Radar System Engineering

SEC. 15.8] CHOICE OF BEAM SHAPE 601
reasonable overlapping of pulses a beamwidth of 0.2° at half power might
be considered adequate.
In order to show clearly the effect of bearnwidth on R-,, it is necessary
to reconsider the range equation [see Eq, (1)],
R— -
PuA ‘j’
= () 4mStipA’
‘~
If we let A = H X W, where
we obtain
H = height of antenna aperture,
W = width of antenna aperture,
‘-= (YT”3’)
(5)
With coverage requirements in height specified, the beamwidth in
elevation angle is fixed; therefore, H,O is a constant. We then have
(6)
holding P and u constant,
where
which is now a constant,
From Eq. (2) we see that Sti, is inversely proportional to the square
root of beamwidth 0. All other factors that enter into the value of S~,.
can now be considered as constants and we can therefore write
where K2 is smother constant. The bearnwidth in radians is A/W to a
good approximation; substituting this expression for e we have
R m!.. = ~2JJ”%x>+, (8)
From Eq. (8) we see that if the beamwidth is sharpened bv decreasing
the \vavelength and holding the antenna width constant, R~., decrrases
slowly, The variation of R~., with antenna width is comparati~rely
rapid, If the bearnw-iclth is sharpened to the point where the number of
pulses per scan on the target (IV,.) is smaller than about 10, Eq. (8] no
longer holds. Then R~.. becomes a more rapid function of k and a
slower fllnction of H’. For values of .Y.. less than about 5, the ~ariation
of Rmx 1~-ithW and k is gi~,cn approximately by