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TOPIC 2
WAVEGUIDE AND COMPONENTS
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COURSE LEARNING OUTCOME (CLO)
CLO1
• Explain clearly the generation of microwave, the effects of microwave radiation and the propagation of electromagnetic in a waveguide and its accessories
CLO2
• Apply given mathematical equations or Smith Chart to solve problem related to microwave propagation.
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CLO3
• Handle systematically the related microwave communication equipment in performing the assigned practical work.
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Understand the characteristic of waveguide
Upon completion of this topic, students should be able to:
1. Define
a) Critical (cut-off) frequency
b) Critical (cut-off) wavelength
2. Explain the following terminologies:
Group velocity, Phase velocity, propagation wavelength, waveguide characteristic impedance
3. Calculate the item no.1 and no. 2 for rectangular and circular waveguide
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With;
a = broad dimension b = narrow dimension x = length waveguide
Rectangular Waveguide
Dimensions of the waveguide which determines the operating
frequency range
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Dimensions of the waveguide which
determines the operating frequency range:
1. The size of the waveguide determines its operating
frequency range.
2. The frequency of operation is determined by the
dimension ‘a’.
3. This dimension is usually made equal to one – half the
wavelength at the lowest frequency of operation, this
frequency is known as the waveguide cutoff frequency.
4. At the cutoff frequency and below, the waveguide will
not transmit energy. At frequencies above the cutoff
frequency, the waveguide will propagate energy.
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Circular waveguide
r = radius
x = length waveguide
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Characteristic of waveguide
• Waveguides are basically a device ("a
guide") for transporting electromagnetic
energy from one region to another.
• They are capable of directing power
precisely to where it is needed, can handle
large amounts of power and function as a
high-pass filter.
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• The waveguide acts as a high pass filter in
that most of the energy above a certain
frequency (the cutoff frequency) will pass
through the waveguide, whereas most of the
energy that is below the cutoff frequency will
be attenuated by the waveguide.
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Critical (cut-off) Frequency, Fc
• The cutoff frequency is the frequency at which
all lower frequencies are attenuated by the
waveguide, and above the cutoff frequency all
higher frequencies propagate within the
waveguide.
• The cutoff frequency defines the high-pass
filter characteristic of the waveguide: above
this frequency, the waveguide passes power,
below this frequency the waveguide
attenuates or blocks power.
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• The cutoff frequency depends on the shape and size of the cross section of the waveguide. The larger the waveguide is, the lower the cutoff frequency for that waveguide is. The formula for the cutoff frequency of a rectangular cross sectioned waveguide is given by:
- permeability
- permittivity
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Rectangular Waveguide
• Let us consider a rectangular waveguide with interior dimensions are a x b,
• Waveguide can support TE and TM modes. – In TE modes, the electric field is transverse to the
direction of propagation. – In TM modes, the magnetic field that is transverse and
an electric field component is in the propagation direction.
• The order of the mode refers to the field configuration in the guide, and is given by m and n integer subscripts, TEmn and TMmn. – The m subscript corresponds to the number of half-
wave variations of the field in the x direction, and – The n subscript is the number of half-wave variations
in the y direction.
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Location of Modes
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Rectangular Waveguide
2 2 2 21
2 2mn
r r
c
m n c m nf
a b a b
• A particular mode is only supported above its cutoff frequency. The cutoff frequency is given by
8where 3 10 m/sc
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Rectangular Waveguide
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Formula
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Dominant Mode
• The dominant mode is the mode with lowest cutoff frequency.
• It’s always TE10
• The order of the next modes change depending on the dimensions of the guide.
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Group and Phase velocity How fast is the wave traveling? • Velocity is a reference distance divided by a
reference time.
• Group velocity is the velocity at which the
energy of the wave propagates. This means that the wave moves at the speed of vg.
• Phase velocity is the speed of movement of a point of constant phase in a continous wave.
• Group and phase velocities have the same value in free space and in parallel wire transmission lines.
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Group and Phase velocity
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The Phase velocity
This is the velocity at which the overall shape of the wave’s amplitudes, or the wave ‘envelope’, propagates. (= signal velocity) Here, phase velocity = group velocity (the medium is non-dispersive)
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Group velocity
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Dispersion: phase/group velocity depends on frequency
Black dot moves at phase velocity. Red dot moves at group velocity. This is normal dispersion (refractive index decreases with increasing λ)
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Rectangular Waveguide
Need to find the fields components of the em wave inside the waveguide
Ez Hz Ex Hx Ey Hy We’ll find that waveguides don’t support TEM waves
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• The m and n represent the mode of propagation and indicates the number of variations of the field in the x and y directions
• Note that for the TM mode, if n or m is zero, all fields are zero.
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Variation of wave impedance
• Wave impedance varies with frequency and mode
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Rectangular Waveguide - Wave Propagation
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Wave Guide Impedance
Wave feature impedance for TE mode is
ZTE =
with; • ZTE = characteristic impedance for TE mode
• 377 = free space feature impedance
• = free space wavelength
• 0 = wavelength cut.
2
0
1
377
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Wave Guide Impedance
Wave feature impedance for TM mode is
ZTM =
where;
• ZTM = characteristic impedance for TM mode
• 377 = free space feature impedance
• = free space wavelength
• 0 = wavelength cut.
2
0
)(1377
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The circular waveguide is used in many special applications in microwave techniques.
It has the advantage of greater power – handling capacity and lower attenuation for a given cutoff wavelength. However, the disadvantage of somewhat greater size and weight.
The polarization of the transmitted wave can be altered due to the minor irregularities of the wall surface of the circular guide, whereas the rectangular wave guide the polarization is fixed
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Description
The wave of lowest frequency or the dominant mode in the circular waveguide is the TE11 mode.
The first subscript m indicates the number of full – wave variations of the radial component of the electric field around the circumference of the waveguide.
The second subscript n indicates the number of half – wave variations across the diameter.
The field configurations of TE11 mode in the circular waveguide is shown in the diagram below
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Applications of circular waveguide Rotating joints in radars to connect the
horn antenna feeding a parabolic
reflector (which must rotate for tracking)
TE01 mode suitable for long distance
waveguide transmission above 10 GHz.
Short and medium distance broad band
communication (could replace / share
coaxial and microwave links)
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• From the cutoff frequencies or the cutoff wavelengths, the phase velocity, the group velocity, the guide wavelength and the wave impedance of each mode can be found using the same equations as those for the rectangular waveguide.
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Cut Off Wavelength
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Example 1
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Example 2
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Solution
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