sel310-A24 Guia met retangular Sel310 612
50 pág.

sel310-A24 Guia met retangular Sel310 612


DisciplinaOndas Eletromagnéticas132 materiais796 seguidores
Pré-visualização3 páginas
m
m
-
1
)
TEM
TE1,0
TE2,0
TE3,0 TE3,1
Freqüência de Corte para Alguns Guias
a
b
Modo TE1,0
0.3
0.4
0.5
0.6
d
e
 
p
r
o
p
a
g
a
ç
ã
o
(
m
m
-
1
)
WR 159
WR 90
WR 62 WR 28
freqüência
06/06/2012 37SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL
EIA: Electronic Industries Association
WR: Waveguide Rectangular
Freqüência (GHz)
0 5 10 15 20 250
0.1
0.2
0.3
C
o
n
s
t
a
n
t
e
d
e
 
p
r
o
p
a
g
a
ç
ã
o
WR 510 Designação
EIA (WR)
Dimensão (a-b) 
(polegadas)
freqüência
de corte
(GHZ)
510 5,100-2,550 1,157
159 1,590-0,795 3,711
90 0,900-0,400 6,557
62 0,622-0,311 9,486
28 0,280-0,140 21,081
Campo Ey do modo TE10
z
amplitude
x
z
y
a
b
x
z
y
a
b
06/06/2012 38SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL
z
x
F
x
a=25,4 mm; b=12,7 mm
f=9 GHz
z
Campo elétrico
06/06/2012 SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL 39
TE31, 32 GHz
http://en.wikipedia.org/wiki/File:Waveguide_x_EM_rect_TE31.gif
www.comsol.com/showroom/gallery/
lrgthumb/1421/4ddf41e2.jpg
Modos TMm,n
( ) ( )
( ) ( )
( ) ( )
0
02
1
02
1
sen sen exp( ),
cos sen exp( ),
sen cos exp( ),
z x y z
z x
x x y z
z y
y x y z
E E k x k y jk z
k k
E j E k x k y jk z
k
k k
E j E k x k y jk z
k
= \u2212
= \u2212 \u2212
= \u2212 \u2212
( ) ( )sen cos exp( ),y
k
H j E k x k y jk z
\u3c9\u3b5
= \u2212
06/06/2012 40SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL
( ) ( )
( ) ( )
02
1
02
1
sen cos exp( ),
cos sen exp( ),
0.
y
x x y z
x
y x y z
z
k
H j E k x k y jk z
k
k
H j E k x k y jk z
k
H
\u3c9\u3b5
\u3c9\u3b5
= \u2212
= \u2212 \u2212
=
Se 0,=n 0
y
k =0
x
k =0,=m ou a solução é trivial
modo TM fundamental é o
11
TM
Impedância de Onda
Modos TE
( )
2
1 c
yx
y x
TE
f
f
z
EE
H H k
Z
Z
\u3c9µ
=
\u2212
= \u2212 = =
Modos TM
2
1yx cz
f
Z Z
E kE \uf8eb \uf8f6\uf8f7\uf8ec \uf8f7\uf8ec= \u2212 \uf8f7= \u2212 = =
06/06/2012 41SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL
/Z µ \u3b5=
Modos TM 1yx cz
y x
TM
f
Z Z
E k
H H f
E
\u3c9\u3b5
\uf8f7\uf8ec \uf8f7\uf8ec= \u2212 \uf8f7\uf8ec \uf8f7\uf8f7\uf8ec\uf8ed \uf8f8
= \u2212 = =
2z
z
TE TM
Z Z
k
Z
k\u3c9µ µ
\u3c9\u3b5 \u3b5
= \u2261=
Potência Média Transportada pela Onda
( ) ( ) ( )1, , , Re , , , ,
2
S x y z t E x y z H x y z
\u2217\uf8f1 \uf8fc\uf8f4 \uf8f4\uf8f4 \uf8f4< >= ×\uf8f2 \uf8fd\uf8f4 \uf8f4\uf8f4 \uf8f4\uf8f3 \uf8fe
( ) ( )
0 0
1
Re , , , ,
2
b a
m
P E x y z H x y z dS
\u2217\uf8f1 \uf8fc\uf8f4 \uf8f4\uf8f4 \uf8f4= × \u22c5\uf8f2 \uf8fd\uf8f4 \uf8f4\uf8f4 \uf8f4\uf8f3 \uf8fe
\u222b \u222b
,dS dAn dydxn= =
\u2322 \u2322
n
\u2322
versor normal à área transversal 
W/m2
W
06/06/2012 42SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL
( ) ( )
0 0
1
Re , , , ,
2
b a
m
z
P E x y z H x y z dydx
\u2217\uf8f1 \uf8fc\uf8ee \uf8f9\uf8f4 \uf8f4\uf8f4 \uf8f4\uf8ef \uf8fa= ×\uf8f2 \uf8fd\uf8f4 \uf8f4\uf8ef \uf8fa\uf8f0 \uf8fb\uf8f4 \uf8f4\uf8f3 \uf8fe
\u222b \u222b
( ) ( ) ( ), , , , x y y x
z
E x y z H x y z E H E H
\u2217
\u2217 \u2217\uf8ee \uf8f9\uf8ef \uf8fa× = \u2212
\uf8ef \uf8fa\uf8f0 \uf8fb
,dS dAn dydxn= = n versor normal à área transversal 
componente na direção z do vetor de Poynting complexo 
x
z
y
a
b
x
z
y
a
b
Potência Média Transportada pelo Modo TE10
{ }
0 0
1
Re
2
b a
m y x
P E H dydx\u2217= \u2212\u222b \u222b
2 2 2
02
1
sen
2
b a
z
m
k x
P H a dydx
a
\u3c9µ \u3c0
\u3c0
\uf8eb \uf8f6\uf8f7\uf8ec \uf8f7= \uf8ec \uf8f7\uf8ec \uf8f7\uf8ec\uf8ed \uf8f8\u222b \u222b
06/06/2012 43SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL
02 0 0
sen
2m
P H a dydx
a\u3c0
\uf8f7= \uf8ec \uf8f7\uf8ec \uf8f7\uf8ec\uf8ed \uf8f8\u222b \u222b
2 2
2
0 1 watt
4
c
m
c
ZabH ff
P
f f
\uf8eb \uf8f6 \uf8eb \uf8f6\uf8f7 \uf8f7\uf8ec \uf8ec\uf8f7 \uf8f7\uf8ec \uf8ec= \u2212\uf8f7 \uf8f7\uf8ec \uf8ec\uf8f7 \uf8f7\uf8f7 \uf8f7\uf8ec \uf8ec\uf8ed \uf8f8 \uf8ed \uf8f8
x
z
y
a
b
x
z
y
a
b
/Z µ \u3b5=
Componentes
06/06/2012 SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL 44
Excitação do modo TE10
y
E E y= \u275
06/06/2012 SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL 45
4
L
\u3bb
\u2264
900 (até parede) + 1800 (reflexão parede)
+ 900 (retornando para a fonte) = 3600 (em fase)
Campos do modo TE10
( )
( )
( )
0
0
0
cos exp( )
sen exp( )
sen exp( )
z x z
x x x z
y y x z
H H k x jk z
H jH k x jk z
E jE k x jk z
= \u2212
= \u2212
= \u2212 \u2212
06/06/2012 46SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL
( )0
0
\u2c6
\u2c6 \u2c6
y y x z
x z y
y
x z
E E H
E E y
H H x H z
= = =
=
= +
Campo Ey
( )
( ) ( ) ( )
0
sen exp
1
exp ex
( )
mas,
p
y y x z
E jE k x j
sen k x jk x jk x
k z
\uf8ee \uf8f9= \u2212 \u2212\uf8ef \uf8fa\uf8f0
= \u2212
\uf8fb
\u2212
06/06/2012 SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL 47
( ) ( ) ( )exp ex
22
\u2c6 \u2c6 \u2c6
p
2
x x zz
x x x
jk x jkjk x jk z yo
y
zyo
E
sen k x jk x
E
e e
jk x
E E e
j
ey y y
\u2212 \u2212\u2212\u2212
\uf8ee \uf8f9= \u2212 \u2212\uf8ef \uf8fa
=
\uf8f0
+
\uf8fb
=
Campos Hx e Hz
( ) ( ) ( )1cos exp ex
como
resulta em
p
2x x x
k x jk x jk x\uf8ee \uf8f9= + \u2212\uf8ef \uf8fa\uf8f0 \uf8fb
06/06/2012 SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL 48
\u2c6 \u2c6
\u2c6
2
2 2
2
\u2c6
x z
z
z
xx z
x
jk x jk z jk x jk zxo
jk x j
xo
jk x jk zo
z
zo
x
k
H x x
H
e e
H
e
H
e e
H
e ez zeH
\u2212 \u2212 \u2212
\u2212 \u2212\u2212
= \u2212
= +
Ondas incidente e refletida
x
1yE
z
x 1H
1k
2yE
z
x
2H
2k
x
Onda 1 Onda 2
06/06/2012 SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL 49
x
z
2H
2k
x
1H1k
2yE
1yE
Polarização
Perpendicular
Ao plano
De incidência
Onda TE
Padrão onda estacionária
x
z
2k 1k
2xk
2zk
1xk
1zk
1 1 1
\u2c6 \u2c6
x z
k k x k z= \u2212 +
2 2 2
\u2c6 \u2c6
x z
k k x k z= +
06/06/2012 SEL310/612 Ondas Eletromagnéticas Amilcar Careli César USP EESC SEL 50
2xk 1xk
x
yE
Polarização perpendicular ao plano de incidência: Onda TE