The electrically small elliptical loop with an oblate spheroidal core

Renewed interest in the use of ferrite-loaded loop antennas in the low part of the HF band (3-30 MHz) led the author to review the available literature (Burgess, R.E., 1946; Wait, J.R., 1953), and to extend the application of quasi-static theory to the definition of frequency bandwidth and efficiency. The spheroidal shape, which leads to closed-form quasi-static solutions for both rotationally symmetric and elliptical loops (Wait), is interesting from a practical standpoint because it can simulate long thin rods (prolate) as well as thin flat disks (oblate). We consider the antenna consisting of an oblate spheroidal core of thickness 2a along the z axis and of maximum diameter 2b excited by an N-turn loop having a pitch, p=2b/N, along the x-axis. For the transmitting case, the turns are treated as separate planar loops, each carrying a current I. Receiving properties follow from reciprocity. Core losses are included.