A New Numerical Design Method for Log-periodic Eleven Feed – The Partial Array Method

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



Outline• Introduction• New Method: the partial array method• Optimization Procedure • Result of Optimization • Simulations and Measurements • Conclusions



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



Introduction - The Eleven Feed

• Simple geometry, small volume– Can be located in

cryostat;• -10 dB reflection

coefficient• Low cross pol. level



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



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



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)



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



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.



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




, ,

, ,

I I I III I

II I II IIII II

S Sb aS Sb a

0

0S=



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



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.



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)


Simulation by CST



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.



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.



Result of Optimization • 14 pairs of folded dipoles with scaling

factor 1 .24.



Result of Optimization • The port impedance is 200 Ohms.



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



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



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



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



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



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



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.



Questions?

A New Numerical Design Method for Log-periodic Eleven Feed – The Partial Array Method

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