numerical analysis of the pyramidal hf absorber anotace annotation

numerical analysis of the pyramidal hf absorber anotace annotation

NUMERICAL ANALYSIS OF THE PYRAMIDAL HF ABSORBER
Eva Kadlecová1 , Martin Zlomek2,Miloslav Steinbauer3, Pavel Fiala4 ,
ANOTACE
Příspěvek přináší výsledky numerického modelování při návrhu a analýze modifikace
mikrovlnného absorberu. Klasické řešení absorberu lze nahradit alterantivním se specifickými
vlastnostmi dostačujícími při vytvoření bezodrazové komory pro testy pulsních mikrovlnných
zdrojů. Pro měření a testy relativistického mikrovlnného pulsního zdroje ve volném prostoru
do mezního pulsního výkonu Pmax=500MW, tp=10-100ns byla navržena stíněná komora
s bezodrazovými elementy. Návrh vznikl jako součást projektu řešeného ve spolupráci s
VTUPV Vyškov, PROTOTYPA a.s. a TESLA Vršovice Praha. Experimentální ověření
navrhovaných jehlanových absorberů se provádělo v laboratořích VA Brno.
ANNOTATION
The paper presents numerical analysis of the microwave absorber design. It is possible to use
modified concept of the absorber. Modified absorber has appropriate properties and it is
possible to use it in non-reflecting chamber construction. The non-reflecting chamber will be
used for open space testing of relativistic microwave pulse generator; Pmax=500MW, tp=10100ns. Presented work is a part of the project conducted in co-operation with VTUPV
Vyškov, PROTOTYPA a.s. and TESLA Vršovice Praha. An experimental testing of the
proposed pyramidal absorbers was done in the laboratories located at VA Brno.
12.ANSYS Users´ Meeting, 30. září-1. října 2004 na Hrubé Skále
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1 INTRODUCTION
It is possible to measure the power supplied by open space impulse by use of the
calorimetric converter. The sensor is connected to the measuring device by help of the coaxial
line of length approximately l = 10 m. The closed space has to be realised as a deaden room,
see Fig.1.
Fig.1. Measurement in non-reflecting shield chamber
The calorimetric sensor has disc design. The carbon with changed crystal lattice is
used as one of the thin layers. Combined calorimetric sensors was designed for microwave
vircator with output power Pmax = 500 MW, length of pulse tp∈<10, 100> ns.
Usually, two types of the absorber materials (non-reflecting) are used. The
polyurethane foam impregnated by graphite is used in high frequency range (more than
1GHz) - the foam employs heat losses in material. The ferrite absorber is used in low
frequency range – the ferrite absorber employs magnetic losses. The mentioned materials are
used to prevent reflection of the electromagnetic waves inside the laboratory.
The idea is to rebuild the laboratory in Fig. 2 to the shielded non-reflecting chamber
for measurements and experiments with power microwave pulse generators Pmax = 500 MW, length of pulse tp∈<1, 100> ns.
1.1 Shielding of the walls
It is possible to define an electromagnetic shielding by help of shielding coefficient τ.
It represents the ratio of the electrical field Et (magnetic field Ht) in the given place of the
chamber to the electrical field Ei (magnetic field Hi) incoming at the absorber.
E
H
τ= t
τ= t
(1)
Ei
Hi
The metal plate is used to prevent the electromagnetic wave go trough the wall. The
damping effect of the metal plate consists of three damping – reflection, absorption and
repeatable reflection.
12.ANSYS Users´ Meeting, 30. září-1. října 2004 na Hrubé Skále
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1.2 Effectiveness of the reflection
Shielding by means of reflection R is caused by partial reflection of the
electromagnetic wave on the impedance boundary. The impedance boundary consists of the
air – characteristic impedance Z0 and metal plate – characteristic impedance ZM. The
characteristic impedances are given
µ0
jωµ
ZM =
(2.2),
(2)
Z0 =
ε0
σ
The amount of the damping is [1]
Z + ZM Z0 + ZM
= R1 + R2 [dB].
R = 20 log 0
2Z M
2Z 0
(3)
Fig.2. The reconstruction of shielded non-reflection laboratory
1.3 Effectiveness of the absorption
When electromagnetic wave travels trough metal plate it is absorbed and it causes heat
losses. Absorption coefficient A of the metal plate is given [1]
A = 20 log e
γt
t
= 20 log e [dB],
δ
(4)
where δ is depth of penetration into the metal plate of thickness t. The depth of
penetration is given
2
δ =
[m],
(5)
ωµσ
where ω is frequency, σ is electrical conductivity, µ is the permeability of vacuum.
After manipulation of (4) we get the absorption coefficient
t
A = 8,69 ⋅ [dB].
δ
(6)
1.4 Pyramidal absorbers
Nowadays, the longitudinal non-homogenous loss environment is made from pyramid
or cylinder Fig. 3. It uses dielectric losses and is made from polystyrene or polyurethane that
is impregnated by graphite. Linearly increasing cross-section of the pyramid serves as an
impedance transformer. The transformer transforms open space impedance to the very low
impedance of the absorber. However, the damping maximum takes place in the back side of
12.ANSYS Users´ Meeting, 30. září-1. října 2004 na Hrubé Skále
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the absorber. It is necessary to have pyramid with height of λ/4 on the lowest working
frequency.
Fig. 3. Multiple reflections in pyramidal absorber
2 MATHEMATICAL MODEL
It is possible to carry out analysis of a MG model as a numerical solution by help of
Finite element method (FEM). The electromagnetic part of the model is based on the sulution
of full Maxwell’s equations.
∂B
∂D
∇ × E = - ∂t , ∇ × H = σ E +
+ Js,
∂t
∇ ⋅ D = ρ,
∇ ⋅ B = 0 in region Ω
(7)
Where E and H is the electrical filed intensity vector and the magnetic filed intensity vector,
D a B are the electrical field density vector and the magnetic flux density vector,, Js is the
current density vector of the sources, ρ is the density of free electrical charge and γ is the
conductivity of the material, Ω is definition area of the model. The relationships between
electrical and magnetic field intensities and densities are given by material relationships
D = ε E,
B = µ H.
(8)
The permittivity ε, the permeability µ and the conductivity γ in HFM are generally tensors
with main axes in the direction of the Cartesian co-ordinates x, y, z. When all the field vectors
performs rotation with the same angular frequency ω, it is possible to rewrite the first
Maxwell equations
∇ × E = − jωµ H ,
∇ × H = ( σ + jωε )E + J s in region Ω
(9)
Where E, H, Js are field complex vectors. Taking into account boundary conditions given in
(7) and after rearranging (9) we get
(10)
( jω ) 2 ε E + σ E + ∇ × µ −1∇ × E = − jω J s .
We apply Galerkin’s method with vector approximation functions Wi. We use vector
form of the Green theorem on the double rotation element [3]. After discretation we get the
expression
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− k 0 [M ]{E } + jk 0 [C ]{E } + [K ]{E } = {F } ,
(11)
where {E} is column matrix of electrical intensity complex vectors. The matrixes [K], [C] and
[M] are in the form that is given in manual [4] and vector {F} is evaluated from expression
{F } = − jk 0 Z 0 ∫ [W i ]{J s }dΩ +
jk 0 Z 0
Ω
∫ [W ]{n× H }dΓ .
(12)
i
Γ0 + Γ1
Vector approximation functions W are given in manual [4], k0 is wave number for vacuum, Z0
is impedance of the free space. The set of equations (11) is independent of time and it gives E.
For transient vector E we can write
{
E = Re E e jωt
}.
(13)
3 GEOMETRICAL MODEL
The geometrical model was created with standard tools in ANSYS with help of
automated mesh and nodes generators. After that the mathematical model was formed. The
applied element is HF120. The model is described by ANSYS characteristic data:
Fig. 3. Multiple reflections in pyramidal absorber
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The geometrical model of HF absorber is shown in Fig. 4. The initial frequency was
taken f=1, 2, 3, 4, 5GHz. The concept of the absorber uses special properties of the
pyrographite. The pyrographite is placed on the pyramid walls with appropriate density. By
means of this concept it is possible to achieve appropriate damping of the incoming
electromagnetic wave.
4 RESULTS OF THE ANALYSIS
In the Fig. 4 there is shown module of vector functions of magnetic intensity H and
electric intensity E. There are results for initial TE plane wave with frequency f=3GHz,
Ex=100V/m. We can see the quality of electromagnetic absorber in one result in Fig. 5. One
can see good absorption of specific power.
a)
H
b)
E
Fig. 4. Evaluation of modules of magnetic intensity H and electric intensity E
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Fig. 5. Evaluation of modules of Poyntings vector Π
The adaptive numerical model of the absorber was created in the ANSYS program
with APDL. It is possible to change the absorber geometry and to perform the optimisation
according to given parameters. The results of the model are used in construction of the
prototype. The prototype will undertake the measurements according to (1) to (6) in the
laboratories at VA Brno.
5 CONCLUSION
Presented work is a part of the project conducted in co-operation with VTUPV
Vyškov, PROTOTYPA a.s. and TESLA Vršovice Praha. The shielded non-reflecting
laboratory for microwave pulse generators is being built. In order to perform the tests of
vircator pulsed generator it is necessary to have a laboratory with shielding up to the
frequency of RTG and the laboratory has to eliminate the reflections of the EMG wave in the
rage f>10MHz. It is necessary to have absorption coefficient of the EMG wave Amin =20dB
for f=10MHz. The HF absorbers were discussed and the analysis of the basic properties was
performed for chosen pyramidal absorber. The absorption coefficient resulting from
numerical analysis is compared with experimental measurement.
References
[1] Svačina, J. Elektromagnetická kompatibilita (Principy a metody). Skripta VUT v Brně; ISBN 80-214-1873-7
[2] Fiala,P.: Koncepce a návrh kalorimetrického čidla ultrakrátkého elektromagnetického impulsu, Výzkumná zpráva, VUT
FEKT Brno, 18.3.2003, 70pgs.
[3] Stratton,J.A: Teorie elektromagnetického pole. SNTL Praha 1961.
[4] ANSYS Theory Reference Manual, Swanson Analysis System , Inc.USA , Huston.
__________________________________________________________________________
1
Ing. Eva Kadlecová, Department of Theoretical and Experimental Electrical Engineering, Brno University of Technology, FECT Brno,
Kolejní 4, 616 00 BRNO, Czech Republic , [email protected]
2
Ing. Martin Zlomek, Department of Theoretical and Experimental Electrical Engineering, Brno University of Technology, FECT Brno,
Kolejní 4, 616 00 BRNO, Czech Republic, [email protected]
3
Ing. Miloslav Steinbauer, Department of Theoretical and Experimental Electrical Engineering, Brno University of Technology, FECT Brno,
Kolejní 4, 612 00 BRNO, Czech Republic, [email protected]
4
Ing. Pavel Fiala, Ph.D., Department of Theoretical and Experimental Electrical Engineering, Brno University of Technology, FECT Brno,
Kolejní 4, 612 00 BRNO, Czech Republic, [email protected]
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