numerical analysis of the pyramidal hf absorber anotace annotation
Transkript
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 -1- 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 -2- 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 -3- 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 12.ANSYS Users´ Meeting, 30. září-1. října 2004 na Hrubé Skále -4- − 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 DISPLAY FEM MODEL SIZE INFORMATION Maximum Node Number Maximum DOF per Node Maximum Element Number = = = 54663 1 37424 *************** MEMORY Requested Initial Work Space ANSYS Scratch Memory Used Maximum Scratch Memory Used STATISTICS *************** = 65011712 Words 248.000 MB = 3493796 Words 13.328 MB = 8317328 Words 31.728 MB ***** Current Database Position DATABASE STATUS ***** = 8215408 Words 31.339 MB ***** SOLUTION MEMORY ***** = 16384 Words 0.063 MB Binary I/O Page Size 12.ANSYS Users´ Meeting, 30. září-1. října 2004 na Hrubé Skále -5- Analysis Type Available Solution Memory Wavefront Available = = = 3 34910309 Words 5887 133.172 MB 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 12.ANSYS Users´ Meeting, 30. září-1. října 2004 na Hrubé Skále -6- 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] 12.ANSYS Users´ Meeting, 30. září-1. října 2004 na Hrubé Skále -7-