Exact solutions of electromagnetic fields in both near and far zones radiated by thin circular-loop antennas: A general representation

Abstract

This paper presents an alternative vector analysis of the electromagnetic (EM) fields radiated from thin circular-loop antennas of arbitrary radius a. This method, which employs the dyadic Green's function in the derivation of the EM radiated fields, makes the analysis more general, compact, and straight-forward than those two methods published recently by Werner and Overfelt. Both near and far zones are considered so that the EM radiated fields are expressed in terms of the vector-wave eigenfunctions. Not only the exact solution of the EM fields in the near and far zones outside the region (where r>a) is derived by the use of the spherical Hankel function of the first kind, but also the closed-series form of the EM fields radiated in the near zone inside the region 0≤r<a is obtained in series of the spherical Bessel functions of the first kind. As an example, a Fourier cosine series is used to expand an arbitrary current distribution along the loop and the exact representations of the EM radiated fields due to the loop everywhere are obtained in closed form. The closed form reduces to those for the sinusoidal current loop and further for the uniform current loop. Validity of the approximate formulas is discussed and clarified. Error analysis based on numerical computations of the radiated fields is also given to show the accuracy of the limiting cases.