Paraxial and source region behavior of a class of asymptotic and rigorous (MoM) solutions in the high-frequency planar limit

Mutual impedance between flush-mounted antennas on convex surfaces has been traditionally computed at high frequencies using the uniform theory of diffraction (UTD) and other high-frequency asymptotic solutions. Motivated by a recent study, the limits of applicability of the existing asymptotic techniques to the calculation of input (or self-) impedance are investigated here. It is shown analytically that UTD and one other asymptotic formulation, in the close vicinity of a source on a perfectly electrically conducting (PEC) circular cylinder, for negligible local surface curvatures, are algebraically identical. For the canonical geometry of an axial magnetic current element on a PEC circular cylinder, it is shown that the additional paraxial correction term in the UTD formulation vanishes in the high-frequency planar limit. Numerical comparisons against rigorous method of moments (MoM) solutions show that the reduced-planar forms are remarkably accurate for source-to-observer separations, t, where 0.02λ_o≤t≤0.08λ_o, and slightly off the axial direction.