V1 - Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...

Computational Electromagnetics 

Ursula van Rienen 

Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics

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 


MEGA 


MEGA 


MEGA 


MEGA 


Concerto 

Radiation 

pattern 

Meander Patch Antenna 

Radiation 

pattern 


OPERA-2d 

Modell 

Radiale Flußdichte 

Vektorpotential 


TOSCA 

Rotor 

Stator 

Coils 

Magn. flux density 

Switched reluctance motor 


TOSCA 

Magnetic flux density on 

surface around air-gap 

Magnetic flux density in 

stator_air-gap_rotor 

neigbourhood 


MAFIA 


MAFIA 


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 ® 


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 

Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics 

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.

V1 - Institut für Allgemeine Elektrotechnik, Uni Rostock - Universität ...

Create successful ePaper yourself

Delete template?

Save as template?