volume | PIER Journals

Abstract

Continuous current spectrum of an integrated open waveguide structure is identified as the branch cut contribution to singularity expansion of those currents in the complex axial transform plane. Those singularities in that plane include poles associated with the guiding structure and branch points contributed by layered background environments. The manner in which singularities in background environments manifest themselves as branch points in the complex axial transform plane is reviewed. Based on spectral integral equation formulation, approximate and analytical expression for spatial microstrip current is obtained. That approximation is based on Maxwellian distribution for the transverse current profile. This result is the representation of currents in terms of proper propagation mode spectrum. During the integration around branch cuts, singularities in the transverse transform plane migrate in a complicated manner. The trajectories of this migration are identified and suitably accommodated during the real axis integration in that plane. This overall procedure leads to a decomposition of the total currents into bound modes and continuous spectrum contributions. This representation is validated by real axis integration in the axial transform plane. The quasi TEM characteristic impedance of bound mode is calculated and validated by comparison with well-known empirical formula.

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