9th INTERNATIONAL WORKSHOP AND TUTORIALS EDM’2008, SESSION III, JULY 1-5, ERLAGOL 159

Calculation of Key Parameters of Installation

of Microwave Dielectric Heating
Vadim V.Tilzo1, Student Member, IEEE, Gennady V. Leonov2.
1
Biysk Technological Institute, Biysk, Russia,
2
Biysk Technological Institute, Biysk, Russia.

Abstract - In paper results of calculation of key

parameters of microwave dielectric heating installation
are presented. Matrix of S-parameters, arrangement and
sizes of communication apertures are calculated.

Index Terms - Microwave, heating, modeling.

I. INTRODUCTION

I N THE COURSE OF synthesis microwave device,

various numerical methods of optimization and the
approximations based on application of computer
modeling are used, allowing to use difficult
mathematical models, and not to use simplified [1]. Fig. 1. Geometrical model of installation.
But use of the simplified mathematical models,
TABLE I
together with computer modeling, allows receiving POWER CHARACTERISTICS OF INSTALLATION
rather simple mathematical description synthesized
microwave devices. Actually, computer modeling Effectiveness of installations: ~40 %
carries out an experiment problem.
More in detail about mathematical models, with Dielectric losses on object: ~66 W
reference to microwave devices and circuits, it is
Non-uniformity of heating on object: ~30 0С
possible to read here [1, 3, 4, 5].
Use of computer modeling has allowed finding
II. PROBLEM DEFINITION
such design of installation which considerably comes
At synthesis of installation of microwave dielectric nearer under the characteristics to shown requirements.
heating of a frictional composition in compression But the bases to believe, that the received system is
mould volume, the following basic demands defined optimum, from the view point of shown requirements,
by a scope last are made: high effectiveness, high there is not, as sizes of the majority of key parameters
uniformity of heating of a frictional composition in of installation are chosen on the basis of experimental
compression mould volume, simplicity of technical data, recommendations from various references.
realization. Therefore use of the simplified mathematical models
Taking into account the results received with use of for calculation of key parameters of installation will
computer modeling, installation, with the certain basic allow with more to confirm reliability about
geometrical sizes, a relative positioning of its separate installation optimality as a whole.
parts and power characteristics has been received. Having assumed as a basis installation model, we
Appearance of model is shown in a Fig. 1 (I - will allocate in it key parameters, it is:
compression mould volume, II - the main waveguide), • Arrangement and the size of communication
the power characteristics received by results of apertures relatively maximum electromagnetic
modeling, are presented to Tab. 1. field defining factor of power transfer;
• Factor of power transfer from the main waveguide
to the compression mould volumes, defining
power effectiveness of installations;

ISSN 1815-3712 ISBN 978-5-7782-0893-3 © Novosibirsk State Technical University

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 160 9th INTERNATIONAL WORKSHOP AND TUTORIALS EDM’2008, SESSION III, JULY 1-5, ERLAGOL

• Distribution of maximum of electric component of received splitter is a basic element, sequence of such
microwave electromagnetic field in a compression splitters form the main part of installation; therefore,
mould, defining uniformity of heating; further we will consider only it.
For the given parameters will be used further the Communication apertures represent as rectangular
simplified mathematical models or the approached waveguides (taking into consideration a thickness of
analytical calculations. walls of the main waveguide) small length, therefore
key parameters of the given waveguides can be easily
III. THEORY calculated by corresponding formulas [3]. Key
parameters, along with some other, are: critical length
1. Arrangement and the size of communication of a wave (λк) (2) in a waveguide and characteristic
apertures resistance (Z):
Zc
For power transfer of microwave electromagnetic Z= (3)
2
field from a waveguide to compression mould ⎛λ ⎞
volumes, from constructive reasons, communication 1 − ⎜⎜ 0 ⎟⎟
apertures has the rectangular form, the waves located ⎝ λк ⎠
in H-plane electromagnetic field are used. Where:
Communication apertures are placed opposite to Zс - resistance of flat electromagnetic waves in
magnitude maximum of electric component of vacuum;
electromagnetic field. λ0 - length of electromagnetic waves in vacuum;
The distance between maximum is defined through λк - critical length of electromagnetic waves in a
wavelength in a rectangular waveguide (Λ), calculated rectangular waveguide.
by the formula [2]: Formulas are valid at µ = ε =1.
λ0
Λ= (1) 2. Factor of power transfer from the main
2
⎛λ ⎞ waveguide to compression mould volumes
1 − ⎜⎜ 0 ⎟⎟
⎝ λк ⎠
Factor of power transfer for a splitter analytically,
2 as a rule, do not calculating, often they are defined by
λк = (2)
2 2 experimental. Therefore, the matrix of S-parameters
⎛ m⎞ ⎛ n⎞
⎜ ⎟ +⎜ ⎟ characterizing both factors of reflexion from
⎝ a ⎠ ⎝b⎠ shoulders, and transfer factors on the normalized
Where: voltage, has been calculated with use of computer
λ0 - length of electromagnetic waves in vacuum; modeling. At presence of matrix S-parameters of
λк - critical length of electromagnetic waves in a device, it is possible to consider, that it is completely
rectangular waveguide; described [2].
m – quantity of half wavelength on width; The S-parameters matrix of a splitter, at length of
n - quantity of half wavelength on height; communication waveguides (l) equal 1 mm, has the
a - width of a waveguide; following values:
b - waveguide height. 0.01 0 0.959 0
Formulas (1), (2) are valid at µ = ε =1.
0.208 0 0.208 0
S= (4)
0.959 0 0.01 0
0.208 0 0.208 0
According to a matrix - shoulders 1 and 3 are used
for supply electromagnetic energy, 2 and 4 for energy
absorbing.
At a known matrix of dispersion, it is possible to
Fig. 2. Geometrical model of a splitter. calculate the power absorbed in shoulders with the
account of reflexion factor from loadings (Гi),
Communication apertures and a part of the main depending on brought power, through the decision of
waveguide form a wave splitter in an H-plane, the Fig. system of the equations (5) [3]:
2 see (Numbers designate splitter shoulders). The

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 TILZO and LEONOV: CALCULATION OF KEY PARAMETERS OF INSTALLATION OF MICROWAVE DIELECTRIC HEATING 161

U1ref U1inc 1. Arrangement and the size of communication

apertures
U 2 ref U 2inc
= S⋅ (5)
U 3ref U 3inc According to (1, 2) volumes of a compression
mould and a communication aperture it is necessary to
U 4 ref U 4inc have on distance of 0.173 m.
2 2 Initially, the sizes of communication apertures
Pi = U iinc − U iref (6)
selected such what to provide the simplest interface of
Where: the main waveguide to compression mould volumes,
Uiinc - normalized incoming voltage to a shoulder i; despite it at modeling admissible results have been
Uiref - normalized reflected voltage from a shoulder received.
i; On the basis of formulas (2, 3) it is possible to
Pi - the power absorbed in i shoulder. come a conclusion that with reduction of the
It is necessary to notice, that return process - geometrical sizes of a waveguide, decreases λк and
device synthesis under the set matrix of dispersion [3] increases Z.
is possible also. So, at m=1, n=0, a=0.03 m., b=0.015 m., λк=0.06
m. that corresponds to frequency of 5 GHz and does
3. Distribution of maximum of electric not allow to extend in current waveguide to a wave
component of microwave electromagnetic field with frequency of 2,45 GHz, full attenuation is
in compression mould volume observed already on distance of 0,015 m. along a
waveguide.
Distribution of maximum of electric component of On the basis of the above-stated, it is possible to
electromagnetic field in compression mould volume come to following conclusions:
can be calculated, being based on point 1 of the given • The sizes of communication waveguides should
section. be as much as possible admissible the big;
The difficult geometrical model of compression • The length of communication waveguides should
mould volume a can be simplified to model of a be is minimum admissible small, in a limit to an
rectangular waveguide. equal thickness of a wall of the main waveguide
The given rectangular waveguide has next sizes: that can be difficultly to technical realization.
a=0.04 m., b=0.015 m., l=0.095 m. Explanatory to a
choice of a value, see Fig. 3. 1. Factor of power transfer from the basic
waveguide to compression mould volumes

According to (4, 5, 6), incoming electromagnetic

wave to a shoulder 1 of splitter of 1 kW energy
capacity, the power absorbs on loadings in shoulders 2
and 4 is ~40 W.
From what it is possible to come a conclusion,
what even the insignificant increase in length of
waveguides of communication leads to reduction of
capacity transfer factor, so in an ideal case, at l=0,
Fig. 3. Explanatory to a choice of a value. value of factor equally ~0.25.
For the received waveguide, all formulas of section
2. Distribution of maximum of electric
1 are correct, but with corrective action needs, because
component of microwave electromagnetic field
the waveguide is filled not by vacuum and the
in compression mould volume
dielectric environment with µ≠ 1 and ε≠ 1. The length
of an electromagnetic wave in dielectric is less in
Values µ and ε for a frictional composition, under
εµ than times [3]. normal conditions, are equal 1.05 and 5.75
accordingly.
IV. DISCUSSION OF RESULTS Value Λ for a waveguide with a dielectric:
Λ = 0.0637 m.

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 162 9th INTERNATIONAL WORKSHOP AND TUTORIALS EDM’2008, SESSION III, JULY 1-5, ERLAGOL

Considering length of a waveguide, we receive [5] Silaev M. A «Application of matrices and diagrams to
analysis of SVH devices». М: Soviet Radio, 1970 – p. 248.
quantity of wavelengths in a waveguide: (in Russian).
l 0.095
= = 1.49
Λ 0.0637 Vadim V. Tilzo has finished the Biysk
Technological Institute in 2006 on
Hence, the quantity of maximum of electric specialty «Information science and
component of electromagnetic field is equal 3 that it is measuring engineering». Now he is the
possible to observe and by results of computer post-graduate student of the second year
modeling, see Fig. 4. training.
Student Member of IEEE from 2006.
After carrying out of modeling of heating process,
non-uniformity of heating on object ~30 0С has been
received. Genadiy V. Leonov (Doctor of
Technical Science, Professor).
He was born on January 29, 1948.
Graduate Leningrad Technological
Institute in 1973. He has defended a
thesis Ph.D in 1976. He has defended a
thesis for a Doctor's degree in1998.
Place of employment: Department of
Methods and Means of Measuring and
Automation, in Biysk Technological
Institute.
Appointment: Rector of Biysk
Technological Institute.

Fig. 4. Electric component of electromagnetic field.

It is possible to come to conclusion, that in this

case, great values µ and ε promote increase in
uniformity of heating, but it is not necessary to forget
that more ε, as a rule, there correspond the bigger
dielectric losses, and demanded uniformity of heating
on length of compression mould volume can not be
reached.

V. CONCLUSION
In work the basic moments, concerning calculation
of key parameters of installation of microwave
dielectric heating, namely parameters only one wave
splitter and loadings have been considered. Calculation
of consecutive connection of such wave splitters will
allow defining matrix S - parameters of the unit as a
whole [4, 5].

REFERENCES
[1] Katz M. V «An Optimal synthesis of SVH devices on T-
waves». М: Radio and Connection, 1984 – p. 288. (in
Russian).
[2] Arhangelskij J.S. «The Plant of dialectic heating. SVH
devices». M: 2004 – p. 279. (in Russian).
[3] Chernushenko A.M. «The designing of screen and SVH
devices». М: Radio and Connection, 1990 – p.352. (in
Russian).
[4] Feldshtejn L.F. «Synthesis of four-lane and eight-lane on
SVH». М: Connection, 1971 – p. 385. / (in Russian).

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