Field patterns of resonant noncircular closed-loop arrays: further analysis

Previous papers have introduced the continuous-current model for resonant closed-loop arrays of cylindrical dipoles and, for a certain class of array shapes, have determined the resulting field patterns analytically. Those analytical calculations involve several approximations. In the present paper, we first study the aforementioned model numerically for the case of elliptical closed-loop arrays. The results-which involve fewer approximations than those of the previous papers, but which refer to different array shapes-imply that elliptical arrays have a bidirectional, highly directive field and, unlike conventional arrays, have no sidelobes. Combining analytical and numerical methods, we then investigate the relationship between the aforementioned continuous-current model and what we call the discrete-current model which, in a certain sense, is more realistic. The results indicate that, subject to suitable conditions, the two models yield virtually identical results. In our analytical investigations, an important tool is the Poisson summation formula for finite sums; we have devoted a stand-alone section to this formula which supplements recent, unrelated publications in antenna theory.