Planar Array 1
Planar Array 1
Planar Array 1
TRACK RF TECHNOLOGIES AND SYSTEMS
Topic 4: Planar Array Antennas
Introduction to linear array antennas
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Index: Introduction to linear arrays
• Array antennas definition
• Arrays theory
• Radiation pattern of an array
• Multiplication patterns principle
• Equispace linear arrays
• Effects of the feeding elements
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What is an array antenna?
• An array antenna is a spatially extended collection of N similar radiating elements,
and the term "similar radiating elements" means that all the elements have the
same radiation patterns, orientated in the same direction in 3D space.
• The elements don't have to be necessary spaced on a regular grid, but it is
assumed that they are all fed with the same frequency.
– Group of individual radiating elements
– Feed from a common terminal
– By linear networks
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Arrays theory: Radiation pattern on an array
• The Multiplication patterns principle, that characterize the arrays antennas, is based on the
superposition principle derived of the Maxwell equations.
• Formulation condition:
– Equal elements
– Equal oriented elements
• An array describes with this principle is characterized by: z
– The position vectors of each elements: IN
I1 r
– The feeding currents of each elements: Ii rN
– The radiation pattern of the radiating element : r1
I2 ri r
r2
ri
Ii
x y
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Arrays theory: Radiation pattern on an array
z
• Radiated field for one element:
I1 IN r
rN
̂⃗ I2
r1
ri r
r2
ri
Ii
x y
Radiated field of an Complex feeding Relative phase for
radiating element coefficient displacement out
in the origin of the origin
𝐹 𝜃, 𝜑 𝐴𝑒 ̂⃗ 𝐸 𝑟, 𝜃, 𝜑 =𝐸 𝑟, 𝜃, 𝜑 𝐹 𝜃, 𝜑
,
In function of:
The radiated field can be expressed as the Element positions
Excitation Ai
product of the element field, situated in the Frequency
E A (r , , ) Ee (r , , ) FA ( , )
• The radiation pattern of an array is the product of the radiation pattern of the single
radiating element and the array factor.
•The total radiated field polarization depends only on the used radiating element (FA is a
scalar value).
• The array factor allow to analyze how is the influence of the geometry and the feeding
on the radiation without considering what kind of radiating element we use.
• For large arrays, FA() varies more than Ee() does, and we can approximate the total
radiation pattern as the array factor.
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Arrays theory: multiplication pattern principle
• Example:
E A (r , , ) Ee (r , , ) FA ( , )
Element radiation pattern Ee
𝑐𝑜𝑠 𝜃 Array Factor FA Array radiation pattern EA
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Arrays theory: Equispaced linear arrays
• Array of N elements separated of a distance d and feed with An
coefficients
𝑟⃗ 𝑖𝑑 𝑧̂ 𝑟⃗ 𝑟̂ 𝑖𝑑 cos 𝜃 ̂⃗
𝐹 𝜃, 𝜑 𝐴𝑒 𝐴𝑒
, ,
DFT 1 An !!
𝐴 𝑎𝑒 𝐹 𝜃, 𝜑 𝑎𝑒 𝑎𝑒
𝜓 𝑘𝑑 cos 𝜃 𝛼 , ,
•As we can see in this expression for FA is the DFT of the excitation law of the array.
•While in signal processing we pass from time domain to frequency spectrum, in arrays
theory we pass from spatial domain (excitation law) to angular spectrum (radiation pattern).
• Thus, all concepts of digital signal can be applied. For instance in digital signals to prevent
the leakage windowing is used, in arrays to reduce side lobes also a windowing of the
feedings is used
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Uniform amplitude
When Ai=(1/N) eji
Uniform amplitude
Progressive phase
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Progressive phase
• The arrays are divided depending on it steering direction in these followings types:
Broadside array : has it radiation maximum in the perpendicular plane of
the array.
Exploration array: steer at a variable direction max fixed by the difference
constant phase . The visible margin is the general one:
Endfire array: has the radiation maximum in the array axis (max = 0 or ).
90
90 90
θ0=90º 120 60
θ0=70º 120 60 θ0=0º 120 60
150 30
180 0
210 330
240 300
270
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Resume: Equispace linear array uniformly feed in
amplitude and the phase is progressive
• FA() is always a periodic function with period =2: the valid margin of
the radiation pattern is the margin with possible values of : between 0 y
Graphic
kd cos representation
FA ( , ) Ai e ji
Broadside
– Phase: 0 kd cos Endfire
Uniform phase
Exploration
kd cos 0, 0 kd 0
– Visible
kd kd kd 2d
margin: Progressive phase
– Maximum: 0 max 2 kd kd 4 d 0
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Effect of non uniformly feeding elements
• A 1 e jn
Uniform feeding: when for i=0 to N‐1
n
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Effect of non uniformly feeding elements
• Triangular feeding: when An=[1‐abs(‐(n‐1)/2+i)/(n/2))] ; for n=0 to i‐1
• Cosines feeding on pedestal:
for i=0 to n‐1
Control the reduced side lobe levels (SLL) N=20
The directivity is reduced d=/2
The beamwidth increase
H=0.5
1 0
0.9 -5 22dB
0.8
0.7 DFT-1-10
-15
0.6 -20
0.5 -25
0.4 -30
0.3 -35
0.2 -40
0.1 -45
0 -50 0 20 40 60 80 100 120 140 160 180
-5 -4 -3 -2 -1 0 1 2 3 4 5
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Effect of non uniformly feeding elements
• Binomial feeding: when
for i=0 to N‐1
The side lobe levels (SLL) disappear
The directivity is reduced N=20
The main beamwidth increase
d=/2
1 0
0.9 without
-5
lobes
0.8 -10
0.7 DFT-1-15
0.6 -20
0.5 -25
0.4 -30
0.3 -35
0.2 -40
0.1 -45
0 -50 0 20 40 60 80 100 120 140 160 180
-5 -4 -3 -2 -1 0 1 2 3 4 5
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Linear array with symmetry amplitude, decreasing from
centre to edge and the phase is constant or progressive
• With a phase variation , we can control the steering direction.
• So with an amplitude variation, we can control the side lobe levels (SLL).
• With symmetry amplitude, decreasing from centre to edge, it achieve to
reduce the side lobe lels (SLL) and wider the main lobe and therefore reduce
the array directivity.
• The side lobe levels (SLL) reduction achieve with symmetry amplitude,
decreasing from centre to edge is equivalent to the problems of signal theory
when we use no rectangular windows like (Hanning, Hamming, Triangular,…).
• As in signal theory, the side lobe levels (SLL) reduction have resolution loss
that is equivalent to wider beamwidth.
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Exercice with theoretical calculation: Linear array
Calculate:
a) Number of elements.
b) ‐3dB beamwidth of the antenna at broadside when
we use uniform feeding network for each elements.
c) Directivity at broadside direction.
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References
• C.A. Balanis. Antenna Theory: Analysis and Design, 3rd Edition. Wiley
2005
• A. Cardama and more. Antenas. 2nd Edition. Ediciones UPC 2002
(spanish)
• W.L. Stutzman and more. Antenna Theory and Design. 3rd Edition
Wiley 2013.
• R. C. Hansen. Phased array antennas. Ed Wiley. 2009
• R.J. Mailloux. Phased array antenna handbook. Ed. Artech House 2005
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