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.Index Terms-Circulant matrices, current, input admittance, loop antennas, method of moments (MoM).

Single-Series Solution to the Radiation of Loop Antenna in the Presence of a Conducting Sphere

“…One can describe the electric field as weighted double sums of the spherical eigenfunctions (1), (2) and deduce the magnetic field via (6), (7). By imposing continuity of the tangential electric and singular discontinuity (due to the point source) of the tangential magnetic field at r = R, the first two boundary conditions are derived.…”

“…In [1] analytical expressions of the near-zone integrals for a loop of arbitrary current are deduced with use of Lommel expansion. In [2] Pocklington's integral equation is formulated and method of moments is applied for the determination of the current on an arbitrarily large ring radiator in terms of step-pulse basis functions. Also in [3] exact series representations and far-zone approximations are given for the field of a loop with traveling-wave current distribution.…”

Accuracy and Complexity Assessment of Sub-Domain Moment Methods for Arrays of Thin-Wire Loops

“…Within the interval of interest 0.1 ≤ κ < 1, (17) holds for G ≥ 5; under this latter condition, the roots given by (16) are real numbers with N − < 0 and N + > 0. Under these circumstances, the inequality…”

“…However, entire-domain schemes are applicable under restrictions upon the size of the loop, mainly due to certain difficulties encountered when attempting to calculate the associated integrals for large mode numbers. On the other hand, subdomain schemes are relatively easy to implement, even for quite large loops [16][17][18].…”

On Block Matrices Associated with Discrete Trigonometric Transforms and Arising in Wave Propagation Theory

“…In particular, block matrices associated with DTT's arise in concrete physical and technological applications including: (i) the solution of wave scattering and radiation problems with the Method of Moments (MoM) [7,8], (ii) the investigation and optimization of numerical methods for electromagnetic scattering problems, such as the Method of Auxiliary Sources (MAS) [9]- [10], (iii) the numerical solution of integral equations with the Boundary Element Method (BEM) [11], (iv) optical imaging [12], (v) image compression [13], (vi) efficient preconditioning of Toeplitz systems [14]. Besides, we point out that these applications exhibit the essential role of the inversion of such types of complex block matrices for the derivation of formulas determining the error bounds of numerical methods as well as for the numerical or semi-analytical computation of solutions [15].…”