A New Approach in Designing Multi-Layer Frequency Selective Surfaces based on Tuning Pole-Zeros of Individual Layers

1394

) 29 (

!"# $

% &

-'$

( )*

+ ,)* '$

- .,/

) 1 (

3 4 54 67 87

) 2 (

) 1 ( '( ) *+ , - . *+

/ 0+ + 12 3 *+ 0+ + /0+ 4 /

) 2 ( ' + , - . *+

/ 12 3 *+ 0+ +

0+ + /0+ 4 /

: 6 7 4 2

/ 5 / 94 :: ; 7 4

2 / 6 / 94

: *-; ,- , - . + ,6 - >* ( 6 3 ?'*+ @ A ,B+ C + D . E F G- H +

I J 1A- , * ( 6 7 4 (

K . 4 LA , * ( 6 7 M 4 N+ O' + + N /

* 4 - >* ( 6 3 ?'*+ LA E F G- H + H P .

E .4 G- . + + / B+ 1 2 0 , * * N Q - + + R+ + 'I ,' ,B+ C

,- 4 -1 .

FSS . 4 ,O1 ,*N I LA N+

S+ -+ T2 K G- * '1 6 E * - ( + K

,- K 2 , C U- '.F+ ,- + 0 + V W 4 X1'?- + N + 'I H + .1 2 . (

.

"8 + .8 :

>* ( 6 3 ?'*+ @ A (FSS)

Y + /, Z6 '1 6 /J '- 'I / N 4 - / .

A New Approach in Designing Multi-Layer Frequency Selective

Surfaces based on Tuning Pole-Zeros of Individual Layers

Mahmoud Fallah(1) Ali Abdolali (2)

(1) Ph.D. Condidate - Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran

[email protected]

(2) Assistant Professor - Department of Electrical Engineering, Shahed University, Tehran, Iran [email protected]

In this paper, a new approach (not new technique) is introduced for designing frequency selective surfaces (FSSs). We try to compose the desired frequency response using the frequency response of each constituent FSS. Also, a new dual-band miniaturized frequency selective surface is proposed. In contrast to the conventional FSS design technique, the presented structure takes advantage of non-resonance elements and has unit cells with a miniaturized dimension. The proposed FSS cells are composed of two complex and inductive planes that act as a dual-band filter through the pass of electromagnetic wave propagation. The performance of this structure toward various angles of incident waves and different polarizations is stable.

Index Terms: Frequency selective surface, miniaturization, periodic structure, radome.

< =>/ ? >

: /0+ + /0+ 4 /0+ + 12 3 *+ / , - . *+ /@V6 [email protected]

1 3 @/ / @ A 3 ?'*+ >* ( 6 d'I+

FSS 1

+ e f\ N+ J '- +

- 2 g g) + g16 hN g* LAg E 0 ( '

, * ( 6 7 + ,

-+ S+ -+ , C U- '.F+ ,g- Kg B

. ( 'g i g( g D 4 'I H + ,g - g( +

0+ -+ N B H + 0+ 3 j N+ k G[4 l m - / * . *+

( N+

FSS

,-0+ 4 . g- S+ -+ Jn D ,B+ C

2 ] 1 /[ g F ] 2 /[ Y + ] 3 /[ D i 1D N+ KI+ 4 ` C T4 + .T ,1[-' `+ ?-, H P qOB -+ 0 'I / g ( gg gg + + gg ] 4 /[ I gg @ Agg >*+ ggr-+ \ gg ) gg gg

, C U-,2 d-3 ]( 5 [/ + V ] 6 [ H'*e / , g4N g + e g ]

7 [

H'g*e g g* g ' ( D \ 0+ 2 ' + ] 8 9 [ Y * + . D 4 . + f\ -D W g4 S g FSS t?g / g *

, ,-( E ,B+ C /J 1A-7

, * ( 6 u 4 `+ g U4

gg +N W gg4 S gg-gg T* . H gg h 'gg - ` gg dI N+ ,gg.

,- 4

FSS

1g 6 ,g * * N g 2 g + ,' 0e H g

g

Xgd* gT4 - N+ g J g1A- , * ( 6 '6 H' + + (

'I .1 2 S - C . K 2 FSS [- + g* + .

g / g[- LAg Eg /J g1A- , * ( 6 7 - M - K . 4 2 N + 4 N+ 'g f\ -)

400

B * E ^ '- ( 2 ` g λ × λ ₁₀ 10 g + H g (

vg 4 g 'I g H m + I w 'I + ^ 4 4 [O N O TD E + g H g P . gi Eg [4 I+ . +

xY + * - ( N+ ,Z

4

H'*e g( H g >* g( 6 g( ,

(

FSS

,g. '.F+ gM* N+ 0 g + g( g + S g 'B+ ,

'g + ,g ( g B W 4 +N `+ U4 T * E] ( *+ ' H P [O Q N 6 TD

^ - ,? * +

] 10 .[ ,B+ C I+

FSS

1 + , '.] g( g

'6 i + _ D 4 - S - C N+ +

'g gM - H g g . +

N+ 3

FSS

0e ( * l+ + ,g * * N 'I g )

h 1 0+ 2 *N

1 N+ / g * - g( '.] g( g + ,

,- K 2 + - 6 2 l g* Hg + N+ . g + g O' + / (

FSS

,- * 4 - Y * f BVA + ]

10 14 .[

y g4 4 * N ) + 'I H + ,B+ C ( z +

5

g

,- \ N g gI Y g3 S g- g3 ` gT2 .

'I

FSS

,- 2 0e KI+ H B

g(

4 S - >* ( 6 ,- J [- 6 2 ,

gD 4 g . * g g

,- S - W 4 >* ( 6 + +Ne Z6 \ N . + { gAI 0+ 4

2 / ( - G'*+

FSS

g 6 Q 2 0+ 2

6

Hg + H g

,- + _ G'*+ { AI 'I g Hg + g3 g - ug_+ * i

g 0e .1 2 ,. 6 K 1[4 + Kg 1[4 g( ( + + - .

,- ( ,F B . (

FSS

Tg Kg 1[4 ,g * * N

' +

7

* N ( + .

W j ,Z g g( ,

0 g( 4 g - + g g I+ g

FSS

, * ( 6 7 ,B+ C ) - / Y )*+ Tg * + g

W 4 +N U4 +

g4 B+ 1 + H P .

λ

08 0/

+ + W ( * g , * ( 6 7 K. -+ .

H'g + * Kg F

^g - gg O ( ^ gm

L

Q

t?gg - |;gB gg ;gi gg* + + /

, * (

] 11 14 .[

Jn D '1 6 g \ g ] N+ O'g + T)- @+ C ( ,

FSS

,- I ( ]

15 23 [ g ,gB+ C g( f\ - / ` g

E4 U4 , * ( 6 7 M 4 'I g ,g g '-+ Eg4

,- Y )*+ g * g \ g g( H + 'I H + 0 \ ] . ;

,g- }g2 g g + X1'?- , '-+ + + g 4 g( g

e 6 K I '-+ 0 e

/J 1A- , * ( 6 7

+ 0e vg 4 N e 6 ( + ] . ( P 0 -N

Y * ,- ` S - Y 4 + 6+ . ;

,- '6 i M* J 1A- , * ( 6 7 E F G- H + >r .

,- J ?'*+ ,[A 'I E E4 , * ( 6 7 M 4 .

i+ D A @ A E4 ` [O H y 4 Y 2 ~ 6 ) 3 . N+ *

uD - 0e v + ( ]

24 25 [ ^A_ O ( + + _

'I J 1A- , * ( 6 7

H + H + , + D+ * .

( + ^ 4 4 1 + ' +

-,- ,6 - + D B+ ( (

* ( 6 , C U- '.F+ S+ -+ K G->

,O1 •+ ,. /H

,B+ C 1 H + N+ O' + >r . + ,*N I •+ 3

FSS

0 + T4 -N ` T- ;i

+ • 4 -+ + .

7 \ N ,. '.F+ , ;i ^ m U4 - , * ( 6

, N + + _ '6 i + . N+ T€- ` dI E

FSS

/ M 4

8

>* ( 6

>* * N ,- 0e , '-+ `+ U4 1

Y )*+ - .

T N , * ( 6 * M 4 + 'I H + , *+ 4 0+ - ,

( , , '-+ N+ ,I U4

. + 0+ - *

* * N+ - ] , * ( 6 7 B B+ C

U4 ,

+N + '6 i + _ : . ( - W 4 ( + . e 'Oi * .

R+ + 'I + €- E 4 ) +

+ H + N

,-H + + O' + K * ' : 7 0 e

, * ( 6 . + * * ] ,'B \ T4 -

( N+ H +

N+ l *

FSS

,-0 'I KI+ S+ -+ ' ( ,-0+ 4 + +

+ 0+ 2 O' + H'*e + Y

+ Y * ,- H P . LA 0+ 4

_ , ' W? + 0 'I E X1'?-

X C N+ ,

v- ,4+ K. k +

1394

) 31 (

K. ) 1 ( : ( K * ' FSS

2 ) , Z6 '1 6 0+

+ ]0 'I E 27

[ .

Fig. (1): Potential application of FSS as a spatial filter in windows or walls of a building [27].

2 3 + ,)* FSS $ " "/

K. 2 3 + T4 - '1 6 ,B+ C + LA B+ 1

0 Eg gB+ 1g Eg N+ M - . + + 0 * ;i

,- 'I N+ J 4 _ K. H + .

4 •* ( ,

,- 16 / + + 0 * ( T ) . g

K.g LAg )

2 ( ) 3 (

C S -0e + N+ 'i ,1 I ( , +

g•+ + + ^ 4 4

*N I ,O1 ,- , K. B+ 1 .

) 2 ( ) 3 ( K

.-9

3 g.

* ,B+ C K. 0 ] i / *+

Hg + g‚ g + g* i

g•+ 0+ g - *+ g' g. + + - ( + H + -+ H + K F .

I g + ` [O N+ Y+ ( ,O1 ,*N ,g g '-+ 1 g

0e ( 3 . N+ + )- C , '-+ T* / ( '

,- M* 3 . ' + + LA . '6 i

K. ) 2 :( B+ 1 * LA

,O1 I + + .

Fig. (2):Unit cell of the inductive plan.

K. ) 3 :( B+ 1 * LA

,*N I I + + .

Fig. (3): Unit cell of the capacitive plan.

3 3 B" C$ FSS < 6$ / $ " "/

,- + T4 - 4 ) + - | g + e Hg + 0 + + _ .

1 N+ K. J ,O1 ,*N I B+

N+ - `

,- / 3 . N+ , ( 1 6 0 g - g'1 6 7g 0+ 4

gT4 - ;gi 1

C ,D - TD i+ . g + gT4 - N+ g'i g ,D g-

/ * ' 'I H + B+ 1

Kg G , * * N 'I /S

-,- I + e + 0e X1 (

K. ) 4 ( K.g g + e + 0e 0N I

) 5 ( ,- K . 4 .

K. ) 4 :( K. B+ 1 0 + + _ ( N+ ( ,O1 J '- + e 2

K . 4 +

.

) 32 (

K. ) 5 :( K. B+ 1 0 + + _ ( N+ ( ,*N I J '- + e 3

+ K . 4 .

Fig. (5) : Periodic capacitive array composed of alongside connected unit cells of the second Fig.

g g / g E] ( 3 . N+ LA 1 6 i+ H +

g

+ _ 0 +

10

,g- g 6 Y g6 ,O1 ,*N I @ A Eg 0+ g4

LC

Eg 0+ g 2 g ( e D S K G N+

-FSS

+ gT4

-,- K 2 0N I X1 H + - ( + H + - '.* ( gC +

( ) + 0 B+ 1 + N+ 'i ,D +

. >* * N

H +

FSS

k 2 ' + ( - ?m )

0e ,g- ƒ g . g

'I

FSS

,O1g LAg /,*N gI LA N+ K . 4

0e H \ N K.

) 6 ( + + 0 * .

K. ) 6 :( W *

. 'I

Fig. (6): 3D presentation of the proposed structure.

K. ) 7 :( + FSS

0 T4 - ;i 1 .

Fig. (7): Equivalent circuit of first-order band-pass filter

H +

FSS

,- + ` [Og N+ Y+ g( g g 2 ,'B+ 0+ 4

*N I ,O1 g \ g N Eg | gC , g( g) + Eg '.F+

.

* 'I K( Y .[' + W + 6+ }2 + e H \ N N+ O' + ] + I 7

.[

K. ) 7 ( +

-FSS

g + 0 g * ,TA_ E4 4

-+ + . + D G'*+ vI + - - H .

2 + - - N+ O' + }

4 'I g ,B+ C K 1[4 u

FSS

' + I C

+ B e 6 , + + I ,B+ C

] 24

25 .[ \ N v G'*+ vI '.F+

E ,- - + 0e gC (

+ h - ?m / \ N E '.F+

gr *+ > g + 0e

r c

Z Z

ε =

,-. + G'*+ vI * 3* * , '*+ , + '

g KgT_ Z6

FSS

0e >*+ ggr-+ gg ,gg +Ne ggZ6 >*+ ggr-+ gg + gg

Ω =₃₇₇

Z + ,- ( A* . N+ N g * - >* * N

6 0N I X1 N+ 4 0e g( ,F G'*+ vI -

g N+ + g

/ ( + D e D

H + . +

-FSS

g) + ^gA_ Eg4 E *+ 4

0 - '1 6 7 0e ) '* ( ( + ;i

.

T * ` [O ` D

,- 0 G'- 2 ,G6+ 0 + V

+ -,* . + + H + 0 + V N+

I 0 * .

'I H +

FSS

+ V U4 T * , * z B 0

.

4 3 "6E F G H

I CST

T + + 6+ Y * N+ 'I N

CST

E ( T N Y 4 S

-11

+ O' + / + .

Y * + 6+

CST

'I B+ 1 E

-FSS

K. k A- + )

8 ( ,- g + g6+ Y g* . g ( W g ` g

1 |+ C+ N - /~ 6 + B+

K A' - ^ .- E `

,- M* D ( i K.g ( + B+ 1 z -

) 8 ( g

g + + 0 * ,4 •* N g- { g ` g

unit

cell

K. k A-)

9 ( Y g* ` g H + . ( J ?'*+ gD '- + g6+

J g '- N - v + ( + I

12

g g . g N g- {

,- B+ 1 ,)* g* ,gm 6 ` [Og 0 g (

•gg* 1 2 ,gg-gg K.gg ) 8

K.gg k ggA- gg + ( )

9 ( gg

`

open(add space)

,)* * ` [O . + _ 1

2 0+ 2

[O S * i ' 6 uT ,g- Kg 2 ( 16 +

gZ6 . g (

D \ ` [O H + ,D I g + I + + _ , C U- '.F+ Jn

[O S+ -+ 4 g 4 +

FSS

'g + g ( g( B

D |VI

FSS

1394

) 33 (

K. ) 8 T K A' - ^ .- ( T •* ) B+ 1 :( . N

Fig. (8): The unit cell geometry inside the simulation air box.

K. ) 9 N - v + . ) N - v + X 4 :( .

Fig. (9): Defining the boundary in the boundary condition setup.

K. ) 10 ,- B+ 1 E X 4 :( + [- * J '- + e E *+ 4

T 0+ 2 \ N + H 4 H P . ( N /J 1A- J 4

,- J '- 'I J 4 . i t? - *+ 4

Fig. (10): Defining a unit cell can simulates the infinite periodic array. The periodicity can also be specified, by setting the size

of the substrate to the desired periodicity.

- v + 2+ gB+ 1g g ( gD g ] g J '- N

\ N - 2+ H P •g* ,)* * ` [O '*+ Jn D

1

2 [O S - I / K .g 4 g[- * LAg E I+ . +

1 N+ K. k A-)

10 T ( . + I N

5 3 + ,)* H G ( > K

. K ) 11 ( ( ,*N I LA , * ( 6 7 , [ O - `

RV2 + + _ +Ne Z6 g _ •g* g ,

-+ + 0 g * +

( ,O1 LA , * ( 6 7 . `

gZ6 gO

g * + + _ +Ne •g* g- _ g' - vgI

g + g + 0 g * .

D 'I , '-+

1 (

. + e

K. ) 11 G- :( \ N EB ,*N I LA , * ( 6 7

,O1 LA , * ( 6 7 N D+ X1'?-.

Fig. (11): Comparison of frequency response of capacitive plane on different rogers substrate and inductance plane.

Table (1): Geometric parameter of capacitive and inductive arrays (unit of millimeter).

) D 1 :( + ,*N I + e , 'O

-,O1 O

( ' 1 - ^ B )

w d r4

r3

r2

r1

0.5 5.5 2 . 8 2.3 1 0.5

s

p

r8

r7

r6

r5

0.5 5.5 2.8 2.3 1 0.5

+ LA H + i+ B + g_ 3 . ( N+ - `

/ g

C C ( >* ( 6 ( Eg] ( LAg 1g 6 ,. '.F+

/ ,- ` H + 0+ 4

>* ( 6 ( -+ N+ A + :

) 1 (

LC f

π ≈

^ m O ( 4 * N

LC

N+ -+ N+ A + :

) 2 (

L C Z

Q_L ≈

e .

L

Q

G] ' / '1 6 4 4 + I . gi+

+ ? '1 6 4

13

' +

L

Q

4 B 0 .-+ w .

H + N N )-C + 4 B 0 .-+ w J ?'*+ ( . H g

+ T* ^ 4 4 . 'I 0N I + G- W + 6+ + ,

,- ~ 6 ( ( K.g ,*N gI LA

) 2 ( g \ N Eg +

( ,( .B E '.F+ K.g . g +

) 12 ( 0+ g g ,g. '.F+

TF ,. | C 16 N+

| . g ) ,*N gI g

N+ g ( ( LAg

K. ) 2 ( M[F + ( H ' + gI + + + 0 g * / 'g

+ + 0 .

,- ( C ,-

g 0+ 4 ~ g6 ^g G4

KI+ N+ 0+ - { AI N+ , * ( ( ' ( T2 E '.F+

^ m i+ B . * 'i E '.F+

g ,*N I 6 ‚ /

H + -e D | .

. 6 + I W + 6+ , +

) 34 (

K. ) 12 :( K. 0+ -,. '.F+ TF

| C 16 | .

) ,*N I N+

( K. + +Ne Z6 .( „] E '.F+

] + + _ K. 25

[.

Fig. (12): Shape of electrical field on the metal edge of each side of capacitive gaps. Free space is on the right and dielectric

in on the left [25].

+ N+ ,gg. ^gg 4 4 H g gg( 4 gg* N x0N ggI + ggG- W + gg6+ gg

g \ g N N+ O'g + / ( ) + + I ^ gm g Eg '.F+

N+ 'i , ;i 1

,- ,*N I LA + K. .

) 11 ( 7g

\ N ,*N I LA , * ( 6 ( g I E '.F+

N D+

14

T O' + - \ N ` d? - . + N

D ) 2 (

] + e

26 + \ N - ?m .[ 5

/ 0 ' 1

-+ '6 i M* .

Table (2): Substrate of the properties of the second FSS used in the simulation of Fig. 11 [26].

D ) 2 :( \ N ` d? ,*N I ` [O

T '6 ( N

K. , * ( 6 7 11

] 26 [ .

? .E B E H G ( LM % N

4 O P $ @/

+ )8$

9 RO3003 3

0.0013

10 RO3006 6.15

0.002

11 RO3010 10.2

0.0022

0 K. ( C )

11 ( ,- ^ m + G- W + 6+

0N I + G- / \ N E '.F+

-…• + '6 W + 6+ LA W + 6+ .

, [ - ^ G'*+ ^ m , * ( 6 7

W + 6+ ,*N I LA

/,. '.F+ , ;i ^ m - @ m

… ,- ,T1A- H ] .

K. ) 13 ( E 0 + + _ N+ K B + T4 - '1 6 , * ( 6 7

'-+ \ N | C ,O1 LA E ,*N I LA D , )

1 ( l * . + + 0 * / H E '.F+

LA

RO3003

- ?m + E '.F+

5 / 0 ,1 - '- ,-.

K. ) 13 :( T S - Y 4 N

FSS

2 W 4 + ^A_ E4

T N+ K B y '* .0e + - - N

Fig. (13): Full-wave numerical simulations for the single-pole FSS at normal incidence compared to the results achieved by

simulating the circuit model of the FSS.

K. ) ,F G'*+ vI - '-+ 6

T 'I ( N

+

Ω =_217/7

Zc /

Ω =₃₇₇

Z

/

nH / L=2 6 /

pF / C=0 5

K. ( )

13 ( 7 + - - H + , * ( 6 7

N+ K B , * ( 6 T

Y * v 4) S - Y 4 N + 6+

CST

(

G-7 . +

Y * v 4 ,F G'*+ vI - , * ( 6 + 6+

ADS

W 0+ 4 D 4 . + -e , [ - ^ - ,

- H + [ / + - - , [ - v 4 S - Y 4 N

.1 2 N

FSS

,- ` T•+ .

6 3 !"# $ ""R$ H ? ) < 6$ / 8" > K

H ,O1 ,*N I LA 1B - gD ` gd? - 0 )

1 (

+ + _ 3 . ( +

FSS

, K . 4 + I + T4 .

H gg gg \ N /LAgg 0e - ?ggm gg( + + gg_ Egg '.F+

mm / h=_{0 5}

+ + LA H 1 6 + e)

,O1g

EB \ N | C ,*N I *+

g'1 6 H + , * ( 6 7 .(

K. ) 14 ( \ N +N+ g e X1'?- , ;i ^ m ,

A + D 4 . + 1

2 g- 0N gI + gG- W + g6+ …

/ 4 g* N •

W ( >* * N >* ( 6 ,- W + 6+ >* * N O ( ^ m

.

K. ) 14 :( , * ( 6 7

FSS

\ N +N+ + T4 -.X1'?-

Fig. (14): Frequency response of FSS for different substrates.

1394

) 35 (

>* ( 6 >* * N

H + ] 'I ^ 4 4 +

GHz / f_r1=_{5 5}

/

GHz f_r2=₄

/

GHz f_r3=₃

GHz / f_r4=_{2 4}

gg . gg

,g / 'I g gB+ 1g g + D 4

mm / D=₁₁₁

0+ g

gg + ^gg 4 4 gg ggB+ 1gg gg + N gg Egg] ( 2

0

1 /

/ D λ =

/

15 0

2 /

/ D λ =

/ 1 0

3 /

/ D λ =

09 0

4 /

/ D λ =

,-.

N+ 0 -'I ,B+ C 'I

+ ( + + \ N

RO3010

,- * * 0+ 2 + i

+ 0e ,g * ( 6 7g B 4

/W 4 +N U4 T * Hg + , * ( 6 7 H + . ( ,

'?- + N +N+ + 'I 1

, 4 S - X K. e

) 15 ( ,- 0 * A* .

( g +N g U4 +N+ g g

4 O N+ W 4 45

D + gI , gI + g N+ , * ( 6 7

.

K. ) 15 (: , * ( 6 7 B ,

FSS

* * + T4 -2

U4

S - W 4 +N .

Fig. (15): Investigating frequency response sensitivity of one order FSS (type 2) versus the variation of wave incident angle.

WI ] 'I . + D 4 90

0e g g 2 [- B D

, * U4 , † [F N+ ,g- / (

Tg Y g)*+ 0 g 0+ g4 N g

6 7 ( + 0 C+ z B 0 + V U4 T * , * (

, * .

7 3 ""R$ H ? ) < 6$ / 8" > K !"# $

( ( /

,g- g'1 6 0N gI U4 + ( 3 + g U4 g gd'- 0+ g4

, '-+

+ ,*N I LA ( G] .

| . g

1 ,*N I ,- W + 6+ 0e ,*N I 6 ‚ + G- W ( B+

.

( ( U4 C ,*N I 1 , '-+ i+ H P C l ( -)

| . g 6 ‚ / g W + g6+ 0e D

,g- W + 6+ * 1 ,*N I g * ,O1g gB+ 1g g- . g

,-( ,-( + 0 0+ 4 „ 'g + W

H g P 0e g

„ ' + C W + 6+ + G-

W + g6+ gB+ 1 , GF+ I ^ m

,g- + g- H + H'6 i M* . vg + N+ 0+ g4

1 2

. 6 i d4 , * ( 6 7 U4 ,3* 3]

\ N H'6 i M*

RO3010

,g- ,gB+ C '1 6 * * g (

, '-+ (

0e ,O1 LA g + 0 g . g

g '-+ .

, LA ,O1 * * H + ,*N I ^g 4 4 g

gD ) 3 (

+ e

\ N ,- 4 - ?m . g + *

mm / h=_{0 5}

+ '6 i M* .

l * '1 6 , * ( 6 7 1

4 3 K. ) 16 ( G- 3 .

. *+ >* ( 6 * * H + >* * N

^ 4 4 +

GHz / f_r1=_{1 8}

/

GHz / f_r2=_{1 5}

GHz / f_r3=₁₂

+ .

+ * * B+ 1

mm D=16 ,-.

* * 0 - N+ 1

4 3 + ,F €- 0+ 2 7g B ,

U4 , * ( 6 * * /W 4 +N

2 ,g- J ?'*+ + K.g . g (

17 ,- 4 O N+ W 4 +N U4 +N+ ( 45

7 D

,- ,_ + , * ( 6 . *

Table (3): Geometric parameters of the inductive and capacitive plane related to first order filter for three designed types 1 to 3

and (unit of millimeter).

D ) 3 :(

,O1 LA ,

'-,*N I * * + T4 - '1 6

,B+ C 1

4 3 ) ' 1 - ^ B (

w d r4 r3 r2 r1 )8 ,)*

1

10 3 2 1.5 0.5 3 $1 .

s p r8 r7 r6 r5 H ; ,)*

0.9 6.2 4.9 4 2.4 1.5 1 .

0.3 7.4 4.3 4 2.8 2.5 2 .

0.1 6.8 4.6 4.5 3.6 3.5 3 .

K. ) 16 :( , * ( 6 7

FSS

* * 1 4 3 '-+ +N+ ,

\ N +N+

X1'?-RO3010

.

Fig. (16): Frequency response of type 1 to 3 FSSs versus different geometric parameters with RO3010 substrate.

K. ) 17 :( , * ( 6 7 B ,

FSS

l * + T4 -2

U4

.S - W 4 +N

) 36 (

* * 4

/ 5 6 \ N H'6 i M* ,gB+ C

+ gD g'1 6 , '-+ 0e ( *+ 4

g4 6 e

+ l * '1 6 , * ( 6 7 . 4

4 6 K. 18 3 .

G-,- ( A* . *+

l * '1 6 O ( ^ m

4 4 6 K( l * '1 6 N+ '.] ( 1

4 3 .

K. ) 18 :( , * ( 6 7

FSS

* * 4 4 6 , '-+ +N+

\ N +N+

X1'?-RO3003

.

Fig. (18): Frequency response of type 4 to 6 FSSs versus different geometric parameters with RO3003 substrate.

>* ( 6 g g* * g H + >* * N

g + ^g 4 4 GHz

/ f_r1=_{2 8}

/

GHz / fr2=3 3

GHz / fr3 =4 1

,-.

Table (4): Geometric parameters of first order filter for types 4 (unit of millimeter).

D ) 4 ( :

'1 6 ,

* * + T4 -4

( ' 1 - ^ B )

w d

r4

r3

r2

r1

1 9.5 3

2 1.5 0.5

s p r8

r7

r6

r5

0.5 5.5 5 4.5 1.5 1

Table (5): Geometric parameters of first order filter for types 5 (unit of millimeter).

D ) 5 ( : +

'1 6 ,

* * + T4 -5

( ' 1 - ^ B )

w d

r4

r3

r2

r1

1 7.5 3 2 1.5 0.5

s p r8

r7

r6

r5

0.5 5.5 4 3.5 1.5 1

Table (6): Geometric parameters of first order filter for types 6 (unit of millimeter).

D ) 6 ( : +

'1 6 ,

* * + T4 -6

( ' 1 - ^ B )

w d

r4

r3

r2

r1

1 5.5 3 2 1.5 0.5

s p r8

r7

r6

r5

0.5 5.5 3 2.5 1.5 1 K.

) 19 :( + ( ,*N I I + + B+ 1 * 'i

0e

+N + N+ ,* ( K T4

α

+ .

Fig. (19): Unit cell of the capacitive plan, larger circle slot

transforms to sector of circle with foreside angel α.

K. ) 20 :( K. B+ 1 0 + + _ ( N+ ( ,*N I J '- + e

19 + K B .

Fig. (20): Periodic capacitive array composed of alongside connected unit cells of figure 19.

* * B+ 1 + 4

/ 5 6 J + ^ 4 4 mm / D₁=_{15 5}

mm / D₂=_{13 5}

/ mm / D₃ =_{11 5}

,-.

g + g 6+ 'I 3 +Ne D E * - .

k gA

K. ) 19 ( Eg K T4 + ,* + /,*N I LA B+ 1

t? - +N 0 (

α

K. . ( )

20 ( J g '- + e *

,- 0 * + B+ 1 H + N+ K B .

,B+ C * * i+ 2

) gD ,g g '-+ )

3 (

+ +N H + N+

π = α

+N+ + , * ( 6 7 / W ( D

]

α

K.g g / g ( X1'?-)

21 ( g + N . g

α

* * 4 >* ( 6 7

4 9 D ) 7 (

+ e

.

U4 F B H +

α

-+ / + W + 6+ + '1 6 T2 >* ( 6 0+ 4

g( ,F gB . g W + g6+ g * '1 6 O ( ^ m B H 2 T K. N ) 14 ( ) 16 ( ^ gm g'1 6 gT2 >* ( 6 W + 6+

,- W ( '1 6 O ( ,- N D+ ( : H + .

(

W ( N * ` `+ g U4 g i g / T2 >* ( 6 W + 6+

. ' + + O ( ^ m , ( , + 6+

1394

) 37 (

K. ) 21 (: , * ( 6 7

G-FSS

l * + T4 -7

4 9

FSS

l * 2

+ N +N+

α

\ N +

X1'?-RO3010

.

Fig. (21): Transmission response of first order FSS type 7 to 9

and type 2 with varying angelαfor RO3010 substrate.

Table (7): Angelα_in capacitive unit cell of filters type 7 to 9.

D ) 7 ( : 0 ( +N

α

'1 6 ,*N I 1 * *

7 4 9

9 8

7 type

5

π

2

π π

10 9

α

4.6 3.7

2.9

r

f

* * 7 , * ( 6 7 B , + + +N U4 T *

,- J ?'*+ /W 4 (

K. . ) 22 ( ,- g U4 +N+ (

4 O N+ W 4 +N 45

,- ,_ + , * ( 6 7 D . *

K. ) 22 (: , * ( 6 7 B ,

FSS

l * + T4 -7

U4

.S - W 4 +N

Fig. (22): Transmission coefficients of the first-order FSS type 7 for different angles of incidence.

,1( g O ( ^ gm >* g* N >* g( 6 gM 4 + F B H 4

,- / '1 6 + 'I g , ` d? - \ N > D 0+ 4

g \ N + . e . + U4 ( g g

^ + gm g Xg1'?- g

,gg- gg F 4 ,gg - ,gg. '.F+ , ;ggi N gg H gg P . * gg

gg U4

, + g „gi g fV€g- . g * [- * * , '-+ , * + ,*N I LA I e 6 N+ ( , - + G- E N+ W 0+ 4

,- K [4 ,B+ C W + g6+ g3 ,F g€- 0+ 2 . + W (

+ l B N+ W ,- }2 B+ 1 ,*

g + g4 g

g ~ g2 gB+ 1g K.g 1( '6 3 . 0 [F gd- Eg g + g @+ C . D+ - WF ] ,B+ C e 6 ` [O , G- \ N > D U4 N+ O' + ,3* 3] H

. ( + _ ,B+ C '-+ 0+ 2

N , ;i ^ m 0 • D 4 €- + \

g F 4 g

( g- O ( ^ m ( - >* ( 6 D 4 @+ C /

\ N I _V2 g Eg * ,g * * N >* g( 6 g( g i + +

' + @+ C J 1A- '1 6 ( - >* ( 6 `+ g U4 + >r .

>* ( 6 ,R D ` [Og ,g gG- / O ( ^ m >* * N

4 * i M .

8 3 U" "M

/ .' + , * * N Q B+ 1 ,6 - F G- H + 9 0 - '1 6 * * g* * . ,B+ C + T4 - ;i

g 1 g4 3 g

\ N

RO3010

0e >* g* N >* g( 6 ( ,B+ C ,g g

0

2 / 1 4 8 / 1 4 4 3 i M

g* * . g 4 g4 6 g g \ g N

RO3003

0e ;i B * * ( ,B+ C g N+ 'g g

,1T_ * * )

L

Q

0e >* g( 6 . + (,1T_ * * N+ ' (

g* * >* * N g

4 g4 6 H g 8 / 2 g4 1 / 4 4 4 g3 i gM

g .

* * ,B+ C 7

4 9 \ N

RO3010

,B+ C

0e >* * N >* ( 6 H

9 / 2 4 6 / 4 4 4 3 i M

Tg * (

+ + ,g1T_ g* *

L

Q

g 4\ g g*+

+ g g * .

* * N+ ,I , * ( 6 W 4 +N U4 T *

Tg Y g)*+

N ` T•+ , .

E :O 1- Frequency-Selective Surfaces

2- Scatterer

3- Artifical Magnetic Conductor; AMC 4- Radom

5- Coupling 6- Passive 7- Quasi-static 8- Tune

9- Complementary 10- Cascading 11- Fullwave

12- Periodic Boundary Condition 13- Sharp

14- Rogers

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