The distribution of support for the radiation of spherical modes on the surface of small antennas

Summary form only given. The expression of antenna radiation in terms of spherical mode expansions (SME), was introduced long ago (J. S. Stratton, Electromagnetic Theory, 1941, Mcgraw-Hill, Chap. VII), (L. J. Chu, “Physical Limitations of Omni-directional Antennas,” Tech. Rept. 64. Lab. Of Electronics, MIT, 1948) but has only occasionally been applied to a practical application (T. Simpson and Y. Chen, “Radiation pattern analysis of arbitrary wire antennas using spherical mode expansions with vector coefficients,” IEEE Trans. Antennas and Propagation, vol. Ap39, pp. 1716-1721, Dec. 1991). More recently, it was shown (Ted Simpson, “Influence of Shape on the Bandwidth of a Rotationally Symmetric Monopole,” IEEE APS/URSI Symposium, 2010) that the pattern variation with frequency was closely related to the width of the SME spectral response. In this paper a method is introduced to determine the strength and location of the contributions to the coefficients of the SME; this is called the mode support distribution (MSD). Restricting discussion to the case of a base-driven rotationally symmetric monopole of arbitrary profile, it is shown that the contributions to (or support for) the radiated field expressed in terms the TM0n modes may be identified with each segment of a moment method solution for the current distribution. Further simplicity results from the additional restriction that the maximum electrical radial dimension, kR , where Rmax is the maximum max radial dimension of the antenna, be less than N + δn where δn is typically 2 or 3 to include a few modes below cutoff to illustrate their small size. For example, for a monopole of height Rmax = 0 . 1m operated at 1431 MHz, so that kRmax = 3, we can safely set N = 5 to include at least one mode below cutoff to establish the trend. Examples will be presented for several electrically small monopole shapes, cylindrical, conical, and disk-loaded. In the ca- e of the disk-loaded monopole, the MSD clearly identifies the part of the antenna supporting radiation as well as the part associated with stored energy and, hence, the reactance. One example will be given of an ice-cream-cone shaped antenna chosen for its UWB characteristics. Since, to the author´s knowledge, the SMD is a new type of antenna property, its practical utility is as yet unclear. On the other hand, like the current distribution, it may provide more insight into the physical relation between antenna shape and performance.