Near Field of a Loaded Circular Toroidal Antenna

In this paper a special toroidal coordinate system is introduced in order to derive general solutions for the electric and magnetic fields from a toroidal antenna. These solutions depend on the current distribution on the toroid and are in integral forms. Some Fourier expansion techniques have been used in order to simplify these integral equations. The surface current is found under the assumption that the thickness of the toroid is thin compared to the wavelength, which leads to an analytic solution for the fields at the center. Many uniform loading impedances are used with the purpose of producing a plane-wavelike field at the center of the toroid. Index Headings: Toroidal antenna Loading impedance Near field With the current interest in electromagnetic effects on electronic equipment, one can simulate a desired waveform using various antenna structures for laboratory testing. The experimental space and the generator power can be significantly reduced if the equipment is located in the near zone of an antenna. However, on many occasions, a plane wave field is required. It is the purpose of this paper to examine the possibility of generating a field distribution in the near zone of an antenna which approximates a free space plane wave to some degree. The antenna considered is a circular toroid fed by a delta-gap generator of voltage V o, as shown in Fig. 1. Under the assumptions of a2>> b z and Ikbt < 1, the current distribution in a circular loop antenna has been extensively studied in the past. The result is summarized in the book by Collin and Zucker [-1]. It is learned in the present paper that the field at the center obtained by using the current solution based upon the above assumptions actually is applicable (with some small errors) to wider ranges, namely, for a 2 > b 2 and Ikbl < 1. Fante et al. [2] have developed some numerical techniques for the near field of a single-frequency loop antenna without load. However, numerical computation for the field at many frequencies is very timeconsuming. So, we will derive here some analytical /•/b z /J o.o ,.~ ,..~ Of voltoge Vo Fig. I. Antenna geometry and the special toroidal coordinate system expressions for the field at the center for convenient reference in the future. Certainly, the method can be extended to the other locations of interest. 1. General Solution for the Fields in a Special Toroidal Coordinate System Figure 1 shows the geometry and coordinate system for a toroidal antenna driven by a delta function generator. According to the electromagnetic theory, one knows that the electric and magnetic fields can