Scott, Kevin James; (1990) Efficient integral equation solutions for electromagnetic modelling of complex printed circuit boards. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Frequencies of 1 GHz or more and high packing densities are becoming common in much electronic equipment, such as mobile communication systems. In these situations, the effect of electromagnetic coupling in the interconnections can seriously degrade performance, and leads to many repeated attempts at a satisfactory design if not understood. This thesis describes several aspects of a method to analyse the complex three dimensional electromagnetic behaviour of printed circuit boards, which is used to understand and correct these problems. An approximate solution to Maxwell's equations in terms of a lumped element equivalent circuit model, using capacitors, inductors and resistors, is first developed. The method employs Green's functions for the electric scalar and magnetic vector potentials. Series solutions for these in situations where there are up to three infinite, planar dielectric layers and two ground planes are developed. They are shown to have good convergence properties, and their use makes the method very efficient. The concept of inductance is examined, and developed to model the inductance of the vias used to connect different layers together. For more general cases of modelling inductance and capacitance, basis functions for rectangular and triangular elements are examined, and efficient subroutines to calculate the potentials due to them are described. The modelling of more general metal shapes than tracks is tackled by describing them in terms of polygons. A comprehensive method for processing these into a set of rectangular and triangular elements is developed, and possible enhancements to this discussed. Results are presented to show that the methods described yield excellent agreement with experimental results, while being extremely efficient in terms of computer time and resources.

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