Radar System Engineering

144 C-W RADAR SYSTE.JfS [SEC. 58
give rise to a beat’ j~, as shown in the bottom graph of Fig. 5.12. Plainly
enough, the greater the target distance, the greater this beat frequency;
its magnitude is then a direct measure of the range. The signal of this
frequency is therefore amplified and limited, and the frequency measured,
usually by a cycle-counting device of some sort. The frequency meter
is then calibrated in terms of range.
.2
Such a system would work, as described, and would also work on
multiple targets. But linear frequency modulation is not easy, and
for single targets the operation is not greatly affected by a change from
linear to sinusoidal frequency modulation. The difference frequency
then varies sinusoidally with time,
but the important point remains,
namely that the mean magnitude
of the difference frequency depends
on the range. Sinusoidal
frequency modulation is therefore e ~
adopted since it requires simpler 2
r
apparatus and accomplishes the ~
same result.
There is one subtlety that is
worth some discussion. If the +
I
mean or carrier frequency were an FIG 5.12.—The upper figure shows, in
integral multiple of the modulator the full line curve, the instantaneous transfrequency,
it is obvious that the
mitter frequency as a function of time. The
dotted curve is the received frequency. The
output of the mixer would be lower figure shows the difference, or beat,
periodic with periodicity correquencies,
between
as
‘ransmi%d
a funct]on
and.
of time.
‘e’eived ‘r!-
The horLsponding
to the modulating fre- zontal axisin the upper figurecorrespondsto
quency. This would mean that
the meantransmitterfrequencyf~.
each modulation period would contain the sa’me number of cycles.
This number is then integral and we see that the frequency meter can
read only 1, 2, . . “ , n times the modulating frequency. Actually,
the same conclusion holds even with no special relation between modulation
and carrier frequencies, if, as is usual, we use a cycle-counting type
of frequency meter. Naturally, it is of interest to translate this stepwise
behavior of the frequency meter into altitude readings. For the
linear-modulation case we easily find j ~= 4j,Ajh/c with f, the modulating
frequency, Af the total frequency swing, f. the beat frequency,
and h the height. Solving for the height and introducing the fact that
f. is quantized in steps of f,, we find for the error 6h
1It isbeats of this sort,whichmay be describedasdueto time-delaydemodulation
of F.M,that are regardedas spurioussignalsin the system describedin Sec. 5.6 and
that must be avoided by reducing FM of the transmitterto the lowest possible
value