PPT Medan 2 - Rectangular Wave Guide.pdf

7/22/2019 PPT Medan 2 - Rectangular Wave Guide.pdf

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Rectangular Waveguides

Irsandi Agustomo(0906529924)

Asep Muhamad A S

(1106050986)


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Waveguide components

Figures from: www.microwaves101.com/encyclopedia/waveguide.cfm

Rectangular waveguide Waveguide to coax adapter

E-teeWaveguide bends


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More waveguides

http://www.tallguide.com/Waveguidelinearity.html


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Uses

To reduce attenuation loss

High frequencies

High power Can operate only above certain

frequencies

Acts as a High-pass filter Normally circular or rectangular

We will assume lossless rectangular


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Rectangular WG

Need to find the fields

components of the

em wave inside thewaveguide

EzHzExHxEyHy

http://www.ee.surrey.ac.uk/Personal/D.Jefferies/wguide.html


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Rectangular Waveguides:

Fields inside

Using phasors & assuming waveguide

filled with

lossless dielectric material and walls of perfect conductor,

the wave inside should obey

ck

HkH

EkE

22

22

22

where

0

0


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Then applying on thez-component

2

2

2

2

2

2

2

2

:obtainwewherefrom

)()()(),,(

:VariablesofSeparationofmethodbySolving

0

kZ

Z

Y

Y

X

X

zZyYxXzyxE

Ekz

E

y

E

x

E

''''''

z

z

zzz

022 zz EkE


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Fields inside the waveguide

0

00

:sexpressionin theresultswhich

2

2

2

2222

2

ZZ

YkYXkX

kkk

kZ

Z

Y

Y

X

X

''

y

''

x

''

yx

''''''

zz

yy

xx

ececzZ

ykcykcY(y)xkcxkcX(x)

65

43

21

)(

sincossincos

22222yx kkkh


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Substituting

zz

yy

xx

ececzZ

ykcykcY(y)xkcxkcX(x)

65

43

21

)(

sincossincos

)()()(),,( zZyYxXzyxEz

zyyxxz

z

yyxxz

zzyyxxz

eykBykBxkBxkBH

eykAykAxkAxkAE

z

ececykcykcxkcxkcE

sincossincos

,fieldmagneticfor theSimilarly

sincossincos

:direction-intravelingwaveat thelookingonlyIf

sincossincos

4321

4321

654321


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Modes of propagation

Boundary Conditions

TEM (Ez=Hz=0) cant propagate.

TE (Ez=0) transverse electric In TE mode, the electric lines of flux are

perpendicular to the axis of the waveguide

TM (Hz

=0) transverse magnetic,Ez

exists In TM mode, the magnetic lines of flux are

perpendicular to the axis of the waveguide.


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TM Mode

Boundary

conditions: ,axE

,byE

z

z

0at0

0at0

Figure from: www.ee.bilkent.edu.tr/~microwave/programs/magnetic/rect/info.htm

zyyxxz eykAykAxkAxkAE sincossincos 4321

zjyxz eykxkAAE sinsin42

From these, we conclude:

X(x) is in the form of sin kxx,

where kx=mp/a, m=1,2,3,

Y(y) is in the form of sin kyy,

where ky=np/b, n=1,2,3,So the solution forEz(x,y,z) is


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TM Mode

Substituting

zj

oz eyb

n

xa

m

EE pp

sinsin


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TM modes

The m and n represent the mode of propagation

and indicates the number of variations of the

field in the xand ydirections

Note that for the TM mode, if n or m is zero, all

fields are zero.

0

sinsin

z

zj

oz

H

eyb

nx

a

mEE

pp

TMmn


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TE Mode

Boundary

conditions: ,axE

,byE

y

x

0at0

0at0

Figure from: www.ee.bilkent.edu.tr/~microwave/programs/magnetic/rect/info.htm

zjyxz eykxkBBH coscos31

From these, we conclude:

X(x) is in the form of cos kxx,

where kx=mp/a, m=0,1,2,3,

Y(y) is in the form of cos kyy,

where ky=np/b, n=0,1,2,3,So the solution forEz(x,y,z) is

zyyxxz eykBykBxkBxkBH sincossincos 4321


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TE Mode

Substituting

Note that n and m cannot be both zero

because the fields will all be zero.

zj

oz eyb

n

a

xmHH

pp

coscos


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TEmn

0

coscos

z

zj

oz

E

eyb

nx

a

mHH

pp


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Conclusion

TEM (Ez=Hz=0) cant propagate.

TE (Ez=0) transverse electric

In TE mode, the electric lines of flux are perpendicular to the axis of thewaveguide

TM (Hz=0) transverse magnetic,Ezexists

In TM mode, the magnetic lines of flux are perpendicular to the axis ofthe waveguide.

The m and n represent the mode of propagation and indicates the number

of variations of the field in the xand ydirections

for the TM mode, if n or m is zero, all fields are zero.

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PPT Medan 2 - Rectangular Wave Guide.pdf