應用於計算任意形狀電源分佈系統轉換阻抗之快速演算法

A Fast Algorithm to Calculate the Transfer Impedance of Arbitrarily Shaped Power Distribution Network

洪國強(Kuo-Chiang Hung 洪國強)

指導教授 ： 林丁丙

國立臺北科技大學/電資學院/電腦與通訊研究所/博士(2010年)

摘要

在本篇論文中，我們運用矩形與等腰三角形架構之二維格林函數，推導雙層電源通道架構之雙重疊加模態展開式。然而，雙重疊加模態展開式需要大量的計算時間，因此，利用傅利葉級數公式，我們提出新的單重疊加模態展開式，可降低計算時間。另外，運用分離變數法結合多個矩形與等腰三角形架構，可獲得任意形狀電源通道架構之阻抗矩陣，以便能夠更加準確地計算電源通道架構之模態影響。最後，配合模擬軟體PowerSI模擬任意形狀電源通道之電流分佈，可正確地分析去耦合電容位置，本論文提出之方法與量測結果比較，利用少數去耦合電容，抑制任意形狀電源通道架構之共振模態影響。

關鍵字

功率完整性 ； 模態展開式 ； 快速演算法 ； 分離變數法 ； 傅立葉級數 ； 肌膚效應 ； 去耦合電容

並列摘要

This dissertation is based on the Green’s function of the 2-D Helmholtz equation to derive the double infinite series summation impedance matrix of rectangular/isosceles triangular power bus. However, a double infinite series summation usually requires long computation time. In order to reduce the calculation time, the double infinite series summation has been reduced to the single finite series summation by using Fourier series summation formulas. Moreover, the segmentation method is very accurate to calculate the impedance matrix of an arbitrarily power-bus by combination of two or more rectangular/isosceles triangular power-buses. Furthermore, to find the optimal positions of decoupling capacitors, the voltage distribution of an arbitrarily power-bus can be simulated by a simulator PowerSI. Finally, the agreement between the measured results and simulated results of the transfer impedance of an arbitrarily power-bus structure can illustrate the applicability to suppress the resonant modes by few decoupling capacitors.

並列關鍵字

Power integrity ； modal expansion ； fast algorithm ； segmentation method ； fourier summation formula ； skin effect ； decoupling capacitor

參考文獻

[1] O. M. Ramahi, V. Subramanian, and B. Archambeault, “A simple finite-difference frequency-domain (FDFD) algorithm for analysis of switching noise in printed circuit boards and packages,” IEEE Trans. Adv. Packag., vol. 2, no. 2, pp. 191 – 198, May 2003.

[2] Y. Xiaoning, M. Y. Koledintseva, L. Min, and J. L. Drewniak, “DC power-bus design using FDTD modeling with dispersive media and surface mount technology components,” IEEE Trans. Electromagn. Compat., vol. 43, no. 4, pp. 579 – 587, Nov. 2001.

[3] Y. Xiaoning, D. A. Hockanson, L. Min, R. Yong, C. Wei, J. L. Drewniak, and R. E. DuBroff, “EMI mitigation with multilayer power-bus stacks and via stitching of reference planes,” IEEE Trans. Electromagn. Compat., vol. 43, no. 4, pp. 538 – 548, Nov. 2001.

[4] E. X. Liu, X. Wei, Z. Z. Oo, and E. P. Li, “An efficient method for power integrity and EMI analysis of advanced packages,” in Proc. Elec. Comp. Technol. Conf., FL, USA, May 2008, pp. 652 – 657.

[5] G. Steinmair, and R. Weigel, “Analysis of power distribution systems on PCB level via reduced PEEC-modeling,” in Proc. Int. Microw., Radar, Wireless Commun. Conf., vol. 1, Warszawa, Poland, May 2004, pp. 283 – 286.