350 PROPAGATION THROUGH 
Multiple Half-Wave 
Long Antennas 
For an antenna of length equal to an integral 
number, 7, of half wavelengths, the radiation field is 
given by: 
1. nis odd: 
cos (2 cos a) (15) 
ja id GOT, ANON? 
d sin 0 
2. nis even: 
sin (Z cos °) (16) 
Ey = 601; 2 /) 
d sin 0 
where d is the radial distance te a field point and 
I; is the input current af the center of one of the 
half-wave elements. 
The radiation patterns are illustrated in Figure 11 
for the doublet, n = 1 (the half-wave dipole), and 
n=2,3,4. 
The radiation resistance, both for integral and 
THE STANDARD ATMOSPHERE 
nonintegral numbers of half wavelengths, is plotted 
in Figure 12. 
20 0 «3.0 40 
LENGTH OF WIRE IN WAVELENGTHS 
Ficure 12. Radiation resistance for linear antennas. 
In Table 1 the radiation resistances and the power 
gains for integral half-wavelength antennas are 
listed. 
Cophased Half-Wave Dipoles 
The directivity and gain of linear antennas may be 
increased considerably by the suppression of alter- 
nate current loops, leaving therefore only loops in 
which the currents are all cophased. The suppressed 
loops are contained in either (1) quarter-wave stubs 
TasiE 1. Comparison of alternate and cophased half-wave dipoles. 
Rn 
Em,n 
Radiation Relative major lobe amplitudes 3 Gn 
n resistance-ohms for same current input Gain (power) 
Half 
waves Alternate Cophased Alternate Cophased Alternate Cophased 
currents currents currents currents currents currents 
it 73.1 73.1 1.0 1 1.09 * 1.09 
2 93 199 1.23 2 1.19 1.47 
3 105 317 1.38 3 1.32 2.09 
4 113 439 1.5 4 1.46 2.67 
5 121 560 1.62 5 1,58 3.26 
G, = Rdoublet (- covet _ doublet ( Em,n y : 
a ae a T, Ry \Z doublet 
Fiaure 13. Cophased half-wave dipoles. 
