動圈式揚聲器非線性參數影響失真之研究

Abstract

早期的研究指出，動圈式揚聲器的非線性失真主要由電磁及機械結構引起，其中磁力系統的力量因子(force factor)和懸吊系統的剛性(stiffness)主導了失真的來源。由於本實驗室並沒有直接量測出非線性參數的儀器，為了實現僅靠測量單體聲壓便能夠得到非線性參數的方法，且縮短得到參數的時間。本研究首先通過建立電-機-聲類比電路之線性系統來模擬揚聲器單體的特性，經過推導整理出類比電路法的數學模型；接著將非線性參數以二次多項式的假設引入模型當中，並使用模擬退火法(simulated annealing)將模型模擬的聲壓與實驗量測到的聲壓不斷進行擬合迭代後，估測出力量因子及剛性之非線性參數的曲線。將模擬與實驗結果進行觀察比較，以確定類比電路法與退火法最佳化之可行性。最後設計並探討非線性參數的曲線形狀對於失真之間的影響。結果顯示當輸入皆為對稱的曲線，並不會產生任何偶次失真分量。而偶次失真將會跟著曲線之頂點偏移的情況出現，且當偏移量變大時，奇次失真變化並不明顯，反之偶次失真則會隨著偏移量變大跟著上升。最後，發現力量因子與剛性曲線之頂點異側偏移的情況，相較於頂點同側偏移，對除了二次互調失真之外的偶次失真皆有明顯的抑制作用。

Early research indicated that the nonlinear distortion in dynamic loudspeakers is primarily induced by both electromagnetic and mechanical structural factors, where the force factor of the magnetic system and the stiffness of the suspension system dominate the sources of distortion. Due to the absence of instruments for directly measuring nonlinear parameters in this laboratory, a method was pursued to obtain nonlinear parameters solely through the measurement of monomer sound pressure, with the goal of reducing the time required to obtain these parameters. In this study, a linear system of electrical-mechanical-acoustic analog circuit was first established to simulate the characteristics of the loudspeaker unit. The mathematical model of the analog circuit approach was derived and organized. Subsequently, nonlinear parameters are introduced into the model through the assumption of a quadratic polynomial, and a simulated annealing algorithm is employed to iteratively fit the simulated sound pressure with experimentally measured sound pressure, thereby estimating the curves of the nonlinear parameters of force factor and stiffness. Simulation results were compared with experimental results to determine the feasibility of the analog circuit approach and annealing optimization. Finally, the design and exploration of the curve's shape of the nonlinear parameters and its impact on distortion are conducted. The results revealed that when the inputs are symmetric curves, no even-order distortion components are generated. And even-order distortion will occur in conjunction with the displacement of the curve's vertex. Furthermore, as the displacement becomes larger, the changes in odd-order distortion are not very noticeable, while even-order distortion will increase as the displacement magnitude increases. Finally, under conditions of curve vertex displacement, the study found that when the vertex is offset in the opposite direction, compared to the same-side offset, there is a significant inhibitory effect on even-order distortion components other than second-order intermodulation distortion.