الفهرس 
Solution of electromagnetic propagation problems in shielded transmission lines using the eigenmode projection technique
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Abstract
In this work, an eigenmode projection technique is utilized to solve the problems of
the electromagnetic wave propagation in shielded transmission lines. The technique is
adopted to solve two sets of problems, non-periodic loaded lines and periodically loaded
lines.
For the first set, a fictitious canonical cavity surrounded by perfect electric surface
is chosen to enclose the line and the fields inside are expanded in terms of of the cavity
solenoidal and irrotational eigenmodes where they are considered as a complete set to
represent any vector field inside the cavity. The fields in Maxwell’s equations inside the
enclosed region are then expanded using the cavity eigenmodes. Finally, a set of equations
for the eigenmodes are resulted by using the fields expansions in Maxwell’s equations of
the cavity where mode projections are done. This set of equations are solved together to
get the line dispersion curve and the propagating modes.
For the second set, the analysis flow is based on expanding the fields in the required
periodic line as Floquet harmonics in terms of the solenoidal and irrotational eigemodes
of a canonical periodic structure. Subsequently, only one cell of the canonical periodic
structure encloses the actual periodic line, the periodic boundary conditions are enforced
in the Floquet harmonics, and the fields eigenmode expansion are used in Maxwell’s
equations. Thus, Maxwell’s equations are projected on the solenoidal and irrotational
eigenmodes to construct a set of equations cast in an eigenvalue problem form. Similarly,
this set of equations are solved together to get the line dispersion curve and the propagating
modes.
In contrast to other numerical techniques, the proposed technique does not require segmentation
and does not use Green’s function in formulation (thus there is no singularities)
and all integrals are frequency independent.