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In search for isotropic radiators with reasonable quality Factor
(

Accumulated experience, empirical and theoretical, with

The peculiarity of the class of isotropic power radiators offered here is that the source has a finite size and that the far-field is analytically solvable. Moreover, it is shown [

The structure of the paper is as follows: in Section

Consider the geometry of a

The geometry of a

The Fourier transform of the tangential electric field on the plane which includes the patch is given by

The complex input power at the antenna terminals is

This expression has real and imaginary parts. The contribution to the real part comes from the radiation into free space and from surface waves excitation effects. In the case of air as a dielectric substrate

Transforming the equation for

In our case

Return back to the

The vertical current can be replaced by two horizontal contributions [

Substituting the surface current densities in the pattern formula, we can calculate the far-field pattern of the idealized

(a)

We present here another current source which radiated its power isotropically. This time the calculations are done in configuration (or real) space. The geometry of the current source is shown in Figure

The geometry of a current source which radiates power isotropically. We put

Hence, the U-shaped

The polarization patterns of the radiator are presented is what. Figures

(a) Schematic view of an observer, of the far-field polarization of the U-shaped power isotropic radiator at the angles

We have found the electric far-fields

The double U-shaped radiator. This radiator is composed of two U-shaped radiators, one radiator is rotated by

The electric far-field components are given by

Figures

(a) Schematic view of an observer, of the far-field polarization of the double U-shaped power isotropic radiator at the angles

We have seen that the U-shaped and the double U-shaped power isotropic radiators have infinite-surface current density. In order to remove this infinity, it is possible to replace the infinite-current density source by a finite-equivalent-current density source. A way to do this is to calculate an equivalent spherical surface current density, where the radius of the sphere is

A finite-size spherical radiator carrying a finite-surface current density, for which its fields outside the sphere are exactly the same as the fields of the U-shaped

Inserting the current density of the U-shaped power isotropic radiator

The details of the calculations are given in [

We can find the coefficients

Figure

Constant amplitude curves of the surface current density on the surface of the spherical radiator drawn in Figure

The far-field can be expressed in terms of the multipole expansion by

Figure

Convergence of the multipole expansion of the far-field power for the isotropic spherical radiator. It is shown in two scales: in a coarse scale (a) and in a fine scale (b), for

The

This paper is devoted to the memory of our great teacher Professore Shmuel Shtrikman of the Department of Complex Systems, Weizmann Institute of Science, Rehovot, Israel, Life Fellow IEEE, who passed away on November 2003.