Responsive image
博碩士論文 etd-0808112-141533 詳細資訊
Title page for etd-0808112-141533
論文名稱
Title
一種處理微波電路模型萃取發散性之數值方法
A Numerical Method to Solve the Divergence Issue of Microwave Circuit Model Extraction
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
64
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2012-07-18
繳交日期
Date of Submission
2012-08-08
關鍵字
Keywords
被動性、因果性、特徵值、奇異值、Hilbert轉換
Singular Value, Eigenvalue, Causality, Passivity, Hilbert Transform
統計
Statistics
本論文已被瀏覽 5696 次,被下載 1181
The thesis/dissertation has been browsed 5696 times, has been downloaded 1181 times.
中文摘要
隨著消費性電子的發展為輕薄短小,電路系統結構更加複雜,因此使用數值電磁演算法進行模擬時可能會產生數值誤差,而造成模擬發散或錯誤。數值誤差主因為被動性與因果性而這兩個問題的產生主要來自於數值計算的瑕疵。本論文即針對這些問題進行探討並提出數值補償方法,被動性的原因是因為數值計算的瑕疵,使得部分頻率點功率為負,這會使得系統不具有收斂性,要改善此問題,進一步的將數學式子推導,在Y參數是由特徵值做被動性的判定與執行,而在S參數則是由奇異值而因果性符合的條件必須滿足符合實部虛部的關係式,像是Hilbert transform或是Kramer-Kronig關係式,都可用來做因果性的判定與執行。
經由一些數值方法,利用現有且常用的模擬軟體如:HFSS、ADS所模擬出來的微波波電路模型萃取,其修改奇異值、特徵值,達成降低數值誤差,使其符合收斂性與避免錯誤結果,並且對原始數據的影響降至最低,才不會改變原始模組的特性,亦可解決被動性與因果性的問題發生。
Abstract
With the development of consumer electronics, the circuitry structure become more complex, For this reason, it might cause numerical errors to be cumulated in the simulation using the numerical electromagnetic algorithm, and result in simulated divergence or error. The two reasons of numerical error are passivity and causality, which priginate from the defect in the numerical calculation. In this thesis, for this problem, investigate the numerical compensation method for passivity, The occurrence of passive will make the frequency point of power is negative, this will makes the system divergence, Improve this problem, passivity verification and enforcement by eigenvalue in the Y-parameter, in the S-parameter by the singular value, causality conditions must be match with the imaginary part and the real part relationship, such as the Hilbert transform or the Kramer-Kronig relation, can be used to make causal verification and enforcement.
Through some numerical methods, used simulation software such as: HFSS, ADS simulation of the microwave circuit model extraction, modified singular value, eigenvalue, and reached to reduce the numerical error, let it satisfy the convergence and avoid incorrect results, and minimize the impact of the initial data, does not change the characteristics of the original module, but also to solve the passive and the issue of causality.
目次 Table of Contents
目 錄
論文審定書………………………………………………………….…………………i
致謝……………………………………………………………………………………ii
中文摘要………………………………………………………...……………………iii
Abstract…………………………………………………………..…………………iv
目錄…………………………………………………………………….……..………vi
圖表索引……………………………………………………………..……………viii
第 一 章 緒論…………………………………………………………………… 1
研究目的與方法………………………………………………………………. 1
第 二 章 向量擬合法 ………………………………………………………………5
2.1向量擬合法…………………………………………………………………5
2.1.1 曲線擬合………………………………………………………………5
2.1.2 極點與留數形式………………………………………………………6
2.1.3 向量擬合法理論………………………………………………………7
2.2 等效模型萃取實例…………………………………………………………9
第 三 章 被動性、因果性與穩定性………………………………………………14
3.1模型萃取產生之問題………………………………………………………14
3.1.1被動性………………………………………………………………14
3.1.2 因果性………………………………………………………………16
3.2 數學定義…………………………………………………………………18
3.2.1 被動性之定義………………………………………………………19
3.2.2 因果性之定義………………………………………………………19
3.2.3 穩定性之定義………………………………………………………19
第 四 章 微波電路模型萃取之實例….…………………………………………..23
4.1 被動性……………………………………………………………………23
4.1.1 在Y參數被動性執行使用之數值方法……………………………23
4.1.2 在S參數被動性執行使用之數值方法……………………………36
4.2 因果性……………………………………………………………………42
4.2.1 Hilber Transform與模型萃取實例…………………………………42
4.2.2 Kronig-Kramer Relation……………………………………………45
第 五 章 結論………………………………………………………………………52
參考文獻…………………………………………………………………….…… 53
參考文獻 References
[1] B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by Vector Fitting,” IEEE Trans. On Power Delivery, vol. 14, no.3, pp. 1052-1061, July 1999
[2] B. Gustavsen and C. Heitz,”Modal verctor fitting:A tool for generating rational models of high accuracy with arbitraty terminal conditions,”IEEE Trans. On Advanced Packaging, vol. 31, no.4, November 2008
[3] B. Gustavsen and C. Heitz,”Fast realization of the modal vector fitting method for rational modeling woth accurate repqresentation of small eigenvalues”IEEE On Power Delivery, vol.24, no.3, July 2009
[4]S. Grivet-Talocia,”Passivity enforcement via perturbation of Hamiltonian matrics”IEEE Trans. On circuits and systems, vol.51, no. 9,sep. 2004
[5] B. Gustavsen,”Passivity enforcement of rational models via modal perturbation”IEEE Trans. On On Power Delivery, vol.23, no.2, April 2008
[6]B. Porkar , M. Vakilian, R. Iravani, M. Shahrtash,”Passivity enforcement using an infeasible-interior-point primal-dual method”IEEE On Power Systems,vol. 23,no. 3,August 2008
[7] B. Gustavsen,”Fast passivity enforcement for pole-residue models by perturbation of residue matrix eigenvalues”IEEE trans. On power delivery, vol.23, no.4 october 2008
[8] B. Gustavsen,”Fast passivity enforcement for S-parameter models by perturbation of residue matrix eigenvalue”IEEE Trans. On advanced packaging, vol. 33,no. 1,Feburary 2010
[9]B. Porkar, M. Vakilian, S. M. Shahrtash,”An adaptive sampling technique to correct large passivity violations”IEEE Power engineering conference, Dec. 2008
[10]J. H. Ryu, Y. S. Kim and B. Hannaford,”Sampled- and continuous-time passivity and stability of virtual environments”IEEE Trans. On robotics, no.4, August 2004
[11]T. D’haene and R. Pintelon,”Passivity enforcement of transfer functions”IEEE Trans. On instrumentation and measurement, vol.57, no.10 ,October 2008
[12]A. Charest, M. Nakhla and R. Achar,”Scattering domain passivity verification and enforcement of delayed rational functions”IEEE microwavw and wireless, vol. 19,no. 10, October 2009
[13]D. Saraswat, R. Achar and M. S. Nakhla,”Fast Passivity verification and enforcement via reciprocal systems for interconnects with large order macromodels” IEEE Trans. On very large scale intergration systems, vol.15, no.1, January 2007
[14]D. Saraswat, R. Achar and M. S. Nakhla,”Global passivity enforcement algorithm for macromodels of interconnect subnetworks characterized by tabulated data”IEEE trans. On very large scale intergration system, vol. 13, no.7, July 2005
[15]A. Charest, M. Nakhla, R. Achar and D Saraswat,”Passivity verification of delayed rational function based macromodels of tabulated networks characterized by scattering parameters”IEEE Trans. On components, packaging, and manufacturing technology, vol. 1,no. 3, March 2011
[16]S. Gao,Y. S. Li and M. S. Zhang,”An efficient algebraic method for the passivity enforcement of macromodels”IEEE Trans. On microwave theory and techniques, vol. 58, no.7, July 2010
[17] B. Gustavsen, A. Semlyen,”Fast passivity assessment for S-parameter rational models via a half-size test matrixIEEE Trans. On microwave theory and techniques, vol. 56, no.12, December 2008
[18]P. Triverio, G. T. Stefano, M. S. Nakhla, F. G. Canavero and R. Achar,”Stability, causality, and passivity in electrical interconnect models”IEEE Trans. On advanced packaging, vol.30, no.4, November 2007
[19]P. perry, T. J. Brazil,”Hilbert-transform-derived relative group delay”IEEE Trans. On microwave theory and techniques, vol.45 no.8, August 1997
[20]P. Triverio, S. Grivet-Talocia,”A robust causality verification tool for tabulated frequency data”IEEE Signal propagation on interconnects, May 2006
電子全文 Fulltext
本電子全文僅授權使用者為學術研究之目的,進行個人非營利性質之檢索、閱讀、列印。請遵守中華民國著作權法之相關規定,切勿任意重製、散佈、改作、轉貼、播送,以免觸法。
論文使用權限 Thesis access permission:自定論文開放時間 user define
開放時間 Available:
校內 Campus: 已公開 available
校外 Off-campus: 已公開 available


紙本論文 Printed copies
紙本論文的公開資訊在102學年度以後相對較為完整。如果需要查詢101學年度以前的紙本論文公開資訊,請聯繫圖資處紙本論文服務櫃台。如有不便之處敬請見諒。
開放時間 available 已公開 available

QR Code