Doctoral Dissertations


Biyao Zhao


"A physics-based circuit modeling methodology for 3D IC/packages is proposed here. The method is based on partial element equivalent circuit (PEEC) and layered Green's function (LGF). The LGFs are calculated from discrete complex image method (DCIM) with three terms, direct coupling, complex images, and surface wave, extracted to analyze the wave behavior. The dominate terms for LGFs are analyzed for four stack-ups in 3D IC/packages. Analytical formulas that include the contribution of complex images are proposed for partial capacitance calculation, with the complex image extracted from LGFs. A chip PDN geometry is used to illustrate the use of LGF in PEEC to validate the proposed method. A good match is observed between the input impedance from the proposed method and full wave simulation.

A physics-based circuit modeling methodology for system-level power integrity (PI) analysis and design is presented herein. The modeling methodology is based on representing the current paths in the power distribution network (PDN) with appropriate circuits based on cavity model and plane-pair Partial Element Equivalent Circuit (PEEC). The PDN input impedance looking from on-chip sources can be computed. A commercial simulation tool is used to corroborate the modeling approach where the system consists of a commercial IC, a complex organic package and a very high-layer-count printed circuit board. Two types of circuit models are proposed from the methodology with physical correspondence maintained in the circuit elements. The circuits can be used to analyze the geometry impact on the PDN impedance and explore design improvements. Voltage ripple simulations are conducted with the circuit models. The simulated results correlated with measurements"--Abstract, page iii.


Fan, Jun, 1971-

Committee Member(s)

Drewniak, James L.
Kim, DongHyun (Bill)
Hwang, Chulsoon
Ruehli, Albert E.
Achkir, Brice
Becker, Wiren Dale


Electrical and Computer Engineering

Degree Name

Ph. D. in Electrical Engineering


National Science Foundation (U.S.)


This dissertation is based upon work supported partially by the National Science Foundation under Grant No. IIP-1440110.


Missouri University of Science and Technology

Publication Date

Spring 2020


xii, 91 pages

Note about bibliography

Includes bibliographic references (pages 84-90).


© 2020 Biyao Zhao, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 11703

Electronic OCLC #