ANTENNA ARRAYS
Array Factor (1)
  ref
H  H f ( , )
n
  ref
E  E f ( ,  )

f ( ,  )   am exp( jko rm .rˆ)
m 1
Phased Array Antennas





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



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

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.

Therefore other effective methods are needed to
account for mutual coupling effects.
Mutual Coupling (cont.)

Finite Array Approach:



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.)

Infinite array assumption:


For large arrays, the central elements that are far
away from edges are affected less
infinite array


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
Mutual Coupling (cont.)
For medium size arrays, the exact AEP
methods are difficult to use and average AEP
method yields in errors in calculating the array
pattern
For these arrays the combination of the two
methods are used to obtain more accurate
results for the array pattern
Array Blindness
•
Direct consequence of mutual coupling
•
Can result in complete cancellation of the
radiated beam at some scan angle
•
Occurs when most of the central elements of the
array have reflection coefficients close to unity
Array Performance
•
•
•
•
•
Array Lattice
Array Bandwidth
Differences Between Single Element and
Array Performances
Amplitude Tapering For Sidelobe Level Control
Wide-Angle Impedance Matching (WAIM)
Array Performance
Array Lattice
The position of the array elements describes the array
lattice and there are basically three types for planar arrays
Array Performance
Array Bandwidth
The bandwidth of the array depends on the
radiators, phase shifters, feeding networks etc.
Phase shifters and feeding networks possess
error transfer functions which grows with
increasing bandwidth.
The error analysis of the effect on the pattern
will determines the bandwidth.
Array Performance
Single Element and Array Performance
Due to the mutual coupling effects in the array
environment the single element performance and the
array performance of most antennas are different
Array Performance
Amplitude Tapering for Sidelobe Level Control
The amplitude tapering in the excitation of the array
elements determines the array sidelobe level, array
gain and the beamwidth.
Stronger tapering results in reduced sidelobe at the
expense of increased beamwidth and reduced gain.
- Powers of cosine
- Taylor distributions
- Modified Sin u/u taper of Taylor distributions
- Dolph-Chebyshev distributions
Array Performance
Modified Sinu/u taper of Taylor Distributions
Array Performance
Dolph-Chebyshev Distributions
Is the optimum distribution in the sense of
narrowest beam for a given SLL
Sidelobes do not decay in amplitude.
The power of percentage in the main beam
varies with the number of elements in the array
for a given SL
Example of illumination coefficients and array
pattern for a 20 dB taper applied to a 16 element
array
Array Performance
Wide-Angle Impedance Matching WAIM
Scan impedance is the impedance of an element
as a function of scan angle with all elements
excited with proper amplitude and phase.
For wide scan angles another mismatch due to
the scan angle occurs.
WAIM techniques are used to overcome this
problem
- Transmission line region techniques
- Free space WAIM techniques
Array Performance
Wide-Angle Impedance Matching WAIM
Transmission Line Techniques
Passsive circuits to control higher order modes
in the aperture
- separate interconnections between the
elements
- active tuning circuits
Free Space Techniques
- Reduced element spacing
- Dielectric slabs or dielectric sheets