  The equivalent external noise temperature of time-varying antennas is studied
using the concept of cross-frequency effective aperture, which quantifies the
intermodulation conversion of external noise across the frequency spectrum into
a receiver's operational bandwidth. The theoretical tools for this approach are
laid out following the classical method for describing external noise
temperature of linear time-invariant antennas, with generalizations made along
the way to capture the effects of time-varying components or materials. The
results demonstrate the specific ways that a time-varying system's noise
characteristics are dependent on its cross-frequency effective aperture and the
broadband noise environment. The general theory is applied to several examples,
including abstract models of hypothetical systems, antennas integrated with
parametric amplification, and time-modulated arrays.
