A rigorous derivation of the relation between the effective area and the directive gain and its extension to lossy antennas

lt is well known that the effective area of a receiving antenna is linearly related to the directive gain of the same antenna in the transmitting mode . Conventionally, this relation is derived by constructing a two-port netwo rk involving the transfer impedance between a pair of antennas. Next, by us e of the Thevenin theorem, the received power is related with the open-circ uit voltage, which in turn is proportional to the transfer impedance, Alter natively, from field analysis, the received power is related to the effecti ve area and the directive gain. Then, the reciprocity theorem is used to eq uate the transfer impedances between a pair of antennas. Based on these, th e area-directivity relation is derived. However, it is indicated that the c ircuit model with the open-circuit voltage is not rigorous. In this investigation, the reciprocity theorem is used ina different way to directly derive the power absorbed at the load in terms of the radiated el ectric held in the transmitting mode. Thereby, the area-directivity relatio n is derived in a straightforward and rigorous manner. In the derivation of the relation, it is seen that the current in the terminal gap should be un iform, Thus, one limitation of this well-known relation is found. The effec t of ohmic loss due to finite conductivity of the antenna material can be t aken into consideration in the derivation. Thus, the area-directivity relat ion is extended such that it is applicable to lossy antennas.