A General Solution of the Thin Circular Loop Radiation

Abstract

A general solution of the thin wire circular loop radiation is offered, without assuming a certain current distribution in advance. The solution is valid for any radius-wavelength ratio and for both near and far field. The field potentials are expressed through the general wave equation basis functions in spherical coordinate system. A zero electric field along the loop is achieved as a sum of the radiation field and time-independent excitation field. The unknown-expansion coefficients are found by the Galerkin method. For highly accurate fulfillment of the boundary condition only twelve modes were required. The current distribution was found uniform for a very small loop, butalso close to uniform for certain much larger electric lengths. It was also found that in a far zone both E ϕ and E θ exist, with E ϕ being some ten times greater than E θ, if the source occupies a very small portion of the loop.