COMSOL Multiphysics RF MODULE M ODEL L IBRARY V ERSION 3.5 How to contact COMSOL: Germany United Kingdom COMSOL Multiphysics GmbH COMSOL Ltd. Benelux Berliner Str. 4 UH Innovation Centre COMSOL BV D-37073 Göttingen College Lane Röntgenlaan 19 Phone: +49-551-99721-0 Hatfield 2719 DX Zoetermeer Fax: +49-551-99721-29 Hertfordshire AL10 9AB The Netherlands [email protected] Phone:+44-(0)-1707 636020 Phone: +31 (0) 79 363 4230 www.comsol.de Fax: +44-(0)-1707 284746 Fax: +31 (0) 79 361 4212 [email protected] [email protected] Italy www.uk.comsol.com www.comsol.nl COMSOL S.r.l. Via Vittorio Emanuele II, 22 United States Denmark 25122 Brescia COMSOL, Inc. COMSOL A/S Phone: +39-030-3793800 1 New England Executive Park Diplomvej 376 Fax: +39-030-3793899 Suite 350 2800 Kgs. Lyngby [email protected] Burlington, MA 01803 Phone: +45 88 70 82 00 www.it.comsol.com Phone: +1-781-273-3322 Fax: +45 88 70 80 90 Fax: +1-781-273-6603 [email protected] Norway www.comsol.dk COMSOL AS COMSOL, Inc. 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Robert Schuman Fax: +46 8 412 95 10 [email protected] F-38000 Grenoble [email protected] www.comsol.com Phone: +33 (0)4 76 46 49 01 www.comsol.se Fax: +33 (0)4 76 46 07 42 For a complete list of international [email protected] Switzerland representatives, visit www.comsol.fr FEMLAB GmbH www.comsol.com/contact Technoparkstrasse 1 CH-8005 Zürich Company home page Phone: +41 (0)44 445 2140 www.comsol.com Fax: +41 (0)44 445 2141 [email protected] COMSOL user forums www.femlab.ch www.comsol.com/support/forums RF Module Model Library © COPYRIGHT 1994–2008 by COMSOL AB. All rights reserved Patent pending The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from COMSOL AB. 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Version: September 2008 COMSOL 3.5 Part number: CM021002 CONTENTS Chapter 1: Introduction Model Library Guide . 2 Typographical Conventions . 6 Chapter 2: Tutorial Models Dielectric Scattering PML 8 Model Definition . 8 Results and Discussion. 9 Modeling Using the Graphical User Interface . 10 Magnetic Frill 14 Introduction . 14 Model Definition . 14 Results and Discussion. 15 Reference . 15 Modeling Using the Graphical User Interface . 15 Microstrip on a Printed Circuit Board 20 Model Definition . 20 Results. 20 Modeling Using the Graphical User Interface . 21 Solving with Lumped Port Termination. 28 Waveguide Optimization 31 Introduction . 31 Model Definition . 32 Results and Discussion. 33 Reference . 34 Modeling Using the Graphical User Interface . 35 CONTENTS | i Calculating the Schumann Resonance Frequencies 42 Introduction . 42 Model Definition . 42 Modeling in COMSOL Multiphysics . 44 Results and Discussion. 45 Modeling Using the Graphical User Interface . 46 Chapter 3: RF and Microwave Models Three-Port Ferrite Circulator 50 Introduction . 50 Model Definition . 51 Results and Discussion. 53 References . 55 Modeling Using the Graphical User Interface . 56 Extracting the S-Parameter Matrix . 63 Exporting S-Parameters versus Frequency to Touchstone . 64 Monoconical RF Antenna 65 Introduction . 65 Model Definition . 65 Results and Discussion. 66 Modeling Using the Graphical User Interface . 70 Antenna Impedance and Radiation Pattern . 75 Far-Field Computation . 77 Transient Analysis with External Circuit . 78 Magnetic Dipole Antenna 80 Introduction . 80 Model Definition . 80 Results and Discussion. 81 Modeling Using the Graphical User Interface . 81 Modeling Using the Programming Language . 85 Optimizing the Shape of a Dipole Antenna 87 Introduction . 87 ii | CONTENTS Model Definition . 87 Results and Discussion. 88 Modeling Using the Graphical User Interface . 89 Thermal Drift in a Microwave Filter 97 Introduction . 97 Model Definition . 97 Results and Discussion. 98 Modeling Using the Graphical User Interface . 101 H-Bend Waveguide with S-parameters 112 Introduction . 112 Model Definition . 113 Results and Discussion. 113 Modeling Using the Graphical User Interface . 114 Waveguide Adapter 117 Introduction . 117 Model Definition . 117 Results. 119 Modeling in COMSOL Multiphysics . 122 Modeling Using the Graphical User Interface . 123 Mode Analysis . 123 S-Parameter Analysis . 126 Creating the Geometry in COMSOL Script or MATLAB . 128 Microwave Cancer Therapy 130 Introduction . 130 Model Definition . 130 Results and Discussion. 134 Reference . 137 Modeling in COMSOL Multiphysics . 137 Modeling Using the Graphical User Interface . 138 Absorbed Radiation (SAR) in the Human Brain 143 Introduction . 143 Model Definition . 143 Results and Discussion. 145 CONTENTS | iii References . 146 Modeling Using the Graphical User Interface . 147 Microwave Oven 157 Introduction . 157 Model Definition . 157 Results. 158 Modeling in COMSOL Multiphysics . 161 Modeling Using the Graphical User Interface . 161 Electromagnetic Analysis . 161 Microwave Filter on PCB 169 Introduction . 169 Model Definition . 169 Results and Discussion. 171 References . 172 Modeling Using the Graphical User Interface . 173 Mechanical Stress Analysis . 179 Balanced Patch Antenna for 6 GHz 183 Introduction . 183 Model Definition . 184 Results and Discussion. 186 Modeling in COMSOL Multiphysics . 188 Reference . 189 Modeling Using the Graphical User Interface . 189 Coaxial to Waveguide Coupling 204 Introduction . 204 Results and Discussion. 204 Modeling Using the Graphical User Interface . 206 Sea Bed Logging 211 Introduction . 211 Model Definition . 211 Results. 211 Modeling in COMSOL Multiphysics . 213 Modeling Using the Graphical User Interface . 213 iv | CONTENTS Chapter 4: Optics and Photonics Models Photonic Microprism 222 Introduction . 222 Model Definition . 223 Results and Discussion. 224 References . 224 Modeling Using the Graphical User Interface . 225 Photonic Crystal 230 Introduction . 230 Model Definition . 231 Results and Discussion. 231 References . 232 Modeling Using the Graphical User Interface . 232 Modeling Using the Programming Language . 238 Bandgap Analysis of a Photonic Crystal 240 Introduction . 240 Model Definition . 240 Results and Discussion. 243 References . 245 Modeling Using the Graphical User Interface . 246 Modeling Larger Sweeps With COMSOL Script . 252 Step-Index Fiber 255 Introduction . 255 Model Definition . 256 Results and Discussion. 256 Reference . 257 Modeling Using the Graphical User Interface . 257 Modeling Using the Programming Language . 260 Stress-Optical Effects in a Silica-on-Silicon Waveguide 262 Introduction . 262 The Stress-Optical Effect and Plane Strain . 262 Perpendicular Hybrid-Mode Waves . 263 CONTENTS | v Modeling Using the Graphical User Interface—Plane Strain Analysis . 264 Modeling Using the Graphical User Interface—Optical Mode Analysis . 272 Convergence Analysis . 275 Stress-Optical Effects with Generalized Plane Strain 279 Introduction . 279 Generalized Plane Strain . 279 Modeling Using the Graphical User Interface—Plane Strain Analysis . 285 Modeling Using the Graphical User Interface—Optical Mode Analysis . 293 Second Harmonic Generation of a Gaussian Beam 296 Introduction . 296 Model Definition . ..