Theory on small radiating apertures in the outer sheath of a coaxial cable

An analytical expression for the aperture field is obtained from an integral equation formulation and a subsequent use of a quasistatic approach in which the dominant part of the solution can be extracted from canonical problems. Unlike the conventional approach of replacing the aperture field by equivalent dipoles, our method retains the basic features of the propagating mode in the coaxial region, and the radiation characteristic of the coaxial cylinder. An equivalent network representation of a small aperture is then derived. The network equivalence of a symmetrical aperture with its axes oriented in the direction of the incident field is shown to consist of a lumped shunt capacitance
C_{b}
and a series impedance
Z
composed of an inductive element
L_{b}
, a capacitive element
C_{T}
and the input admittance
Y_{b\infty}
of the external antenna, all in parallel.