
107Waveguides
P E H dxdy
ba
= ×
∫∫
Re ( ) *1 2
00
/
(3.45)
In view of Equations 3.23b and 3.23c written in the modied form as
E
y
= E
y0
sin(x
π
/a) e
−j
β
z
and H
x
= H
x0
sin(
π
x/a) e
−j
β
z
,
P E x a e H x a e dxdy
y
j z
x
j z
ba
= ×
−
∫∫
Re ( ) sin( ) sin( )1 2
0 0
00
/ / /π π
β β
(3.46)
Since H
x0
= E
y0
/Z
z
(TE) = −E
y0
/Z
z
(TE).
In view of Equation 3.28, H
x0
= −(
β
/
ωμ
) E
y0
.
Thus, Equation 3.46 becomes
P E x a dxdy E
y
ba
y
= × −
=
∫∫
Re ( ) ( )sin ( )1 2
1
4
0
2 2
00
0
2
/ / /β ωε π
β
ω
µµ
ab
(3.47)
3.3.10 Attenuation in Waveguides
The attenuation in waveguides is mainly due to its nite conductivity. It
results in some (small) surface resistance in t