ANTENNA ARRAYS ANTENNA ARRAYS

Array Factor (1)Array Factor (1)

)ˆ.exp(),(1

rrjkaf mo

n

mm

),( fHH ref

),( fEE ref

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 a certain angleangle can also have other peak values can also have other peak values depending on the spacing between depending on the spacing between the the antenna elements.antenna elements.

Grating LobesAF for uniform excitation:

))(exp()( oom uudjmkaf

oou sin sinuAF will have a maximum when exponent is a multiple of 2

pd

o

2)sin(sin2

grating lobes will occur at:d

pop

sinsin

to avoid grating lobes:

oo

d

sin1

1

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)

030030030

Mutual CouplingMutual Coupling

element pattern of the antenna changes element pattern of the antenna changes from its free space (isolated) value when from its free space (isolated) value when it is inserted into an arrayit is inserted into an array

this coupling effect will be different for this coupling effect will be different for each element of the array. each element of the array.

iit may be necessary to use the concept t may be necessary to use the concept of “of “active element patternactive element pattern””

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

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 effective methods are needed to needed to account foraccount for mutual coupling mutual coupling effects.effects.

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

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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 is calculated separately for

each element in the arrayeach element in the array.. these patterns are added up to obtain thethese patterns are added up to obtain theoveralloverall array array

pattern.pattern.

may imply simultaneous solution of thousands of equations

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

Infinite array assumption:Infinite array assumption: For large arraysFor large arrays,, the central elements that are the central elements that are

far away from edges are affected lessfar away 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 It is assumed that for all elements the currents are currents are similarsimilar except except for for some complex some complex constants. 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

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 AEP method yields in errors in calculating the array pattern calculating the array pattern

For these arrays the combination of the For these arrays the combination of the two methods are used to obtain more two methods are used to obtain more accurate results for the array patternaccurate results for the array pattern

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

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

• Array LatticeArray Lattice• Array BandwidthArray 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

ControlControl• Wide-Angle Impedance Matching (WAIM)Wide-Angle Impedance Matching (WAIM)

Array PerformanceArray Performance

The position of the array elements describes the The position of the array elements describes the array lattice and there are basically three types for array lattice and there are basically three types for planar arraysplanar arrays

Array PerformanceArray PerformanceArray LatticeArray Lattice

The bandwidth of the array depends on the The bandwidth of the array depends on the radiators, phase shifters, feeding networks etc.radiators, 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 PerformanceArray BandwidthArray Bandwidth

Due to the mutual coupling effects in the array Due to the mutual coupling effects in the array environment the single element performance environment the single element performance and the array performance of most antennas and the array performance of most antennas are differentare different

Array PerformanceArray PerformanceSingle Element and Array PerformanceSingle Element and Array Performance

The amplitude tapering in the excitation of the The amplitude tapering in the excitation of the array elements determines the array sidelobe array elements determines the array sidelobe level, array gain and the beamwidth.level, array gain and the beamwidth.

Stronger tapering results in reduced sidelobe at Stronger tapering results in reduced sidelobe at the expense of increased beamwidth and the expense of increased beamwidth and reduced gain.reduced gain.

- Powers of cosine- Powers of cosine- Taylor distributions- Taylor distributions- Modified Sin - Modified Sin u/u/u taper of Taylor u taper of Taylor

distributionsdistributions- Dolph-Chebyshev distributions- Dolph-Chebyshev distributions

Array PerformanceArray PerformanceAmplitude Tapering for Sidelobe Level Amplitude Tapering for Sidelobe Level ControlControl

Array PerformanceArray PerformanceModified SinModified Sinu/u/u taper of Taylor u taper of Taylor DistributionsDistributions

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 The power of percentage in the main beam varies with the number of elements beam varies with the number of elements in the array for a given SLin the array for a given SL

Array PerformanceArray PerformanceDolph-Chebyshev DistributionsDolph-Chebyshev Distributions

Example of illumination coefficients and Example of illumination coefficients and array pattern for a 20 dB taper applied to a array pattern for a 20 dB taper applied to a

16 element array16 element array

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 For wide scan angles another mismatch due to the scan angle occurs.to 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 PerformanceWide-Angle Impedance Matching WAIMWide-Angle Impedance Matching WAIM

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 PerformanceWide-Angle Impedance Matching WAIMWide-Angle Impedance Matching WAIM