Radar System Engineering

SEC. 16.2] BASIC PRINCIPLES OF MTI 629
heard in the phones. The echo frequency is given by the well-known
doppler formula
fl=
gf.
The beat frequency
is then
Since the target velocity v is very small compared
light c, this can be written as
with the velocity of
For v in miles per hour and k in cm this becomes
f,=E
x“
See, for example, Fig. 5.12.
A
~h
=f~f
FIG. 16.3.—Doppler effect with c-w system.
The arrangement of Fig. 16.3 gives no range information. This
can be remedied by chopping up the outgoing train of waves as in Fig.
16.4. The beats in the telephones now consist of a succession of pulses
whose envelope has the doppler frequency f~. Note that the doppler
effect can be viewed as causing a phase shift of the echo from pulse to
pulse. It is easy to calculate this phase change and to show that it is
equivalent to the frequency shift. The distance traveled by the target
between pulses is uT, where T is the repetition period. Hence each
pulse travels a distance 2vT less than the preceding pulse. This is
2vT/h wavelengths, so that the phase change is 2r2vT/h between each
pulse and the next. The beat frequency is then 2v/k, as before.