120th AES 6840 : Analysis and Optimal Design of Miniature Loudspeakers Mingsain R. Bai and Rong-Liang Chen Department of Mechanical Engineering, National Chiao-Tung University, 1001 Ta-Hsueh Road, Hsin-Chu 300, Taiwan Objective Using the optimal design to improve the output performance of the miniature loudspeaker with minimal distortion penalty. Summary ■ The miniature loudspeaker discussed in this paper is dynamic moving-coil type. Due to size limitation, miniature loudspeakers suffer from the problem of low output level. ■ The optimization procedure is based on an electro-acoustic model established by using the test-box method to experimentally identify the Thiele and Small parameters. ■ The optimization procedure is carried out by using a nonlinear constrained optimization algorithm. ■ Objective function: Pressure sensitivity ■ Constraints: maximum displacement of diaphragm, magnetic flux density, mechanical compliance, acoustic resistance and resonance frequency. ■ Design variables include magnetic flux density, mechanical compliance and acoustic resistance. ■ The results revealed that the optimal design effectively enhanced the output performance with little distortion penalty. Voice-coil impedance measurement 2.8cc test-box loudspeaker

■ The Hessian matrix can be updated by using the BFGS method. ■ T-S parameters of the miniature ■ EMA analogy of a moving loudspeaker loudspeaker ■ Loudspeaker response functions: voice-coil impedance transfer function velocity of the diaphragm on-axis pressure response Optimization design ■ Sequential quadratic optimization theory The Sequential Quadratic Programming (SQP) algorithm in nonlinear programming is employed to tackle this constrained nonlinear optimization problem. ■ nonlinear programming problem ■ Lagrangian function where and are the Lagrange multipliers, are the slack variable. ■ QP subproblem Rg － + ic eg RE LE ZAF ZAB -UD UD － + + － uD ■ The Hessian matrix can be updated by using the BFGS method. where ■ The solution of dk is used to update the estimate of x

Optimization syntax ■ The maximum displacement Simulation and Experiment ■ THD and IMD measurement of the loudspeakers ■ The responses of the original design, the optimized design, and the measurement of the miniature loudspeaker are compared.