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Waveguides
Rectangular Waveguides
TEM, TE and TM waves
Cutoff Frequency
Wave Propagation
Wave Velocity,
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2. Waveguides
Circular waveguide
Rectangular
waveguide
In the previous chapters, a pair of conductors was used to guide electromagnetic wave propagation. This propagation was via the transverse electromagnetic (TEM) mode, meaning both the electric and magnetic field components were transverse, or perpendicular, to the direction of propagation.
In this chapter we investigate wave-guiding structures that support propagation in non-TEM modes, namely in the transverse electric (TE) and transverse magnetic (TM) modes.
In general, the term waveguide refers to constructs that only support non-TEM mode propagation. Such constructs share an important trait: they are unable to support wave propagation below a certain frequency, termed the cutoff frequency.
Optical Fiber
Dielectric Waveguide

3. 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.
A particular mode is only supported above its cutoff frequency. The cutoff frequency is given by
Location of modes

4. Rectangular Waveguide
The cutoff frequency is given by
Rectangular Waveguide
Location of modes
Table 7.1: Some Standard Rectangular Waveguide
Waveguide
Designation a
(in) b t
fc10
(GHz)
freq range
WR975
9.750
4.875
.125
.605
.75 – 1.12
WR650
6.500
3.250
.080
.908
1.12 – 1.70
WR430
4.300
2.150
1.375
1.70 – 2.60
WR284
2.84
1.34
2.08
2.60 – 3.95
WR187
1.872
.872
.064
3.16
3.95 – 5.85
WR137
1.372
.622
4.29
5.85 – 8.20
WR90
.900
.450
.050
6.56
8.2 – 12.4
WR62
.311
.040
9.49

5. To understand the concept of cutoff frequency, you can use the analogy of a road system with lanes having different speed limits.

6. Rectangular Waveguide
Let us take a look at the field pattern for two modes, TE10 and TE20
In both cases, E only varies in the x direction; since n = 0, it is constant in the y direction.
For TE10, the electric field has a half sine wave pattern, while for TE20 a full sine wave pattern is observed.

7. Rectangular Waveguide
Example
Let us calculate the cutoff frequency for the first four modes of WR284 waveguide. From Table 7.1 the guide dimensions are a = mils and b = mils. Converting to metric units we have a = cm and b = cm.
TM11
TE10:
TE10
TE20
TE01
TE11
TE01:
TE20:
TE11:
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