x z y 0 a b 0 0 a x EyEy z rectangular waveguides TE 10 mode.

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