Active antenna designs allow antennas of limited size to have a wider frequency range (bandwidth) than passive antennas, and are primarily used in situations where a larger passive antenna is either impractical, such as inside a portable radio or on a vehicle, or impossible, such as in a suburban residential area with restrictions on large outdoor antennas.
The active circuit compensates for the signal attenuation caused by the mismatch between antenna size and signal wavelength.
This arrangement is especially useful for constructing low frequency antennas which, due to budgetary, spatial, or practical requirements, must be kept compact.
[1] Antennas containing active impedance translating and (optionally) amplifying stages are usually used only for receiving, since operation of such stages is unidirectional.
Ulrich L. Rohde: Active Antennas, RF Design, May/June 1981 Ulrich L. Rohde, Magdalena Salazar Palma, Tapan K. Sarkar: Electrically short antennas, [1], Feb 11, 2016