Civil Engineering Reference
In-Depth Information
the guide with little attenuation. If it is below the cutoff frequency, the
wave is described as evanescent and will be attenuated strongly within a
short distance.
For a homogeneously filled waveguide, the cutoff frequency,
f
c
, is given by
1
f
c
=
2
2
m
a
π
n
b
π
2
πεε
+
00
where
a
and
b
are the dimensions of the waveguide, and
m
and
n
are the
mode indices. The cutoff frequency characteristic of a waveguide must be
used to choose the appropriate waveguide and horn for a specific frequency
and microwave mode.
The propagation modes in the waveguides vary with the polarisation,
shape, and size of the waveguide. The longitudinal mode is a particular
form of standing wave pattern developed by waves confined in the cavity.
On the other hand, the transverse modes include transverse electric (TE)
modes, transverse magnetic (TM) modes, and transverse electromagnetic
(TEM) modes. TE and TM modes have, respectively, no electric field and
no magnetic field in the direction of propagation. TEM modes have neither
electric nor magnetic field in the direction of propagation. Finally, hybrid
modes are the propagation modes with both electric and magnetic field
components in the direction of propagation. In the hollow waveguides used
in the transmission lines of microwave-assisted demolition tools, TEM
modes are not possible. This is because obtaining the TEM modes as the
solution of Maxwell's equations requires the electric field to have zero
divergence and zero curl and be equal at the boundaries, requiring it to be
equal to zero. Because of the boundary conditions, the waves that propa-
gate inside a homogeneously filled waveguide are different from the TEM
waves and are known as TE waves and TM waves. TE waves have
E
x
= 0;
TM waves have
H
x
= 0. For TE waves, there is a component of
H
along the
direction of propagation; for TM waves, it is the
E
component that exists in
the same direction. In both cases, energy is carried by the electric and mag-
netic fields associated with the wave. It is possible to have several modes
of propagation inside a particular waveguide. The mode that has the low-
est frequency in a particular waveguide is known as the dominant mode.
Generally, the waveguide used for microwave heating has dimensions such
that only the dominant mode propagates along it. The fundamental TE and
TM modes, TE
10
and TM
11
, respectively, are usually the two most domi-
nant modes [16]. The TE
10
mode is the dominant mode excited by most of
the basic microwave heating systems available today. Field lines for the TE
10
mode in a rectangular waveguide are shown in Figure 3.23. In the example
problem used in the present chapter, the rectangular waveguides used are
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