Small magnetic toroid antenna imbedded in a highly conducting half space

Abstract

The ante nna co nsider ed co nsists of a s mall toroidal core of magnetic materi al, upon whic h a uni· formly di stribute d driving wi ndin g is pl aced. Thin laye rs of in s ulation se parate th e windin g fro m th e core and from the hi ghly conduc tin g me dium in whic h th e ante nna is situ a te d. The exte rnal fi elds for th e drive n a nte nna are es timated using a sta ti c fi eld so luti on e mploying toroid al coordinates. The dri vin g-poi nt admitt a nce is th e n d ete rmined from th ese fi eld s. Th e effec tiv e electri c c urre nt mome nt of th e ante nn a is es timated by dualit y with the electric curren t loo p. Th e drivin g-point ad mitt a nce a nd the effecti ve mo me nt are the n combi ned to es ti mate the effective length a nd the re la tiv e effecti ve a rea of a tor o id a nt en na orie nt e d suc h t hat the e lectric mome nt prod uced is para ll el to t he su rface of the cond uct in g ha lf space. Wh ile the effective lengt h of a tu ned toroid antenn a ca n be made muc h greater th a n the e ffective length of an elect ric-di po le-in .radome ante nn a, t he effective areas of the t wo a nten na types are of t he same orde r of magnitud e if th e max imum exte ri or dimens ions are equal.

Metallic and Dielectric Antennas in a Conducting Environment

“…Since the frequencies used are generally very low and since the antenna dimensions are small with respect to the local wavelength, it seems convenient to fully develop the simpler static case. This is obviously a known approach for antennas whose dimensions are small with respect to the skin depth of the wave [Swain, 1965;Williams et al, 1965]. However, we make not a quasi-static, but a rigorously static approach, even for the effective height; then we show to what extent static results are valid in the dynamic case.…”

Small prolate spheroidal antenna in a dissipative medium

“…Combining the results of Swain [1965], who discusses a toroid in a dissipative medium, and the results of this paper, an equivalent circ uit valid for the small toroid-driven prolate spheroidal antenna is shown in figure 6. The meaning of the various circuit parameters is described below: RI is the s elf-resistance of the N -turn pnmary winding on the toroid .…”

“…(derived by Swain [1965]). t::.G is the increase in conductance caused by the presence of the spheroid given by (29).…”

“…These effects can be introduced into the equivalent circuit in fi gure 6 by the addition of appropriate circ uit paramete rs. Swain [1965] shows how to introduce a capacitor to correspond to parasitic capacities, and this paper shows how to introduce an inductance (Lp) to correspond to magnetic energy storage in the di ssipative medium. Several other effects could be introduced depending upon the user's application and desire for refinement.…”

“…The expression for Yo in (27) is that part of the total admittance Yin which is due to a magnetic toroid alone in a conducting medium. The quantity Yo has real and imaginary components and has been determined by Swain [1965]. The l:,.G expression in (28) is the contribution to the total admittance Yin due to the presence of the conducting prolate spheroid.…”