Page 243 - Maxwell House

Chapter 5 223

because for both of them () = sin, = /2 and = 4 ≅ 1.2732 or 1.05 dBi. For
⁄
0
Huygens’ radiator () = 1 + sin, = /2 and = 16 ≅ 5.1 or 7.07 dBi.
⁄
0
One more critical antenna dimensionless parameter is called antenna gain G and defined as
how much more power some lossy antenna delivers to the observation point in comparison to
an isotropic antenna emitting the same power as a directional antenna. Since according to
(5.18) the antenna radiated power is = input , we obtain
Σ
= < � (5.49)
[dBi] = 10 log 10

As we have shown before in this chapter (Section 5.2.3) the part of power input coming to an
antenna from a generator might be reflected back and absorbed in the matching and/or generator
circuitry. Evidently, this mismatch loss primarily depends on the antenna’s layout because as a
general rule, the generator circuitry is developed independently by different group of engineers
and considered as a given instance for antenna designers. If so, it is reasonable to define one

more parameter called realized gain that includes the return loss (5.13) as
2
= (1 − | | ) (5.50)

5.2.11 Antenna Effective Aperture
The concept of antenna effective aperture came to electrodynamics from the analogy between
an ideal isotropic antenna and physical abstraction called “black body.” The black body like
14
a perfect isotropic receiving antenna absorbs all incident electromagnetic radiation, regardless
of frequency or angle of incidence. Note that the term comes from the fact that a cold black
body appears visually black. According to the Rayleigh-Jeans Law [36] of thermodynamics,
the average power absorbed by the black body is equal to

3
4 4
≅ = (5.51)
Σ 2 2

Here is the effective absorption surface or aperture of the black body and is the absolute

temperature of the black body. The simple equation in (5.51) is the fair approximation of
Planck’s Law [36] and works quite well while the quantum effects can be neglected. Eventually,
the black body captures power from passing waves and transfers their energy into the energy
Σ
heating the black body and increasing its noise temperature. A similar effect in antennas was
described (see (5.35)) in the Section 5.2.8. Therefore, it must be = noise or
Σ
4 = (5.52)
2
From this equity the effective aperture of the black body or equivalent isotropic radiator
can be found as

14 http://www.pnas.org/content/106/15/6044.full.pdf : “Among all known materials, we found that a forest
of vertically aligned single-walled carbon nanotubes (see Figure 3.3.7 in Chapter 3) behaves most
similarly to a black body, a theoretical material that absorbs all incident light …across a very wide spectral
range (0.2–200 m).”