**Authors:** Everett G. Farr

**Source:** FERMAT, Volume 7, Article 1, Jan-Feb., 2015

**Abstract:** We introduce here a simple theory of antenna
radiation and scattering that fully extends into the time
domain a number of standard antenna terms, including
gain, realized gain, effective length, antenna pattern,
beamwidth, scattering cross section, and radar cross
section. Power wave theory applies to linear reciprocal
antennas of all feed impedances and feed types, including
waveguide feeds. It also applies to antennas embedded in
any lossless medium. The theory also leads to a natural
definition of mutual coupling coefficient in antenna
arrays. The approach is analogous to that used to describe
circuits with generalized scattering parameters, with
different reference impedances at each port. We identify
receiving and transmitting impulse responses, and prove
that they always have a simple relationship to each other,
provided that the antenna has no nonlinear or
nonreciprocal components. We also identify a scattering
impulse response that can be applied to either an antenna
or an arbitrary scatterer. From these functions, we build
a Generalized Antenna Scattering Matrix (GASM), which
provides a complete description of antenna response in the
far field. This establishes a formalism that allows one to
calculate antenna response under a variety of conditions,
including, for example, a source or load of arbitrary
impedance. The approach simplifies and clarifies
terminology for characterizing antenna performance in
both the time and frequency domains.

**Index Terms:**Antenna Characterization, Frequency
Domain, Time Domain, Antenna Impulse Response,
Scattering Impulse Response, Generalized Antenna
Scattering Matrix (GASM), Antenna Equation.

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