Transcript ARRAY THEORY-1

ANTENNA ARRAYS
A Short Review
Array Factor (1)
  ref
H  H f ( , )
n
  ref
E  E f ( ,  )

f ( ,  )   am exp( jko rm .rˆ)
m 1
Uniform, Linear Array
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Equally spaced elements along the z-axis
n
1
j ( m 1)(  kd cos )
f ( ,  )   e
n m1
Different radiation patterns can be obtained by changing d and 
Phased Array Antennas
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Each antenna element can be controlled
individually by phase or time delay.
By changing the feeding it is possible to construct
a directive beam that can be repositioned
electronically.
Amplitude control can be used for pattern
shaping
The beam can be pointed to new direction,
narrowed or widened in microseconds.
An array that has a main peak at a certain angle
can also have other peak values depending on
the spacing between the antenna elements.
Grating Lobes
AF for uniform excitation:
f ( )   am exp(jmko d (u  uo ))
uo  sin  o
u  sin 
AF will have a maximum when exponent is a multiple of 2
d
2 (sin   sin  o )  2p

grating lobes will occur at:
to avoid grating lobes:
p
sin  p  sin  o 
d
d
1

o 1  sin  o
8 element array with /d=1
and for uo=0.5 (scan angle of 30o)
300
uo=0 (broadside)
uo=0.5 (scan angle of 30 degrees)
Mutual Coupling
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element pattern of the antenna changes from
its free space (isolated) value when it is
inserted into an array
this coupling effect will be different for each
element of the array.
it may be necessary to use the concept of
“active element pattern”
Element pattern of a dipole located as a center element
of a 7X9 array
Analysis Including Mutual Coupling
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In a strong mutual couping environment
array pattern = element pattern X array factor
does not work ! Solving the problem using
numerical methods is not practical.
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Therefore other effective methods are needed to
account for mutual coupling effects.
Mutual Coupling (cont.)
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Finite Array Approach:
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Used for small and medium arrays.
Active element pattern is calculated separately for each
element in the array.
these patterns are added up to obtain theoverall array
pattern.
n 

Etot   Ei
i 1
may imply simultaneous solution of thousands of equations
Mutual Coupling (cont.)
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Infinite array assumption:
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For large arrays, the central elements that are far
away from edges are affected less
infinite array
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concept can then be used
It is assumed that for all elements the currents are
similar except for some complex constants.
When this approach is used, it is sufficient to
analyze only one element completely
Array Blindness
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Direct consequence of mutual coupling
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Can result in complete cancellation of the
radiated beam at some scan angle
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Occurs when most of the central elements of the
array have reflection coefficients close to unity