Hertzian dipoles and microstrip circuits on arbitrarily oriented biaxially anisotropic media

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Antennas, Hertzian dipoles, Microstrip, Biaxially anisotropic

Subject Categories

Electrical and Computer Engineering | Engineering


This dissertation presents radiation field analyses of Hertzian dipoles positioned above, in, and on layered isotropic-biaxially anisotropic media as well as spectral-domain full-wave analyses of microstrip transmission lines and microstrip dipoles on arbitrarily oriented conductor-backed biaxial slabs.

First, an overview of biaxially anisotropic media is presented. Included in the discussion are the multi-sheeted wave vector surface and birefringence. Next, the two dyadic Green's function formulations used for the dipole and transmission line analyses are presented. Reciprocity formulations needed for radiation-field analysis are developed. Likewise, methods of ensuring the continuity and stability of the Green's function calculations for large spectral values are developed. Detailed analyses of the branch-point and surface-wave-pole singularities associated with arbitrarily oriented biaxial media and the multilayer geometry are given.

With the biaxial media properties addressed and the dyadic Green's functions in hand, the radiation fields of Hertzian dipoles in one- and two-layer geometries are calculated using asymptotic techniques in conjunction with an eigenvector dyadic Green's function integral formulation. The sensitivity and the symmetry of the radiation fields due to the position of the Hertzian dipole, the source's orientation, the biaxial medium's thickness, and the orientation of the medium itself are thoroughly investigated. Indeed, the fields are shown to be asymmetric when the biaxial medium is arbitrarily oriented.

Following the radiation field analysis, the microstrip transmission line and dipole antennas are analyzed utilizing a transition-matrix dyadic Green's function formulation appropriate for the layered structure in conjunction with Galerkin's method to determine the unknown currents. The integrals pertinent to the research are formulated and evaluated entirely in Cartesian coordinates. All relevant singularities are identified and appropriate numerical methods are applied to ensure analytic results are obtained. Detailed analyses and simulation results of bound-mode effective propagation constants, current distributions, and characteristic impedances of microstrip lines on conductor-backed arbitrarily oriented biaxially anisotropic slabs are presented. Likewise, the current distribution, input impedance, efficiency, and gain of microstrip dipoles on conductor-backed arbitrarily oriented biaxial slabs are obtained. The results clearly show that the biaxial medium's orientation can be used to modify microstrip circuit parameters and, thereby, potentially enhance device performance.


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