FDTD演算法的缺點為模擬時間較長，及較難對複雜電路結構進行模擬。主要的改善模擬的效率有放大時間步階、增加網格切割大小及預測後段的時間序列。我們使用Prony’s Method對於FDTD運算出的時域資料作預測，以減少FDTD演算法的運算時間。

而Prony’s Method運算所花費的時間相當少，且對於資料波形為週期性振盪的預測結果特別良好。所以將針對Prony’s Method的訓練起始點及訓練區間寬度的選擇建立一套規則，應用於輸出波形為週期性振盪的電路結構，減少其FDTD運算時間，而達到實用性的目的。

The disadvantage of FDTD method is that it needs a long simulation time, and it is difficult to simulate a complex circuit. The methods to improve the efficiency in FDTD simulation are increase in width of time step, enlargement in space grid and extrapolation of late time records. In this paper, we predict the late time record in FDTD simulation by applying Prony’s method, and save the computation time of FDTD simulation.

The cost of computation time of Prony’s method is low, and it has a good result that applying Prony’s method at predicting a waveform which resonates with period. In this paper, we try to make a rule for finding training start point and width of training period in Prony’s method. The result of prediction with a short period of time records under the rule is accurate and reliable

目錄....…………………………………………………………………………….....iii
圖表目錄……………………………………………………………………………...iv
第一章 序論…………………………………………………………………………1
1-1 概述…………………………………………………………………………1
1-2 論文大綱……………………………………………………………………2
第二章 FDTD演算法……………………………………………………………….3
2-1 FDTD公式………………………………………………………………….3
2-2 Courant穩定準則…………………. ……………………………………….4
2-3 吸收邊界條件……………………. …………………………………….….4
2-3-1 Mur一階吸收邊界………………………………………………….5
2-3-2 Anisotropic PML吸收邊界…………………….…………………..6
2-4 集總元件模擬………………………………………………………….8
2-4-1 電阻……………………….…………………….…………………10
2-4-2 電容……………………….…………………….…………………10
2-4-3 電感……………………….…………………….…………………11
2-4-4 阻抗性電壓源……….….…………………….…………………11
第三章 Prony演算法…………………………………………...………………….13
3-1 Prony’s Method介紹………………………..……………………………13
3-2 應用Prony’s Method於波形預測………….………………………….14
3-3 Bairstow’s Method………………………..……………………………17
3-4 波形預測的模擬驗証………………………..……………………………22
3-4-1 訓練區間起始點的影響……………………….………………….22
3-4-2 訓練區間寬度的影響……………………….…………………….24
3-4-3 其它函數的測試……………………….………………………….27
第四章 Prony’s Method和FDTD的結合……………………………………..31
4-1 波形預測自動化……………………….……..………………………….31
4-2 Case 1 微帶線帶通濾波器1……………………….……..………………39
4-3 Case 2 標準型表面聲波共振濾波器….…………………….……..….…42
4-4 Case 3 微帶線帶通濾波器2……………………….……..………………51
第五章 結論………………………………………………………………………..56
附錄A：三次仿樣曲線(cubic spline) ………………………….……………………57
參考文獻……………………………………………………………………………..63

[1] K. S. Yee, “Numerical solution of initial boundary value problems involving
Maxwell’s equation in isotropic media”, IEEE Trans. Antennas Propagat., vol.14,
No.3, pp.300-307, May 1966.
[2] J. K. Wolf, “Decoding of Bose-Chaudhuri-Hocquenghem codes and Prony's
method for curve fitting”, IEEE Transactions on Information Theory, vol. 13,
Issue 4, pp.608-608, Oct 1967.
[3] A. Taflove, Computational Electrodynamics The Finite-Difference Time-Domain
Method, Boston, MA: Artech House, 1995.
[4] G. Mur, “Absorbing boundary conditions for the finie-difference approximation
of the time-domain electromagnetic field equations”, IEEE Trans.
Electromagnetic compatibility, vol. EMC-23, pp.377-382, Nov. 1981.
[5] Z. Bi, K. Wu, C. Wu, and j. Litva, “A dispersive boundary condition for
microstrip component analysis using the FD-TD method”, IEEE trans. Antennas
and propagate., vol. MTT-40, no. 4, pp. 774-777, Apr. 1992.
[6] O. M. Ramahi, “Complementary operators: A method to annihilate artificial
reflections arising from the truncation of the computational domain in the
solution of patial differential equations,” IEEE Trans. Antennas and Propagat.,
vol. 43, pp. 697-704, Jul. 1995.
[7] J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic
waves,” J. Computat. Phys., vol. 114, pp. 185-200, 1994.
[8] Z. S. Sacks, D.M. Kingsland, R. Lee, and J. F. Lee, “A perfectly matched
anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans.
Antennas and Propagat., vol. 43, pp. 1460 –1463, Dec. 1995.
[9] S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the
truncation of FDTD lattices,” IEEE Trans. Antennas and Propagat., vol. 44, pp.
1630 -1639, Dec. 1996.
[10] W. Sui , D. A. Christensen , and Carl H. Durney , “Extending the
Two-Dimensional FDTD Method to Hybrid Electromagnetic System with Active
and Passive Lumped Elements ,” IEEE Transactions on Microwave Theory
Tech. , vol. 40 , No. 4 , April 1992 .
[11] M. P. May , A. Taflove , and J. Baron , “FD-TD Modeling of Digital Signal
Propagation in 3-D Circuits with Passive and Active Loads ,” IEEE Transactions
on Microwave Theory and Techniques , vol. 42 , No. 8 , August 1994 .
[12] B. Toland, B.Houshmand, and T. Itoh, “Modeling of nonlinear active regions
with the FDTD method,” accepted for publication in IEEE Microwave and
Guided Wave Letters., Vol. 3, Issue 9, pp. 333-335, Sept. 1993.
64
[13] D. B. Choate, J. B. Y. Tsui, “Note on Prony’s Method”, IEE Proceedings-F,
vol.140, No. 2, April 1993.
[14] 施澄鐘, “數值分析”, 松崗電腦圖晝資料股份有限公司, 1993.
[15] W. L. Ko, R. Mittra, “A Combination of FD-TD and Prony’s methods for
Analysis Microwave Integrated Circuits”, IEEE Transactions on Microwave
Theory and Techniques , vol. 39, No. 12, pp. 2176-2181, Dec. 1991.
[16] T. Shibata, T. Hayashi, and T. Kimura, “Analysis of Microstrip Circuits Using
Three-Dimensional Full-Wave Electromagnetic Field Analysis in the Time
domain”, IEEE Transactions on Microwave Theory and Techniques, vol. 36,
No.6, June 1988.
[17] K. Lan, S. K. Chaudhuri, S. Safavi-Naeini, “Application of C-COM for
Microwave Integrated-Circuit Modeling”, IEEE Transactions on Microwave
Theory and Techniques , vol. 51, No. 4, pp. 1289-1295, Apr. 2003.
[18] K. Y. Lin, K. H. Lin, “A Study of Crosstalk Effects on the Packaged SAW by the
FDTD Method”, IEEE Transactions on Ultrasonics, Ferroelectrics, and
Frequency Control, vol. 52, No. 3, pp. 445-454, Mar. 2005.
[19] T. P. Budka, E. M. Tentzeris, S. D. Waclawik, N. I. Dib, L. P. B. Katehi, G. M.
Rebeiz, “An experimental and theoretical comparison of the electric fields above
a coupled line bandpass filter”, Microwave Symposium Digest, 1995., IEEE
MTT-S International, vol. 3, pp. 1487-1490, May 1995.