2. Array Factor (1)
Array Factor (1)
)
ˆ
.
exp(
)
,
(
1
r
r
jk
a
f m
o
n
m
m
)
,
(
f
H
H ref
)
,
(
f
E
E ref
3. Phased Array Antennas
Phased Array Antennas
Each antenna element can be controlled
Each antenna element can be controlled
individually by phase or time delay
individually by phase or time delay.
.
By changing the feeding it is possible to
By changing the feeding it is possible to
construct a directive beam that can be
construct a directive beam that can be
repositioned electronicall
repositioned electronically.
y.
A
Amplitude control
mplitude control can be
can be used for pattern
used for pattern
shaping
shaping
The beam can be pointed to new direction,
The beam can be pointed to new direction,
narrowed or widened in microseconds.
narrowed or widened in microseconds.
An array that has a
An array that has a main
main peak at
peak at a certain angle
a certain angle
can also have other peak values depending on
can also have other peak values depending on
the spacing between
the spacing between the
the antenna elements.
antenna elements.
4. Grating Lobes
AF for uniform excitation:
))
(
exp(
)
( o
o
m u
u
d
jmk
a
f
o
o
u
sin
sin
u
AF will have a maximum when exponent is a multiple of 2
p
d
o
2
)
sin
(sin
2
grating lobes will occur at:
d
p
o
p
sin
sin
to avoid grating lobes:
o
o
d
sin
1
1
5. 8 element array with /d=1
and for uo=0.5 (scan angle of 30o
)
uo=0 (broadside) uo=0.5 (scan angle of 30 degrees)
0
300
300
30
6. Mutual Coupling
Mutual Coupling
element pattern of the antenna changes
element pattern of the antenna changes
from its free space (isolated) value when it is
from its free space (isolated) value when it is
inserted into an array
inserted into an array
this coupling effect will be different for each
this coupling effect will be different for each
element of the array.
element of the array.
i
it may be necessary to use the concept of
t may be necessary to use the concept of
“
“active element pattern
active element pattern”
”
8. Analysis Including Mutual Coupling
Analysis Including Mutual Coupling
In a strong mutual couping environment
In a strong mutual couping environment
array pattern = element pattern X array factor
array pattern = element pattern X array factor
does not work
does not work ! Solving
! Solving the
the problem
problem using
using
numerical methods is not practical.
numerical methods is not practical.
Therefore other
Therefore other effective methods are needed
effective methods are needed
to
to account for
account for mutual coupling effects.
mutual coupling effects.
9. Mutual Coupling (
Mutual Coupling (cont.
cont.)
)
n
i
i
tot E
E
1
Finite Array Approach:
Finite Array Approach:
Used for small and medium arra
Used for small and medium arrays.
ys.
A
Active element pattern
ctive element pattern is calculated separately for each
is calculated separately for each
element in the array
element in the array.
.
these patterns are added up to obtain the
these patterns are added up to obtain theoverall
overall array pattern.
array pattern.
may imply simultaneous solution of thousands of equations
10. Mutual Coupling (
Mutual Coupling (cont.
cont.)
)
Infinite array assumption:
Infinite array assumption:
For large arrays
For large arrays,
, the central elements that are far
the central elements that are far
away from edges are affected less
away from edges are affected less
infinite array
infinite array concept
concept can
can then
then be
be used
used
It is assumed that for all elements the currents
It is assumed that for all elements the currents
are
are similar
similar except
except for
for some complex constants.
some complex constants.
When this
When this approach is used
approach is used,
, it is
it is sufficient
sufficient to
to
analyze only one element completely
analyze only one element completely
11. For medium size arrays, the exact AEP
For medium size arrays, the exact AEP
methods are difficult to use and average
methods are difficult to use and average
AEP method yields in errors in calculating
AEP method yields in errors in calculating
the array pattern
the array pattern
For these arrays the combination of the two
For these arrays the combination of the two
methods are used to obtain more accurate
methods are used to obtain more accurate
results for the array pattern
results for the array pattern
Mutual Coupling (
Mutual Coupling (cont.
cont.)
)
12. Array Blindness
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
13. • Array Lattice
Array Lattice
• Array Bandwidth
Array Bandwidth
• Differences Between Single Element and
Differences Between Single Element and
Array Performances
Array Performances
• Amplitude Tapering For Sidelobe Level
Amplitude Tapering For Sidelobe Level
Control
Control
• Wide-Angle Impedance Matching (WAIM)
Wide-Angle Impedance Matching (WAIM)
Array Performance
Array Performance
14. The position of the array elements describes the array
The position of the array elements describes the array
lattice and there are basically three types for planar
lattice and there are basically three types for planar
arrays
arrays
Array Performance
Array Performance
Array Lattice
Array Lattice
15. The bandwidth of the array depends on the radiators,
The bandwidth of the array depends on the radiators,
phase shifters, feeding networks etc.
phase shifters, feeding networks etc.
Phase shifters and feeding networks possess error
Phase shifters and feeding networks possess error
transfer functions which grows with increasing
transfer functions which grows with increasing
bandwidth.
bandwidth.
The error analysis of the effect on the pattern will
The error analysis of the effect on the pattern will
determines the bandwidth.
determines the bandwidth.
Array Performance
Array Performance
Array Bandwidth
Array Bandwidth
16. Due to the mutual coupling effects in the array
Due to the mutual coupling effects in the array
environment the single element performance and
environment the single element performance and
the array performance of most antennas are
the array performance of most antennas are
different
different
Array Performance
Array Performance
Single Element and Array Performance
Single Element and Array Performance
17. The amplitude tapering in the excitation of the array
The amplitude tapering in the excitation of the array
elements determines the array sidelobe level, array
elements determines the array sidelobe level, array
gain and the beamwidth.
gain and the beamwidth.
Stronger tapering results in reduced sidelobe at the
Stronger tapering results in reduced sidelobe at the
expense of increased beamwidth and reduced gain.
expense of increased beamwidth and reduced gain.
- Powers of cosine
- Powers of cosine
- Taylor distributions
- Taylor distributions
- Modified Sin
- Modified Sin
u/
u/
u taper of Taylor distributions
u taper of Taylor distributions
- Dolph-Chebyshev distributions
- Dolph-Chebyshev distributions
Array Performance
Array Performance
Amplitude Tapering for Sidelobe Level Control
Amplitude Tapering for Sidelobe Level Control
19. Is the optimum distribution in the sense of
Is the optimum distribution in the sense of
narrowest beam for a given SLL
narrowest beam for a given SLL
Sidelobes do not decay in amplitude.
Sidelobes do not decay in amplitude.
The power of percentage in the main beam
The power of percentage in the main beam
varies with the number of elements in the
varies with the number of elements in the
array for a given SL
array for a given SL
Array Performance
Array Performance
Dolph-Chebyshev Distributions
Dolph-Chebyshev Distributions
20. Example of illumination coefficients and array
Example of illumination coefficients and array
pattern for a 20 dB taper applied to a 16 element
pattern for a 20 dB taper applied to a 16 element
array
array
21. Scan impedance is the impedance of an
Scan impedance is the impedance of an
element as a function of scan angle with all
element as a function of scan angle with all
elements excited with proper amplitude and
elements excited with proper amplitude and
phase.
phase.
For wide scan angles another mismatch due to
For wide scan angles another mismatch due to
the scan angle occurs.
the scan angle occurs.
WAIM techniques are used to overcome this
WAIM techniques are used to overcome this
problem
problem
- Transmission line region techniques
- Transmission line region techniques
- Free space WAIM techniques
- Free space WAIM techniques
Array Performance
Array Performance
Wide-Angle Impedance Matching WAIM
Wide-Angle Impedance Matching WAIM
22. Transmission Line Techniques
Transmission Line Techniques
Passsive circuits to control higher order modes in
Passsive circuits to control higher order modes in
the aperture
the aperture
- separate interconnections between the elements
- separate interconnections between the elements
- active tuning circuits
- active tuning circuits
Free Space Techniques
Free Space Techniques
- Reduced element spacing
- Reduced element spacing
- Dielectric slabs or dielectric sheets
- Dielectric slabs or dielectric sheets
Array Performance
Array Performance
Wide-Angle Impedance Matching WAIM
Wide-Angle Impedance Matching WAIM
Editor's Notes
#2:. The field excited from each antenna element interferes
with each other. This interaction depends on the phase and
amplitude of the contributor and can be either constructive or
destructive. In one direction interaction can be destructi
ve causing
nulls of the radiation pattern while in some other dire
ction the fields may add up and produce the maxi
mum of antenna pattern.
