The performance of a slot antenna situated on infinite conic metal surface
with circular cross-section is shown to be similar to that of situated on the infinite flat
metal surface. The proof is based on the transition from a V-shaped magnetic radiator to
a double-sided slot cut in the mentioned surface. If, to simplify the design, metal and
slot radiators are placed along the regular pyramid sides, the antenna performance
changes but remains close to that of the self-complementary antenna. Flux density
distribution over long line cross section is analyzed. The transition from the parabolic
problem to the flat one is done.
Keywords: Complementary principle, Directivity of 3-dimensional radiator,
Duality principle, Double-sided slot, Electric V-shaped radiator, Finite dimensions
of the radiator, Flux density distribution over long line cross section, Magnetic Vshaped
radiator, Metal sheet as a set of divergent wires, Parabolic long line,
Parabolic problem, Phantom model, Phantom vessel shape as an example of a
parabolic surface, Pyramid-shaped volume radiator, System of parabolic
coordinates, Three-dimensional radiator, Transformation of variables, Transition
from a paraboloid to a cylinder, Two slot antennas on curvilinear metal surfaces.
