Computational Electromagnetics

Computational Electromagnetics Ursula van Rienen

Overview 1. Introduction 2. Maxwell s Equations 3. Finite Integration Technique 4. Finite Element Methods 5. Boundary Element Methods 6. Grid Generation 7. Further Numerical and Semi-Analytical Methods

Handouts Please find copies (pdf) of the slides together with brief notes, each under: http://www-ae.e-technik1.uni-rostock.de/lehre/ce.html

1. Introduction Most practical problems in electromagnetics cannot be solved purely by means of analytical methods, e.g.: radiation caused by a mobile phone near a human head shielding of an electronic circuit by a slotted metallic box etc. In many of such cases, numerical methods in electromagnetics can be applied in an efficient way to come to a satisfactory solution. The course deals with some of the most successful numerical methods in electromagnetics.

Discretization example: TEMF, TU Darmstadt Finite Difference Method (FD) Finite Element Method (FEM) Boundary Element Method (BEM) Finite Integration Technique (FIT)

HFSS - a Finite Element Tool for RF Problems http://www.ansoft.com/welcome2.html

Concerto Radiation pattern Meander Patch Antenna Radiation pattern 11

OPERA-2d Modell Radiale Flußdichte Vektorpotential 12

TOSCA Rotor Stator Coils Magn. flux density Switched reluctance motor 13

TOSCA Magnetic flux density on surface around air-gap Magnetic flux density in stator_air-gap_rotor neigbourhood 14

MAFIA-S Magnetostatics: Electrostatics: Flux density in Permanent-magnet motor Field distribution in and around a sparking plug

MAFIA-S Stationary currents: Temperature (stationary): Current density distribution in a circuit breaker Temperature: equipotential surface around CPU of a PC

MAFIA-W3 und -E Eddy current problems: Eigenmodes: Eddy current sensor RF-Resonator

MAFIA-T3 Waveguide branch: Plug: Horn antenna: Patch Antenna:

CST Microwave Studio

Waveguide Junction CST-Demo

Waveguide Junction CST-Demo Port 1 Port 3

The Human Body Model HUGO in MWS TM HUGO: based on Visible Human Data Set of the National Library of Medicine, Maryland 40 tissues 7 detail level: min/max-voxel size 1x1x1 mm (361 MB) 8x8x8 mm ( 0,7 MB) C/C++ programming interface convertable in STL format

HUGO and RF-Waves of a WLAN-Card Magnetic field Magnetic field Magnetic energy density Magnetic energy density V.Motrescu, G.Pöplau, UvR

Examples for Parameter Extraction PCB RJ45 connection CST-Demo isolator ε = 2,1; µ = 1 r r transmission lines ε = 2, 4 ; µ = 1 r r connector PEC PCB, socket & connector ε = 2, 2 ; µ = 1 r r

RJ45 Connector Extraction of some SPICE-compatible network model based on the computation of S-parameters : Definition of excitation sources: all wires are terminated with discrete ports the ports are excited sequentially with a Gaussian pulse yields broadband results for all wires 46.464 mesh points CST-Demo

RJ45 Connector Ports 1 and 6 CST-Demo

IC Package ε r = Box 4 104 ports, 190.333 mesh points Substrat Silicon ε = 12,3 PEC wires and traces r ε = 9, 2 r CST-Demo

IC Package CST-Demo

Parasitic Effects in IC s Current density of an IC at 5 GHz T. Wittig, I. Munteanu, T. Weiland, TU Darmstadt

CST Design Studio TM

Coupled S-Parameter Calculation Coupled S-Parameter Calculation H.-W. Glock, K.Rothemund, UvR 98-dato

0.912 GHz f 1.68 GHz Example: Test Resonator f=1.442 GHz

2. Maxwell s Equations B curl E = t D curl H = + J t div D = ρ div B = 0 Die Maxwellschen Gleichungen beschreiben das Verhalten elektromagnetischer Felder und deren Wechselwirkungen untereinander. Zur analytischen Lösung werden sie in integraler oder differentieller Form dargestellt. Elektromagnetische Felder können in folgende Klassen aufgeteilt werden: Statische Felder, Stationäre Felder, Quasistationäre Felder, Schnell veränderliche Felder. Diese Feldklassen erfordern jeweils unterschiedliche Lösungswege. Die analytische Lösung der Maxwellschen Gleichungen ist nur für einfache geometrische Anordnungen möglich. Zur Feldberechnung für praktische Aufgabenstellungen werden daher numerische Methoden verwendet.

Maxwell s Equations B curl E = t D curl H = + J t div D = ρ div B = 0 Faraday s induction law: Electric curl field = inductive flux density Ampère s law with Maxwell s extension: Magnetic curl field = Displacement current density + current density Gauss law for electricity: Electric flux out of any closed surface is proportional to the Gauss total charge law for enclosed magnetism: within Net the magnetic surface flux out of any closed surface is zero (always) Die Maxwellschen Gleichungen beschreiben das Verhalten elektromagnetischer Felder und deren Wechselwirkungen untereinander. Zur analytischen Lösung werden sie in integraler oder differentieller Form dargestellt. Elektromagnetische Felder können in folgende Klassen aufgeteilt werden: Statische Felder, Stationäre Felder, Quasistationäre Felder, Schnell veränderliche Felder. Diese Feldklassen erfordern jeweils unterschiedliche Lösungswege. Die analytische Lösung der Maxwellschen Gleichungen ist nur für einfache geometrische Anordnungen möglich. Zur Feldberechnung für praktische Aufgabenstellungen werden daher numerische Methoden verwendet.