指導教授：江簡富臺灣大學：電信工程學研究所羅育聰Lo, Yu-TsungYu-TsungLo2014-11-302018-07-052014-11-302018-07-052014http://ntur.lib.ntu.edu.tw//handle/246246/264324在本篇論文中，我們提出了一個改良式的Y 參數模型去模擬耦和震盪器陣列的行為。當把震盪頻率的隨機性納入考量時，我們所提出的行為模型可以應用在蒙地卡羅模擬中去分析大型的震盪器陣列。為了分析在不同的耦合強度下耦合震盪器的行為，我們提出了一個可調式耦合網路，能夠確保震盪器在不同的耦合強度下都能夠震盪。震盪器及耦合網路的設計是基於台積電0.18微米製程，Y參數在10GHz附近出萃取以用在之後的數值模擬。描述耦合震盪器陣列的方程式可以用四階的隆格-庫塔法求解。本模型可以得到比傳統Y參數模型更加的準確度並且比用全電路模擬節省時間。本模型可以用在找出耦合震盪器陣列所能達到的最大震盪器個數。我們發現強耦合可以容許約11個震盪器的同步。此外，因為我們提出是一個時域的模型，可以讓我們易於判定穩定性並且可以得到在鎖定過程中頻率對時間的響應。於相位陣列系統時，藉由調整陣列前後兩端震盪器的自震頻率，可調整震盪器間的相位差。我們分析出可以藉由注入相位的方式，使不同的震盪器陣列同步，進而產生一個更大的耦合震盪器陣列。In this thesis, a modified Y-parameters approach is proposed to model the behavior of coupled oscillator arrays (COA’s). A better behavior model enables us to investigate a large oscillator array with random free-running frequency distribution by using Monte-Carlo simulation. A coupling network with tunable coupling strength is proposed, so the phenomena of a COA under different coupling strengths can be observed. The parameters of oscillators and the coupling network are obtained based on the TSMC 0.18 μm process, and their Y parameters are extracted around 10 GHz for numerical solution. The governing equation of the proposed Y parameters approach is solved by using fourth-order Runge-Kutta method. The results are verified with full-circuit simulations and compared to other behavior models, including the Adler’s equation and the conventional Y-parameters approach. Our approach provides better accuracy than other behavior models as well as saves much simulation time comparing to full-circuit simulation. Our proposed method is applied to estimate the maximum allowable number of oscillators that can be synchronized. We discover that stronger couple leads to a larger allowable size up to 11. Since our approach is a time domain model,it provides easy check of stability as well as enable us to observe the frequency transition of the COA during the synchronization process. The inter-element phase shift of a COA is controlled by tuning the free-running frequencies of oscillators at both ends. We propose a phase injection scheme to synchronize multiple COA’s by injection and control the signal with variable phase to the center oscillator of each COA. Hence, the effective maximum number of oscillators can be significantly increased.1 Introduction 1 1.1 Oscillator Arrays for Beam-Steering . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Motivation and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Behavior Models of COA’s 7 2.1 Y-Parameters Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Adler’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Modified Y-Parameters Approach . . . . . . . . . . . . . . . . . . . . . . . . 11 3 Design and Modeling of Coupling Network and VCO 14 3.1 The Coupling Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Voltage-Controlled Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4 Verification of Modified Y -Parameters Approach 27 4.1 Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.2 Analytic Solution to the Simplified Model . . . . . . . . . . . . . . . . . . . 31 5 Synchronization of Multiple COA’s 34 5.1 Randomness of Free-Running Frequencies . . . . . . . . . . . . . . . . . . . . 36 5.2 Synchronization by Phase Injection . . . . . . . . . . . . . . . . . . . . . . . 39 6 Conclusion 43 Bibliography 47 Publicatio list of Yu-Tsung Lo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553211331 bytesapplication/pdf論文公開時間：2016/07/22論文使用權限：同意有償授權(權利金給回饋學校)震盪器陣列相位陣列耦合蒙地卡羅分析thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264324/1/ntu-103-D98942006-1.pdf