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研究生:林逸彥
研究生(外文):Yih-Yan Lin
論文名稱:壓電變壓器設計流程相關之理論建模與實驗應證
論文名稱(外文):Theoretical Modeling and Experimental Varifications for Developing Design Flow of Piezoelectric Transformers
指導教授:葉超雄葉超雄引用關係
指導教授(外文):Chau-Shioung Yeh
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:應用力學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:123
中文關鍵詞:設計流程等效電路升壓比效率壓電變壓器
外文關鍵詞:equivalent circuitdesing flowpiezoelectric transformerefficiencystep-up ratio
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  • 被引用被引用:4
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本論文由傳統以等效電路描述壓電變壓器作出發點,成功地推導負載效應對壓電變壓器之升壓比、效率、輸入相位差、輸入與輸出阻抗之影響。經由進一步深究壓電變壓器之等效電路,亦可求得壓電變壓器的輸出阻抗與其輸出端負載阻抗相等時,將可達成阻抗匹配的狀態。此時,整個系統具有最佳的功率傳輸效率。然而本論文亦發現,礙於電路分析理論的限制,傳統壓電變壓器之等效電路無法有效預測壓電變壓器在高功率運作下,最佳效率時的工作頻率。因此,以實驗討論此一主題是必要的。
本論文在實驗上利用阻抗分析儀完成壓電變壓器在低功率工作時,等效電路參數的量測。並且經由壓電變壓器在高功率運作下的實驗發現,當輸入功率高達五瓦時,壓電材料的行為尚未進入非線性區。因此低功率下所量測的等效電路參數,尚能有效並準確預估壓電變壓器的電子特性。而經由此實驗亦發現壓電變壓器在最佳效率下工作時,工作頻率發生於共振頻右側,在輸入與輸出電壓相位差45°時之效率,可維持在其最佳效率的95%以上。此一經由實驗而歸納出的結論,亦可經由等效電路的推導,在理論上得到支持。基於工程上的需求,儘管點亮冷陰極燈管需要高電壓,但當冷陰極燈管點亮而達穩定狀態時,應追求整個系統在能量傳輸上的高效率。根據此一目標,將相位差鎖定於45°之概念,對於設計壓電變壓器驅動電路將有決定性的突破。
為了改善一般壓電變壓器驅動電路無法確實使得壓電變壓器在最佳效率下運作的缺失,本論文提出一雙模式驅動的控制策略,可有效改善過往在驅動電路上所無法達成的目標。此外,本論文由理論推導與實驗結果,滙整出一系統化的設計流程。若壓電變壓器在力學的振動上,可以簡化為一二階振動系統,則依循本文所提出的設計流程,將可確保整個系統在最佳效率下運作。


To start with the equivalent circuit to model the behavior of the piezoelectric transformer, it was derived that the loading effect influences the step-up ratio, power efficiency, phase differences, input impedance and output impedance of the piezoelectric transformer. To explore further about the equivalent circuit, it was found that once the output impedance equals to the load resistor, i.e., the impedance-matched resistor, the piezoelectric transformer is then operate in optimal condition. In this optimal condition, the system was shown to have maximum power efficiency. Due to the limitation of the electronic circuit analysis, the equivalent circuit of the piezoelectric transformer cannot predict the operating frequency of the optimal condition. Therefore, an experimental set-up is needed to examine this topic.
The measurement of RLC equivalent circuit parameters of piezoelectric transformer was accomplished by using an impedance analyzer under low power condition. It was found by the experiments that the piezoelectric material remains in the linear region even when the device is operated at high input power such as 5.0W. Hence, the equivalent circuit model measured under low power condition can be used to predict the electric characteristics of the piezoelectric transformer under 5.0W input power. It was also discovered that the operating frequency of the maximum power efficiency occurs after the resonant frequency. Once the phase difference between input and output voltage is 45°, the power efficiency of the piezoelectric transformer is higher than 95% to its maximum value. The above conclusions were also supported by the theoretical derivations of the equivalent circuit. Based on the application requirements, the cold cathode fluorescent lamp requires high voltage to light up and high power efficiency in steady state. According to this requirement, the concept of 45° phase angle becomes the best choice to design the control strategy of the driving circuit for piezoelectric transformer.
The driving circuit of piezoelectric transformers which presented in past decades fails to make sure the piezoelectric transformer operate in optimal condition. A dual-mode control strategy was presented to solve this problem. Additionally, a design flow was summarized by the theoretical predictions and experiment results in this thesis. Once the piezoelectric transformer can be simplified to a second order vibration system, the system can be preserved in the most efficient condition by following this design flow.


CHAPTER 1 - 1 -
1.1 HISTORY - 2 -
1.2 MARKET TREND - 5 -
CHAPTER 2 - 9 -
2.1 THE CONSTITUTIVE EQUATIONS OF PIEZOELECTRIC MATERIALS - 10 -
2.2 THEORETICAL ANALYSIS OF PIEZOELECTRIC TRANSFORMERS - 18 -
2.3 ELECTROSTRICTIVE SIDED-PLATED BAR - 20 -
2.4 ENDED-PLATED PIEZOELECTRIC BAR - 28 -
2.5 LOSSES - 34 -
2.6 EQUIVALENT CIRCUIT OF ROSEN-TYPE PIEZOELECTRIC TRANSFORMER - 38 -
2.7 SIMPLIFIED MECHANICAL CIRCUIT OF ROSEN-TYPE PIEZOELECTRIC TRANSFORMER - 40 -
CHAPTER 3 - 51 -
3.1 STEP-UP RATIO - 52 -
3.2 IMPEDANCE WITH LOADING EFFECT - 59 -
3.2.1 Input Impedance - 59 -
3.2.2 Output Impedance - 62 -
3.3 PHASE ANGLE DIFFERENCE - 65 -
3.3.1 Phase Difference between Input and Output Voltage - 65 -
3.3.2 Phase Difference between Input Voltage and Current - 67 -
3.3.3 Phase Difference between Input Voltage and Current - 70 -
3.3.4 Phase Difference between Output Voltage and Current - 71 -
3.4 POWER EFFICIENCY - 74 -
CHAPTER 4 - 79 -
4.1 HISTORY - 80 -
4.2 GOVERNING EQUATION OF PIEZOELECTRIC TRANSFORMERS - 81 -
4.3 MODAL ACTUATOR AND QUASI-MODE PIEZOELECTRIC TRANSFORMER - 86 -
CHAPTER 5 - 89 -
5.1 THE EQUIVALENT CIRCUIT MEASUREMENT FOR PIEZOELECTRIC TRANSFORMERS - 90 -
5.2 ELECTRICAL CHARACTERISTICS MEASUREMENT OF PIEZOELECTRIC TRANSFORMERS - 94 -
5.3 EXPERIMENTAL RESULTS OF ELECTRICAL CHARACTERISTICS MEASUREMENT - 96 -
5.3.1 Step-up Ratio - 96 -
5.3.2 Power Efficiency - 97 -
5.3.3 Phase difference between input and output voltage - 101 -
5.3.4 Input phase - 102 -
5.3.5 Output phase - 102 -
5.3.6 Input impedance - 104 -
5.3.7 Input voltage and current - 105 -
CHAPTER 6 - 107 -
6.1 OPTIMAL OPERATING POINT - 108 -
6.2 CONTROL STRATEGY OF THE DRIVING MODULE - 109 -
6.2.1 Variable-frequency control - 109 -
6.2.2 Self-resonance control - 111 -
6.2.3 Dual-mode control - 114 -
6.3 DESIGN FLOW OF THE PIEZOELECTRIC TRANSFORMER - 116 -
CHAPTER 7 - 119 -

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