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 length2din 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 areaandb, respectively, then the limiting case ofb rightarrow inftyis an infinite dipole in free space. Numerical results for the admittance are given as a function ofka (0.01 leq ka leq 0.50)with parameterb/a = 2, 5,10and 50 for the coaxial guide. For the infinite dipole the admittance is presented as a function ofd/a (10^{-3} leq d/a leq 10)withkaas a parameter (0.001 leq ka leq 0.1).