WAVEGUIDES
Parallel-wire transmission lines, including
coaxial cables, cannot effectively
propagate electromagnetic energy above
approximately 20 GHz, because of the
attenuation caused by skin effect and
radiation losses.
A waveguide is a hallow conductive tube,
usually rectangular in cross section, but
sometimes circular or elliptical.
Waveguides
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The dimensions of the cross section are
selected such that electromagnetic waves can
propagate within the interior of the guide.
A waveguide does not conduct current.
If the wall of the waveguide is a good
conductor and very thin, little current flows in
the interior walls and, consequently, very
little power is dissipated.
Waveguides are generally restricted to
frequencies above 1 GHz.
Waveguides
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Rectangular waveguides are the most
common form of waveguide.
Transverse electromagnetic wave cannot
have a tangential component of the electric
field at the walls of the waveguide
To successfully propagate a TEM wave
through a waveguide, the wave must
propagate down the guide in a zigzag
manner, with the electric field maximum in
the center of the guide and zero at the
surface of the walls.
Rectangular Waveguide
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In waveguide, the velocity varies with
frequency.
There are two different kinds of velocity:
- Phase Velocity
- Group Velocity
Waveguide Velocities
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Phase velocity is the apparent velocity of
a particular phase of the wave.
It is the velocity with which a wave
changes phase in a direction parallel to
conducting surface, such as the walls of a
waveguide.
Phase Velocity
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v ph = fl
where: vph = phase velocity, (m/s)
f = frequency, (Hz)
λ = wavelength, (m)
Phase Velocity
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Group velocity is the velocity of a group of
waves.
Group velocity is the velocity at which
information signals of any kind are
propagated.
Group velocity can be measured by
determining the time it takes for a pulse
to propagate a given length of waveguide.
Group Velocity
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vg v ph = c 2
where: vph = phase velocity, (m/s)
vg = group velocity, (m/s)
c = 3 x 10^8 m/s
Group Velocity
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The phase velocity is always equal to or
greater than the group velocity, and their
product is equal to the square of the free-
space propagation velocity.
Phase velocity may exceed the velocity of
light.
Phase Velocity
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v ph
lg = lo
c
where: λg = guide wavelength, (m)
λo = free space wavelength, (m)
vph = phase velocity, (m/s)
c = 3 x 10^8 m/s
Guide Wavelength
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Cutoff frequency is the minimum
frequency of operation of a waveguide.
Frequencies below the cutoff frequency
will not be propagated by the waveguide.
The minimum wavelength that a
waveguide can propagate is called the
cutoff wavelength.
Only frequencies with wavelengths less
than the cutoff wavelength can propagate
down the waveguide.
Cutoff Frequency and Cutoff
Wavelength
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c
fc =
2a
Where: λc = cutoff wavelength, (m)
a = cross-sectional length, (m)
Cutoff Frequency
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c lo
lg = =
1 - ( fc f )
2 2
f - fc
2
where: λg = guide wavelength, (m)
λo = free space wavelength, (m)
f = frequency of operation, (Hz)
fc = cutoff frequency, (Hz)
c = 3 x 10^8 m/s
Guide Wavelength
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c (l g ) c
v ph = =
lo 1 - ( fc f ) 2
where: vph = phase velocity, (m/s)
f = frequency of operation, (Hz)
fc = cutoff frequency, (Hz)
Phase Velocity
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377 lg
Zo = = 377
1 - ( fc f ) lo
2
where: Zo = characteristic impedance,
ohms
f = frequency of operation, (Hz)
fc = cutoff frequency, (Hz)
Characteristic Impedance of
waveguide
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For a rectangular waveguide with a wall
separation of 3 cm and a desired
frequency of operation of 6 GHz,
determine
A. Cutoff frequency
B. Cutoff wavelength
C. Group velocity
D. Phase velocity
E. Characteristic impedance
Example #1
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