電聲元件之分析、評估與最佳化設計

Abstract

本文主要目的在建立電聲元件的分析、設計與評估方法，近幾年來，微型揚聲器已為3C手持式產品的主要元件，由於受限於體型微小的關係，微型揚聲器會有低輸出功率與非線性失真的問題，為求改善這種複雜問題，可從事微型揚聲器機電參數的最佳化設計，由微型揚聲器的電阻抗、頻率響應與諧波失真等特徵去評估其最佳化結果，由最佳化結果顯示，揚聲器的輸出性能與振膜行程有明顯的改善。另外，對微型揚聲器而言，振膜不僅造成聲音輻射，而且具有懸吊的功能，因此對於微型揚聲器的整體響應與性能而言，振膜形狀的設計也就顯的重要。對集中參數的模擬方式而言，微型揚聲器的高頻模態是無法被模擬出來的，因此本文乃利用有限元素分析與機電聲電路的結合方式，成功模擬出振膜高頻的模態。首先由有限元素分析的方式求得機械阻抗，再將此機械阻抗取代機電聲電路中集中參數的機械阻抗，根據有限元素分析結合機電聲電路的技術，振膜的形狀與刻痕數目，就可以由田口法與靈敏度分析得到最佳化的設計。 此結合有限元素分析與機電聲電路的方法，也可以應用在壓電蜂鳴器的設計與駐極體揚聲器的分析上。首先由壓電振膜從事有限元素分析，求得機電雙埠的阻抗矩陣，並將此阻抗矩陣代入機電聲電路中，即可模擬到壓電振膜的電阻抗。其中壓電振膜的機電參數可由質量增加法來鑑別，因此整體壓電蜂鳴器的電阻抗與軸向聲壓，可由機電聲電路的迴圈方程式求得。其次，駐極體材料具有輕、薄和可撓性的特性，做成揚聲器非常具有空間上的優勢及應用，根據駐極體揚聲器電阻抗的量測，其電系統與機械系統的耦合效應很弱，因此一般適用於揚聲器的參數鑑別方法並不適用於此結構，因此可用有限元素分析來從事此種揚聲器的動態響應分析，並針對簡化模型與整體模型做分析，有限元素簡化模型僅針對駐極體薄膜進行分析，其餘接觸部分設為固定邊界。有限元素整體模型乃針對駐極體薄膜、支撐與背板組合的模型進行分析。因此由有限元素簡諧分析可求得其機械阻抗，並結合背後腔體與出氣孔的聲學阻抗及正面的聲音輻射阻抗，求得駐極體揚聲器的薄膜體速度以及軸向聲壓，此模擬結果與實驗量測結果相當吻合。 最後，限制條件的最佳化技術也可以應用在壓電蜂鳴器與出音孔音響空間最佳化設計，此最佳化乃根據振動吸振器理論，求得電聲元件的腔體與出音孔結構之最佳設計參數。其中整體系統的電路可視為串聯與並聯兩個振盪器電路的耦合，因此根據振動吸振器理論可推導出機械系統與聲學系統耦合的特徵方程式，再根據機電聲模擬平台與機械與聲學系統特徵方程式，可繪出其設計圖表，由此設計圖表找出實現低頻延伸最大輸出的最佳設計參數。除此之外，限制條件最佳化設計方法也可以設計出，在適當的音響空間或機械系統等限制條件下，得到最佳的聲學性能輸出，而且其最佳化設計結果也經由實驗證實，其結果顯示最佳化設計也確實改善了原始的設計。

The goal of this thesis is to establish the analysis, design and evaluation of electro-acoustical transducers. In recent years, microspeakers are key components of many 3C products especially for portable devices. Due to size limitation, microspeakers suffer from the problem of low output level and nonlinear distortion. To address the issue, an optimization technique is presented for design of microspeaker. The optimization procedure is based on an electro-mechano-acoustic (EMA) model and electro-mechanical parameters. Characteristics including voice-coil impedance, frequency response and harmonic distortion are evaluated. The results show that significant improvement in output performance and excursion limitation has been gained by using the optimal design. On the other hand, the diaphragm serves as not only a sound radiator but also the suspension. Thus, the pattern design of the diaphragm is crucial to the overall response and performance of a microspeaker. Traditional approach for modeling microspeakers using lumped-parameter models is generally incapable of modeling flexural modes in high frequencies. In this thesis, a hybrid approach that combines finite element analysis (FEA) and EMA analogous circuit is presented to provide a more accurate model than the conventional approaches. The mechanical impedance obtained using FEA is incorporated into the lumped parameter model. On the basis of this simulation model, the pattern design and optimal number of the diaphragm is optimized using the Taguchi method and sensitivity analysis. The combination of FEA and EMA analogous circuit technique is also can be used in the piezoelectric buzzer design and electret loudspeaker simulation. The analysis starts with modeling the diaphragm structure by using FEA model. The FEA model is then converted into electro-mechanical two-ports to fit into the EMA analogous circuit. Electrical impedance of the piezoelectric diaphragm is simulated using the model. An ‘added-mass’ method is developed to identify the lumped parameters of the piezoelectric diaphragm. Electrical impedance and on-axis sound pressure level (SPL) of a piezoelectric buzzer (containing the diaphragm and case) can be simulated by solving the loop equations of the analogous circuits. On the other hand, the loudspeaker made of thin, light and flexible electret material lends itself well to the space-concerned applications. Electrical impedance measurement reveals that the coupling between the electrical system and the mechanical system is weak, which renders conventional parameter identification and electroacoustic modeling procedures used in voice-coil loudspeakers impractical. To predict the loudspeaker’s dynamic response, FEA is conducted on the basis of a simple model and a full model. In the simple model, FEA is applied to model the electret membrane, leaving the rest of system as rigid parts. In the full model, FEA is applied to model the entire membrane-spacer-back plate assembly. The mechanical impedance is calculated with the FEA harmonic analysis. The mechanical impedance is combined with the acoustical impedance due to the back cavity and pores as well as the radiation loading at the front side to predict the volume velocity of the membrane and the resulting on-axis SPL. The response data predicted by the simulation compare very well with experimental measurements. The constrained optimization technique also can be applied piezoelectric buzzers and vented box system design. This technique aims at finding the optimal parameters of the cavity and vented box configuration of electro-acoustical transducers using a systematic design procedure based on vibration absorber theory, where the system is viewed as two coupled serial and parallel oscillators. The characteristic equation of the mechanical and acoustical system can be derived form the vibration absorber theory. Based on the EMA simulation platform and characteristic of the mechano-acoustical system, a design chart is devised to determine the parameters such that the system delivers the maximal output at the low-frequency end. In addition, constrained optimization is also applied to best reconcile the acoustic output and the housing constraints. Experiments were conducted to justify the optimal design. The results showed that the performance was significantly improved using the optimal design over the original design.