The admittance of bare circular loop antennas in a dissipative medium

The normalized input admittance of thin bare circular loop antennas has been evaluated from the theory of T. T. Wu. Computations have been made for loops in air and in an infinite homogeneous isotropic dissipative medium. A comparison is also made with Storer's theory of the loop. Numerical results are given in the form of graphs for several wire sizes and for loops up to two and one-half wavelengths in circumference. The properties of the medium are represented by the ratio
\alpha/\beta
in the range from zero (perfect dielectric) to one (good conductor);
\alpha
and
\beta
are the imaginary and real parts of the complex propagation constant
k=\beta-j\alpha = \omega\sqrt{\mu(\epsilon-j\sigma/\omega)}
where
\mu
is the permeability,
\epsilon
the dielectric constant, and
\sigma
the conductivity of the medium.