At the receiving end, dB ?V ?dBm (decibels above 1 ?V ?decibels above 1 mW) A receiving antenna at a distance r from the transmitting antenna with an aperture A will receive power P _r

where ? is the Poynting vector.

We can also obtain the received power from Fig. D.1c

where V is the induced voltage in volts. For a maximum power delivery ZL = Z _a ^[1], where the notation ^[1] indicates complex conjugate. Then, we obtain Z _L + Z _a = 2R _L, where R _L is the real-load resistance. Equation (D-2) becomes

Assume that a dipole or a monopole is used as a receiving antenna. The induced voltage V can be related to field strength E as ^[1]

Where E is expressed in volts or microvolts per meter. Substitution of Eq. (D-3) into Eq. (D-4) yields

If we set R _L = 50 ?, P _r in decibels above 1 m, and E in decibels (microvolts per meter), Eq. (D-5) becomes

Figure D.l: An actual antenna and its equivalent circuit, (a) An actual antenna; (b) equivalent circuit of a transmitting antenna; (c) equivalent circuit of a receiving antenna

The notation "dB?V" in Eq. (D-6) is a simplification of decibels above 1 ?V/m and has been accepted by the Institute of Radio Engineers. We can find the equivalent aperture