Page 280 - Maxwell House

260 ANTENNA BASICS

to only a particular frequency rate. The whole bank simultaneously maps the set of signals from
multiple far and near-range targets. As long as a satellite radar can “see” the targets emitting
the train of coherent pulses, the energy of multiple pulses is accumulated by each filter and thus
grows. In other words, long target visibility provides a definite measurement of even slight
differences in adjacent filter outputs and high azimuth resolution, i.e. resolution along the
ground swath. The degree of improvement is customary characterized by the so-called antenna
synthetical aperture length showing the ratio between the azimuth resolution with and without
the Doppler beam sharpening procedure. It is possible to show [21] that the synthetical L and
actual antenna length are related as ≤ ⁄ . For example, if = 1 (antenna with wide
⁄
0
beam that ensures longer target visibility) and = 100 km the length L can reach 100 km
0
There is no way to put something even close in size on satellite or aircraft.
5.5.8 Linear Array with Multiple Simultaneous Beams
One of the unique and significant advantages of linear arrays is their ability to simultaneously
generate a grid of independent beams but not in sequence as shown in Figure 5.4.1c. They may
be fixed in space, steered independently, or steered as a group. To demonstrate this
phenomenon, assume that the linear array of (N + 1) elements is excited simultaneously by two
signals of unit magnitude at the same frequency, i.e.

() = ∑ −(cos−cos 1 ) + ∑ −(cos−cos 2 ) = ∑ −cos � cos 1 +
Σ
=0
=0
=0
cos 2 � (5.101)
Here 1,2 = cos is the inter-element time delay provided by the first and second TTD
1,2
unit, respectively. The summands in the parenthesis of (5.101) can be transformed as
cos 1 + cos 2 = (cos 1 +cos 2 )/2 � (cos 1 −cos 2 )/2 + −(cos 1 −cos 2 )/2 �
Applying Euler’s formula we obtain

(cos 1 −cos 2 )/2 −(cos 1 −cos 2 )/2 � = 2cos((cos − cos )/2)
� + 1 2
Then (5.101) yields

() = 2 ∑ −(cos−(cos 1 +cos 2 )/2) cos((cos − cos )/2) (5.102)
=0
Σ
1
2
This expression clearly shows that dual signal excitation (5.101) is equivalent to
1. The progressive time delay over the array with the inter-element delay of = (cos +
1
cos )/2.
2
2. The inter-element magnitude modulation defined by the expression cos((cos −
1
cos )/2). The equivalent circuit of such excitation is similar to the depicted in Figure
2
2
5.5.5 where the power is divided not equally and accordingly to cos ((cos −
1
cos )/2), = 0,1,2, … , . Figure 5.5.9a demonstrates the necessary power distribution
2
in 12 elements array if = 50° and = 60°.
1
2
3. If so, according to (5.93) and (5.101) the array pattern is superposition of two beams