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研究生:梁慧鐘
研究生(外文):Leong, Hui-Zhong
論文名稱:用於線焊積體電路的電源墊放置演算法
論文名稱(外文):On Power Supply Pads Planning for Wire-bonded IC
指導教授:陳宏明陳宏明引用關係
指導教授(外文):Chen, Hung-Ming
口試委員:李育民陳宏明林昌賜
口試委員(外文):Lee, Yu-MinChen, Hung-MingLin, Chang-Tzu
口試日期:2018-10-02
學位類別:碩士
校院名稱:國立交通大學
系所名稱:電子研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2018
畢業學年度:107
語文別:英文
論文頁數:32
中文關鍵詞:電源墊電壓降電源供應網絡
外文關鍵詞:IO padIR droppower delivery network
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在引線鍵合技術中,輸入及輸出焊盤位於積體電路的外圍,因此電源焊盤的放置受限於可用的輸入焊盤。電源焊盤通過電源供應網絡供電,因此電源焊盤的不足可能導致積體電路故障。為了克服這個問題,我們提出了一種用於引線鍵合技術的電源焊盤放置演算法。實驗結果證明,我們所提出的演算法能夠有效地決定電源焊盤數和電源焊盤的位置。此外,積體電路的最差電壓降保證少於電源電壓的3%。
In wire-bonding technology, Input/Output (I/O) pads are located along the peripheral of integrated circuit (IC) and power pad placement is limited by available I/O pad candidates. Power pads supply voltage to the IC through power delivery network (PDN), hence insufficient power pads may cause IC failure. To overcome this problem, we proposed a power pad placement algorithm for wire-bonding technology. Experimental results show that the proposed algorithm determines both power pad counts and power pad locations effectively for a given power delivery network. In addition, the worst voltage drop for the IC is guaranteed to be less than 3% of the supply voltage.
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Our Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Formulation of Effective Resistance . . . . . . . . . . . . . . . . . . . . . . 6
2.2 IR Drop Analysis Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Fast Placement Optimization Method [1] . . . . . . . . . . . . . . . . . . . 8
2.4 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Chapter 3 Methodologies and Algorithm . . . . . . . . . . . . . . . . . . 11
3.1 Definition of Effective Region . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Formulation of Cost Function . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Our Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 18
4.1 Information of Four Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 Experimental Results of Four Cases . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Validate Results Using VOLTUS . . . . . . . . . . . . . . . . . . . . . . . 22
4.3.1 IR drop distribution of Case 1 . . . . . . . . . . . . . . . . . . . . . 24
4.3.2 IR drop distribution of Case 2 . . . . . . . . . . . . . . . . . . . . . 25
4.3.3 IR drop distribution of Case 3 . . . . . . . . . . . . . . . . . . . . . 26
4.3.4 IR drop distribution of Case 4 . . . . . . . . . . . . . . . . . . . . . 27
4.4 Comparison of IR Drop Distribution between VOLTUS and Voltage Drop
Analysis Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Chapter 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 6 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
[1] Y. Zhong and M. D. F. Wong, “Fast placement optimization of power supply pads,”
in Asia and South Pacific Design Automation Conference, pp. 763–767, Jan 2007.
[2] R. Gonzalez, B. M. Gordon, and M. A. Horowitz, “Supply and threshold voltage
scaling for low power cmos,” IEEE Journal of Solid-State Circuits, vol. 32, pp. 1210–
1216, Aug 1997.
[3] X. . S. Tan and C. . R. Shi, “Fast power/ground network optimization based on equivalent
circuit modeling,” in Proceedings of the 38th Design Automation Conference,
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[4] C. Huang, C. Lin, W. Liao, C. Lee, H. Chen, C. Lee, and D. Kwai, “Improving power
delivery network design by practical methodologies,” in IEEE 32nd International
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[5] X. Wu, X. Hon, Y. Ca, C. K. Cheng, J. Gu, and W. Dai, “Area minimization of
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[7] P. Du, S.-H. Weng, X. Hu, and C. Cheng, “Power grid sizing via convex programming,”
in 9th IEEE International Conference on ASIC, pp. 337–340, Oct 2011.
[8] T. Hayashi, M. Fukui, and S. Tsukiyama, “A new power grid optimization algorithm
based on manufacturing cost restriction,” in European Conference on Circuit Theory
and Design, pp. 703–706, Aug 2009.
[9] M. Fukui, H. Miki, M. Yoshikawa, and S. Tsukiyama, “A power grid optimization
algorithm considering via reliability,” in 20th European Conference on Circuit Theory
and Design, pp. 809–812, Aug 2011.
[10] J. Singh and S. S. Sapatnekar, “Partition-based algorithm for power grid design using
locality,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems, vol. 25, pp. 664–677, April 2006.
[11] M. Zhao, Y. Fu, V. Zolotov, S. Sundareswaran, and R. Panda, “Optimal placement
of power-supply pads and pins,” IEEE Transactions on Computer-Aided Design of
Integrated Circuits and Systems, vol. 25, pp. 144–154, Jan 2006.
[12] T. Sato, H. Onodera, and M. Hashimoto, “Successive pad assignment algorithm to
optimize number and location of power supply pad using incremental matrix inversion,”
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[13] K. Wang, B. H. Meyer, R. Zhang, K. Skadron, and M. Stan, “Walking pads: Fast
power-supply pad-placement optimization,” in 19th Asia and South Pacific Design
Automation Conference, pp. 537–543, Jan 2014.
[14] T. Yu and M. D. F. Wong, “A novel and efficient method for power pad placement
optimization,” in International Symposium on Quality Electronic Design, pp. 158–
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[15] S. Köse and E. G. Friedman, “Fast algorithms for ir voltage drop analysis exploiting
locality,” in 48th ACM/EDAC/IEEE Design Automation Conference, pp. 996–1001,
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[16] “Cadence Voltus IC Power Integrity Solution.” https://www.cadence.com/tw/
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