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

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.

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?