Practical_Antenna_Handbook_0071639586

C h a p t e r 3 : A n t e n n a B a s i c s 105
RF energy on an antenna, however, moves at a velocity somewhat less than that of
the radiated energy in free space because the antenna’s dielectric constant, e, is greater
than the e 0 of free space.
Because of the difference in velocity between the wave in free space and the wave
on the antenna, the physical length of the antenna no longer corresponds to its electrical
length. An antenna that is exactly a half-wavelength electrically will be somewhat
shorter than this physically. This is also reflected in the formula for the velocity of electromagnetic
waves,
vP = f λ
(3.30)
Circumference wavelengths
where n P is the velocity of propagation, ƒ is the frequency, and l is the wavelength.
Since the frequency of the RF energy must remain constant, a decrease in the velocity
results in a decrease in the wavelength. Therefore, the RF wave traveling in an antenna
has a shorter wavelength than the same wave traveling in free space, and the physical
length of a l/2 dipole will be shorter.
The actual difference between the physical length and the electrical length of the
antenna depends on several factors. A thin wire antenna, for example, has less effect on
wave velocity than an antenna with a large cross section. As the circumference of the
antenna increases, the wave velocity becomes progressively lower relative to its freespace
velocity. The effect of antenna
circumference on wave velocity is illustrated
in the graph of Fig. 3.12.
Other factors can also lower wave
velocity on the antenna. Stray capacitance,
for example, increases the dielectric
constant. In many installations
this capacitance is dominated by the
insulators used to give physical support
to the antenna, as well as nearby
objects made of metallic or high dielectric
materials. The change in velocity
resulting from stray capacitance
is called end effect because the ends of
.01
the antenna act as though they are farther
apart electrically than they are
.005
physically. End effect for a typical dipole
of wire that is thin compared to
its length is counteracted by making
the physical length about 5 percent
.002
shorter than the electrical length, as
expressed in the formula
.001
0 .2 .4 .6 .8 1.0
Wave velocity
Free-space velocity
Figure 3.12 Effect of antenna
circumference on wave velocity.