Masters Theses


"This thesis presents modeling approaches for fast calculation of signals in dense via arrays in high speed printed circuit boards (PCBs) and model to hardware correlation study of solid and perforated disk resonators. A 2D finite difference (FD) method to extract the via capacitance which includes the via pad capacitance obtained by solving the laplace equation in the via domain in multi-layer geometries is presented and validated with analytical formulation for via capacitance. Next, closed-form expression for the impedance of an infinitely large parallel plane pair is derived and validated by comparing with cavity model for several numerical examples. The infinitely large parallel plane pair model is applicable to practical printed circuit board (PCB) design problems where there are multiple shorting vias around the signal vias of interest. With the presence of multiple shorting vias, reflections from the plane pair edges can be neglected since the shorting vias prevent the electromagnetic energy from leaking away from the local cavity around the signal vias. Next, improved multiple scattering method for fast calculation of signals in via arrays in plane pair is derived using analytical expressions. Parallel plate modes expressed as cylindrical waves are excited by the magnetic frill currents in via holes (antipads). Multiple scattering of these modes among vias as well as from the edge boundaries of the plate pair are rigorously considered with the addition theorem of the cylindrical waves. In the final part of this thesis, different approaches mentioned here are applied to study solid and perforated disk resonator behaviors and to correlate the simulated and measured results"--Abstract, page iii.


Fan, Jun, 1971-

Committee Member(s)

Zhang, Yaojiang
Drewniak, James L.


Electrical and Computer Engineering

Degree Name

M.S. in Electrical Engineering


Missouri University of Science and Technology

Publication Date

Fall 2009

Journal article titles appearing in thesis/dissertation

  • 2D finite difference method to obtain the via capacitance
  • Impedance of an infinitely large parallel plane pair and its applications in engineering modeling
  • Multiple scattering method for analyzing via arrays in circular/irregular plane pair and its quantifaction with physics based circuit model
  • Disk resonator study using boundary element method, multiple scattering method, and effective dielectric medium approach


xii, 92 pages


© 2009 Arun Reddy Chada, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Printed circuits -- Design and construction -- Mathematical models
Signal integrity (Electronics)

Thesis Number

T 9570

Print OCLC #


Electronic OCLC #