= 
ANTENNAS 349 
-;(2% (xb 
B= — pon eG) 4h GT, (12) 
a b 
Hy = -j2 [EO EE GD], (13) 
4n Lr r 
By the reciprocity theorem a small current length 
I,dz = I; cos [(21/d)z]- dz induces a voltage (— dV;) 
at the input point which is equal to the voltage 
dV, = E,dz induced in dz by a small current length 
T,dz taken at the input point. Hence 
E,dz _ — dV; 
Tele TI; cos (= :) - dz 
and the total input voltage is 
z=A/4 
Vz= i ~ 8, cs (2%). de. 
z=0 Xr 
Carrying out the operation indicated and dividing 
by I; gives the impedance of the half-wave dipole as 
Z = 73.1 + 742.5 ohms. (14) 
The dipole thus has an inductive reactance of 42.5 
ohms if a sine distribution of current amplitudes is 
assumed. 
The reactance can be altered by changing the 
length of the wire. Increasing the length increases 
the inductance; decreasing the length decreases the 
inductance, first to zero for resonance, and then 
for still shorter lengths to a capacitive reactance. 
Changes in length of only 4 to 5 per cent will pro- 
duce large changes in the reactance. 
Modifications of the 
Half-Wave Dipole 
Two modifications will be given. 
1. Quarter-wave dipole with artificial ground. A 
convenient device for doubling the effective length 
DOUBLET 
(CIRCLE) 
of a dipole is to use an artificial ground plane. It 
usually takes the form of a number of grounded 
rods spreading radially from the base of the antenna 
(Figure 9). If the antenna is a quarter-wave dipole 
the effect of the artificial ground is to produce an 
image quarter-wave dipole; the radiation resistance 
and the radiation pattern of the system are those of a 
half-wave dipole. 
Fieure 9. Quarter-wave dipole with artificial ground. 
2. Folded dipole. Another variant of the dipole 
antenna is the folded dipole, shown in Figure 10. 
It is essentially a center-fed half-wave dipole with a 
parasitic counterpart “dummy” (see page 360 ) 
in its immediate neighborhood and connected to the 
latter at the ends of the dipole. The induced current 
in the dummy has the same distribution as, and is in 
phase with, that of the primary dipole. Hence the 
radiation pattern is essentially that of a simple half- 
wave dipole. The radiation resistance is four times 
that of the ordinary dipole. 
! 
iN PUT 
Ficurt 10. Folded dipole. 
| 1,38 
| 
1 4 
( 
\ 
aaa 
! I; 
| 
| 
| n=3 
Figure 11. Antenna radiation patterns (relative field strength). 
