Design Of Slot X-Polarized Microstrip Patch Antenna At ISM Band

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D -POLARIZEDMICROSTRIPPATCHANTENNAATI SM D

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ii i v

S T N E T N O C F O E L B A T

CHAPTER TITLE PAGE

T C E J O R

P TITLE i

M R O F N O I T A M R I F N O C T R O P E R S U T A T

S ii

T E E H S L A V O R P P

A i ii

T E E H S N O I T A R A L C E

D i v

T N E M E G D E L W O N K C

A v

T C A R T S B

A v i

K A R T S B

A vii

S T N E T N O C F O E L B A

T v iii

F O T S I

L TABLES xii

S E R U G I F F O T S I

L x iii

F O T S I

L ABBREVIATIONS /SYMBOLS xvi

F O T S I

L APPENDICES x iv i

I INTRODUCTION 1

1 .

1 BACKGROUND 1

2 .

1 PROBLEMSTATEMENT 2

3 .

1 OBJECTIVES 2

4 .

1 SCOPEOFWORKS 3

5 .

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x i

I

I LITERATUREREVIEW 6

.

2 1 PARAMETEROFANTENNA 6

1 . 1 .

2 RadiaitonPattern 6

2 . 1 .

2 Driecitvtiy 10

3 . 1 .

2 G ain 1 0

4 . 1 .

2 Bandwidth 1 1

5 . 1 .

2 Pola irzaiton 1 2

1 . 5 . 1 .

2 Linea rPola irzed 1 3

2 . 5 . 1 .

2 Cricula rPola irzed 1 4 3

. 5 . 1 .

2 Elilpitca lPolairzed 1 5 2

.

2 MICROSTRIPPATCHANTENNA 1 6 3

.

2 RECTANGULARMICROSTRIPPATCH 21 4

.

2 QUARTERWAVELENGTHTRANSFORMER 24 1

. 4 .

2 SingleSeciton 2 5

2 . 4 .

2 MulitpleSecitonAndBinomia lDesign 2 5 5

.

2 SLOTTYPESOFMICROSTRIPPATCHANTENNA 2 6 1

. 5 .

2 U- S lot 2 7

2 . 5 .

2 C- S lot 2 8

3 . 5 .

2 MulitpleSlots 2 9

4 . 5 .

2 DiamondSlot 2 9

5 . 5 .

2 Slo tLoaded 3 0

6 . 5 .

2 Dua lSlot 3 1

6 .

2 ISMBAND 3 1

I I

I METHODOLOGY 3 3

1 .

3 FLOWOFMETHODOLOGY 3 3

2 .

3 MICROSTRIPPATCHANTENNADESIGN 3 3 1

. 2 .

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x

2 . 2 .

3 Microst irpFeedLine 3 4 3

. 2 .

3 Inse tFeed 3 5

4 . 2 .

3 � 54 0Pola irzedMicrost irpPatch a

n n e t n A

6 3

5 . 2 .

3 X- Pola irzedMicrost irpPatchAntenna 3 7 6

. 2 .

3 Slo tMicrost irpPatchAntenna 3 8 3

.

3 SIMULATION 4 1

4 .

3 FABRICATIONPROCESS 4 5

5 .

3 MEASUREMENTPROCESS 46

V

I RESULTANALYSISANDDISCUSSION 4 7

1 .

4 RESULTANALYSIS 4 7

2 .

4 SIMULATION 4 7

1 . 2 .

4 SingleMicrost irpPatchAntenna 4 7 2

. 2 .

4 � 54 0Pola irzedMicrost irpPatch Antenna 4 9 3

. 2 .

4 Slo tSingleMicrost irpPatchAntenna 5 3 1

. 3 . 2 .

4 Veritca lSlo tMicrost irpPatch 5 3 2

. 3 . 2 .

4 Ho irzonta lSlotMicrost irpPatch 5 4 3

. 3 . 2 .

4 Slan tSlo tMicrost irpPatch 5 6 4

. 3 . 2 .

4 DoubleSlo tMicrost irpPatch 5 7 4

. 2 .

4 X- Pola irzedMicrost irpPatchAntenna 5 9 5

. 2 .

4 Slo tX-Pola irzedMicrost irpPatchAntenna 6 1 1

. 5 . 2 .

4 X- Slo tX-Pola irzedMicrost irpPatch a

n n e t n A

1 6

2 . 5 . 2 .

4 T- Slo tX-Pola irzedMicrost irpPatch a

n n e t n A

3 6

3 . 5 . 2 .

4 SimulaitonResul tFo rT-Slo tX-Pola irzed a

n n e t n A h c t a P p ir t s o r c i M

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i x

3 .

4 MEASUREMENT 6 8

1 . 3 .

4 X- PolairzedMicrost irpPatchAntenna 6 8 2

. 3 .

4 T- Slo tX-Pola irzedMicrost irpPatchAntenna 6 9

V CONCLUSIONANDRECOMMENDATION 7 1

1 .

5 CONCLUSION 71

2 .

5 RECOMMENDATION 7 2

S E C N E R E F E

R 7 3

S E C I D N E P P

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ii x

S E L B A T F O T S I L

E L B A

T TITLE PAGE

.

2 6 Frequencybandi nI SMband 3 2

6 . 2 .

3 Dimensionmicrost irppatch 4 0

.

4 22 . Compairsons imulaitonr esutlf ors inglemicrost irppatchand

� 54 0pola irzedmicrost irppatchantenna

2 5

4 . 2 .

4 Simulaitonr esutlf o rX-pola irzedmicrost irppatchantenna 6 1 3

. 5 . 2 .

4 Simulaitonresutlf o rT-slo tX-polairzedmicrost irppatch a

n n e t n a

7 6

1 . 3 .

4 Measurementr esutlf o rX-pola irzedmicrost irppatchantenna 6 9 2

. 3 .

4 Measurementr esutlf o rT-slo tX-pola irzedmicrost irppatch a

n n e t n a

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ii i x

S E R U G I F F O T S I L

E R U G I

F TITLE PAGE

1 Flowo fmethodology 5

) a ( 1 . 1 .

2 Fieldpatterni n ilnears cale 7

) b ( 1 . 1 .

2 Powe rpatterni n ilnears cale 7

) c ( 1 . 1 .

2 Powe rpatterni ndBs cale 8

) d ( 1 . 1 .

2 Radiaitonpattern 9

) 3 ( 1 . 1 .

2 Linea rplo to fpowe rpattern 9

4 . 1 .

2 Bandwidth 1 2

5 . 1 .

2 Propagaitono fwave 1 3

1 . 5 . 1 .

2 Thepropagaitonwaveo filnea rpola irzed 1 4 2

. 5 . 1 .

2 Thepropagaitonwaveo fcricula rpola irzed 1 5 3

. 5 . 1 .

2 Thepropagaitonwaveo felilpitca lpola irzed 1 6 )

a ( 2 .

2 Microst irppatchantenna 1 7

) b ( 2 .

2 Sideview 1 7

) c ( 2 .

2 Shaper adiaitngpatch 1 8

) d ( 2 .

2 Typicalf eed sfo rmicrost irppatchantennas 2 0 )

e ( 2 .

2 Equivalentf ort ypicalf eeds 2 0 )

a ( 3 .

2 Singlemicrost irppatchantenna 2 2 )

b ( 3 .

2 Microst irpfeed il ne 2 3

) c ( 3 .

2 Inset dfee length 2 4

4 .

2 Thequa tre rwavelength rtansformer 2 5 2

. 4 .

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v i x

1 . 5 .

2 U-slo tdesign 2 8

2 . 5 .

2 C-slo tdesign 2 8

3 . 5 .

2 Mul itples lots 2 9

4 . 5 .

2 Diamonds lo tdesign 3 0

5 . 5 .

2 Slotl oadeddesign 3 0

6 . 5 .

2 Duals lo tdesign 31

4 . 2 .

3 � 54 0pola irzedmicrost irppatchantenna 3 7 5

. 2 .

3 X-pola irzedmicrost irppatchantenna 3 8 )

a ( 6 . 2 .

3 Slot singlemicrost irppatchantennawtihva irou sshapes 3 9 )

b ( 6 . 2 .

3 S tlo X-pola irzedmicrostirppatchantenna 4 1 )

a ( 3 .

3 Microst irppatchantenna 4 2

) b ( 3 .

3 Potrs rtucturei nCST 4 3

) c ( 3 .

3 � 54 0pola irzedmicrost irppatchinCST 4 3 )

d ( 3 .

3 Sidev wi e inCSTf o rX-pola irzedmicrost irppatch 4 4 )

e ( 3 .

3 Bottomvi ewinCSTf o rX-pola irzedmicrost irppatch 4 4 )

f ( 3 .

3 Fron tvi ewinCSTf o rX-pola irzedmicrost irppatch 4 5 5

.

3 Measurements etitng 4 6

) a ( 1 . 2 .

4 Singlemicrost irppatchantenna 4 8 )

b ( 1 . 2 .

4 Simulaitonr esutls inglemicrost irppatchantenna 4 9 )

a ( 2 . 2 .

4 � 54 0pola irzedmicrost irppatchantenna 5 0 )

b ( 2 . 2 .

4 Simulaitonr esutl� 54 0pola irzedmicrost irppatchantenna 5 2 )

a ( 1 . 3 . 2 .

4 Veritcals lo tmicrost irppatch 5 4

) b ( 1 . 3 . 2 .

4 Resu tlf o rbandwidthandgainwhenl engths lot ,Lsi sva ired 5 4 )

a ( 2 . 3 . 2 .

4 Ho irzontals lo tmicrost irppatch 5 5 )

b ( 2 . 3 . 2 .

4 Resu tlf o rbandwidthandgainwhenwidthslot ,Wsi sva ired 5 5 )

a ( 3 . 3 . 2 .

4 Slants lo tmicrost irppatch 5 6

) b ( 3 . 3 . 2 .

4 Resutlf o rbandwidthandgainwhenlengthslot ,Lsi sva ired 5 6 )

a ( 4 . 3 . 2 .

4 Doubles lo tmicrost irppatch 5 7

) b ( 4 . 3 . 2 .

4 Resu tlf o rbandwidthandgainwhenlengthslot ,Ls1andLs2 e

r

a va ired

8 5

) c ( 4 . 3 . 2 .

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v x

e r

a va ired )

a ( 4 . 2 .

4 X-pola irzedmicrost irppatchantenna 5 9 )

b ( 4 . 2 .

4 Simulaitonr esutlfo rX-pola irzedmicrost irppatchantenna 6 0 )

a ( 1 . 5 . 2 .

4 X-slo tX-pola irzedmicrost irppatchantenna 6 2 )

b ( 1 . 5 . 2 .

4 Resu tlf o rbandwidthandgainwhenl engths lot ,Ls1and d

e g n a h c s i 2 s L

3 6

) a ( 2 . 5 . 2 .

4 T-slo tX-pola irzedmicrost irppatchantenna 6 4 )

b ( 2 . 5 . 2 .

4 Resu tlf o rbandwidthandgainwhenl engths lot ,Ls2 i s d

e g n a h c

5 6

) c ( 2 . 5 . 2 .

4 Resu tlf o rbandwidthandgainwhenwidths lot ,Ws1i s d

e g n a h c

5 6

3 . 5 . 2 .

4 Simulaitonresutlf o rT-slo tX-polairzedmicrost irppatch a

n n e t n a

7 6

1 . 3 .

4 Measurementr esutlf o rX-pola irzedmicrost irppatch a

n n e t n a

8 6

2 . 3 .

4 Measurementr esutlf or T- ts X-lo pola irzedmicrost irppatch a

n n e t n a

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i v x

S L O B M Y S / S N O I T A I V E R B B A F O T S I L

S P

D - Driec tBroadcas tSatellties S

C

P - Persona lCommunicaitonSystem S

T M

U - Universa lMoblieTelecommunicaitonSystem N

A L

W - Wrieles sLoca lAreaNetwork S

P

G - Globa lPosiitoningSatellties C

E

P - Perfec tElect ircConductor M

S

I - Indust iral ,Scienit ifcandMedical 4

R

F - FlameResistant 4 B

d - Decibel

εr - Dielect ircConstan tO fMate iral εe ff - EffecitveDielect ircConstant

𝜆g - WaveguideWavelength

𝜆 - WavelengthI nFreeSpace

𝜇o - Permeablitiyo fvacuum

εo - Permtiitvtiyo fvacuum

F

R - RadioFrequency B

C

P - P irntedCricui tBoard T

S

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ii v x

S E C I D N E P P A F O T S I L

X I D N E P P

A TITLE PAGE

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1 1 R E T P A H C N O I T C U D O R T N I 1 .

1 Background

d n a e fi l e l p o e p n i t n a c if i n g i s y r e v g n i m o c e b e r a s e c i v e d c i n o rt c e l e y lt n e r r u C o t e u D . n o it a c il p p a s s e l e ri w d n a s m e t s y s n o it a c i n u m m o c , s m e t s y s r e t u p m o c n i r a l u p o p s s e l e ri w s u o ir a v n i t n e m p o l e v e d d i p a r e h

t communicaiton systems ,al o to fmethodhave

o t h t d i w d n a b y c n e u q e r f d e c n a h n e d n a e z i s d e c u d e r h ti w a n n e t n a p o l e v e d o t d e t s e g g u s e li b o m , r a l u ll e c e li b o m s a h c u s s m e t s y s e li b o m f o s t n e m e ri u q e r y c n e i c if f e e h t e v e i h c a ) S P D ( s e ti ll e t a s t s a c d a o r b t c e ri d , s s e l d r o

c , persona lcommunicaiton system (PCS) ,

k r o w t e n a e r a l a c o l s s e l e ri w , ) S T M U ( m e t s y s n o it a c i n u m m o c e l e t e li b o m l a s r e v i n u m e t s y s s s e l e ri w n o it a r e n e g t x e n r e h t o d n a ) S P G ( s e ti ll e t a s g n i n o it i s o p l a b o l g , ) N A L W ( .] 1 [ n i d e s u y l e d i w e r a s a n n e t n a h c t a p p ir t s o r c i

M wrieles scommunicaiton system .

, d a e h n a m u h e h t o t g n il p u o c c it e n g a m o rt c e l e w o l s a h c u s s e g a t n a v d a s ti o t e u d s i s i h T e c n a m r o f r e p h g i h n i a t n i a m o t y ti li b a p a c d n a t s o c w o l , y ti li b a il e r l a c i n a h c e m d e s a e r c n i e t s y s n o it a c i n u m m o c n I . s e i c n e u q e r f f o d n a b e d i w r e v

o m ,wide bandwidth i sa main

n o it a c il p p a e s o p r u p it l u m n i d e s u e b n a c a n n e t n a h c t a p e h t e k a m o t t n e m e ri u q e r t n e m e l e p ir t s o r c i m r o f e g a t n a v d a s i d r o j a m a s i h t d i w d n a b w o r r a N . y c n e i c if f e e r o m e t a r e p o d n a ] 2 [ a n n e t n a h c t a

(19)

2 o p o r p n e e b e v a h s e u q i n h c e t l a r e v e

S sedbyr esearcher spreviouslyt o i ncreaset he

r e y a l r e h t o n a n i r e h ti e s e h c t a p c it i s a r a p g n i s u y b s i d o h t e m l a n o it n e v n o c e h T . h t d i w d n a b e h t e s a e r c n i ll i w s d o h t e m h t o B . ) y rt e m o e g r a n a l p o c ( r e y a l e m a s r o ) y rt e m o e g d e k c a t s ( r c n i o s l a l li w p a g r i A . e z i s a n n e t n

a easet hebandwidthbutt hi smethodr equrie sadjusitng

d o h t e m r e h t o n A . e c it c a r p n i k s a t y s a e n a t o n s i h c i h w , y ll a c i n a h c e m h t d i w p a g r i a e h t d n u o r g r e v o t h g i e h h c t a p g n i s a e r c n i s i h t d i w d n a b e h t e s a e r c n i o t d e s u e b n a c s i h c i h w e t a rt s b u s r e w o l a g n i s u , e n a l

p permtiitvtiyandcutt hes lo tont hepatch[ 5][6]..

2 .

1 ProblemStatement

, h t d i w d n a b w o r r a n s a h c u s s e g a t n a v d a s i d f o t o l a s a h a n n e t n a h c t a p p ir t s o r c i M n o i s s i m s n a rt w o r r a n s a h o s l a s i ti , s e d i s e B . s e it il i b a p a c g n il d n a h r e w o p w o l d n a n i a g w o l p e h T . l a n g i

s ola irzaiton o fwave radiated in convenitona lmicrost irp antenna i s ilnea r l li w l a n g i s h c t a m s i m e s u a c e b s e s s o l e c u d o rt n i l li w n o it a z ir a l o p e p y t s i h T . d e z ir a l o p f o e g a t n a v d a s i d n i a m a s i h t d i w d n a b w o r r a n A . l a n g i s n o i s s i m s n a rt g n ir u d r u c c o a h c t a p p ir t s o r c i

m ntenna i n pracitca lappilcaiton normally a few pe rcen taround 2% -

m , e r o f e r e h T . %

3 anymethod shaveproposed t oenhance t he performanceo fmicrost irp h t d i w d n a b y ll a i c e p s e a n n e t n a h c t a

p . The narrow bandwidth wli l ilmtis t he funciton o f

i a n n e t n a p ir t s o r c i

m nt hepresen tmoderncommunicaitons ystem.

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t band i s2.4 GHz .Anothe rgoal i nt hi sproject i st o enhance

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t c e j o r p s i h

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s thepatch .Thi sprojec tha sdesignedand simulated byusing CST2009 so tfware y c n e u q e r f g n it a r e p o e h T . h t d i w d n a b d n a n i a g , n r e tt a p n o it a i d a r ,s s o l n r u t e r e h t n i a t b o o t i m s i h t r o

f cros irp patch antenna usedi n ISM band appilcaiton i s2.4GHz .The mate ira l s i t n a t s n o c c ir t c e l e i d e h t s i h c i h w 4 R F s i a n n e t n a h c t a p e h t f o e t a rt s b u s e h t r o f d e il p p a e t a c ir b a f o t d e s u s a h d o h t e m g n i h c t E . 9 1 0 . 0 s i s s o l t n e g n a t d n a m m 6 . 1 s i s s e n k c i h t , 4 . 4 i h

t santenna .Fo rmeasuremen treturn loss ,radiaiton pattern ,gain and bandwidth o f . d e r u s a e m e b l li w a n n e t n a h c t a p 5 .

1 Projec tMethodology

a n n e t n a h c t a p s e p y t t o l s d n a a n n e t n a h c t a p p ir t s o r c i m e h t t u o b a n o it a m r o f n i ll A h c u s s e c r u o s l a r e v e s m o r f g n ir e h t a g e r

a as j ournal ,reference book and pape rwhich i s

e h t t u o b a n o it a m r o f n i e h t n i a t b o o t r a l u p o p t s o m e h t t u B . e ti s b e w y n a n i a t b o n a c n I . e r o l p x e E E E I m o r f e r a a n n e t n a h c t a p p ir t s o r c i m t o l s d n a a n n e t n a h c t a p p ir t s o r c i m r p m i o t w o h n o it a m r o f n i e h t , e r u d e c o r p s i h

t ove the characte irsitc o fmicrostirp patch

e h t m o r F . d e s o p o r p d n a d e t a g it s e v n i n e e b s a h n i a g d n a h t d i w d n a b s a h c u s a n n e t n a . y d u t s c ir t e m a r a p g n i s u y b n w o h s s a w t o l s n g i s e d o t d o h t e m e h t , w e i v e r e r u t a r e ti l f o c it s ir e t c a r a h c d n a n g i s e d e h t o t g n i d r o c c a s i t c e j o r p s i h t r o f n g i s e d e h T X , a n n e t n a h c t a p p ir t s o r c i m l a n o it n e v n o

c -pola irzed microst irp patch antenna and slo t

l a r e v e S . w e i v e r e r u t a r e ti l m o r f d e n i a t b o s i n o it a m r o f n i l l A . a n n e t n a h c t a p p ir t s o r c i m s d o h t e

m can be used to design antenna such a scalculaiton ,paramet irc study and o t d e s u e b l li w y d u t s c ir t e m a r a p d n a n o it a l u c l a c , t c e j o r p s i h t n I . h c a o r p p a l a c ir i p m e n a c e n il p ir t s o r c i m d n a d e e f t e s n i , h c t a p n o i s n e m i D . a n n e t n a h c t a p p ir t s o r c i m e h t n g i s e d l u c l a c e

b ated and designed using approximate equaiton from ltierature review .Slo t d n a t o l s l a c it r e v e l b u o d , t o l s X , t o l s l a t n o z ir o h s a h c u s e p a h s y n a d e n g i s e d e b n a c e p a h s e r o f e r e h T . t o l s f o n o i s n e m i d e n i m r e t e d o t n o it a u q e e t a m i x o r p p a t o n s a h e r e h T . t o l s T t e m a r a

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4 X d n a h c t a p p ir t s o r c i

m -pola irzed microst irppatch antenna t oanalyze t he effect so fslo t . t o l s ) h t g n e l( s L d n a ) h t d i w ( s W g n i y r a v y b n i a g d n a h t d i w d n a b n o s a h t c e j o r p s i h

T been simulated in the microwave appilcaiton so tfware ,CST

. 9 0 0

2 In thi sso tfware ,the paramete ro fantenna can be observed .Thi sparamete ri s n o it i d n o c d o o g n i d n a t n e i c if f e , ll e w g n it a r e p o s i a n n e t n a e h t t a h t e r u s n e o t t n a tr o p m i a c ir b a f o t e u n it n o c e r o f e

b itngprocess .The paramete rantenna suchas r adiaiton pattern ,

. d e z y l a n a y l n o m m o c s i h t d i w d n a b d n a y ti v it c e ri d , n i a g , s s o l n r u t e r o t d e tr e v n o c s i n o it a l u m i s m o r f n g i s e d , s s e c o r p g n it a c ir b a f n

I dxf flie and p irn t

p s n a rt s i h T . r e p a p y c n e r a p s n a rt e h t n o t u

o arencypaperi spatchedont hes ubs rtatebefore

4 R F , t c e j o r p s i h t n I . e t a c ir b a f o t d e s u e b n a c s l a ir e t a m e t a rt s b u s e p y t l a r e v e S . e t a c ir b a f s i e t a rt s b u s s s e n k c i h t , 4 . 4 s i t n a t s n o c c ir t c e l e i d s a h e t a rt s b u s s i h T . d e t c e l e s s a h e t a rt s b u s s s o l t n e g n a t d n a m m 6 .

1 i s0.019 .Thi ssubsrtate wli lbe etching using chemical i n t he

. y r o t a r o b a l , r e z y l a n A k r o w t e N . y r o t a r o b a l e h t n i e n o d n e e b s a h t i , t n e m e r u s a e m r o F k r o w t e N g n i s u y B . t n e m e r u s a e m r o f d e s u e r a r e n i a r T a n n e t n A d n a r e z y l a n A m u rt c e p S n r u t e r , h t d i w d n a b , r e z y l a n

A los sand r esonance f requency o fantenna wli lbe measured .

. d e s u s i r e n i a r T a n n e t n A y ti v it c e ri d d n a n i a g , n r e tt a p n o it a i d a r e r u s a e m o T i h

T s i sthe ifna lstep in thi sprojec.t Al linformaiton abou tltierature review , l a n if s i h t n i d e v a s d n a d e t c e ll o c n e e b s a h t n e m e r u s a e m d n a e t a c ir b a f , n o it a l u m i s , n g i s e d . d e r a p m o c d n a d e z y l a n a s i t n e m e r u s a e m d n a n o it a l u m i s r o f t l u s e r e h T . g n it ir w t r o p e r p m i o t k r o w e r u t u f e h t r o f n o it s e g g u s e h

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6 2 R E T P A H C

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.

2 1 Parameter soft heantenna

e h t f o n o it a r e p o d n a e c n a m r o f r e p e h t e b ir c s e d o t d e s u s i a n n e t n a e h t f o r e t e m a r a P e h T . ll e w g n it a r e p o s i a n n e t n a e h t t a h t e r u s n e o t d e s u e b n a c r e t e m a r a p s i h T . a n n e t n a n o it a i d a r , y ti s n e d r e w o p n o it a i d a r , n r e tt a p n o it a i d a r s a h c u s a n n e t n a e h t f o s r e t e m a r a p m a e b , n i a g , y c n e i c if f e a n n e t n a , s e u q i n h c e t l a c ir e m u n , y ti v it c e ri d , h t d i w m a e b , y ti s n e t n i n e i c if f e n o it a i d a r a n n e t n a , e c n a d e p m i t u p n i , n o it a z ir a l o p , h t d i w d n a b , y c n e i c if f

e cy and

, n i a g , n r e tt a p n o it a i d a r s i d e s u y l n o m m o c r e t e m a r a p e h T . e r u t a r e p m e t a n n e t n a .] 7 [ n o it a z ir a l o p d n a h t d i w d n a b 1 . 1 .

2 Radia itonpa ttern

Radiaiton pattern can be de ifned a sa graphica lrepresentaiton o fthe radiaiton

a s a a n n e t n a e h t f o s e it r e p o r

p funciton o fspace coordinates .The radiaiton pattern can

x u lf r e w o p s a h c u s n r e tt a p n o it a i d a r f o s e it r e p o r p e h T . n o i g e r d l e if r a f e h t e n i m r e t e d . n o it a z ir a l o p d n a y ti v it c e ri d , h t g n e rt s d l e if , y ti s n e t n i n o it a i d a r , y ti s n e

d A rtace o fthe

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r e tt a

p n anda graphof t hespaital va iraitonof t hepowe rdenstiyalong aconstant r adiu s

e d u ti l p m a n a d e ll a c s

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) B d ( s l e b i c e

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r a l u g n a e h t f o n o it c n u f a s a d l e if c it e n g a m r o c ir t c e l e e h t f o e d u ti n g a m e h t f o t o l

p space .

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r a l u g n a e h t n o it c n u f a s a d l e if c it e n g a m r o c ir t c e l e e h t f o e d u ti n g a m e h t f o e r a u q s e h t

s e r p e r ) c ( 1 . 1 . 2 e r u g i F n i d e t a c i d n i e l a c s B d n i n r e tt a p r e w o P . e c a p

s ents t he magntiude

.] 7 [ e c a p s r a l u g n a e h t f o n o it c n u f a s a d l e if c it e n g a m r o c ir t c e l e e h t f o

r a e n il n i n r e tt a p d l e i F : ) a ( 1 . 1 . 2 e r u g i F

e l a c s

r a e n il n i n r e tt a p r e w o P : ) b ( 1 . 1 . 2 e r u g i F

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