雖然對具有不規則板形和多層堆疊的印刷電路板（PCB）進行電源分布網路（PDN）的建模與阻抗曲線模擬是一項艱鉅的任務，但這仍是電源分布網路（PDN）設計和性能評估的關鍵過程。在特定頻率範圍內，PCB板的阻抗曲線需要滿足目標阻抗的要求。本文提出了一種新的深度學習方法PIPPON來預測PDN阻抗，該方法包含了一個專門處理阻抗曲線極點範圍的候選網絡(proposal network)。實驗結果顯示，PIPPON不僅比先前的深度學習方法能產生更準確的阻抗預測結果，還保持了與先前方法同等級的快速計算時間。同時，因PIPPON專注於阻抗的極點部分，使得在判斷阻抗曲線是否符合目標阻抗要求時擁有更為準確的判定。

While it is a difficult task to model and simulate a power distribution network’s (PDN) impedance profile for printed circuit boards (PCBs) with irregular board shapes and multi-layer stackup, it is a crucial process for the design and performance evaluation of the PDN. This paper proposes a new deep learning method PIPPON for PDN impedance prediction which contains a proposal network that specializes in the prediction of impedance profile in the range around a pole point. The result shows that PIPPON not only produces more accurate results (with 30% relative error reduction) than the previous deep learning method but also maintains the same level of fast computation time as the previous method. Meanwhile, PIPPON focuses on impedance pole points resulting in a more accurate picture of whether the impedance profile meets the target impedance requirement.

[1] Sergio Franco. (2018, July). Playing with poles and zeros. EDN. https://www.edn.com/playing-with-poles-and-zeros/
[2] J. Kim, L. Ren and J. Fan, "Physics-Based Inductance Extraction for Via Arrays in Parallel Planes for Power Distribution Network Design," in IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 9, pp. 2434-2447, Sept. 2010, doi: 10.1109/TMTT.2010.2058278.
[3] J. Kim, K. Shringarpure, J. Fan, J. Kim and J. L. Drewniak, "Equivalent Circuit Model for Power Bus Design in Multi-Layer PCBs With Via Arrays," in IEEE Microwave and Wireless Components Letters, vol. 21, no. 2, pp. 62-64, Feb. 2011, doi: 10.1109/LMWC.2010.2100079.
[4] L. Wei et al., “Plane-Pair PEEC Model for Power Distribution Networks With SubMeshing Techniques,” IEEE Trans. Microw. Theory Tech., vol. 64, no. 3, pp. 733¬ 741, March 2016.
[5] Y. Zhang, G. Feng, and J. Fan, “A Novel Impedance Definition of a Parallel Plate Pair for an Intrinsic Via Circuit Model,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 12, pp. 3780-3789, Dec. 2010.
[6] M. Friedrich and M. Leone, “Boundary-Element Method for the Calculation of Port Inductances in Parallel-Plane Structures,” IEEE Trans. Electromagn. Compat., vol. 56, no. 6, pp. 1439-1447, Dec. 2014.
[7] C. M. Schierholz, K. Scharff, and C. Schuster, “Evaluation of Neural Networks to Predict Target Impedance Violations of Power Delivery Networks,” 2019 IEEE 28th Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS), Montreal, QC, Canada, 2019.
[8] S. Sourav, A. Roy, Y. Cao, and S. Pandey, “Machine Learning Framework for Power Delivery Network Modelling,” 2020 IEEE International Symposium on Electromagnetic Compatibility & Signal/Power Integrity (EMCSI), Reno, NV, USA, 2020, pp. 10-15.
[9] H. Park et al., “Deep Reinforcement Learning-Based Optimal Decoupling Capacitor Design Method for Silicon Interposer-Based 2.5-D/3-D ICs,” IEEE Trans. Compon. Packaging Manuf. Technol, vol. 10, no. 3, pp. 467-478, March 2020.
[10] R. Cecchetti et al., “Effective PCB Decoupling Optimization by Combining an Iterative Genetic Algorithm and Machine Learning,” Electronics 9.8, 1243, 2020.
[11] L. Zhang, Jack Juang, Zurab Kiguradze, Bo Pu, Shuai Jin, Songping Wu, Zhiping Yang, and Chulsoon Hwang, “Fast PDN Impedance Prediction Using Deep Learning,” International Journal of Numerical Modelling: Electronic Networks, Devices, and Fields, vol. 10, issue 2, March/April 2022.
[12] L. Zhang et al., "Efficient DC and AC Impedance Calculation for Arbitrary-Shape and Multilayer PDN Using Boundary Integration," in IEEE Transactions on Signal and Power Integrity, vol. 1, pp. 1-11, 2022, doi: 10.1109/TSIPI.2022.3164037.
[13] R. Girshick, "Fast R-CNN," 2015 IEEE International Conference on Computer Vision (ICCV), 2015, pp. 1440-1448, doi: 10.1109/ICCV.2015.169.
[14] S. Ren, K. He, R. Girshick and J. Sun, "Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks," in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 39, no. 6, pp. 1137-1149, 1 June 2017, doi: 10.1109/TPAMI.2016.2577031.
[15] Ioffe Sergey and Szegedy Christian. 2015. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In Proceedings of the International Conference on Machine Learning. ACM, New York, NY, 448–456.
[16] Xu, B.; Wang, N.; Chen, T.; Li, M. Empirical evaluation of rectified activations in convolutional network. arXiv 2015, arXiv:1505.00853.