Radar System Engineering

SEC. 85] INDEPENDENCE OF IN TERROOA TION AND REPLY 255
range, Eq. (1) gives
(2)
In Eq. (2) R: is the maximum free-space range for interrogation of the
beacon; when it is at greater ranges it will not be triggered.
The corresponding expression for the reply link is
[$
h’: = & $+(G,,) m.x(G.s)me.x
(3)
[ Sr 1
In Eq. (3), P!, is the peak value of the available received power
required to give a satisfactory beacon signal on the indicator of the
interrogating system, due account being taken of scanning losses and
other circumstances of use. The range R; is the greatest one for which
reply signals from triggered beacons will be usable. This cannot be
defined as clearly as is R! since having a signal “satisfactory” is less
definite than having it either present or absent. The other quantities
in Eq. (3) are of obvious significance if it is kept in mind that the subscript
r refers to the reply link.
In the preceding paragraphs it was assumed that the triggering of the
beacon and the intensity of the displayed reply depend on the pulse
powers of the two pulses. This implies that both the receiver in the
beacon and the one in the interrogating system have a bandwidth sufficient
to insure that both received signals rise to a value that depends on
the pulse po\ver and is independent of the length of the pulse \vithin wide
limits. This condition is usually the desired one and the receivers are
designed accordingly. If a receiver of very narrow bandwidth should
be used, however, the peak value of its output would then depend upon
the energy of the pulse, rather than upon the pulse power. For such
cases Eqs. (2) and (3) would be modified by substituting the transmitted
and received values of the energies per pulse for the respective pulsepower
values.
It is sensible to design the system so that R; N R: since there is no
use in having replies that are too weak to be observed even though the
beacon is being interrogated, as can be the case if R: < R?. Likewise
nothing is gained by making provision for strong replies if they are absent
because of the failure of the interrogation. This situation can arise if
R: > R!. The common value of R! = R$ must be made equal to the
desired maximum range, and indesd somewhat larger if a reasonable
factor of safety is desired. It is sometimes useful to make R; somewhat
larger than R: iu order to facilitate recognition by the operator of beacon
signals in the noise.