ANTENNAS 
5,0 
n=5 
n=6 
Ficure 14. Cophased half-wave dipoles (relative fields). 
or (2) short inductive elements, as indicated in 
Figure 13. The suppressed loops are practically 
nonradiative. 
The radiation field at distance d is the vector sum 
of the fields from the n half-wave elements. The 
contribution from each element lags that of the next 
element above by an angle 
a= > cos 6- = = 7 cos @ radians, (17) 
determined by the extra distance [(A/2) cos 6] 
which it must travel. The radiation field is then 
equal to the radiation field of one half-wave element 
(as a function of angle @) multiplied by the vector 
resultant for the n elements. Thus 
ats 
601, cos gq 6088 
DS a sin 8 
[e? + eit 4 oa eeteete eXtra] 
us | Na (18) 
601, cos ( 2 cos a) sin 5) 
=F) . 5 a i 
d sin 0 sin 2 
REACTANCE IN OHMS 
The radiation patterns for various values of n are 
plotted in Figure 14. Table 1 gives the radiation 
resistances, relative lengths of major lobes, and the 
gains, with comparative figures for the doublet and 
the multi-half-wave antennas discussed on page 350. 
Effects of Finite Diameter 
on Center-Fed Linear Antennas 
Figure 15 shows the input reactance, and Figure 16 
the input resistance of a center-fed antenna of 
arbitrary length. The input impedance is a series 
combination of the two components. The important 
regions of the curves correspond to antenna. half- 
lengths near \/4 and near \/2. The former repre- 
sents a center-fed half-wave antenna, whereas the 
latter represents a pair of end-fed half-wave antennas 
excited in phase. The half-length of the antenna was 
used in plotting, because in these terms the reactance 
curves resemble those for an open-ended trans- 
mission line. 
In the regions of principal interest the reactance 
curves are nearly straight lines whose slopes depend 
on the diameter of the antennas expressed in wave- 
lengths. The slopes of the reactance curves decrease 
SS A 
Va a Ze a 
HALF-LENGTH OF ANTENNA 
Ficure 15. Reactance at input of a center-fed antenna of arbitrary length. 
