Radar System Engineering

SEC. 165] STABILITY REQUIREMENTS 639
as
y = y~ Cos l+, (1)
where VOis the i-f amplitude and 1#1is the phase difference between the
i-f echo signal and the reference signal. Now @ depends, as we have
already seen, only on the number of cycles executed by the stable local
oscillator and the coherent oscillator during the echo-t ime t1. Thus
where w and w are the angular frequencies of the stable local oscillator
and the coherent oscillator, respectively. The positive sign is to be
taken when the local oscillator is tuned below the magnetron frequency,
the negative sign when it is above. If either oscillator varies in frequency
between pulses by an amount Au, the phase change produced is then
If the frequency
drifts at a uniform rate, then
where T is the repetition period. Thus
(2)
Now, from Eq. (l),
we obtain, for the fractional change in beat amplitude,
which has a maximum value equal to A+. For a high-performance
MTI system a value of 6 per cent for Ay/yo could be tolerated since this
represents the maximum residue of clutter amplitude left after cancellation.
The average residue will then be considerably less than 6 per
cent. The corresponding value of A@ is 0.06 radian or ~ cycle. On
substituting this value in Eq. (2) we get for the allowable rate of drift of
frequency
df= 1
z 100Tt,”
For example, this has the value 20 kc/see’ for T = 1000 ~sec (PRF of
1000) and t,= 500 psec (target at range of 50 miles). It will be seen
later that such a low rate of drift cannot be obtained in a local oscillator
without some special means of stabilization. In the case of the coherent
oscillator, on the other hand, the figure is readily attainable with a wellconstructed
oscillator circuit.
(3)