both simulation results were verified against experimental results. The proposed LPM can predict the sound pressure level (SPL) by making use of the BAR parts dimension and material property. In addition, the previous analysis method, FEM/BEM, took 36 h, while the proposed LPM takes 1 h. So the proposed LPM can be used to check the BAR parts’ dimension and material property influence on the SPL and develop the BAR product efficiently.

Efficient approximation of the Struve functions Hn occurring in the calculation of sound radiation quantities

The Struve functions H_n(z), n=0, 1, ...  are approximated in a simple, accurate form that is valid for all z≥0. The authors previously treated the case n = 1 that arises in impedance calculations for the rigid-piston circular radiator mounted in an infinite planar baffle [Aarts and Janssen, J. Acoust. Soc. Am. 113, 2635-2637 (2003)]. The more general Struve functions occur when other acoustical quantities and/or non-rigid pistons are considered. The key step in the paper just cited is to express H₁(z) as (2/π)-J₀(z)+(2/π) I(z), where J₀ is the Bessel function of order zero and the first kind and I(z) is the Fourier cosine transform of [(1-t)/(1+t)]^1/2, 0≤t≤1. The square-root function is optimally approximated by a linear function ĉt+d̂, 0≤t≤1, and the resulting approximated Fourier integral is readily computed explicitly in terms of sin z/z and (1-cos z)/z². The same approach has been used by Maurel, Pagneux, Barra, and Lund [Phys. Rev. B 75, 224112 (2007)] to approximate H₀(z) for all z≥0. In the present paper, the square-root function is optimally approximated by a piecewise linear function consisting of two linear functions supported by [0,t̂₀] and [t̂₀,1] with t̂₀ the optimal take-over point. It is shown that the optimal two-piece linear function is actually continuous at the take-over point, causing a reduction of the additional complexity in the resulting approximations of H₀ and H₁. Furthermore, this allows analytic computation of the optimal two-piece linear function. By using the two-piece instead of the one-piece linear approximation, the root mean square approximation error is reduced by roughly a factor of 3 while the maximum approximation error is reduced by a factor of 4.5 for H₀ and of 2.6 for H₁. Recursion relations satisfied by Struve functions, initialized with the approximations of H₀ and H₁, yield approximations for higher order Struve functions.