Radar System Engineering

32 THE RADAR EQUATION [SEC.28
first amplifier stage-are taken into account, together with the fact that
the input impedance of microwave receivers is not unlimited, the optimum
value of R turns out to be finite. The condition R = Z is, in fact, not
unusual. This condition, in our ideal system of Fig. 2.3, leads to
(21)
A question of fundamental interest, though not as yet of much
practical moment, is the one raised eaiiier about the temperature to be
assigned to the antenna radiation resistance. This is certainly not in
general the temperature of the metal parts of the, antenna. The reader
may correctly surmise, from what has been said, that the effective temperature
of this element of the circuit is that of any surroundings of the
antenna with which the antenna can exchange energy by radiation—that
is to say, it is the temperature (or a suitable average of the temperatures)
of whatever would absorb energy radiated by the antenna as a transmitter.
This has indeed been demonstrated experimentally. It has been
shown 1that a microwave antenna pointed at the sky receives only a very
small amount of radiation, corresponding to an absolute temperature of
at most a few degrees. If our receivers were very nearly ideal this would
have the practical result of making it much easier to detect aircraft
appearing at high angles of elevation. In the best existing receivers the
reduction in noise output which could be obtained by pointing the antenna
upward would amount to some 10 per cent.
The foregoing somewhat academic discussion of thermal noise would
be inappropriate in this place were it not for two facts. First, microwave
receivers, even as this is written, have been brought so close to the
pinnacle of ideal performance that it is well for the radar engineer to
appreciate the nearness, and the finality, of the goal. Second, thermal
noise, although it is not wholly to blame for the noise background in
microwave receivers, provides a very convenient standard in terms of
which the performance of an actual receiver can be specified.
We shall define, as the over-all noise jigure N of a receiver, the ratio of
signal power available from the antenna to kZ’@, 2 when the mean noise
power and the signal power are equal as observed at some stage in the
receiver where both have been amplified so highly as to override completely
any noise introduced by succeeding stages. In framing the definition
so broadly we have in effect included, under “receiver,” not only the
rnixer but all associated r-f circuits. It is well to do so at this stage, for the
analysis of the contribution of each part of the input system to the over-
I R. H. Dicke, ‘(The Measurementof Thermal Radiation at Microwave Frequencies,”
RL Report No. 787. See also Dicke etal., Phys. Rsu., 70, 340 (1946).
2In thisdefinitionT is customarily,and arbitrarily,takento be 291“K