A New Numerical Design Method for Log-periodic Eleven Feed – The Partial Array Method
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Transcript of A New Numerical Design Method for Log-periodic Eleven Feed – The Partial Array Method
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
A New Numerical Design Method for Log-periodic Eleven Feed – The Partial
Array Method
Jian Yang, Associate ProfessorChalmers University of Technology
Sweden
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Outline• Introduction• New Method: the partial array method• Optimization Procedure • Result of Optimization • Simulations and Measurements • Conclusions
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Introduction - The Eleven Feed• Two unique characteristics
over decade bandwidth– Constant beam width;– Fixed phase center location
-150 -100 -50 0 50 100 150-30
-25
-20
-15
-10
-5
0
Theta (deg)
Am
plitu
de (d
B)
2GHz3GHz4GHz5GHz6GHz7GHz8GHz9GHz10GHz11GHz12GHz13GHz
dipoles
Ground planePhase center
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Introduction - The Eleven Feed
• Simple geometry, small volume– Can be located in
cryostat;• -10 dB reflection
coefficient• Low cross pol. level
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Introduction - challenge• Minimizing reflection
coefficient is needed.• Challenge: Eleven feed
is very large at highest frequency.
• New method for global optimization scheme.
Photo of the 2-13 GHz Eleven feed
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
New Method - Partial array method Scaled S-parameters due to scaled geometry• If the log-periodic array is infinite, we have
the frequency scaling on s-parameters as:
( ), ( )
( ), ( ) /iport idipole n jport jdipole n
niport idipole jport jdipole
s f
s f k
idipole
jdipole
jdipole+n
idipole+n
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Partial Array Method: Scaled S-parameters
• example:
D1D2D3
D4D5
D6
1 2 12 2 2 2 21 1 1 1
2 1
2 3 4 5 6 7 8 9 10 11 12-35
-30
-25
-20
-15
-10
-5
0
Frequency (GHz)
Am
plitu
de (d
B)
S1(3)1(3)(f)
S1(4)1(4)(f)
S1(3)1(3)(f/k)
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
2 4 6 8 10 12 13-40
-30
-20
-10
0
Frequency (GHz)
Mut
ual c
oupl
ing
(dB
)
S1(4)2(3)
S1(6)2(1)
Partial Array Method: far separated mutual couplings very low
D1D2D3
D4D5
D6
1 2 12 2 2 2 21 1 1 1
2 1
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Partial Array Method
• We can predict the S matrix for the whole array using S parameters in a small part of the array by– Scaling S parameters;– Ignoring mutual coupling between far
separated elements.
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Partial Array MethodImplementation
, ,
, ,
I I I III I
II I II IIII II
S Sb aS Sb a
Port definition
S1(3)2(4)
port1 port2
dipole3 dipole4
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Partial Array Method
, ,
, ,
I I I III I
II I II IIII II
S Sb aS Sb a
0
0S=
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Partial Array Method• Formula
, ,
, ,
I I I III I
II I II IIII II
S Sb aS Sb a
, ,
, ,
I I I III I
II I II IIII II
S Sb aS Sb a
1(1)1(1) 1(1)2( ),
2( )1(1) 2( )2( )
NI I
N N N
s ss s
S
1(1)2(1) 1(1)1(2) 1(1)2( 1) 1(1)1( ),
2( )2(1) 2( )1(2) 2( )2( 1) 2( )1( )
N NI II
N N N N N N
s s s ss s s s
S
2(1)1(1) 2(1)2( )
1(2)1(1) 1(2)2( )
,
2( 1)1(1) 2( 1)2( )
1( )1(1) 1( )2( )
N
N
II I
N N N
N N N
s ss s
s ss s
S
2(1)2(1) 2(1)1(2) 2(1)2( 1) 2(1)1( )
1(2)2(1) 1(2)1(2) 1(2)2( 1) 1(2)1( )
,
2( 1)2(1) 2( 1)1(2) 2( 1)2( 1) 2( 1)2( )
1( )2(1) 1( )1(2) 2( )2( 1) 2( )2( )
N N
N N
II II
N N N N N N
N N N N N N
s s s ss s s s
s s s ss s s s
S
1
, , , ,I I I II II II II I
S S S D S S
0 1 0 0 0 01 0 0 0 0 00 0 0 1 0 00 0 1 0 0 0
0 0 0 0 0 0 10 0 0 0 0 1 0
D
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Partial Array Methodfor details
, ,
, ,
I I I III I
II I II IIII II
S Sb aS Sb a
J. Yang and P.-S. Kildal, “Optimizing large log-periodic array by computing a small part of it”, appears in IEEE Trans. on Antennas Propag. Special Issue on Antennas for Next Generation Radio Telescopes, vol. 59, no. 3, March 2011.
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Example
, ,
, ,
I I I III I
II I II IIII II
S Sb aS Sb a
Reflection coefficient of a 14-element log-periodic Eleven antenna array based on simulation of a 6-element array
2 3 4 5 6 7 8 9 10 111213-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
Frequency (GHz)
Ref
lect
ion
Coe
ffici
ent (
dB)
Partial Array Method
Simulation by CST
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Optimization Procedure Genetic Algorithm
• Six parameters are optimized:– scaling factor k, – dipole length L, – arm width w, – arm spacing da, – transmission line gap dc, – height above ground plane h.
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Optimization• GA is used for minimizing S11 in a 6-element folded
dipole array. • Elite crossover, Roulette wheel selection, crossover
and mutation are used in GA.– population size: 50;– 5 generations;
• Simulation tool is CST MS and the optimization is done by in-house Matlab program.
• Computation Time– Each case 1 hours;– Fully optimized 1 week.
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Result of Optimization • 14 pairs of folded dipoles with scaling
factor 1 .24.
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Result of Optimization • The port impedance is 200 Ohms.
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Simulated and Measured ResultsReflection coefficient including centre puck
2 3 4 5 6 7 8 9 10 11121314-20
-15
-10
-5
0
Frequency (GHz)
Ref
lect
ion
Coe
ffici
ent (
dB)
Simulation by using CST
Mea. for pol 1 of Vertex feed at OSO
Mea. for pol 2 of Vertex feed at OSO
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Radiation Measurement at Technical University of Denmark
• φ : 0-360o with step 1o.
• θ : 0-180o with step 1o.
• Frequency: 2–15 GHz with step 0.1 GHz.
• Spherical near field measurement
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Efficiencies based on measured patterns in reflector with subtended semi-angle of 60 deg
3 4 5 6 7 8 9 1011121314-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Frequency (GHz)
Effi
cien
cies
(dB
)
e
epolespeBOR1eilleap
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Efficiencies based on Simulated patterns in reflector with subtended semi-angle of 60 deg
3 4 5 6 7 8 9 10 11121314-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Frequency (GHz)
Effi
cien
cies
(dB
)
e
epol
esp
eBOR1
eill
eap
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Radiation Patterns of BOR1 component
-150 -100 -50 0 50 100 150-30
-25
-20
-15
-10
-5
0
Theta (deg)
Am
plitu
de (d
B)
2GHz3GHz4GHz5GHz6GHz7GHz8GHz9GHz10GHz11GHz12GHz13GHz
-150 -100 -50 0 50 100 150-30
-25
-20
-15
-10
-5
0
[o]
Rel
ativ
e le
vel [
dB]
2.00 GHz2.18 GHz2.38 GHz2.60 GHz2.83 GHz3.08 GHz3.37 GHz3.67 GHz4.01 GHz4.37 GHz4.77 GHz5.20 GHz5.68 GHz6.20 GHz6.76 GHz7.37 GHz8.04 GHz8.76 GHz9.57 GHz10.43 GHz11.39 GHz12.42 GHz
Measured Simulated
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Directivity
2 3 4 5 6 7 8 9 10111213144
5
6
7
8
9
10
11
12
13
14
Frequency (GHz)
Dire
ctiv
ity (d
Bi)
MeasuredSimulated
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Conclusions• The reflection coefficient is below -10 dB for 2 – 13
GHz.• The radiation pattern is constant for 2 – 13 GHz.• BOR1 efficiency is
– > -0.5 dB for most part of 2 – 13 GHz, – > -1.5 for 2 –13 GHz.
• Directivity is about 11 dBi.• Aperture efficiency is better than – 3 dB for 2 – 13
GHz.
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2010 SKA Africa Bursary Conference
Chalmers University of Technology
Questions?