Closed-form model of extremely thin conformal magnetic antenna with high Gain-Bandwidth Product

A model of the input impedance of the toroidal permeable antenna, which is the dual of the conventional metal loop antenna, is derived, starting from Schelkunoff's transmission line description of the loop antenna instead of the electrically small limit model. The input impedance for the dipole mode is expressed in a form that has a frequency independent resistor terminating a reactive network which is called the Darlington form. Since such a circuit mimics the input impedance of the dipole modes of the spherical mode expansion, it works very well as we go beyond the electrically small limit even for magnetic antennas as large as multiple wavelengths. The realistic feed loop contribution is explicitly accounted for and results are compared with fullwave simulations of a typical toroidal antenna which shows good agreement well beyond the electrically small limit.