PHYSICS

Foster’s theorem for a free-space antenna

S. L. Solovtsov^a, I. A. Fanyaev^a, V. P. Kudin<sup>b

a</sup> Francisk Skorina Gomel State University
^b Sukhoi State Technical University of Gomel

Abstract: A generalization of Foster’s theorem to the case of an antenna radiating into free space is considered. It is demonstrated that the frequency derivative of the phase of the antenna input reflection coefficient is a positive quantity and is proportional to the time delay of the radiated radio pulse. By employing the Lorentz reciprocity lemma and analyzing the energy balance within a volume surrounding the antenna, a relationship is derived that links this time delay to the stored reactive energy in the antenna’s near field. The obtained relation enables experimental determination of the time delay from measured reflection coefficient parameters and permits the use of this quantity as a diagnostic and comparative metric for antennas. The theorem holds practical significance for antenna design and for understanding fundamental physical limitations.

Keywords: Foster’s theorem, antenna, Poynting vector, reflection coefficient phase, delay time, radio pulse.

UDC: 537.87:621.396.67

Received: 10.10.2025

DOI: 10.54341/20778708_2025_4_65_47