Graphics Programs Reference
In-Depth Information
The AM signal
E
()
can then be written as
E
()
E
0
=
cos
(
ω
s
t
ϕ
)
=
E
0
ε
e
cos
ω
s
t
+
E
0
ε
a
sin
ω
s
t
(9.3)
where is a constant called the error slope, is the scan frequency in radi-
ans per seconds, and is the angle already defined. The scan reference is the
signal that the radar generates to keep track of the antennaÓs position around a
complete path (scan). The elevation error signal is obtained by mixing the sig-
nal
E
0
ω
s
ϕ
E
()
with
cos
ω
s
t
(the reference signal) followed by low pass filtering.
More precisely,
1
---
E
0
1
---
E
e
()
E
0
=
cos
(
ω
s
t
ϕ
)
cos
ω
s
t
=
cos
ϕ
+
cos
(
2ω
s
t
ϕ
)
(9.4)
and after low pass filtering we get
1
---
E
0
E
e
()
=
cos
ϕ
(9.5)
Negative elevation error drives the antenna beam downward, while positive
elevation error drives the antenna beam upward. Similarly, the azimuth error
signal is obtained by multiplying
E
()
by
sin
ω
s
t
followed by low pass filter-
ing. It follows that
1
---
E
0
E
a
()
=
sin
ϕ
(9.6)
The antenna scan rate is limited by the scanning mechanism (mechanical or
electronic), where electronic scanning is much faster and more accurate than
mechanical scan. In either case, the radar needs at least four target returns to be
able to determine the target azimuth and elevation coordinates (two returns per
coordinate). Therefore, the maximum conical scan rate is equal to one fourth of
the PRF. Rates as high as 30 scans per seconds are commonly used.
The conical scan squint angle needs to be large enough so that a good error
signal can be measured. However, due to the squint angle, the antenna gain in
the direction of the tracking axis is less than maximum. Thus, when the target
is in track (located on the tracking axis), the SNR suffers a loss equal to the
drop in the antenna gain. This loss is known as the squint or crossover loss.
The squint angle is normally chosen such that the two-way (transmit and
receive) crossover loss is less than a few decibels.
9.2. Amplitude Comparison Monopulse
Amplitude comparison monopulse tracking is similar to lobing in the sense
that four squinted beams are required to measure the targetÓs angular position.
The difference is that the four beams are generated simultaneously rather than
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