Radar System Engineering

140 C-W RADAR SYSTEMS [SEC 37
and jO f ~D, jO + j, f $Dr, from the target, with ~D and ~D~very slightly
different because of the difference in transmitter frequencies. This
slight difference in doppler frequencies leads to a phase difference between
the two doppler-frequency outputs which is a linear function of time,
just as the target range is a linear function of time for constant radial
velocity. This suggests that the phase difference is a measure of the
range.
This is in fact the case, as may be shown analytically, or qualitatively
by the following argument. If the target is very close to the system,
the number of wavelengths from transmitter
to target and back will be the
same, even though the two transmitter
wavelengths differ slightly. Thus the
leakage and target signals will be in
phase or out of phase at the two receivers
simultaneously and the doppler
outputs will be in phase for this range.
As the target gets further away, this
phase difference increases, finally becoming
27rwhen the number of wavelengths
to the target and back is one
greater for j, + j, than for fo. Analytically
one easily finds that the
range is given by
FIG, 5.8.—The upper figure shows
(5)
the frequencies present in the transmitter
spectrum. The lower gives the
same information for the receiver. with @ the phase shift between the two
Frequenciesfo andfo +/, in the receiver
are dueto leakagefrom the transmitter; doppler frequencies.
the samefrequenciesffD come from the This is a perfectly feasible system
target.
and has worked in the field. It is
not nearly so complicated as appears from the description since the two
transmitters can be combined, as also can most parts of the receivers.
The apparatus is essentially like that of the system described in Sec. 5.6
with the addition of a modulator for the transmitter, another audio
channel, and a phase meter. No detailed description will be given
because, as yet, no great practical application of the method has been
made. The principal difficulty at present is the lack of a well-developed
phase meter that will work over a range of both frequent y and amplitude.
Nevertheless, some further discussion is in order both because of the
principles involved and because some future use may be made of the
idea.
Four points of principle should be noted. First, to measure the