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Consider a volume v bounded by a closed surface s. The complex power Ps delivered by the sources in v equals the sum of the power Pf flowing out of s, the time-average power Pdav dissipated in v, plus the time-average stored power in v: P s = Pf + Pd + J'2w(Wm - We ) BV BV BV (1-28) The complex power flowing out through closed surface s is found from Pf = ! Jr 2:tr. E x H* • ds (1-29) where ds = dso and 0 is the unit normal to the surface directed out from the surface. Note that E and H are peak phasors, not rms, leading to 112 in power expressions.

In addition, the term absolute gain, which is synonymous with gain, is sometimes used. 9 ANTENNA IMPEDANCE, RADIATION EFFICIENCY, AND mE SHORT DIPOLE The input impedance of an antenna is the impedance presented by the antenna at its terminals. Thus, suitable terminals must be defined for an antenna. The input impedance will be affected by other antennas or objects that are nearby, but for this discussion we assume that the antenna is isolated. Input impedance is composed of real and imaginary parts: (1-165) The input resistance RA represents dissipation, which occurs in two ways.

At lower frequencies, where the antenna can be small compared to the wavelength, the far-field distance may have to be greater than 2D2/A in order that all conditions in (1-99) are satisfied. See Prob. 7-4. The concept of field regions was introduced in Sec. 6 and illustrated with the fields of an ideal dipole. We can now generalize that discussion to any finite antenna of maximum extent D. The distance to the far field is 2D 2/A. This zone was historically called the Fraunhofer region if the antenna is focused at infinity; that is, if the rays at large distances from the antenna when transmitting are parallel.

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