Radar System Engineering

SEC. 16.8] RECEIVER CHARACTERISTICS 647
input of the receiver, the total increment in amplitude can be written as
Ax=kx+N,
where kz is the amplitude component of the clutter fluctuation and N is
the component of the i-f noise vector in the direction of x. The output
fluctuation Ay is given by
Ay = $
Ax,
and we require it to be independent of the clutter amplitude z. Thus we
have
dy= K
z kx + N’
where K is the (constant) value of Ay. Integrating this equation with the
condition that y = O when z = O, we get the following expression for the
characteristic of the i-f amplifier:
(12)
For values of x giving a fluctuation kx considerably less than noise, the
characteristic is linear. For large values of x it is logarithmic. A
receiver with this characteristic is called a lin-log receiver.
The output of the lin-log i-f amplifier has to be added to the reference
signal and then detected. Since the clutter varies in phase as well as
amplitude, its phase variations are converted by the detector, when the
reference signal is present, into amplitude variations, which unfortunately
are not independent of the size of the clutter. It can be shown, however,
that no serious harm results if the reference signal level is kept somewhat
smaller than the maximum amplitude of the linear portion of the receiver
characteristic.
The second method of obtaining uniform output fluctuations depends
on the fact that the rms phase variation of the clutter is independent of
the size of the clutter. Thus all that is.required is a limiting i-f amplifier
to remove the amplitude variations, followed by a phase-sensitive detector
to convert the phase variations into uniform amplitude variations. To
obtain the maximum sensitivityy for targets moving in the clutter it is
necessary that the phase-sensitive detector should have a linear characteristic—that
is, the output amplitude variation should be proportional to
the input phase variation. This can be achieved by using a balanced
detector for mixing the reference signal with the output of the limiting
i-f amplifier.
The relative advantages of the two types of receiver will now be
considered. If the lin-log receiver is used, it is possible to dispense with