Radar System Engineering

SEC. 5.6] SIMPLE DOPPLER SYSTEM 137
where ~(z) is the dish illumination as a function of x, the transverse
distance from the axis of rotation; k = 27r/i; and dO/dt is the angular
rate of rotation. Now E is zero outside the range x = ~ d/2 for a dish
with diameter d and so g(u) is zero for kd ~ < w. This corresponds,
incidentally, to the doppler frequency associated with the motion of the
edge of the dish or, what is usually about the same thing, the number of
beamwidths scanned per second. Although this calculation is more
complicated for separate transmitter and receiver dishes, etc., the
important general conclusion stands—namely that, in so far as the
approximations used are good, the spectrum produced by scanning is
definitely confined to a finite frequency range.
Another lower limit on bandwidth is set by the modulation due to
fluctuation in target cross sections. If the target is an airplane, for
example, inspection of Fig. 3.8 shows that even moderate yawing will
introduce large fluctuations in returned signal. The frequency spread
so introduced depends on the rate of yaw and on the ratio of the target
dimensions to the wavelength, this ratio determining the number of
pattern lobes per radian. Calculations are difficult because of lack of
data, but experimentally a value of about 30 cps at x = 10 cm is found.
Another and equivalent point of view is that when the plane is turning
different parts have different doppler frequencies.
Finally there is, in principle, a limit set by target acceleration.
Thus if we have an accelerating target it may happen that the doppler
frequency will transit the pass range of the band-determining filter
before the filter has time to build up, in which case the signal may be
missed. If the acceleration is a, and the band is Av, so that we require a
buildup time of l/Av, we then find
A, , 60a 34
(4)
() -r
\tith a in ft/sec2. and A in cm.
Apparatus Considerations. —Having blocked out the system and
determined the leading design constants, we can now proceed with the
detailed engineering. Figures 5.6 and 5.7 show the final result; there
follow a few remarks as to the more important ways in which the engineering
technique for this system cliffers from that used in pulse systems.
There are no high pulse powers and both intermediate- and audiofrequency
amplifiers are narrow-band. Gains per stage are limited by
stability rather than by bandwidth; in other words, the technique is
like that of ordinary radio rather than like that of television. Because
of the large size of the leakage signal relative to the target signal, only