Fast, simple and accurate computation of the currents on an arbitrarily large circular loop antenna

Abstract

This paper is presenting a very efficient method for computing the currents on a circular loop antenna with arbitrarily large size. Pocklington's integral equation is formulated for the circular loop geometry, and the method of moments with point matching is applied to cast the equation's discrete counterpart. The basis functions are chosen in such a way that the relevant square matrix is circulant, and therefore amenable to exact eigenvalue analysis. Subsequently, the matrix is diagonalized and inverted analytically, yielding simple, analytical expressions for the weights of the basis functions, and hence the current and the input admittance of the antenna. The algorithm utilizes mainly elementary mathematical functions, as opposed to already known expressions in the literature, and yields results in the form of a rapidly convergent, single series, applicable to extremely large loops.