Radar System Engineering

130 C-W RADAR SYSTEMS [sm. 53
pointed out in Chap. 4, l/T is also the maximum rate at ~rhich information
can be received.
When frequency modulation is used, the variation of a with u depends
on the form of modulation just as it depends, in the amplitude-modulation
case, on the pulse shape. Usually the frequency is varied either (a)
sinusoidally or (b) in a sawtooth manner. The results are shown qualitatively
in Figs. 5.4a and 5.4b, which are drawn for the normal case in which
the frequency deviation is large compared to the modulation frequency.
Also, only the envelope of the la. Ihas been drawn. The actual la.1 fluctuate
irregularly belo~v this value.
For pulse modulation, the phases
are such as to make the component
waves add to a maximum periodically.
For example, if one pulse is
centered on time t = O, the phases
(a)
are all zero. In the frequency-modulation
case, the phases are such
that the various components add to
give a result that varies more or less
sinusoidally with time, but with constant
amplitude.
Of course there are many possible
types of modulation besicfcs simple
AM and FM but these will not be
treated here.
5.3. Effect of Target.—The effect
of reflection from the target on this
spectrum will now be considered.
(b-)
FIG. 54.-Appr0ximate frequenr>spectra
for frequency modulation, (a)
with sinusoidaland (b) with hnear sawtooth
variation of instantaneous frequency.
More precise figures would
show a few sidebands outside Af, the
maximum frequency deviation, and tbe
intensities of the various sidebands as
fluctuating irregularly about the mean
value here shown.
First, all amplitudes are greatly reduced,
as is discussed in detail in
Chap. 2. Second, the scattering
cross section of the target is, in
general, a function of o; the various
amplitudes are therefore not equally reduced. This effect can be
expected to be notable only when the target extent is comparable to c
divided by the bandwidth. Third, there is a phase change, linear in w,
with proportionality constant depending on the distance. Fourth, all
frequencies are shifted by the doppler frequency. Finally the scattering
cross section varies with time; this introduces an additional modulation
which broadens each of the returned sidebands by an amount depending
on the rate of the fluctuation. (All this is for a single target. Usually
there are many targets, in which case the above specification
complicated by a summation over all targets.)
is further