時域有限差分法 ( Finite-Difference Time-Domain, FDTD )為一套非常有效的全波分析電磁現象的數值方法，由於它的適應性，所以可以解決在各種不同介質中的電磁散射問題，如微波電路、生物組織電磁吸收的問題。

但是使用FDTD法在微波積體電路時，往往需要冗長的計算時間，若所要模擬的結構很複雜，而且又想要得到正確的頻率響應時，則模擬的時間將會過長而顯得效率不彰。因此，在本論文中，吾人介紹一種類神經網路的方法「有限脈衝響應類神經網路」可以增加FDTD法的計算速度，當FDTD模擬一足夠的時間步階時便停止計算，使用FIRNN來預測之後時間步階的訊號，因此可以改善FDTD的模擬效率。

The Finite-Difference Time-Domain Method (FDTD) is a very powerful numerical method for the full wave analysis electromagnetic phenomena. Due to its flexibility, it can be used to solve numerous electromagnetic scattering problems on microwave circuits, dielectrics, and electromagnetic absorption in biological tissue at microwave frequencies.

However, it needs so much computation time to simulate microwave integral circuits by applying the FDTD method. If the structure we simulated is complicated and we want to obtain accurate frequency domain scattering parameters, the simulation time will be so much longer that the efficiency of simulation will be bad as well. Therefore, in the thesis, we introduce an artificial neural networks (ANN) method called “Finite Impulse Response Neural Networks (FIRNN)” can speed up the FDTD simulation time. In order to boost the efficiency of the FDTD simulation time by stopping the simulation after a sufficient number of time steps and using FIRNN as a predictor to predict time series signal.

第一章序論……………………………………………………………………………1
1.1 概序………………………………………………………………………….1
1.2 論文大綱…………………………………………………………………….2
第二章 類神經網路(Artificial Neural Network ,ANN)……………………………...3
2.1生物神經系統簡介…………………………………………………………..3
2.1.1神經細胞(neuron)…………………………………………………………..4
2.1.2神經細胞系統的工作機制………………………………………………...4
2.2 類神經網路由來…………………………………………………………….5
2.3類神經元 (Artificial Neuron)………………………………………………..6
2.4 類神經網路………………………………………………………………….9
2.5類神經網路應用……………………………………………………………12
2.6類神經網路優缺點…………………………………………………………12
2.7類神經網路的學習訓練(training)………………………………………….13
第三章 有限脈衝響應類神經網路Finite Impulse Response FIR Neural Network
……………………………………………………………………………..20
3.1 動態的類神經元…………………………………………………………...20
3.2有限脈衝響應的模型Finite-duration Impulse Response FIR model ……..21
3.3 有限脈衝響應類神經網路FIR Neural Network …………………………23
3.4 時間回傳學習Temporal Back-Propagation Learning……………………..23
第四章 時域上的預測………………………………………………………………30
4.1 時間序列預測的目的……………………………………………………...30
4.2要如何實現函數g呢?...................................................................................30
4.3 重要參數的設定……………………………………………………...……33
4.3.1學習率 (learning rate) η..............................................................................34
4.3.2機率演算法……………………………………………………………….37
4.3.3 慣性項(momentum)α…………………………………………………….38
4.3.4隱藏層層數……………………………………………………………….40
4.3.5隱藏層神經元的個數與FIR filter的長度……………………………….41
4.3.6 間隔取樣…………………………………………………………………43
4.3.7 學習訓練的終止…………………………………………………………46
第五章 有限脈衝響應類神經網路與時域有限差分法的結合……………………48
5.1封裝蕭基二極體……………………………………………………………48
5.2 邊耦帶通濾波器(edge coupled bandpass filter)…………………………...50
5.3 表面聲波濾波器(Surface Acoustic Wave, SAW filter)…………………...54
5.4 接收模組的模擬…………………………………………………………...58
第六章 結論………………..………………………………………………………..66
附錄A 三次仿樣曲線(cubic spline)..……………………………………………….67
附錄B 片段三次Hermite內插法(Piecewise Cubic Hermite Interpolation, PCHI)...73

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