ANTENNA ARRAYS engg notes from antenna and microwave engineering

ANTENNA ARRAYS

1. ANTENNA ARRAYS ANTENNA ARRAYS

2. Array Factor (1)Array Factor (1)
)ˆ.exp(),(
1
rrjkaf
mo
n
m
m




),(fHH
ref

 ),(fEE
ref



3. Phased Array AntennasPhased Array Antennas

Each antenna element can be controlled Each antenna element can be controlled
individually by phase or time delayindividually 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 electronicallrepositioned electronically.y.

AAmplitude control mplitude control can becan be used for pattern used for pattern
shapingshaping

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 aAn array that has a main main peak at peak at a certain anglea 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()(
oom
uudjmkaf 
oou sin sinu
AF will have a maximum when exponent is a multiple of 2
p
d
o

 2)sin(sin2 
grating lobes will occur at:
d
p
op

 sinsin
to avoid grating lobes:
oo
d
 sin1
1



5. 8 element array with /d=1
and for u
o
=0.5 (scan angle of 30
o
)
uo=0 (broadside)
uo=0.5 (scan angle of 30 degrees)
0
30
0
30
0
30

6. Mutual CouplingMutual 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 arrayinserted 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.

iit may be necessary to use the concept of t may be necessary to use the concept of
““active element patternactive element pattern””

7. Element pattern of a dipole located as a center element
of a 7X9 array

8. Analysis Including Mutual CouplingAnalysis Including Mutual Coupling

In a strong mutual couping environmentIn a strong mutual couping environment
array pattern = element pattern X array factor array pattern = element pattern X array factor
does not workdoes not work ! Solving ! Solving the the problemproblem 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 foraccount for mutual coupling effects. mutual coupling effects.

9. Mutual Coupling (Mutual Coupling (cont.cont.))



n
i
itot EE
1


Finite Array Approach:Finite Array Approach:

Used for small and medium arraUsed for small and medium arrays.ys.

AActive element patternctive element pattern is calculated separately for each is calculated separately for each
element in the arrayelement in the array..

these patterns are added up to obtain thethese patterns are added up to obtain theoveralloverall 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 arraysFor large arrays,, the central elements that are far the central elements that are far
away from edges are affected lessaway from edges are affected less

infinite arrayinfinite array concept concept can can then then be be usedused

It is assumed that for all elements the currents It is assumed that for all elements the currents
are are similarsimilar except except for for some complex constants. some complex constants.

When thisWhen this approach is used approach is used,, it is it is sufficientsufficient 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 patternresults for the array pattern

Mutual Coupling (Mutual Coupling (cont.cont.))

12. Array BlindnessArray 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 LatticeArray Lattice
•Array BandwidthArray Bandwidth
•Differences Between Single Element and Differences Between Single Element and
Array PerformancesArray Performances
•Amplitude Tapering For Sidelobe Level Amplitude Tapering For Sidelobe Level
ControlControl
•Wide-Angle Impedance Matching (WAIM)Wide-Angle Impedance Matching (WAIM)
Array PerformanceArray 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
arraysarrays
Array PerformanceArray Performance
Array LatticeArray 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 PerformanceArray Performance
Array BandwidthArray 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
differentdifferent
Array PerformanceArray Performance
Single Element and Array PerformanceSingle 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 distributionsu taper of Taylor distributions
- Dolph-Chebyshev distributions- Dolph-Chebyshev distributions
Array PerformanceArray Performance
Amplitude Tapering for Sidelobe Level ControlAmplitude Tapering for Sidelobe Level Control

18. Array PerformanceArray Performance
Modified SinModified Sinu/u/u taper of Taylor Distributionsu taper of Taylor Distributions

19. Is the optimum distribution in the sense of Is the optimum distribution in the sense of
narrowest beam for a given SLLnarrowest 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 SLarray for a given SL
Array PerformanceArray Performance
Dolph-Chebyshev DistributionsDolph-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
arrayarray

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
problemproblem
- Transmission line region techniques- Transmission line region techniques
- Free space WAIM techniques- Free space WAIM techniques
Array PerformanceArray Performance
Wide-Angle Impedance Matching WAIMWide-Angle Impedance Matching WAIM

22. Transmission Line TechniquesTransmission Line Techniques
Passsive circuits to control higher order modes in Passsive circuits to control higher order modes in
the aperturethe aperture
- separate interconnections between the elements- separate interconnections between the elements
- active tuning circuits- active tuning circuits
Free Space TechniquesFree Space Techniques
- Reduced element spacing - Reduced element spacing
- Dielectric slabs or dielectric sheets - Dielectric slabs or dielectric sheets
Array PerformanceArray Performance
Wide-Angle Impedance Matching WAIMWide-Angle Impedance Matching WAIM