ANTENNAS 363 
These formulas correspond to the case of nearly 
uniform illumination of the reflector from the source 
at the focus. In practice a source that concentrates 
the field toward the center of the parabola is used 
in order to reduce the magnitude of the side lobes, 
The half-power angle is then more nearly equal to 
6 = 0.6\/D. 
The maximum gain of a parabolic reflector is 
(Jw 
For D = 2 meters and \ = 0.1 meter, the gain is 
approximately 1,000. 
HORNS 
Types of Horns 
Many of the antennas previously described are 
used in the high-frequency [HF] and very high- 
frequency [VHF] bands of frequencies. Horns cannot 
readily be used at these frequencies because the sizes 
required would be excessive. 
But at the microwave frequencies, the size of the 
horn is small and it is easy to feed energy to it 
through a wave guide. In this arrangement the 
horn acts as transition between the impedance of 
the wave guide and the 377 ohms impedance of 
free space and thus reduces to a minimum the 
reflection of energy backward into the guide (such 
as would occur if the wave guide ended in an open 
pipe). 
Common types of horns are sectoral (discussed 
in next section ), pyramidal, conical, biconical, etc. 
Only the first type is discussed in this section. 
Sectoral Horn with TE,, Wave 
For this case the horn is flared only in width and 
is an extension of the wave guide of width b and 
depth a. For the TH,» wave the electric field is 
parallel to the dimension a and varies in strength 
cosinusoidally across the wave guide and horn open- 
ing, as shown in Figure 44. The length of the horn 
is R and the flare angle is ?. 
Figure 44. Sectoral horn. 
Figure 45 illustrates the pattern shapes in the 
plane parallel to dimension b for various flare angles. 
For this type of wave, the cutoff frequency of the 
wave guide is 
Ee 1s 
43 
Banh (43) 
Se 
with b in meters. The operating frequency should 
be near but not greater than twice this value. 
The gain depends upon the length R and the flare 
angle ¢, and is plotted in Figure 46. 
Qos $:76 SS g-90° 
Ficure 45. Radiation pattern for a sectoral horn hav- 
ing various flare angles. 
Power Gain for 9 =1 
(0) 10 20 30 40 S50 
Flare Angle ,Degrees 
Power Gain for 4/4 =1 
Fa 
SOON aE 
Fania as 
4 6 8 10 15 20 30 
Horizontal Aperture in A 
Ficure 46. Gain of sectoral horn with TF1,0 wave. 
(These curves are for a vertical aperture ratioa /A = 1. 
For other ratios the gain given should be multiplied by 
a/X.) (From Radio Engineers’ Handbook by Terman.) 
