Page 333 - Maxwell House

FEED LINE BASICS 313

1. The axial ratio defined in Section 5.1.2 is frequency and coordinate dependable.
2. The function tan (/) describing the magnetic magnitude ratio is positive while x < a/2
and we are in the right half of WR. Then the polarization is right-handed and elliptical as
soon as | | ≠ 1. The observer looks down along the y-axis (see Figure 6.6.6) while
⁄

the wave propagates over positive direction of the z-axis, i.e. is positive. We will call
such wave forward.
3. tan (/) < 0 as x > a/2. Thus, the polarization of the forward wave in the left half of
WR becomes left-handed and elliptical as soon as | | ≠ 1.
⁄

4. Now let change the direction of wave propagation to backward, i.e. putting → − in
(6.32). The right-handed polarization in right part of WR becomes left-handed and vice
versa.
5. Evidently, both polarizations are CP if and only if | | = 1 or |sin (/)| = /2.
⁄

To estimate the average power carried by the TM -mode we can put (6.32) into (3.49) from
10
Chapter 3 and obtain
2

0

∗
∗
= ∯ ( x )/2 ∘ = ∫ ∫ = 4 � (6.33)
Σ

0
0

2
= �1 − ( 2) > while < 2
⁄
⁄

0
0
Here is so-called WR characteristic impedance and ≅ 120 is the wave impedance of
0

free space. Under standard WR dimensions b = a/2 and = 0.7 we have = 1.13 ∙
Σ
10 ( ) [W]. Therefore, the maximum power (as = 3 MV/m) that can be transported is
2
−4
0 0
92 MW at = 30 cm and drops to 100 W at = 1 mm. Note that the permissible power could
be 2 – 3 time less. Evidently, the weakest area of WR susceptible to the breakdown is the middle
of the broad wall where the E-field intensity is highest. The breakdown strength can be
enhanced by rising the air pressure in WR or filling it up with special pressured or unpressured
gases like Sulfur Hexafluoride (SF ) that provides 2 – 3 time better breakdown protection than
6
air. Although this gas is a non-toxic, it must be handle with caution. By displacing oxygen in
the lungs, it carries the risk of asphyxia if too much is inhaled. This gas is most commonly used
in hermitized high voltage power line equipment.
If we aim to transmit through WR the power close to the limit, we must acute care of the WR
fabrication process, namely the cleaning of the inner metal surface. Such technology as
electrochemical polishing lets improves the metal micro-profile leveling its micro-peaks and
valleys (look at Figure 4.4.3 of Chapter 4). Moreover, this polishing process allows removing
from a conductive surface the tiny metal particles sometimes remaining after WR machining.
The probability is very high that these microparticles if they left, would be moved from the
surface by strong E-field and then accelerated causing the undesired extra ionization and
following breakdown.
The next topic is the dissipation loss in hollow WR. Recall that the magnetic components

and are the source of the surface currents (see Figure 6.6.6 and check the boundary

conditions in Table 2.2 of Chapter 2). Evidently, the higher current density means higher loss.
Due to the skin effect, the heat energy releases into the WR metal walls commonly of high
thermal conductivity and spreads there almost instantaneously and practically uniformly.
Meanwhile, to prevent overheating the WRs can be incorporated into water jacket, have the