Page 232 - Maxwell House

212 ANTENNA BASICS

1
= � + − � sin (−)
0 () 2 () 3 ⎫

1 (−) ⎪
= � + () 2 − () 3 � cos (5.20)
0

1 (−) ⎬
= 0 � + � sin

() 2 ⎪
= = = 0 ⎭

The magnitude of E- and H-field components denoted by symbol 0 in subscripts does not
depend on time and coordinates. According to (4.60), all of them are mutually related through
∆. Note, that Figure 4.3.1a is the graphical representation of (5.20) while
the same factor
the expression (4.68) follows from (5.20) as → ∞.
2. Clearly, the dominant describing near-field terms in (5.20) are when → 0 are
1 (−)
~− sin

0
() 3 ⎫
⎪
1 (−)
~− 0 () 3 cos (5.21)

⎬
1 (−) ⎪
~ sin
0 () 2 ⎭
Therefore, the intensity of an E-field is proportional to 1 () and much surpasses the
3
⁄
intensity of H-field proportional to 1 () only. It means that in the balance of energy near
2
⁄
the dipole ≫ and thus the input impedance of the dipole is mostly capacitive.

Meanwhile, a phase shift of 90° between the E- and H-fields in (5.21) is evidence that the
nearby Poynting’s vector is purely imaginary quantity. Therefore, the portion of the active (i.e.
radiated by the dipole) power is much lower than the reactive one accumulated nearby. The
field zone where
ℑ( ) ≫ ℜ( ) (5.22)

is customarily called the near-field zone. If so, for a short electric dipole this zone is the
bounding sphere of radius ≪ . A good rule of thumb is < /50. Note that the criteria
(5.22) can be applied to any electrically small antennas.
3. The transition zone is defined as the bounding sphere where
ℑ( ) ≅ ℜ( ) (5.23)

A rule of thumb for a short electric dipole is /5 > > /50.
4. Finally, the far field zone is the region where the radiated power prevails or

ℜ( ) ≫ ℑ( ) (5.24)