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EEE 171 [Fall 1997: ekim] Receiving Antenna 3 Dec 1997 RECEIVING PROPERTIES OF ANTENNAS In the discussion of antennas and antenna arrays, we have analyzed their operation in the transmitting mode. In the transmitting mode, a voltage source is applied to the input terminals of the antenna, setting up currents and charges on the antenna. The time-varying currents and charges radiate electromagnetic waves, which carry energy. A transmitting antenna can then be regarded as a device that transforms energy form a source (generator) to energy associated with an electromagnetic wave. A receiving antenna, on the other hand, extracts energy from an incident electromagnetic wave and delivers it to a load. By invoking reciprocity relations, it is possible to justify the following: 1. The equivalent generator impedance of an antenna in the receiving mode is equal to the input impedance of the antenna in the transmitting mode. 2. The radiation pattern of an antenna for reception is identical with that for transmission. For a receiving antenna weakly coupled to a transmitting source, an approximate Thévenin's equivalent circuit at the receiving end is shown below in Figure 1, where VOC is the open-circuit voltage induced in the receiving antenna, Zg is the equivalent generator internal impedance of the antenna in the receiving mode (equal to its input impedance in the transmitting mode), and ZL is the load impedance. I Z V OC L g Z L V L Figure 1. Thévenin's Equivalent Circuit For A Receiving Antenna With Load Recall that the effective aperture of an antenna (transmitting or receiving), Ae, is defined as, Ae Pavg S PL [m2], S (1) where PL is the power delivered to a matched load and S is the time-average power density of the incident electromagnetic wave at the antenna. Under conjugate-matched condition, ZL = Zg * = Zi* , (2) 1 EEE 171 [Fall 1997: ekim] Receiving Antenna 3 Dec 1997 where Zi* is the antenna input impedance in the transmitting mode. Neglecting losses, the antenna input impedance Zi in the transmitting mode can be written as, Zi = Rrad + jXi , (3) where the radiation resistance Rrad and Prad 2 I in Prad is the power radiated by the antenna in the transmitting mode Iin is the rms input current to the antenna in the transmitting mode. In view of Equations (2) and (3), the induced open circuit voltage, VOC in Figure 1 appears across a total resistance of 2Rrad , and the average power delivered to the matched load is, F IJR G H K 1 VOC PL 2 2 Rrad 2 rad 2 V OC . 8 Rrad (4) Let Ei equal the amplitude of the electric field intensity at the receiving antenna. The timeaverage power density at the receiving site is S Ei2 E2 . i 2 240 (5) The open circuit voltage across a receiving antenna can then be determined using Equations (4) and (5). 2