An asymptotic closed-form paraxial formulation for surface fields on electrically large dielectric coated circular cylinders
Ertürk, Vakur B.
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Investigation of surface fields excited on material coated perfectly conducting (PEC) circular cylinders is a problem of interest (i) due to its application in the design and analysis of conformal microstrip antennas and arrays, and (ii) it acts as a canonical problem useful toward the development of asymptotic solutions valid for arbitrarily convex material coated smooth surfaces. Nevertheless, integral equation based solutions that use the eigenfunction representation of the appropriate dyadic Green’s function, as well as pure numerical solutions become intractable when the geometry of interest is electrically large. A few asymptotic solutions have been suggested in the literature to overcome this problem. However, these solutions are not accurate within the paraxial (nearly axial) region of the cylinder. This is a well known problem that has been observed for PEC and impedance cylinders in the past as well. Recently, a novel paraxial space-domain representation for the surface fields has been presented by Ert¨urk et. al. (IEEE Trans. Antennas and Propagat., 11, 1577-1587, 2002), which is much faster than the well-known eigenfunction solution. However, in this representation the fi- nal expressions for the surface fields have some special functions which involve Sommerfeld type integrals to be evaluated numerically. In this thesis, using the final results of this paraxial space-domain formulation as a starting point, a relatively simple closed-form asymptotic representation for the surface fields of a dielectric coated, electrically large circular cylinder is developed. The large parameter in this asymptotic development is the separation between the source and observation points. The solution uses the fact that existing special functions in the previously developed paraxial formulation are in similar forms when compared to the special functions used in the Sommerfeld integral representation for the single layer microstrip dyadic Green’s function for the planar case. Furthermore, when the radius of the cylinder goes to infinity, using the leading terms of Debye representations for the Hankel and Bessel functions (as well as their derivatives), cylindrical special functions recover their planar counterparts. Therefore, first a steepest descent path representation of these special functions is obtained. Then, using the method suggested by Barkeshli et. al. (IEEE Trans. Antennas and Propagat., 9, 1374-1383, 1990) closed-form expressions are achieved. Numerical results in the form of mutual coupling between two tangential electric current modes have been obtained using these closed-form expressions and compared with the previously developed paraxial formulation as well as eigenfunction solution to assess the accuracy and efficiency of these closed-form solutions. Details of the formulation is presented.