隨著半導體技術的不斷進步，時脈頻率的增加以及電路板上的元件變得越來越複雜。為了使系統正常工作，對電壓噪聲的要求變得更加嚴格，使得配電網絡（PDN）的設計更加複雜和具有挑戰性。
在本文中，我們詳細描述了PDN在設計過程中會遇到的電源完整性問題，並從物理角度進行分析，提出了一種基於物理的高效設計方法來減輕電源完整性問題的影響。實驗結果表明，與基於機器學習的方法相比，我們的方法可以顯著降低所需的時間複雜度，並且保持相同的解決方案。

With the continuous advancement of semiconductor technology, the increase in clock frequency and components on circuit boards become more and more complex. For the system to work correctly, the requirements for voltage noise become more stringent, making the power distribution network's (PDN's) design more complex and challenging. In this thesis, we describe the power integrity issues that PDN will encounter during the design process and analyze them from a physical perspective, and we propose an efficient physics-based design method to alleviate the impact of the power integrity issues. The results show that compared to ML-based methods, our method can significantly reduce the required time complexity while maintaining the same solution.

[1] Huabo Chen, Jiayuan Fang, and Weimin Shi. Effective decoupling radius of decoupling capacitor. In IEEE 10th Topical Meeting on Electrical Perfor- mance of Electronic Packaging (Cat. No. 01TH8565), pages 277–280. IEEE, 2001.

[2] Jonghyun Cho, Siqi Bai, Biyao Zhao, Albert Ruehli, James Drewniak, Matteo Cocchini, Samuel Connor, Michael A Cracraft, and Dale Becker. Modeling and analysis of package pdn for computing system based on cavity model. In 2017 IEEE International Symposium on Electromagnetic Compatibility & Signal/Power Integrity (EMCSI), pages 213–218. IEEE, 2017.

[3] Surendra Hemaram and Jai Narayan Tripathi. Optimal design of a decoupling network using variants of particle swarm optimization algorithm. In 2021 IEEE International Symposium on Circuits and Systems (ISCAS), pages 1–5. IEEE, 2021.

[4] Douglas Samuel Jones. The theory of electromagnetism. Elsevier, 2013.

[5] Jack Juang, Ling Zhang, Zurab Kiguradze, Bo Pu, Shuai Jin, and Chulsoon Hwang. A modified genetic algorithm for the selection of decoupling capacitors in pdn design. In 2021 IEEE International Joint EMC/SI/PI and EMC Europe Symposium, pages 712–717. IEEE, 2021.

[6] Cheng-Hsueh Lu, Ling-Yu Tseng, Shih-Chieh Chang, and Shih-Hsien Wu. Pippon: Improve impedance prediction of power distribution network using pole proposal network. In 2023 IEEE Symposium on Electromagnetic Com- patibility Signal/Power Integrity (EMC+SIPI), pages 705–711, 2023.

[7] Hyunwook Park, Junyong Park, Subin Kim, Daehwan Lho, Shinyoung Park, Gapyeol Park, Kyungjun Cho, and Joungho Kim. Reinforcement learning- based optimal on-board decoupling capacitor design method. In 2018 IEEE 27th Conference on Electrical Performance of Electronic Packaging and Sys- tems (EPEPS), pages 213–215. IEEE, 2018.

[8] Clayton R Paul. Inductance: loop and partial. John Wiley & Sons, 2011.

[9] Madhavan Swaminathan and Ege Engin. Power integrity modeling and design
for semiconductors and systems. Pearson Education, 2007.

[10] Ling Zhang, Jack Juang, Zurab Kiguradze, Bo Pu, Shuai Jin, Songping Wu, Zhiping Yang, and Chulsoon Hwang. Fast pdn impedance prediction using deep learning. arXiv preprint arXiv:2106.10693, 2021.

[11] Ling Zhang, Jack Juang, Zurab Kiguradze, Bo Pu, Shuai Jin, Songping Wu, Zhiping Yang, Er-Ping Li, Jun Fan, and Chulsoon Hwang. Efficient dc and ac impedance calculation for arbitrary-shape and multilayer pdn using boundary integration. IEEE Transactions on Signal and Power Integrity, 1:1–11, 2022.