十九世紀以來，線性理論支配著科學領域的發展，然而以現代科學的觀點來看，它只是非線性理論的一個特例。非線性理論發展過程中最具研究價值的部份可說是混沌的探討，因此近年來各個研究領域均對其感到興趣。這當中包括了物理、化學、社會學、經濟學、生態學及工程等，其中在工程方面又以電子電路上的研究最為科學家所廣泛探討。然而從已發表的文獻中觀察到，所探討的電子電路大部份為非實用電路，因此本論文特別以通信系統中的重要裝置─振盪電路之考畢子振盪器為對象研究其非線性混沌現象。
振盪器在使用上經常會發生頻率偏移及產生多個振盪頻率的現象而影響通信品質，對於這個問題，一般總是歸究於雜訊或是干擾所造成，本論文嘗試以不同角度探討發生的原因；在做法上，從應用Lur’e系統建構法快速尋獲電路引起混沌現象之主要參數，再藉由自律型與非自律型考畢子振盪電路模擬及實際電路研製驗證其可行性。
　　本論文主要貢獻有：（一）應用Lur’e系統建構法於考畢子振盪器尋找引起混沌參數之可行性；（二）驗證考畢子振盪器參數值變動所造成非線性混沌現象變化的範圍，提供工程師未來設計相關電路之參考依據；（三）應用Matlab軟體自行開發驗證電路中非線性混沌現象之程式；（四）完成自律型28MHz高頻(HF)頻段、0.3GHz微波(Microwave)頻段與非自律型28MHz高頻(HF)頻段混沌式考畢子振盪器硬體實作與量測，對未來製作更高層次的混沌電路具有實值的經驗與幫助。

　　The development of the science has been dominated by the linear theory from the nineteenth century. However, from the advanced science point of view, the linear theory is a special case of the nonlinear theory. Chaos is a part of the nonlinear theory with the most use in research. Therefore, in recent years many researches of different territories have involved in the chaos, such as physics, chemistry, sociology, economics and engineering etc. Among them, the chaotic phenomena in electric circuits of engineering have been extensively discussed. However, in these published paper electric circuits discussed which generate chaotic phenomena are almost unpractical circuits. As a result, a practical circuit, the oscillator widely used in communication system, is discussed here.
The frequency shift and multiple oscillation frequencies generated in the oscillator are often occurred. Concerning this problem, it results from noise or perturbation. In this dissertation, we try to discuss reasons from the different point of view. At first, the dominated components which cause chaotic phenomenon can be determined by modeling the oscillator as a combination of linear and nonlinear subsystem (called Lur’s system), then Simulations and experiment results of autonomous and nonautonomous oscillator verify this developed criteria of prediction of chaos.
The main contribution in this dissertation are: (1) the dominated components which cause chaotic phenomenon in Colpitts oscillator can be determined by modeling it as a Lur’s system (2) Though this study, it provide a reference which can assist engineers in design more qualified oscillator; (3) Applied Matlab to develop a chaotic verification program (4)Via an experience implementation of autonomous (28MHz, HF; 0.3GHz, Microwave) and nonautonomous chaotic Colpitts oscillator; We have leaned how to design high level chaotic circuits.
It is believed our approach can help those people who desire to understand the chaotic phenomena in oscillator.

　　　　　　　　　　　　　　目　錄
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　頁次
中文摘要………………………………………………………………………i
英文摘要………………………………………………………………………iii
誌謝……………………………………………………………………………v
目錄……………………………………………………………………………vii
表目錄…………………………………………………………………………x
圖目錄…………………………………………………………………………xi
第一章 緒論……………………………………………………………………1
1.1 研究背景…………………………………………………………1
　　　 1.1.1 振盪器概述………………………………………………1
　　　 1.1.2 非線性混沌現象概述……………………………………4
　　　 1.2 研究動機…………………………………………………………6
　　　　　 1.2.1 問題描述…………………………………………………6
　　　　　 1.2.2 解決方案…………………………………………………7
　　　 1.3 論文架構…………………………………………………………9
第二章 非線性混沌現象之探討……………………………………………10
　　 　2.1 混沌理論的發展過程……………………………………………10
　　　 2.2 混沌的特性………………………………………………………12
　　　 2.3 預測混沌產生的方法……………………………………………17
2.3.1 諧波平衡法………………………………………………17
　　　　　 2.3.2 Lur’e系統建構法………………………………………19
　　　 2.4 驗證混沌的方法…………………………………………………23
　　　　　 2.4.1 定量法則…………………………………………………23
　　　　　 2.4.2 定性法則…………………………………………………26
　　　 2.6 混沌的應用………………………………………………………32
第三章 考畢子振盪器之非線性混沌現象分析……………………………34
　　　 3.1 自律型考畢子振盪器……………………………………………34
　　　 　　3.1.1 高頻(HF)頻段……………………………………………34
　　　　　 3.1.2 微波(Microwave)頻段……………………………………41
　　　3.2 非自律型考畢子振盪器…………………………………………46
第四章 模擬結果與分析……………………………………………………49
　　　 4.1 自律型高頻頻段考畢子振盪器之模擬結果與分析……………49
　　　 4.2 自律型微波頻段考畢子振盪器之模擬結果與分析……………59
　　　 4.3 非自律型考畢子振盪器之模擬結果與分析……………………63
第五章 實體電路驗證………………………………………………………75
　　　 5.1 自律型考畢子振盪器之實驗與比較……………………………75
　　　 5.2 非自律型考畢子振盪器之實驗與比較…………………………99
第六章 討論與結語…………………………………………………………114
6.1 討論……………………………………………………………114
6.2 結語……………………………………………………………115
參考文獻……………………………………………………………………118
附錄A 自律型高頻頻段考畢子振盪器之Lur’e系統型式推導…………123
附錄B 自律型微波頻段考畢子振盪器之Lur’e系統型式推導…………126

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