TWI423686B - Parameter identification method and its optimization method for electret speaker simulation platform - Google Patents
Parameter identification method and its optimization method for electret speaker simulation platform Download PDFInfo
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本發明係有關一種揚聲器參數鑑別以模擬其聲壓響應之技術，特別是指一種應用於駐極體揚聲器之參數鑑別方法，可提高模擬之真實度，並提出最佳化之方法。The invention relates to a technique for discriminating a speaker parameter to simulate its sound pressure response, in particular to a parameter identification method applied to an electret speaker, which can improve the realness of the simulation and propose a method for optimization.
按，駐極體又稱永電體，其體績小、耗電低且具有可撓式特性，用其製做喇叭之振動振膜，可使駐極體喇叭在外觀造型上不受拘束，挑戰更小、更時尚多變之造型而不會影響音質。According to the electret, the electret is also known as the permanent electric body. It has small physical performance, low power consumption and flexible characteristics. The vibrating diaphragm made of the horn can make the electret horn unconstrained in appearance. Challenge smaller, more stylish and versatile shapes without affecting sound quality.
第1圖為推挽式駐極體揚聲器之結構示意圖，包括兩正負電極10及置中之駐極體振膜12，駐極體振膜12與電極10之間距為d，駐極體振膜12所受的力為F，兩端電極10受到電壓響應為espk ，使駐極體振膜12受力F產生振動，駐極體揚聲器可利用機電聲類比電路進行模擬，如第2圖所示之機電聲類比電路示意圖，包括電系統14、機械系統16及聲學系統18，將機械系統16與聲學系統18映射至電系統14之類比電路示意圖如第3圖，ein 為輸入之電壓值，Zmot 為運動阻抗(motional impedance)，是機械系統與聲學系統18映射至電系統後的等效阻抗，可由下列公式(1)求得，並利用公式(2)求得短路機械阻抗Zms 。1 is a schematic structural view of a push-pull electret speaker, comprising two positive and negative electrodes 10 and a centering electret diaphragm 12, and the distance between the electret diaphragm 12 and the electrode 10 is d, the electret diaphragm The force received by 12 is F, and the voltage at both ends of the electrode 10 is e spk , so that the electret diaphragm 12 is vibrated by the force F, and the electret speaker can be simulated by using an electromechanical acoustic analog circuit, as shown in Fig. 2. electromechanical acoustic analog circuit schematic diagram of, including an electrical system 14, mechanical system 16 and the acoustic system 18, mechanical system 16 to the acoustic system 18 is mapped to an electrical system of analog 14 of a circuit diagram as Fig. 3, e in the voltage value input of the Z mot is the motion impedance, which is the equivalent impedance after the mechanical system and the acoustic system 18 are mapped to the electrical system. It can be obtained by the following formula (1), and the short-circuit mechanical impedance Z ms is obtained by the formula (2). .
其中SD 為駐極體振膜12之振膜面積，ZA 為聲學阻抗，ZM 為開路機械阻抗，CE 為靜電容值，ω為角頻率，Zms 為短路機械阻抗，由於駐極體揚聲器的電-力轉換因子(voltage-force conversion factor)Ψ極小，因此Zmot 極大，使得Zmot 如同一個開路電路，因此電系統不受機械系統的影響，電阻抗將無法顯示機械系統的特性，傳統揚聲器之參數鑑別是利用電阻抗量測來進行，而這個方法不完全適用於駐極體揚聲器之參數鑑別。Where S D is the diaphragm area of the electret diaphragm 12, Z A is the acoustic impedance, Z M is the open mechanical impedance, C E is the electrostatic capacitance value, ω is the angular frequency, Z ms is the short-circuit mechanical impedance, due to the electret the speaker body electrically - power conversion factor (voltage-force conversion factor) Ψ extremely small, thus greatly Z mot, Z mot such as an open circuit, and therefore unaffected by the electrical system of the mechanical system, the electrical impedance characteristics of the mechanical system can not be displayed The parameter identification of the traditional speaker is performed by the electrical impedance measurement, and this method is not completely suitable for the parameter identification of the electret speaker.
因此，本發明即提出一種應用於駐極體揚聲器模擬平台之參數鑑別方法及其最佳化方法，以有效克服上述之該等問題，具體架構及其實施方式將詳述於下。Therefore, the present invention proposes a parameter identification method and an optimization method for the electret speaker simulation platform to effectively overcome the above problems, and the specific architecture and its implementation will be described in detail below.
本發明之主要目的在提供一種應用於駐極體揚聲器模擬平台之參數鑑別方法，其係將電系統與聲學系統映射整合至機械系統中，整合之系統可簡化，利用雷射速度量測儀量測振膜有、無測試箱時的速度響應，可得到精確的參數，利用此模擬平台可以準確模擬出駐極體揚聲器的聲壓響應，與實驗結果一致。The main object of the present invention is to provide a parameter identification method applied to an electret speaker simulation platform, which integrates an electrical system and an acoustic system into a mechanical system, and the integrated system can be simplified, and the laser speed measuring instrument is utilized. The speed response of the vibration measuring film with and without the test box can obtain accurate parameters. The simulation platform can accurately simulate the sound pressure response of the electret speaker, which is consistent with the experimental results.
本發明之另一目的在提供一種最佳化方法，對駐極體揚聲器的結構做最佳化設計，其利用模擬退火方法將設計參數予以最佳化，其參數最佳化之設計方案分為單一變數之最佳化及多變數之最佳化，利用最佳化之參數來設計駐極體揚聲器可提升駐極體揚聲器之性能。Another object of the present invention is to provide an optimization method for optimizing the structure of an electret speaker, which utilizes a simulated annealing method to optimize design parameters, and a design scheme for optimizing parameters thereof is divided into The optimization of single variables and the optimization of multiple variables, the use of optimized parameters to design electret speakers can improve the performance of electret speakers.
為達上述之目的，本發明提供一種應用於駐極體揚聲器模擬平台之參數鑑別方法，駐極體揚聲器包含一電系統、一聲學系統及一機械系統，可用機電聲類比電路來進行分析模擬。首先利用量測電阻抗響應以及變壓器輸出端響應求得電系統中必要的參數值，接著將電系統及聲學系統映射至機械系統中，將機械系統與聲學系統耦合成一二階系統；由於機電聲類比電路之電-力轉換因子(voltage-force conversion factor)極小，可將機電聲類比電路簡化，接著將駐極體揚聲器置入一氣密之測試箱中，量測有無測試箱時之振膜速度響應，求出電-力轉換因子之數值與機-聲系統之參數後代入機電聲類比電路中，建立完整的機電聲類比電路，以用於駐極體揚聲器之聲壓響應之模擬。本發明更提供將駐極體揚聲器之結構進行最佳化之方法，調整振膜與電極板之間距及等效阻尼、順性、質量，可提升駐極體揚聲器之聲壓響應及工作頻寬。To achieve the above object, the present invention provides a parameter identification method applied to an electret speaker simulation platform. The electret speaker comprises an electrical system, an acoustic system and a mechanical system, and the electromechanical acoustic analog circuit can be used for analysis and simulation. Firstly, the measured electrical impedance response and the output of the transformer are used to obtain the necessary parameter values in the electrical system. Then the electrical system and the acoustic system are mapped into the mechanical system, and the mechanical system and the acoustic system are coupled into a second-order system; The circuit's voltage-force conversion factor is extremely small, which simplifies the electromechanical acoustic analog circuit. Then the electret speaker is placed in an airtight test box to measure the diaphragm speed response with or without the test box. Find the value of the electro-mechanical conversion factor and the parameters of the machine-acoustic system into the electromechanical acoustic analog circuit to establish a complete electromechanical acoustic analog circuit for the simulation of the acoustic pressure response of the electret speaker. The invention further provides a method for optimizing the structure of the electret speaker, adjusting the distance between the diaphragm and the electrode plate and equivalent damping, compliantness and quality, and improving the sound pressure response and working bandwidth of the electret speaker. .
本發明更提供一種應用於駐極體揚聲器模擬平台之最佳化方法，於駐極體揚聲器之結構中預設至少一設計變數及至少一目標函數，再利用以模擬退火法(Simulated Annealing,SA)針對駐極體揚聲器之結構設計進行最佳化。The invention further provides an optimization method for an electret speaker simulation platform, which presets at least one design variable and at least one objective function in the structure of the electret speaker, and then uses the simulated annealing method (Simulated Annealing, SA) ) Optimized for the structural design of the electret speaker.
底下藉由具體實施例詳加說明，當更容易瞭解本發明之目的、技術內容、特點及其所達成之功效。The purpose, technical content, features and effects achieved by the present invention will be more readily understood by the detailed description of the embodiments.
本發明提供一種應用於駐極體揚聲器模擬平台之參數鑑別方法及其最佳化方法，第2圖為駐極體揚聲器之機電聲類比電路，其中包含電系統14、機械系統16及聲學系統18，求出其中各項參數值，以將機電聲類比電路用於如第1圖中之駐極體揚聲器之響應模擬中。The invention provides a parameter identification method and an optimization method thereof for an electret speaker simulation platform, and FIG. 2 shows an electromechanical acoustic analog circuit of an electret speaker, which comprises an electric system 14, a mechanical system 16 and an acoustic system 18 The values of the various parameters are determined to use the electromechanical acoustic analog circuit in the response simulation of the electret speaker as shown in FIG.
雖然先前技術中利用電阻抗量測的參數鑑別方法並不完全適用於駐極體揚聲器，但藉由電阻抗量測可發現此電阻抗響應如同一個電容器，因此可推得駐極體揚聲器之靜電容值CE ，如下式(3)。Although the parameter identification method using the electrical impedance measurement in the prior art is not completely suitable for the electret speaker, it can be found that the electrical impedance response is like a capacitor by the electrical impedance measurement, so the static electricity of the electret speaker can be derived. The capacitance C E is as shown in the following formula (3).
CE =(ω|ZE |)-1 ................................................................(3)C E =(ω|Z E |) -1 ..................................... ..........................(3)
其中|ZE |為在頻率為ω時的電阻抗大小值。Where |Z E | is the magnitude of the electrical impedance at a frequency of ω.
請同時參考第1圖及第2圖，在第2圖中，RE 和LE 分別為一變壓器的內電阻與內電感，當變壓器與駐極體揚聲器連結時，駐極體揚聲器之電極板10端點的電壓響應為二階低通系統，因此電極板10的電壓響應可以用下式(4)來模擬，利用電極板10的電壓響應量測結果可在下式(5)、(6)中推得內電阻RE 和內電感LE 之值。Please refer to Fig. 1 and Fig. 2 at the same time. In Fig. 2, R E and L E are the internal resistance and internal inductance of a transformer respectively. When the transformer is connected with the electret speaker, the electrode plate of the electret speaker The voltage response of the 10th terminal is a second-order low-pass system, so the voltage response of the electrode plate 10 can be simulated by the following formula (4), and the voltage response measurement result by the electrode plate 10 can be used in the following formulas (5), (6). The values of the internal resistance R E and the internal inductance L E are derived.
LE =(ωE0 2 CE )-1 ...........................................................(5)L E =(ω E0 2 C E ) -1 ..................................... .....................(5)
RE =(QE ωE0 CE )-1 .............................................................(6)R E =(Q E ω E0 C E ) -1 ..................................... ........................(6)
其中ωE0 為此二階低通系統的共振頻率，QE 為共振頻率時的品質因子。Where ω E0 is the resonant frequency of the second-order low-pass system, and Q E is the quality factor at the resonant frequency.
完成電系統之參數鑑別後，接著進行機聲系統之參數鑑別。將駐極體揚聲器的類比電路中的電系統14及聲學系統18映射至機械系統16，且機械系統16與聲學系統18係耦合並用二階系統來模擬，在電路中用電阻、電感以及電容串階而成的二階系統模擬，如第4圖所示，其中MM 、RM 及CM ’ 為機械系統16與聲學系統18之耦合，分別為機械系統與聲學系統耦合後之等效阻尼、等效質量以及等效順性，耦合的部分相當於ZM ＋ZA ×SD 2 ，而u代表駐極體振膜之運動速度。當電-力轉換因子Ψ很小時，RE Ψ2 ≒0且LE Ψ2 ≒0，因此可將機電聲類比電路簡化為第5圖所示之簡化電路。After the parameter identification of the electrical system is completed, the parameter identification of the machine sound system is performed. The electrical system 14 and acoustic system 18 in the analog circuit of the electret speaker are mapped to the mechanical system 16, and the mechanical system 16 is coupled to the acoustic system 18 and simulated with a second order system using resistors, inductors, and capacitors in the circuit. The second-order system simulation is shown in Fig. 4, where M M , R M and C M ' are the coupling of the mechanical system 16 and the acoustic system 18, respectively, the equivalent damping of the mechanical system coupled with the acoustic system, etc. The effective mass and the equivalent compliantness, the coupled part is equivalent to Z M + Z A × S D 2 , and u represents the moving speed of the electret diaphragm. When the electric-force conversion factor Ψ is small, R E Ψ 2 ≒ 0 and L E Ψ 2 ≒ 0, the electromechanical acoustic analog circuit can be simplified to the simplified circuit shown in FIG.
由第5圖中駐極體揚聲器的振膜速度響應可以求得，列於下式(7)。The diaphragm velocity response of the electret speaker in Fig. 5 can be obtained and is listed in the following equation (7).
其中ω0 基本共振頻率，Qu 為速度響應在ω0 時的品質因子，而CM 為與CM ’串聯後的等效順性。將駐極體揚聲器鑲嵌於一個內無添加任何吸音材的測試箱上，並使測試箱氣密，此測試箱將會改變駐極體揚聲器之等效順性，並使駐極體揚聲器之基本共振頻率變更至較高頻，接著再利用雷射速度量測儀分別量測有、無測試箱時之振膜速度響應，等效順性CM 可由下式(8)求得。Where ω 0 is the fundamental resonance frequency, Q u is the quality factor of the velocity response at ω 0 , and C M is Equivalent conformity after concatenation with C M '. The electret speaker is mounted on a test box without any sound absorbing material and the test box is airtight. This test box will change the equivalent compliance of the electret speaker and make the electret speaker basic. The resonance frequency is changed to a higher frequency, and then the diaphragm speed response of the test chamber with and without the test box is measured by the laser speed measuring instrument, and the equivalent compliance C M can be obtained by the following formula (8).
其中ω0B 為有測試箱時的基本共振頻率，ΔCM 為測試箱所造成的機械順性，可由下式(9)求得。Where ω 0B is the basic resonance frequency when there is a test box, and ΔC M is the mechanical compliance caused by the test box, which can be obtained by the following formula (9).
其中Vbox 為音箱容積，ρ為空氣密度，c為空氣中聲速，SD 為振膜有效面積，接著，RM 、MM 、CM ’可由下面的公式(10)、(11)、(12)求得。Where V box is the volume of the speaker, ρ is the air density, c is the speed of sound in the air, and S D is the effective area of the diaphragm. Then, R M , M M , C M ' can be given by the following formulas (10), (11), ( 12) Get it.
MM =(ω0 2 CM )-1 .........................................................(10)M M = (ω 0 2 C M ) -1 ...................................... ...................(10)
RM =(ω0 Qu CM )-1 .........................................................(11)R M =(ω 0 Q u C M ) -1 ..................................... ....................(11)
此外，電-力轉換因子ψ亦可利用下式(13)求得。Further, the electric-force conversion factor ψ can also be obtained by the following formula (13).
其中u(ω0 )為駐極體揚聲器在基本共振頻率時的速度大小值，ein 為輸入之電壓值。Wherein u (ω 0) of the electret loudspeaker velocity magnitude value at a substantially resonant frequency, e in the input voltage value.
如此，第4圖所示之駐極體揚聲器的機電聲類比電路即可被建立，並用於駐極體揚聲器的響應模擬。第6圖為駐極體揚聲器的聲壓(Sound pressure level,SPL)實驗量測(虛線)與用機電聲類比電路模擬出來的結果(實線)，可以發現此參數鑑別法可以準確鑑別有關駐極體揚聲器的各項參數並準確模擬出聲壓響應。Thus, the electromechanical acoustic analog circuit of the electret speaker shown in Fig. 4 can be established and used for the response simulation of the electret speaker. Figure 6 shows the sound pressure level (SPL) experimental measurement (dashed line) of the electret speaker and the result simulated by the electromechanical acoustic analog circuit (solid line). It can be found that this parameter identification method can accurately identify the relevant station. The parameters of the polar body speaker accurately simulate the sound pressure response.
若是欲提升駐極體揚聲器之性能響應，本發明更提供一種駐極體揚聲器結構最佳化之方法，其係利用模擬退火(Simulated annealing,SA)法來進行駐極體揚聲器結構最佳化設計。模擬退火是一種隨機求解的演算法，適用於多個設計變數之問題。在尋求最佳解的過程中，模擬退火演算法在初始求解階段有一定的機率可以接受較差的解，此可避免求解過程陷入區域的最佳解而找不到整體區域的最佳解，在最後求解階段幾乎不會接受較差的解，而會鎖定一個最好的解。在模擬退火演算法中必須設定一個目標函數以及至少一個設計變數。本案例的最佳化設計有兩個設計方案，分別為單一變數最佳化及多變數最佳化。In order to improve the performance response of the electret speaker, the present invention further provides a method for optimizing the structure of the electret speaker, which uses the Simulated Annealing (SA) method to optimize the design of the electret speaker structure. . Simulated annealing is a stochastic solution algorithm that is applicable to multiple design variables. In the process of seeking the best solution, the simulated annealing algorithm has a certain probability to accept a poor solution in the initial solution stage, which can avoid the optimal solution of the solution process into the region and can not find the best solution of the overall region. The final solution phase will almost never accept a poor solution, but will lock a best solution. An objective function and at least one design variable must be set in the simulated annealing algorithm. The optimized design of this case has two design schemes, which are single variable optimization and multivariate optimization.
單一變數最佳化之設計變數僅有駐極體振膜與電極板之間距d，目標函數為提昇聲壓響應以及高頻-3dB截止頻率點的延伸，其最佳化流程如第目標函數以及限制條件如下：The design variable of single variable optimization only has the distance d between the electret diaphragm and the electrode plate. The objective function is to enhance the sound pressure response and the extension of the high frequency -3dB cutoff frequency point. The optimization process is as the objective function and The restrictions are as follows:
G2 =fuc ...............................................................(15)G 2 =f uc ............................................. ..................(15)
其中G1 與G2 為兩個子目標函數，G1 為計算頻率800Hz到5000Hz聲壓之均方根值，fuc 為高頻區域的-3dB截止頻率點，G1 與G2 均為愈大愈好，GTG 為主目標函數，主目標函數越小越好，w為G2 倒數的權重。整個退火的過程是從初始溫度Ti 至終止溫度Tf 結束，降溫過程由降溫因子α來決定，若在公式(17)範圍內隨機選擇的間距d所計算出之主目標函數GTG 超出約束範圍，則將其丟棄，並再次選擇一個隨機的間距d重新計算，直到溫度小於終止溫度Tf 時結束。在演算過程中可能會出現壞解，但此壞解並非不可被接受，因為在其附近可能有較佳解，因此演算法是否接受較壞的解由下式(18)來決定。Where G 1 and G 2 are two sub-objective functions, G 1 is the root mean square value of the sound pressure of the calculated frequency from 800 Hz to 5000 Hz, and f uc is the -3 dB cutoff frequency point of the high frequency region, and both G 1 and G 2 are more The bigger the better, G TG is the main objective function, the smaller the main objective function is, the better, w is the weight of the inverse of G 2 . The whole annealing process is from the initial temperature T i to the end temperature T f . The cooling process is determined by the cooling factor α. If the randomly selected spacing d within the range of the formula (17) is calculated, the main objective function G TG exceeds the constraint. For the range, discard it and re-calculate a random spacing d again until the temperature is less than the termination temperature Tf . A bad solution may occur during the calculation, but this bad solution is not unacceptable because there may be a better solution in its vicinity, so whether the algorithm accepts a bad solution is determined by the following equation (18).
P為是否接受壞解的機率函數，ΔG為目前與前一個目標函數的差值，T為目前溫度，γ為區間(0,1)之內的任意值，此外限制條件如式(17)所示，最佳化過程時，振膜最大位移量不能超過間距d。P is the probability function of accepting the bad solution, ΔG is the difference between the current and the previous objective function, T is the current temperature, γ is any value within the interval (0, 1), and the limiting condition is as shown in equation (17). It is shown that the maximum displacement of the diaphragm cannot exceed the spacing d during the optimization process.
單一設計變數最佳化結果如第7圖所示，最佳化後的間距為0.86公釐(mm)，因為聲壓提昇與高頻響應的延伸為互相矛盾之設計函數，因此最佳化結果可有效提昇，但些許的頻寬被犧牲。The optimization result of the single design variable is shown in Fig. 7. The optimized pitch is 0.86 mm (mm), because the sound pressure boost and the extension of the high frequency response are contradictory design functions, so the optimization result Can be effectively improved, but a small amount of bandwidth is sacrificed.
多變數最佳化之設計變數有振膜與電極板之間距d、機械與聲學系統耦合後之等效阻尼RM 、等效質量MM 以及等效順性CM ’，目標函數為提昇聲壓響應、高頻以及低頻-3dB截止頻率點的延伸，因此多加的一個子目標函數及主目標函數如下式所示：The design variables of multivariate optimization have the distance d between the diaphragm and the electrode plate, the equivalent damping R M coupled with the mechanical and acoustic system, the equivalent mass M M and the equivalent cisness C M ', and the objective function is the lifting sound. The pressure response, high frequency and low frequency -3dB cutoff frequency point extension, so the additional sub-objective function and main objective function are as follows:
G3 =f1c ................................................................(19)G 3 =f 1c ............................................. ...................(19)
其中f1c 為低頻區域的-3dB截止頻率點，GTM 為主目標函數，主目標函數越小越好，w1 為G1 倒數的權重，w2 為G2 倒數的權重。此最佳化的限制條件Where f 1c is the -3dB cutoff frequency point of the low frequency region, G TM is the main objective function, the smaller the main objective function is, w 1 is the weight of the reciprocal of G 1 , and w 2 is the weight of the reciprocal of G 2 . The constraints of this optimization
最佳化的結果參數示於下表一，聲壓響應如第8圖所示，可以發現最佳化的結果因為間距減小，所以振膜受力大，可以產生較大的聲壓，但也犧牲了高頻響應的延伸的需求；而順性的增大，使得基本共振頻率往低頻延伸，達到低頻響應延伸的要求。The optimized result parameters are shown in the following table 1. The sound pressure response is shown in Fig. 8. It can be found that the optimized result is because the pitch is reduced, so the diaphragm is stressed and can generate a large sound pressure, but The need for the extension of the high frequency response is also sacrificed; and the increase in the cisness causes the fundamental resonance frequency to extend to the low frequency, achieving the requirement of low frequency response extension.
綜上所述，本發明所提供之應用於駐極體揚聲器模擬平台之參數鑑別方法係將駐極體揚聲器之機電聲類比電路中之電系統及聲學系統映射到機械系統中，再利用雷射速度量測儀在有、無測試箱時分別對駐極體揚聲器做振膜速度響應量測，可有效鑑別出駐極體揚聲器之各項參數，將參數代入機電聲類比電路可有效模擬出駐極體揚聲器之聲壓響應。此外，利用模擬退火法可對單一設計變數及多設計變數之問題進行最佳化，有效找出整體區域之最佳解以對駐極體揚聲器之結構做最佳化設計，且駐極體揚聲器經過最佳化後可提昇聲壓響應並達到低頻響應延伸的設計需求。In summary, the parameter identification method applied to the electret speaker simulation platform of the present invention maps the electrical system and the acoustic system in the electromechanical acoustic analog circuit of the electret speaker to the mechanical system, and then uses the laser. The speed measuring instrument performs the diaphragm speed response measurement on the electret speaker in the presence or absence of the test box, which can effectively identify the parameters of the electret speaker, and substitute the parameters into the electromechanical acoustic analog circuit to effectively simulate the station. The sound pressure response of the polar body speaker. In addition, the simulated annealing method can be used to optimize the problem of single design variables and multiple design variables, effectively finding the best solution for the overall region to optimize the structure of the electret speaker, and the electret speaker Optimized to increase the sound pressure response and achieve the design requirements of low frequency response extension.
唯以上所述者，僅為本發明之較佳實施例而已，並非用來限定本發明實施之範圍。故即凡依本發明申請範圍所述之特徵及精神所為之均等變化或修飾，均應包括於本發明之申請專利範圍內。The above is only the preferred embodiment of the present invention and is not intended to limit the scope of the present invention. Therefore, any changes or modifications of the features and spirits of the present invention should be included in the scope of the present invention.
10．．．電極板10. . . Electrode plate
12．．．駐極體振膜12. . . Electret diaphragm
14．．．電系統14. . . Electric system
16．．．機械系統16. . . computer system
18．．．聲學系統18. . . Acoustic system
第1圖為駐極體揚聲器之結構示意圖。The first picture shows the structure of the electret speaker.
第2圖為駐極體揚聲器之電系統、機械系統及聲學系統之類比電路示意圖。Figure 2 is a schematic diagram of an analog circuit of an electrical system, a mechanical system, and an acoustic system of an electret speaker.
第3圖為先前技術中將機械系統與聲學系統映射至電系統之類比電路示意圖。Figure 3 is a schematic diagram of an analog circuit for mapping a mechanical system and an acoustic system to an electrical system in the prior art.
第4圖為本發明中將電系統與聲學系統映射至機械系統之類比電路示意圖，且機械系統與聲學系統耦合。Figure 4 is a schematic diagram of an analog circuit for mapping an electrical system and an acoustic system to a mechanical system in the present invention, and the mechanical system is coupled to the acoustic system.
第5圖為第4圖之簡化電路示意圖。Figure 5 is a simplified circuit diagram of Figure 4.
第6圖為聲壓實驗量測與模擬比較之曲線圖。Figure 6 is a graph of sound pressure experimental measurement and simulation comparison.
第7圖為單一變數最佳化中改變間距之結果與初始設計比較之曲線圖。Figure 7 is a graph comparing the results of changing the spacing in a single variable optimization with the initial design.
第8圖為多變數最佳化之結果與初始設計比較之曲線圖。Figure 8 is a graph comparing the results of multivariate optimization with the initial design.
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