Effect of gap length on the input admittance of center fed coaxial waveguides and infinite dipoles

The input admittance of a coaxial waveguide fed by a gap of length
2d
in the center conductor is evaluated using the dyadic Green's function of the guide and a band of equivalent magnetic surface current proportional to the gap's axial electric field via the equivalence principle. The axial electric field is expressed in terms of a rapidly convergent series of ultraspherical polynomials whose weighting function satisfies the edge conditions at each end of the gap. If the inner and outer radii of the coaxial guide are
a
and
b
, respectively, then the limiting case of
b \rightarrow \infty
is an infinite dipole in free space. Numerical results for the admittance are given as a function of
ka (0.01 \leq ka \leq 0.50)
with parameter
b/a = 2, 5,10
and 50 for the coaxial guide. For the infinite dipole the admittance is presented as a function of
d/a (10^{-3} \leq d/a \leq 10)
with
ka
as a parameter (
0.001 \leq ka \leq 0.1
).