Page 277 - Maxwell House

Chapter 5 257

5.5.6 Within-Pulse Scan Technique

One more frequency scan approach that can be called a frequency modulated scan is illustrated
in Figure 5.5.7a. According to this drawing the traditional phase shifters or TTD units are
replaced with frequency progressive shifters delivering signals to the radiators with

frequency + ∆, = 0,1,2, … , . Assuming for simplicity that ∆ ≪ and = 1, =
0
0

0,1,2, … , we can obtain from (5.89)
() = ∑ ( 0 +(∆+)) = 0 ∑ (∆+) (5.97)
Σ
=0
=0
0 1 2 3 … N =1/ ,
N

Power Divider 1 : N+1
~ Main Beam Trace

v
a) b)

Figure 5.5.7 a) Schematic diagram of frequency modulated scan, b) Time-space scan
illustration

∆
⁄
Here = −cos = − �1 + � cos ≅ − cos since ∆ ≪ 1 while =
0
0
0
0
0
⁄ . Applying to (5.97) the same expression for a geometric progression sum as in (5.87) we
0
can write the array factor omitting all phase terms as
sin ((+1)(∆− 0 cos)/2) sin ((+1) 0 (−cos)/2)
(, ) = = (5.98)
sin ((∆− 0 cos)/2) sin ( 0 (−cos)/2)
∆ 2
We denote with the symbol = = ∆ the constant which depends on the frequency
0 0
shift choice and linear array geometry. As usual, the peak of main beam is formed when −
−1
cos = 0 or at the angle = cos () where 0 ≤ ≤ 1. This means that the linear
array with feed shown in Figure 5.5.7a continuously steers its beam to cover a wide angular
sector as depicted in Figure 5.5.7b. The areas in blue indicate the sidelobe traces. It is quite a
remarkable fact that such a scan can be done without phase shifters or TTD units. The array
swings its beam between 0° and 90° for the time period between t = 0 and = 1/ =
. To illustrate how fast it can be done suppose that /2 = 0.5 and ∆ = 10 kHz
0 /2
∆ 0
(even low-band surveillance radars typically work at frequencies above =150 MHz).
0
Then = 50µs only. It means that the 90°-scan can be provided during the duration of a
single radar pulse. That is why such ultra-fast beam steering is often called a within-pulse scan
allowing us to revisit the same target repeatedly. The proper subsequent signal processing
greatly improves recognition of the final target or group of targets. We refer the reader to [30]
for more information.