a new numerical design method for log-periodic eleven feed – the partial array method
DESCRIPTION
A New Numerical Design Method for Log-periodic Eleven Feed – The Partial Array Method. Jian Yang, Associate Professor Chalmers University of Technology Sweden. Outline. Introduction New Method: the partial array method Optimization Procedure Result of Optimization - PowerPoint PPT PresentationTRANSCRIPT
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
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
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
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
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
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
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)
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
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.
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
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=
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
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.
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
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.
2010 SKA Africa Bursary Conference
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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.
2010 SKA Africa Bursary Conference
Chalmers University of Technology
Result of Optimization • 14 pairs of folded dipoles with scaling
factor 1 .24.
2010 SKA Africa Bursary Conference
Chalmers University of Technology
Result of Optimization • The port impedance is 200 Ohms.
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
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
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
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
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
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
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.
2010 SKA Africa Bursary Conference
Chalmers University of Technology
Questions?