ANTENNAS 347 
if I; is the effective value of the input current, 
Bi 
Rk, =—. 1 
a (l) 
The radiation resistance of the doublet antenna is 
stated in equation (9) in Chapter 2 to be 
R, = sox (2) ohms. (2) 
Influence of Near-by 
Conducting Bodies 
The impedance of an antenna is affected by the 
presence of conductors in the vicinity and depends 
upon the mutual impedances between the conductors 
and the antenna. The mutual impedance decreases 
with increasing distance so that for conducting 
bodies of comparable size the effect is negligible for 
distances greater than, perhaps, 2 to 3 wavelengths. 
But for conductors set less than a wavelength 
apart, such as an antenna and reflector (or director) 
combination or as antenna arrays, the mutual 
effect plays an important role and modifies the 
input impedance of the antenna. 
For an antenna set near a large conducting body, 
such as a large metallic sheet or the earth, the mutual 
effect is cared for in a different way. If the earth, for 
instance, is assumed plane and perfectly conducting, 
its effect is the same as that of the mirror image 
of the antenna in the ground. As shown in Figure 4, 
wine 
ft ANTENNA 
7; 
i PLANE EARTH 
ay PERFECT CONDUCTOR 
4 Ife IMAGE ==—— 
l u 
VERTICAL HORIZONTAL 
Figure 4. Method of images. 
the image of a vertical antenna is a similar antenna 
with current in the same direction, while the current 
is reversed for a horizontal antenna. The radiation 
field at any point above ground is obtained by 
summing the radiation fields of antenna and image. 
STANDING-WAVE ANTENNAS 
Linear Antennas 
A linear antenna is a straight thin rod supplied 
with alternating current. According to whether the 
connection to the antenna is made at the middle or 
at the end, center-fed and end-fed antennas are 
distinguished. Center-fed linear antennas are also 
called dipole antennas. 
Typical current amplitude distributions are illus- 
trated in Figure 5. The amplitude is always zero 
—_ 
=— 
= 
Fee Le 
END FED GENTER FED 
ALTERNATE CURRENTS CO-PHASED CURRENTS 
Ficure 5. Distribution of current amplitudes with 
linear antennas. 
at the open end while the amount at the input point 
depends on the position of the input connection. For 
thin wires, compared with the length, the distribu- 
tion of amplitudes is approximately sinusoidal. 
Half-Wave Antennas 
Figure 6 illustrates two types of half-wave dipole 
or center-fed antennas and one end-fed antenna, 
together with their lumped-circuit analogues. The 
ACTUAL CIRCUIT 
ft 
vee z “Itt 4f 
CURRENT-FED OR DIPOLE VOLTAGE-FED OR 
CENTER-FED DIPOLE END FED 
SCHEMATIC CIRCUIT 
2 eat earl aa 
A B Cc 
LUMPED-CIRCUIT ANALOGUE 
af 
Figure 6. Three methods of exciting half-wave an- 
tennas and their analogues in lumped-constant resonant 
circuits. : 
SERIES RESONANCE PARALLEL RESONANCE 
input current required varies with the position of 
the input point. The voltage distribution in general 
has a maximum at the points of current zero and 
has a minimum where the current is maximum. 
Half-Wave Dipole 
The half-wave dipole, shown in A and B of 
Figure 6 and in Figure 7, is the type most frequently 
used in the 100 to 3,000 me range. In this range the 
