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Submitted to:-

Anshul Gupta

Jyoti PushpamB.Tech III year

ECE(A2)

Roll no-

09mubECE030

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A waveguide consists of a hollow metallic tube used toguide an electromagnetic wave.

Normally circular or rectangular.

Used principally at frequencies in the microwaverange.

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If the waves are propagating in the positive z-direction, then 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,Ezexists In TM mode, the magnetic lines of flux are

perpendicular to the axis of the waveguide.

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The in a rectangular wave guide is characterized by=0. must exist. By Helmholtz eqn:-

2=2

A solution in the form of-

=[ sin(

) + cos(

)] [ sin(

) +

cos(

)]

For lossless dielectric, Maxwells curl eqn. in the frequency

domain are = =

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Boundary

conditions: ,axE

,byE

y

x

0at0

0at0

From these, we conclude:

X(x) is in the form ofcos kxx,

where kx=mp/a, m=0,1,2,3,Y(y) is in the form ofcos 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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Substituting

Note that n and m cannot be both zerobecause the fields will all be zero.

22

2

againwhere

coscos

b

n

a

mh

ey

b

n

a

xmHH zjoz

pp

pp

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Other components are

z

oy

zox

z

oy

z

ox

eb

yn

a

xmH

b

n

h

jH

ebyn

axmH

am

hjH

eb

yn

a

xmH

a

m

h

jE

eb

yn

a

xm

Hb

n

h

j

E

ppp

ppp

ppp

ppp

sincos

cossin

cossin

sincos

2

2

2

2

0

coscos

z

zj

oz

E

eyb

nx

a

mHH

pp

y

H

hH

x

H

hH

x

H

h

jE

y

H

h

j

E

zy

zx

zy

z

x

2

2

2

2

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The cutoff frequency for the TE mode

fc,mn

attenuation Propagation

of mode mn

=1

2[

+

]

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Wave in the dielectric

medium

Inside the waveguide

/'

'/' u

2

1

'

f

fc

TE

2

1

'

f

fc

/

1'

2

f

f

u

c

p

2

1'

f

fc

fu /''

/1'/' fu

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The dominant mode is the mode with lowestcutoff frequency.

Its always TE10 The order of the next modes change depending on

the dimensions of the guide.

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