x z y 0 a b 0 0 a x eyey z rectangular waveguides te 10 mode
TRANSCRIPT
xz
y
0 a
b
0
0a
x
Ey
z
rectangular waveguidesTE10 mode
rectangular waveguides
TE10 mode2
c a
1
2
1f
2
c b
1
2
1f
y
xz 0 a
b
0
y
b
xz 0 a0
yb
xz 0 a0
a = 2b
a2
cfc
cf2
ca
2
λc
xz
y
0 a
b
02
c a
m1
2
1f
2
c a
m1
2
1f
28
a
m
2
103
28
03.0
1
2
103
2
1010 9 GHz 5
a = 3 cm
rectangular waveguides
TE10 mode
xz
y
0 a
b
0
222
a
222y
2x kk
22
a
22
c a
c
rectangular waveguides
TE10 mode
rectangular waveguides
TE10 mode
y
b
xz 0 a0
22
a
v2
2
a
2
2 a1
1
c
2
fa2c
1
c
2
a21
c
rectangular waveguides
TE10 mode
y
b
xz 0 a0
22
a
v2
a21
c
f
vg
2
2
a21
xz
y
0 a
b
0
0a
x
Ey
z
rectangular waveguidesTE10 mode
g
rectangular waveguides
xz
y
0 a
b
0
TE10 mode
a
πxsin
a
Bj-Ey
a
πxsin B
aπjβ
Hx
2
c1c
a
πxcos BHz
x
yTE H
EZ
2
c
ωω
1cω
ωμ
B
aπjβ
B
aπ
jωωμ
β
ωμ
2
c
c
ωω
1
Z
Movie to illustrate phase mixing of two propagating sinewaves in a dispersive media.
c
Study of an amplitude modulated pulse
Movie to illustrate the propagation of an amplitude modulated pulse in a
waveguide
dispersion ztje
z
z
z
t1
t2
t3
z
z
z
t1
t2
t3
z
z
z
t1
t2
t3
dispersion ztje
z
z
z
t1
t2
t3 T tjtj dteeA o
0)(
2
)(
eA2
2
)('())((
2),(
ztztj ooo
ee
tzA
xz
y
0 a
b
0
rectangular waveguidesTE10 mode
8.8.e. The transmission analogy can be applied to the transverse field components, the ratios of which are constants over guide cross sections and are given by wave impedances. A rectangular waveguide of inside dimensions [a = 4, b = 2 cm] is to propagate a TE10 mode of frequency 5 GHz. A dielectric of constant r=3 fills the guide for z>0 with an air dielectric for z<o.
rectangular waveguides
xz
y
0 a
b
0
TE10 mode
x
yTE H
EZ
2
c
c
ωω
1
Z
2
c
2aλ
1
Z
.06105
103λ
9
8
vac
.035ε
λλ
r
vacdielectric
570
86
1
377Z
2air
241
83.5
1
3377
Z2dielectric
rectangular waveguides
xz
y
0 a
b
0
TE10 mode
by,ax
0y,0x
*xy dxdyHERe
2
1power
abHEpower oo
a
πxsin
a
Bj-Ey
a
πxsin B
aπjβ
Hx
xz
y
0 a
b
0
lossy dielectric
The wave will attenuate as it propagates.
rectangular waveguidesTE10 mode
xz
y
0 a
b
0
rectangular waveguidesTE10 mode
Loss in walls due to finite conductivity of metal surfaces
Tangential H surface current js
Ohmic power loss
Attenuation of the em wave
xz
y
0 a
b
0
0a
x
Ey
z
rectangular waveguidesTE10 mode
matching
xz
y
0 a
b
0
rectangular waveguides
8.8a. For f=3 GHz, design a rectangular waveguide with copper conductor and air dielectric so that the TE10 wave will propagate with a 30% safety factor (f = 1.30fc) but also so that wave type with next higher cutoff will be 30% below its cutoff frequency.
cm 10103
103λ
9
10
c
c
f
f
λ
λ
2aλ10TEc
2bλ01TEc
cm 13 λ 1.3 λ want10TE
cm 7.7 1.3
λ λ want
01TE
a = 6.5 cm
b = 3.85 cm
Cylindrical Waveguides
ztje a
z zzt EE 222
zzt HH 222
Cylindrical Waveguides
ztje a
z
011 22
2
2
2
zzz EE
rr
Er
rr
0222 zzt EE
nrkAJE cz cos0
Bessel function
J0(x)
J1(x)
0
0
10 20
1
Cylindrical Waveguidesa
z
00 akAJE cz
c
aak cc
nrkAJE cz cos0
.... ;TM ;TM ;TMTM 110201nl
c
a
2
0J of zero
J0(x)
J1(x)
0
0
10 20
1
n is angular variation
l is radial variation
Cylindrical Waveguides
ztje a
z
011 22
2
2
2
zzz HH
rr
Hr
rr
0222 zzt HH
nrkBJH cnz cos
Cylindrical Waveguides
ztje a
z
n
dr
rkdJB
k
jE cn
c
cos
0cos n
dr
akdJB
k
jE cn
c
.... ;TE ;TE ;TETE 110201nl
n is angular variation
l is radial variation
J0(x)
J1(x)
0
0
10 20
1
mode TE01
mode TE11
Loss decreases as frequency increases
Field distribution is similar to TE10 mode in rectangular waveguide
vg
v
v c
1
c
a
z
