An Improved Antenna Scattering Model: An equivalent model based on the reciprocity theorem

The Thévenin and Norton equivalent models of a receiving antenna cannot be used to calculate the antenna's scattered power because they are too simplistic. Based on the reciprocity theorem, a more elaborate equivalent model, consisting of a passive distributed transformer, is proposed for wire antennas in both the transmit and receive modes. The model parameters are derived from the antenna's transfer admittance parameters, the latter obtained under short circuit loading conditions in transmit mode only. A method is then applied to determine the new admittance parameters when the antenna is perturbed by an arbitrary load, which allows the receive-mode current distribution on the antenna to be calculated. Once the receive-mode current is known,scattered power can be calculated with a formula that avoids integration over the far-field sphere. The method has been applied to a λ/2dipole, λ-dipole, and three-element Yagi antenna for resistive loads spanning up to nine decades. Calculated scattered-power values are shown to agree almost perfectly with values obtained using a commercial simulator, thus demonstrating that it is possible to calculate scattered power based on the characterization of the antenna in transmit mode only. Results indicate that the aperture efficiency of a dipole antenna can exceed 50% when it is connected to a mismatched load. Finally, a newly defined transducer efficiency is presented, which can be used to choose an optimum load to obtain the best compromise between the aperture and scattering areas.