Multiconductor transmission lines in multilayered dielectric media over a gridded ground plane

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Roger F. Harrington


Bethe's small aperture theory

Subject Categories

Electrical and Computer Engineering


We consider multiconductor transmission lines in multilayered dielectric media for which the normal ground plane is replaced by a gridded ground plane. The gridded ground plane consists of uniform arrays of holes running parallel to the transmission lines. They are treated using Bethe's small aperture theory, which replaces each hole with an equivalent set of electric and magnetic dipoles. Arrays of holes, running parallel to the transmission lines, are then two-dimensionalized using a Fourier series method developed here. This two-dimensional approximation we dub the average dipole density approximation. With this in hand, the charge on each conductor and the bound charge at each dielectric interface are obtained using a standard subsectional basis and the appropriate boundary conditions. This determines the electro-static capacitance matrix. The inductance matrix is obtained by artificially imposing a set of conditions which yield a modified freespace capacitance matrix. This modified matrix is the inverse of the inductance matrix. Sample calculations are presented for different geometries.


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