The Electrically Small Multi-Turn Loop Antenna with a Spheroidal Core

A complete analysis of the electrically small multi-turn loop antenna with a spheroidal core is presented, using quasistatic electromagnetic theory (QS). Its use as a primary design tool for later use in conjunction with a large finite-element (FEM) program for full-wave analysis of a practical loop with a cylindrical core is illustrated. Previously unavailable components of the equivalent circuit, including conductor and core losses, inductance, and capacitance, are derived. The accuracy of this circuit for practical use is demonstrated by comparison with results obtained from an FEM analysis of a cylindrical loop of equal volume and aspect ratio. All results are obtained in closed form: these include expressions for the dependence of the impedance, bandwidth, and efficiency upon the frequency, volume, aspect ratio, permeability, and number of turns. Although attention is focused on the design of a 2 MHz transmitting antenna, the theory is sufficiently general for application to the design of electrically small receiving or transmitting antennas at other frequencies