Microwave heating cavities and applicators - Microwave-Assisted Concrete Technology: Production, Demolition and Recycling - page 216

The cavity is assumed to operate at 2.45 GHz and TE 324 mode. The TE 324 is
a transverse electric (TE) mode, which by definition has no electric field in
the z direction and has 3, 2, and 5 variations in the x , y , and z directions,
respectively. As shown in Chapter 1, the energy density in an electromag-
netic field is proportional to the square of the electric field intensity norm.
Therefore, it can be assumed that the energy density in the multimode cav-
ity shown in Figure 6.17a is proportional to the norm of the intensities of
the x and y electric field components, that is, EE
x

2 + . By taking this into
account, a numerical simulation of the microwave field shows that the nor-
malised power density at the observation plane located in parallel to the x - z
surface in the center of the cavity follows the 3D plot shown in Figure 6.17b
[6]. As shown, there are three and four obvious variations along the x and
z directions, respectively. This indicates poor power uniformity within the
cavity as the power density can vary from a maximum value to a minimum
of zero every few centimetres. Using Equation 6.6, the field uniformity can
be estimated as 100%, which is the worst-possible uniformity for an appli-
cator. However, as discussed previously, the nonuniformity of a microwave
field is undesired in most heating applications. Thus, maximising the field
uniformity is one of the main objectives in the design of multimode cavities.
In the following, various techniques for improving the field uniformity in
multimode cavities are discussed.

y

6.4.1.1 Resonant frequency and possible modes
Identifying the relationship between the excited mode, resonant frequency,
and cavity dimensions is crucial in designing efficient multimode cavities.
In general, such a relationship should be determined by finding the eigenval-
ues of the general wave equations in the phasor form, expressed as follows:

2 2

+= EkE 0 (6.7)

2 2

HkH + = 0 (6.8)

where ∇ is the Laplacian operator, and k is the wave number, which has
the following relationship with the angular frequency (ω = 2πf ) in radians/
second, permittivity ε in farads/metre (F/m), and magnetic permeability μ
in henries/ metre (H/ m).

k =ω ε (6.9)

When considering an empty rectangular cavity, the following analytical
solution for the relationship between mode number, cavity dimensions, and
resonant frequency can be easily obtained [4]: