Radar System Engineering

256 RADAR BEACONS [SEC.85
In the case of beacons interrogated and received bya radar set, ~,is
nearly equal to X,; (Gd ~.. usually equals (GE,)~.. since the same antenna
is likely to be involved; and (GR,)~~.usually equals (G~,)~,. since beacon
antennas for receiving and transmitting need to have the same radiation
pattern and are therefore alike. The condition for balance of the two
links, namely that R: equal R:, then becomes
The receiver of the beacon is almost always less sensitive than that of the
radar, either by necessity (because of the greater bandwidth), or by
choice to avoid undesired triggering (see below); hence P:, < P~i. In
the balanced system, then, the transmitter of the beacon may as well be
less powerful than that of the radar in the same proportion.
In actual cases, Eq. (1) and a corresponding equation for the received
power in the reply link involve two additional factors. One of these is a
geometrical factor that expresses the effects of interference and diffraction.
The other takes account of the attenuation of the radiation in the
atmosphere. These matters as they pertain to radar echoes are discussed
in Sees. 2“12 and 2.15. It should be noted, however, that the
numerical factors appropriate here are the square roots of those for radar
signals, when for the latter the effects on both the transmitted and
reflected pulses are lumped together. These factors drop out of the
expression (4) just as the antenna gains do, since they have the same value
for both links. In any beacon system in which the frequencies of interrogation
and reply are substantially different, however, all of the factors
in Eqs. (2) and (3) must be retained and these additional ones must be
added. The two links have to be designed separately to get proper
operation at all ranges up to some fixed value or to meet other particular
requirements.
It is apparent from Eq. (1) that another consequence of the independence
of the two links is a different law for the relation between signal
strength and range. Radar echoes vary in pulse power as the inverse
fourth power of the free-space range, whereas beacon replies vary only as
the inverse square. In general, beacon signals do not vary as much
between particular values of range, do not cut off as abruptly with
increasing range, and do not give as deep interference minima as radar
signals do.
A zimuth.—One further consequence of the separation of the two links
is that the scanning sector through which beacon replies are obtained is
limited either in the interrogation link or in the reply link according to
circumstances. Equation (1) becomes more generally
(4)
(5)