Doctoral Dissertations


Ling Zhang


"In power distribution networks (PDN), there are two main challenges nowadays. One challenge is how to efficiently model and calculate the impedance for arbitrary-shape and multi-layer PDN systems. The second challenge is the optimization of decoupling capacitors in the pre-layout stage. This dissertation proposes novel solutions to these two challenges. To tackle the first challenge, a boundary element method (BEM) is utilized to calculate the quasi-static inductances between vertical vias for arbitrary-shape planes. Then a specialized circuit solver is developed to solve the equivalent circuit of inductances and capacitances for multi-layer PDN structures. Also, a contour integral method (CIM) is used to calculate the DC IR drop. Therefore, both DC and AC impedance can be calculated very efficiently. Afterward, over one million printed circuit boards (PCBs) are generated with different board shapes, stackups, IC location, and decap placement. A deep learning model is trained with the generated data to predict the impedance for any new board using just 0.1 seconds. What’s more, deep reinforcement learning (DRL) is adopted to accelerate the decap optimization process. Large amounts of PCBs with different shapes, stackups, IC location, VRM location, and decap locations are generated and used to train a DRL model. The trained DRL can predict a near-optimal solution to satisfy a target impedance for any new board that has not been used for training within 0.1 seconds. Then the solution is fed to a genetic algorithm (GA) as a seed solution, which can greatly reduce the search time for the GA. The modeling method and the machine learning techniques proposed in this work are novel and valuable to the efficiency improvement of pre-layout decap optimization and post-layout performance evaluation for PDN systems"--Abstract, page iv.


Hwang, Chulsoon
Fan, Jun, 1971-

Committee Member(s)

Drewniak, James L.
Kim, DongHyun (Bill)
Achkir, Brice
Yin, Zhaozheng


Electrical and Computer Engineering

Degree Name

Ph. D. in Electrical Engineering


Missouri University of Science and Technology

Publication Date

Spring 2021

Journal article titles appearing in thesis/dissertation

  • Efficient DC and AC impedance calculation for arbitrary- shape and multi-layer PDN using boundary integration
  • Fast PDN impedance prediction using deep learning
  • PCB-level decap placement using deep reinforcement learning


xiii, 74 pages

Note about bibliography

Includes bibliographic references.


© 2021 Ling Zhang, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11861

Electronic OCLC #