Radar System Engineering

596 EXAMPLES OF RADAR SYSTEM DESIGN [SEC. 155
elevation angle, and (6) wavelength. We shall make use of the equation
that gives the maximum detection range of a system as a function of the
system parameters.
The range equation (see Sec. 2.4) can be written as
where
P = pulse power
a = radar cross section of target
A = area of antenna aperture
f is a dimensionless constant dependent on the efficiency of the
antenna aperture. It is equal to about 0.6 for a simple
paraboloidal reflector, and its value is approximately the same
for the parabolic cylinder used for the lower beam of the
set described here. If the reflector is distorted to spread the
beam, as was done for the upper beam of the set under consideration,
A and j cannot be used in the normal way.
Sti = minimum detectable signal power. It varies directly with the
bandwidth B of the receiver, assuming that B is properly
adjust ed for the pulse length, and, to a good approximation
for the problem under consideration, it varies inversely with
the square root of the number of pulses per scan on the target.
Acceptable values for u and Sti. are now reasonably well established,
and, since other quantities determining R-, can be readily measured,
Eq. (1) can be used with some confidence for an absolute determination
of range. The safer practice, however, is to compute coverage relative
to the range performance on similar targets of a system with a similar
scan, which has been carefully checked as to component performance.
This procedure will be followed, and Eq. (1) will be used only for the
relationships it establishes among the system parameters.
15-5. Choice of Pulse Length.-The pulse length is convenient for
first consideration since its relations with the other parameters are
relatively simple. It enters the range equation through its effect on the
value of S~~; this quantity normally varies inversely with pulse length
since the receiver bandwidth, if chosen for optimum performance, is an
inverse function of pulse length.
Before proceeding further with the analysis, a discussion of other
quantities ~hat influ~nce the value of Stim will be useful. To a good
approximation for the problem under consideration, the value of S~~
varies inversely with the square root of the number of pulses per scan on
the target.
(1)