GELOMBANG DATAR SERBASAMA

7/21/2019 GELOMBANG DATAR SERBASAMA

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1

GELOMBANG DATAR

SERBASAMA

Achmad Mauludiyanto

Lab. Antena & Po!a"a#iRuan" B$%'



(

Gelomban" data #eba#ama

) Salah #atu bentu* "elomban"

ele*toma"neti*

)Rambatan ene"i EM

) Dianali#a den"an !e#. Ma+,ell



%

A*an Di!ela-ai

) Siat$#iat "el. Ele*toma"neti* / *on#e! *ece!.ambat ambat "elomban"0 !an-an" "elomban"0im!edan#i0 !ha#e dan edaman

) Siat$#iat ambatan"ea* "el. Dalam beba"aimedia / uan" ham!a0 diele*ti* #em!una0diele*ti* meu"i0 !en"hanta bai* dan!en"hanta #em!una

) Men"enal daya 2Poyntin" Theoema3

) Pantulan dan tan#mi#i "el EM. 4an" datan"!ada !ebata#an ( media 5 Aah *edatan"an / nomal0 dan menyudut



6

Macam$macam Gelomban"

) Gel. Suaa 2a*u#ti*3 "el. Lon"itudinal

) Gel. 7ahaya0 "el adio 2EM3 "el.

Tan#8e#al



9

Gelomban" data

) Gel. 7ahaya0 "el. Radio yan" bea#al dai#umbe yan" -auh

) Gel. EM tedii dai !a#an"an medan E dan :

) :a#il !e*alian #ilan" E&: menentu*an aah!eambatan ene"i EM

) Gel. TEM 2tan#8e#e electical Ma"netic3 "el.yan" mem!unyai E dan : te"a* luu# aah

ambat) Seba#ama ; bidan" E&: m!* bidan" data

*on#tan



'

Gea* "el. Dalam uan" ham!a

( ) ( ) ( ) ( )

( ) ( ) ( )

).(.

.

).(.

.

0.,

0.,

,,0,0

2

2

00

2

2

2

00000

2

0

2

2

00

2

000

2

0

0

00

Helmholtz pers H medan gelombang perst

H H

t

H

t

H

t E

t H H

t

E H

Helmholtz pers E medan gelombang pers

t

E E

t

E

t H

t B

t E E

t

B E

E

t

H

t

B E

H t

E

t

D H

Maxwell pers

v

−−−−→∂∂

=∇∴

∂∂

−=

∂∂

−∂∂

=×∇∂∂

=∇−∇∇→

∂∂

×∇=×∇×∇

−−−−→∂

∂=∇∴

∂∂

∂∂

−=×∇∂∂

−=×∇∂∂

−=∇−∇∇→

∂∂

×−∇=×∇×∇

=∇

∂

∂−=

∂

∂−=×∇

=∇∂∂

=∂∂

=×∇

−====

ε µ

ε µ µ ε ε ε

ε µ

ε µ µ

µ

ε

µ µ ε ε ρ σ



<

Pe#. Ma+,ell dlm bentu* !ha#o

[ ] [ ][ ]

[ ] [ ] [ ]

jwt

s

jwt

s

jwt

s

jwt

s

jwt

s

jwt

s

jwt

s

e jwH e E

e jwH e H

t

e E

e H t

e E t

H E

0

00

00

ReReRe

ReRe

µ

µ µ

µ µ

−=×∇∴

−=

∂

∂−=×∇

∂∂

−=×∇→∂∂

−=×∇

0,

0,

0

0

=⋅∇=×∇→=⋅∇−=×∇→

s s s

s s s

H E jw H

E H jw E

ε

µ



=

Pe#. Gel. Dalam bentu* !ha#o

( ) ( ) ( ) ( ) s s s s s E jw jw E E H jw E 00

2

0 ε µ µ −=∇−⋅∇∇→×∇−=×∇×∇

H gel pers H w H E gel pers E w E

s s

s s

−−→−=∇−−→−=∇..

..

00

22

00

22

ε µ ε µ



>

) Mi#al aah ambat "el. !d. aah ?@ ada

E+ dan :y #a-a

) t* "el. Data #eba#ama

E+ ta*beubah thd. +0 :y ta* beubah thd y

z jw z w

xs

xs xs

xs xs

xs xs

Ae Ae E

umuman penyelesaimempunyai

E wdz

E d atau

E wdz

E d E w

z

E

00002

:

000

2

2

2

00

2

2

2

00

2

2

2

ε µ ε µ

ε µ

ε µ ε µ

−−−

==

−−

=+→

−=→−=∂∂



1

) Dalam bentu* #e#aat 2time domain3

[ ]

)(cos()(

)cos()(

Re)(

000

00

ε µ

ε µ

z t w E t E

z wwt At E

e E t E

x x

x

jwt

xs x

−=

−=

=



11

Paamete lain di udaa

000:tan ε µ β w propagasitakons =−

Ω===−−

×==−−

377120:

/1031

:tan

0

0

0

8

00

π ε

µ

η

ε µ

udaradiimpedansi

smcdiudararambat kecepa



1(

Peambatan dalam diele*ti* meu"i0,0 =≠ v ρ σ

( ) ( ) ( ) ( ) ( )

( )

( )

( )ε σ µ γ

γ ε σ µ

γ ε σ µ

ε σ µ µ µ

µ

ε σ

jw jwdengan

H H H jw jw H

E E E jw jw E

E jw jw H jw E E H jw E

E H jw E

H E jw H

Maxwell pers

s s s s

s s s s

s s s s s

s s s

s s s

+=

=∇→+=∇∴

=∇→+=∇∴

+−=×∇−=∇−∇∇→×∇=×∇×∇

=∇−=×∇=∇+=×∇

−

2

222

222

2

:

.

0.,

0.,)(

[ ]

β

α

β α γ

:]/[tan

:]/[tan

:tan 1

mrad fasatakons

m eper redamantakons

jm propagasitakons

−

−+=− −



1%

) Mi#al aah ambat "el. !d. aah ?@ ada E+ dan

:y #a-a

) t* "el. Data #eba#ama E+ ta* beubah thd.

+0 :y ta* beubah thd y

z j z

x

z

x xs

xs xs

xs xs

xs xs

ee E e E E

umuman penyelesaimempunyai

E dz

E d atau

E dz

E d E w

z

E

β α γ

γ

γ ε µ

−−− ==−−

=−→

=→−=∂∂

00

2

2

2

2

2

2

00

2

2

2

:

0

( ) z wt e E eee E e E t E sesaat nilai z

x

jwt z j z

x

jwt

xs x β α β α −===− −−− cos]Re[]Re[)(: 00



16

Paamete lain

) ece!atan !ha#a /

β

wv =

)Cm!edan#i intin#i* /

ε σ

µ η

jw

jw

+=



1'

) t* "el. 4" meambat *e aah ?@

( ) sesaat z t E E

phasor e E E

gelombang bentuk

z dz

E d

z dz

E d

x x

z j

x xs

xs xs

→−=→=

−−=→−=

−

β ω

β µε ω

β

cos

:

0

0

2

2

22

2

2

)Paamete lainnya /

r r

r

r r r r r

r r r

rinsik impedansi

f

c f gelombang panjang

ccrambat kecepa

ε

η

ε

µ η η

ε

λ

ε µ

λ

ε µ ν λ

ε ε µ µε β

ω ν

0

0

00

:int

/:

1:tan

≈=−

≈===−

≈===−



1<

Rambatan "el. Dlm.diele*ti* bai*

) 7ii / 1⟨⟨ωε σ

µε ω ωε

σ µε ω β

ε

µ σ

ωε

σ µε ω α

ωε

σ

ωε

σ µε ω

ωε

σ µε ω γ

≈

+≈

≈

−≈

+

+−=−=

2

2

8

11

22

8

1

211

j j

j j j j

)on#tanta !o!a"a#i

/



1=

Paamete lain

) Cm!edan#i intin#i*

) ece!atan a#a

+≈ ωε

σ

ε

µ

η 21 j

022

2

0

22

2 8

11

8

11

1ν

ε ω

σ ν

ε ω

σ µε

ν ≈

−≈

+

=



1>

Rambatan dlm.!en"hanta bai*

) 7ii /

) on#tanta !o!a"a#i

1⟩⟩ωε

σ

( )

2

2

1

2

1

2

1

211

2/1

ωµσ µσ π β

ωµσ µσ π α

µσ π γ

ωµσ ωε

σ µε ω

ωε

σ µε ω

ωε

σ µε ω γ

≈≈

≈≈

+≈

−≈−≈

−=−=

f

f

f j

j j j j j j j j

GELOMBANG DATAR SERBASAMA

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