The Radiation Resistance of an Antenna in an Infinite Array or Waveguide

The electromagnetic field in front of an infinite flat array of antennas can be subdivided into wave channels, each including one of the antennas. Each channel behaves like a hypothetical waveguide similar to a transmission line made of two conductors in the form of parallel strips. A simple derivation then leads to the radiation resistance of each antenna and to some limitations on the antenna spacing. In the usual flat array of half-wave dipoles, each allotted a half-wave-square area, and backed by a plane reflector at a quarter-wave distance, the radiation resistance of each dipole is 480/π = 153 ohms. In a finite array, this derivation is a fair approximation for all antennas except those too close to the edge. This derivation also verifies the known formula for the directive gain of a large flat array in terms of its area. The same viewpoint leads to the radiation resistance of an antenna in a rectangular waveguide, which has previously been derived by more complicated methods.