Comsol Acdc Rf v43a

102
t t + = × = × = = E J B B E B E 0 0 0 0 0 ε µ µ ε ρ Electromagnetics Modeling in COMSOL Multiphysics

Transcript of Comsol Acdc Rf v43a

Page 1: Comsol Acdc Rf v43a

t

t

∂∂+=×∇

∂∂−=×∇

=⋅∇

=⋅∇

EJB

BE

B

E

000

0

0

εµµ

ερ

Electromagnetics Modeling in COMSOL Multiphysics

Page 2: Comsol Acdc Rf v43a

COMSOL is a Fully Integrated Software Suite

• All modeling steps are available from one and the same environment: – CAD Import and Geometry Modeling – Meshing – Multiphysics problem setup – Solving – Visualization – Postprocessing – Export/Import of data

Based upon the finite element method, COMSOL is designed from the ground up to address arbitrary combinations of physical equations

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COMSOL Multiphysics 4.3a Product Suite

COMSOL, COMSOL Multiphysics, COMSOL Desktop, and LiveLink are registered trademarks or trademarks of COMSOL AB. AutoCAD and Inventor are registered trademarks of Autodesk, Inc. LiveLink for AutoCAD and LiveLink for Inventor are not affiliated with, endorsed by, sponsored by, or supported by Autodesk, Inc. and/or any of its affiliates and/or subsidiaries. CATIA is a registered trademark of Dassault Systèmes S.A. or its affiliates or subsidiaries. SolidWorks is a registered trademark of Dassault Systèmes SolidWorks Corporation or its parent, affiliates, or subsidiaries. Creo is a trademark and Pro/ENGINEER is a registered trademark of Parametric Technology Corporation or its subsidiaries in the U.S and/or in other countries. Solid Edge is a registered trademark of Siemens Product Lifecycle Management Software Inc. SpaceClaim is a registered trademark of SpaceClaim Corporation. MATLAB is a registered trademark of The MathWorks, Inc. Excel is a registered trademark of Microsoft Corporation.

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Electromagnetics in the COMSOL Multiphysics Core Package is extended by various Modules

1) Start Here

2) Add Modules based upon your needs

4) Interface with your CAD data and MATLAB

3) Additional Modules extend the physics you can address

COMSOL, COMSOL Multiphysics, COMSOL Desktop, and LiveLink are registered trademarks or trademarks of COMSOL AB. AutoCAD and Inventor are registered trademarks of Autodesk, Inc. LiveLink for AutoCAD and LiveLink for Inventor are not affiliated with, endorsed by, sponsored by, or supported by Autodesk, Inc. and/or any of its affiliates and/or subsidiaries. CATIA is a registered trademark of Dassault Systèmes S.A. or its affiliates or subsidiaries. SolidWorks is a registered trademark of Dassault Systèmes SolidWorks Corporation or its parent, affiliates, or subsidiaries. Creo is a trademark and Pro/ENGINEER is a registered trademark of Parametric Technology Corporation or its subsidiaries in the U.S and/or in other countries. Solid Edge is a registered trademark of Siemens Product Lifecycle Management Software Inc. SpaceClaim is a registered trademark of SpaceClaim Corporation. MATLAB is a registered trademark of The MathWorks, Inc. Excel is a registered trademark of Microsoft Corporation.

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Types of Electromagnetics Modeling

Static Low Frequency Transient High Frequency

0=∂∂

tE ( )tωsinE ( )tE ( )tωsinE

Electric and magnetic fields do not vary in time.

Fields vary sinusoidally in time, but there is negligible radiation.

Fields vary arbitrarily in time, radiation may or may not be significant. Objects can be moving.

Fields vary sinusoidally in time, energy transfer is via radiation.

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Static Field Modeling

• DC Electric Currents solves for current flow in conductors • Electrostatics solves for electric fields in perfect insulators • Magnetostatics solves for the magnetic fields around magnets, and the fields around

current carrying objects

Inductor, DC current flow and Magnetostatics Parallel Plate Capacitor, Electrostatics Permanent Magnet, Magnetostatics

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Mutual Inductance, Magnetic Fields Analysis

Low Frequency Modeling

• AC Electric Currents considers both conduction and displacement currents in conductive and insulating media

• The Magnetic Fields can be solved for in the frequency domain to find the conduction, displacement, and induction currents

• The Magnetic and Electric fields can be solved for, if skin effects in coils require a high accuracy model

Inductive Heating, Magnetic Fields Inductor, Magnetic and Electric Fields

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Transient Modeling

• Transient Electric Currents solves for displacement and conduction currents in insulators and conductors

• Transient Magnetic Fields is suitable for modeling current pulses and nonlinear material response to field strength

• Rotating Machinery considers rotary velocity and acceleration • Transient electromagnetics solves for nonlinear wave phenomena

Second Harmonic Generation, Transient Electromagnetics E-Core Transformer, Transient Magnetic Fields Generator, Rotating Machinery

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High Frequency Modeling

• Electromagnetic Waves formulation solves for the electric and magnetic fields under the assumption that the energy transfer is via radiation

– Frequency domain and eigenfrequency (resonant mode) analysis

Optical Scattering Coplanar Waveguide Filter Microstrip Patch Antenna Array

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Whenever there are electromagnetic losses, there is a rise in temperature

Joule Heating Induction Heating Microwave Heating

Specialized user interfaces and solvers address the two-way coupled frequency-domain electromagnetic and time-domain thermal problems

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Additional Formulations

Electric Circuits Transmission Line Equations

The Electric Circuits formulation can model a lumped system of circuit elements and couple this to the finite element model

The Transmission Line Equation formulation solves for the electric potential along transmission lines

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Formulations per Module

COMSOL Multiphysics1 AC/DC Module RF Module

Static Electric Currents

Static Joule Heating

Electrostatics

Magnetic Fields2

Electric Currents in Solids

Electric Currents in Shells

Joule Heating Electrostatics

Magnetic Fields Induction Heating

Magnetic and Electric Fields Rotating Machinery Electric Circuits

Electromagnetic Waves Microwave Heating Transient EM Waves Time Explicit EM Waves Transmission Line Equations Electrical Circuits

1) Core package contains a reduced set of boundary conditions for these formulations 2) 2D and 2D-axisymmetric geometries and static and low frequency formulations only

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Finite Element Based Solutions

2D: Triangular & Quadrilateral Elements

3D: Tetrahedral, Hexahedral, Triangular Prismatic, & Bricks

1st, 2nd, & 3rd order isoparametric (curved) elements represent geometry to high accuracy and the mesh is fully user-controllable

State of the art direct and iterative solvers can address models with millions of unknowns

x =A-1b

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Feature Overview: Boundary Conditions

• Voltage source, Current source, & Insulating surfaces • Thin layers of electrically resistive, or conductive, material • Thin layers of high, or low, permittivity materials • Thin layers of high, or low, permeability materials • Perfectly conducting boundaries • Symmetry and periodicity conditions • Connections to external circuit models • Lumped, Coaxial, and other Waveguide feeds • Electromagnetic wave excitations • Radiating boundaries to infinity

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Feature Overview: Domain Conditions

• Background and Scattered Field excitations • Single Turn, Multi-Turn, and Coil Group Excitations • Infinite Elements and Perfectly Matched Layers

Iron sphere in a uniform magnetic field, surrounded by Infinite Elements

Single Turn, Multi-Turn, and Coil Group Excitations

Gold Sphere illuminated by a background plane wave

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Feature Overview: Material Models

• All material properties can be: – Constant or nonlinearly dependent upon the fields – Isotropic, Diagonal, or Fully Anisotropic – Defined via Rule-of-Mixtures models – Bi-directionally coupled to any other physics, e.g. Temperature, Strain – Fully User-Definable

• AC/DC Module supports magnetic nonlinearities, B-H curves

• RF Module supports loss tangents and dispersion models

– Drude-Lorentz, Debye, and Sellmeier dispersion

rr

r

DEDPED

ED

+=+=

=

εεε

εε

0

0

0

rr

r

BHBMHB

HB

+=+=

=

µµµµ

µµ

0

00

0

EJ σ=

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Feature Overview: Data Extraction

Magnetic Forces Far-Field Radiation Pattern

2221

1211

SSSS

Lumped Parameters

• Resistance, Capacitance, Inductance, & Mutual Inductance • Impedance, Admittance, and S-parameters • Force calculation due to electric and magnetic fields • Far-field plots for radiation

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Additional Modules for Electromagnetics Plasma Module1 MEMS Module2 Particle Tracing Module3

Micro-Electro-Mechanical Sensor Inductively Coupled Plasma Magnetic Lens

Solves DC Discharge, Capacitively Coupled Plasmas, Inductively Coupled Plasmas, and Microwave Plasmas.

Couples structural mechanics and electrostatics for the modeling of electroactuation, as well as piezoelectric devices.

Computes paths of charged particles through electric and magnetic fields as well as fluid fields.

1) Depending upon the type of plasma being modeled, the AC/DC or the RF Module may also be needed 2) Contains the same 3D electrostatic, electric currents in solids, and electric circuits capabilities as the AC/DC Module

3) Does not require any other Modules

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3D CAD File Formats ACIS® Catia® V5 Creo™ Parametric IGES Inventor® Parasolid® (read & write) Pro/ENGINEER® SolidWorks® STEP

LiveLink™ Interface Products LiveLink™ for AutoCAD® LiveLink™ for Creo™ Parametric LiveLink™ for Inventor® LiveLink™ for Pro/ENGINEER® LiveLink™ for SolidWorks® LiveLink™ for SpaceClaim®

Partner Meshing Products Mimics Simpleware

2D CAD File Formats DXF

E-CAD File Formats GDS/NETEX-G ODB++

Mesh File Formats NASTRAN STL (read & write) VRML

CAD & Meshing Interoperability

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MATLAB Based Scripting

All the functionality in the COMSOL GUI is equivalently available via the Live-Link for MATLAB which also allows for scripting and automation of model generation, results extraction, and design optimization

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Example Models, AC/DC Module

Resistors

Capacitors

Inductors and Coils

Magnets

Motors and Actuators

Electromagnetic Heating

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Resistor and Capacitor Modeling

• DC Resistive device analysis assumes that all materials are conductors, and solves the equation:

• Electrostatic analysis assumes all materials are insulators, thus:

• AC resistive and AC capacitive devices are both solved in the frequency domain

using the same governing equation:

• Transient analysis also uses the same governing equation:

( ) 0=∇⋅∇− Vσ

( ) 00 =∇⋅∇− Vrεε

( )( ) 00 =∇+⋅∇− Vj rεωεσ

( ) 00 =

∂∂+∇⋅∇− Vt

V rεεσ

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Electrostatic, Transient, and Frequency Domain modeling of a Parallel Plate Capacitor • A parallel plate capacitor is modeled under

electrostatic, frequency domain, and transient conditions

• Fringing fields and domain size effects on capacitance are studied

• Frequency domain modeling resolves the losses in dielectric materials

• Transient modeling of the charging behavior agrees with analytic solution

http://www.comsol.com/showroom/gallery/12695/

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Modeling of Thin Conductive or Resitive Layers

• Layers of highly conductive material relative to the surroundings can be modeled with an Electric Shielding boundary condition

• Layers of highly resistive material relative to the surroundings can be modeled with a Contact Impedance boundary condition

• These boundary conditions will reduce the mesh and problem size

http://www.comsol.com/showroom/gallery/12623/ http://www.comsol.com/showroom/gallery/12621/

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Modeling of Thin Layers of Dielectric Material

• Thin layers of high dielectric material relative to the surroundings can be modeled with a Dielectric Shielding boundary condition

• Thin layers of relatively low dielectric material can be modeled with a Thin Low Permittivity Gap boundary condition

• These boundary conditions will reduce the mesh and problem size

http://www.comsol.com/showroom/gallery/12651/ http://www.comsol.com/showroom/gallery/12625/

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MEMS Capacitor

http://www.comsol.com/showroom/gallery/123/

• A representative Micro-Electro-Mechanical-System (MEMS) capacitor composed of two plates

• The objective is to compute the device capacitance

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Inductor and Coil Modeling

BHABJH

1−=×∇==×∇

µ

Static Magnetic Fields are computed by solving:

Where A is the Magnetic Vector Potential, and J is the current density, which can be solved simultaneously, or in a separate analysis

( )

BHAB

JHA

1

2

−=×∇=

=×∇+−

µ

εωωσj

AC Magnetic Fields are computed by solving:

The additional terms represent the induced and the displacement currents

BHAB

JHA

1−=×∇=

=×∇+∂∂

µ

σt

The displacement currents are not included in the governing equations

Transient Magnetic Fields are computed by solving:

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Mutual Inductance between Axisymmetric Coils

• A single turn primary coil generates a magnetic field • The secondary coil has one, several, and many turns • The mutual inductance and induced currents are computed • Agreement with analytic mutual inductance is demonstrated

http://www.comsol.com/showroom/gallery/12687/ http://www.comsol.com/showroom/gallery/12679/ http://www.comsol.com/showroom/gallery/12653/

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http://www.comsol.com/showroom/gallery/129/

• Static analysis of an inductor using the Magnetic and Electric fields formulation to find the currents and the magnetic fields

• The objective is to compute the device inductance

Integrated Square-Shaped Spiral Inductor

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Inductance of a Power Inductor

• At the operating frequency (1kHz) of this power inductor, the skin depth in the coil is comparable to the thickness of the current-carrying wires

• The Magnetic and Electric fields interface is used to capture the skin effect in the wires

• The admittance and inductance is computed

http://www.comsol.com/showroom/gallery/1250/

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E-core Single Phase Transformer

E-core

Primary winding

Secondary winding

http://www.comsol.com/showroom/gallery/5700/

• Full non-linear time domain analysis at 50 Hz is solved for the induced voltages • Non-linear magnetic material (with saturation effect) is used for the magnetic core • Windings are treated as coil bundles, without modeling each turn of wire

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Inductor in Amplifier Circuit

• A nonlinear 2D axisymmetric finite element model is combined with a lumped circuit model

• A 1000 turn coil is wrapped around a core with nonlinear magnetic response, the multi-turn coil domain is used

• A DC bias is applied, and the AC response at this bias is computed • The voltage and current in the device is predicted over time

http://www.comsol.com/showroom/gallery/990/ http://www.comsol.com/showroom/gallery/2128/

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Transponder antenna

~1-2 cm

~ 1-2 m

Reader antenna

Modeling of an RFID system

• RFID systems typically consist of a small (~1cm) antenna and a larger (~1m) reader antenna

• Here, both antennas are modeled as zero-thickness lines, the larger reader antenna has a driving current applied

• The intercepted magnetic flux is used to compute the mutual inductance between antennas

http://www.comsol.com/showroom/gallery/1264/

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Multi-Turn Coil Above an Asymmetric Conductor Plate

http://www.comsol.com/showroom/gallery/13777/

• The model calculates the eddy currents and magnetic fields produced when an aluminum conductor is placed asymmetrically above a multi-turn coil carrying an AC current

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If there is no current flow in the model, solve: Where Vm is the Magnetic Scalar Potential

Magnets, Motors & Actuators

( )mV∇==⋅∇

HH 0µ

When modeling rotating objects, solve for the transient magnetic fields and induced currents in the conductive and current carrying domains, but only the magnetic fields only in the surrounding air

( )mV∇==⋅∇

HH 0µ

BHAB

JBvHA

1−=×∇=

=×−×∇+∂∂

µ

σσt

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The Magnetic Field from a Permanent Magnet

http://www.comsol.com/showroom/gallery/78/

• Introductory example for magnetic field modeling considers a typical horseshoe magnet and iron bar

• Symmetry is used to reduce problem size • The magnetic fields and forces are computed

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• An expression is used to set up a laterally periodic magnetization: • M = ( Mpresin(kx) , 0 , Mprecos(kx) ) • The magnet interacts with a plate of nonlinear permeability:

• Flux and forces are computed

One-sided Magnet

http://www.comsol.com/showroom/gallery/213/

Page 38: Comsol Acdc Rf v43a

Magnetic Prospecting of Iron Ore Deposits

• Underground iron ore deposits result in magnetic anomalies • Here, disturbances in the background magnetic field of the Earth, due to the

presence of a ore deposit are computed • The Reduced Field formulation solves for small perturbations to a background field

http://www.comsol.com/showroom/gallery/3807/

Assumed ore deposit

Page 39: Comsol Acdc Rf v43a

Simulating the Moving Parts of a Generator

http://www.comsol.com/showroom/gallery/2122/

• The Rotating Machinery, Magnetic interface solves for rotating 2D and 3D domains composed of magnetic materials

• The finite element mesh is allowed to slide at the interface • Nonlinear magnetic materials are included in the model • Induced voltages as a function of rotational speed are computed

Page 40: Comsol Acdc Rf v43a

Simulating a Generator Made From Nonlinear Materials

http://www.comsol.com/showroom/gallery/462/

• A fully 3D static analysis of the magnetic fields around the rotor and stator • Permanent magnets and nonlinear magnetic materials are included in the model • Material nonlinearity is modeled via an interpolation function

Page 41: Comsol Acdc Rf v43a

Magnetic Damping of Vibrating Conducting Solids

http://www.comsol.com/showroom/gallery/12437/

• A metallic cantilever beam is placed in a strong magnetic field • A sinusoidal force excites the beam • Although the displacements are small, the velocities are significant • Currents are induced in a conductors moving through a magnetic field • The induced currents in the vibrating solid create a damping effect

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Electromagnetic Heating

Displacement Current Losses Dipolar molecules rotate in time varying electric field

e- Conduction Current Losses Electrons moving through a conductor lose energy

Induction Current Losses Time varying magnetic fields induce currents in a conductor

J(t) H(t)

All of the above losses can be included in the generalized heat transfer equation ( )

LossesneticElectromagp QTk

tTC =∇⋅∇−

∂∂ρ

+ E(t)

Page 43: Comsol Acdc Rf v43a

Electrical Heating of a Busbar

• Direct current flows through a copper busbar • Resistive losses raise the temperature • The objective of this model is to find the peak temperature under

steady-state conditions • This is the introductory example to the COMSOL Multiphysics

Product Suite

http://www.comsol.com/products/tutorials/introduction/page2/

Page 44: Comsol Acdc Rf v43a

Inductive Heating of a Copper Cylinder

• A 2D axisymmetric model of a coil around a cylinder of copper • The Induction Heating interface solves the frequency-domain electromagnetic and

time-domain thermal problem in a two-way coupled approach • The electric conductivity varies as the temperature increases • The rise in temperature over time is computed

http://www.comsol.com/showroom/gallery/148/

Page 45: Comsol Acdc Rf v43a

Example Models, RF Module

Antennas

Waveguides & Transmission Lines

Scattering Problems

Periodic Problems

Electromagnetic Heating

Resonant Structures

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Resonant Structure Example Models

• COMSOL can find the resonant frequency and Quality factor of an closed and open cavity structures by solving the eigenvalue problem:

• Typical examples: – Microwave Cavities – Optical Resonators – Filters – Coil Resonance

( ) ( )δωλ

ωεσεµ+−=

=−−×∇×∇ −

jjk r 0EE 0

20

1

Page 47: Comsol Acdc Rf v43a

Verification of eigenvalue solvers

http://www.comsol.com/showroom/gallery/9618/

• Rectangular, cylindrical, and spherical air-filled metal cavities • The resonant frequency and Q-factor are computed • Mesh refinement studies are performed • Results show agreement with analytic solutions • C.A. Balanis, Advanced Engineering Electromagnetics, Wiley, 1989

Page 48: Comsol Acdc Rf v43a

Evanescent Mode Cylindrical Cavity Filter

• A cylindrical cavity is partially filled with Teflon which will shift the resonant frequency down

• A slot coupled microstrip line feed with lumped ports is used • S-parameters are computed

http://www.comsol.com/showroom/gallery/12015/

Page 49: Comsol Acdc Rf v43a

Cascaded Rectangular Cavity Filter

• Three slot coupled cascaded rectangular cavity filters • Slot coupled microstrip line feed with lumped port • Insertion loss <2dB, -10dB S11 bandwidth ~15MHz • Much better out-of-band rejection is computed compared to a single cavity model

http://www.comsol.com/showroom/gallery/12018/

Page 50: Comsol Acdc Rf v43a

Finding the resonant frequency of a coil

• A copper coil in an air domain • A perfectly matched layer domain models the surrounding

free space • Eigenvalue analysis find the resonant frequency and the

Q-factor • Frequency domain analysis also finds the resonance, and

Q-factor • Driving and tuning elements can be added to the model

http://www.comsol.com/showroom/gallery/6126/

Page 51: Comsol Acdc Rf v43a

Modeling of a Fabry-Perot Cavity

• A Fabry-Perot cavity is a slab of dielectric in air • The simplest optical resonator • Objective is to find resonant frequency and Q-factor • Frequency-Domain and Eigenvalue solutions are shown

http://www.comsol.com/showroom/gallery/10005/

Page 52: Comsol Acdc Rf v43a

Tunable Evanescent Mode Cavity Filter Using a Piezoelectric Device

http://www.comsol.com/showroom/gallery/12619/

• Tunable the capacitance inside the cavity by the piezoelectric device • The resonant frequency is controlled by the capacitance • Higher voltage, thinner gap, more reactance, and lower frequency resonance

Page 53: Comsol Acdc Rf v43a

Antenna Example Models

• Antennas transmit and/or receive radiated electromagnetic energy. COMSOL can compute the radiated energy, far field patterns, losses, gain, directivity, impedance and S-parameters by solving the linear problem for the E-field:

• Typical examples: – Microstrip Patch Antenna – Vivaldi Antenna – Dipole Antenna

( ) ( ) 0EE =−−×∇×∇ −0

20

1 ωεσεµ jk r

Page 54: Comsol Acdc Rf v43a

Microstrip Patch Antenna

http://www.comsol.com/showroom/gallery/11742/

• A low profile, planar, narrow bandwidth antenna that is easy to design and fabricate on a PCB, used in many applications.

• There is an optimum feed point between the center and edge • An inset feeding strategy is used that does not require any additional matching

parts

Page 55: Comsol Acdc Rf v43a

4 x 2 Microstrip Patch Antenna Array

• Slot-coupled 4x2 array of patch antennas • Controlling the phase and magnitude assigned to each element can steer the beam • Far-Field radiation pattern is computed

http://www.comsol.com/showroom/gallery/12021/

Page 56: Comsol Acdc Rf v43a

Biconical Antenna

• A wide-band antenna with omni-directional radiation pattern in azimuth angle (H-plane)

• A coaxial feed with better than -10 dB S11 in the simulation frequency range

http://www.comsol.com/showroom/gallery/12075/

Page 57: Comsol Acdc Rf v43a

Radome with Double-layered Dielectric Lens

• A dielectric radome is an RF-transparent enclosure for antennas • Such structures can be designed to minimize transmission losses and increase

directivity

http://www.comsol.com/showroom/gallery/12027/

Page 58: Comsol Acdc Rf v43a

Dipole Antenna with a Coaxial Balun

• A λ/4 coaxial balun (1:1) prevents undesirable currents on the outside of the feed cable

1mm Thickness Enclosure

Shorted to The Coax Outer Conductor

Feed Point

λ/4

λ/4

λ/4

http://www.comsol.com/showroom/gallery/12313/

Page 59: Comsol Acdc Rf v43a

Dielectric Resonator Antenna with Parasitic Array

• A quartz dielectric resonator above a radiating element increases directivity and gain • Additional passive metallic antenna elements are patterned on the dielectric block • Far-field patterns and antenna impedance are computed

http://www.comsol.com/showroom/gallery/12042/

Page 60: Comsol Acdc Rf v43a

http://www.comsol.com/showroom/gallery/12045/

Electromagnetic Band Gap Meta-material

• A periodic mushroom structure has a band gap that provides increased isolation between two antenna elements

Decoupling Band

With EBG

Without EBG

Page 61: Comsol Acdc Rf v43a

Balanced Patch Antenna

http://www.comsol.com/showroom/gallery/782/

• A fractal antenna has multiple resonances that can operate at several bands • A patch antenna is formed on top of a printed circuit board • Antenna is driven by two coaxial feeds • The full details of the feeds are modeled • Near and Far-Fields are plotted

Page 62: Comsol Acdc Rf v43a

Sierpinski Fractal Monopole Antenna

http://www.comsol.com/showroom/gallery/12721/

• A fractal antenna has multiple resonances that can operate at several bands

Page 63: Comsol Acdc Rf v43a

Dipole Antenna with Conductive Surfaces

http://www.comsol.com/showroom/gallery/8715/

• The most straightforward antenna configurations which is realized with two thin metallic rods

• A sinusoidal voltage difference applied between two rods • The model computes input impedance and 3D far-field pattern

Page 64: Comsol Acdc Rf v43a

Spiral Slot Antenna

http://www.comsol.com/showroom/gallery/12315/

• A spiral slot antenna provides a wide-band impedance matching and bi-directional radiation pattern

Page 65: Comsol Acdc Rf v43a

Vivaldi Antenna

http://www.comsol.com/showroom/gallery/12093/

• A tapered slot antenna, also known as a Vivaldi antenna • Useful for wide band applications • An exponential function is used for the taper profile

Page 66: Comsol Acdc Rf v43a

Helical Antenna

http://www.comsol.com/showroom/gallery/13681/

• A helical antenna has two major modes; normal mode and axial mode. • At the normal mode, torus-shaped radiation pattern • At the axial mode, similar to an end-fire array generating a directive radiation pattern

Page 67: Comsol Acdc Rf v43a

Waveguides and Transmission Lines

• Any structure that guides electromagnetic waves along its structure can be considered a waveguide. COMSOL can compute propagation constants, impedance, S-parameters by solving:

• Typical examples: – Coaxial cable – Optical fibers and waveguides

( ) ( )( )

z

r

jyx

jk

δβλλ

ωεσεµ

−−==

=−−×∇×∇ −

z)exp( ,0

20

1

EE0EE

Page 68: Comsol Acdc Rf v43a

Lossy Ferrite 3-Port Circulator

• A microwave circulator uses an anistropic and lossy ferrite • A ferrite post, under an assumed externally biasing magnetic field is at the center of

the circulator • Non-reciprocal behavior provides isolation

http://www.comsol.com/showroom/gallery/10302/

Page 69: Comsol Acdc Rf v43a

Coupled Line Filter

• A narrowband bandpass filter is realized using cascaded coupled microstrip lines, each approximately a half-wavelength long

• Input matching is better than -15dB around the center frequency • Low insertion loss and good out-of-band rejection

http://www.comsol.com/showroom/gallery/12012/

Page 70: Comsol Acdc Rf v43a

Coplanar Waveguide Bandpass Filter

• A Coplanar Waveguide bandpass filter can be realized using Interdigital Capacitors and Short-circuited Stub Inductors

• S-parameters are computed

http://www.comsol.com/showroom/gallery/12099/

Page 71: Comsol Acdc Rf v43a

Branch Line Coupler

• A Four-port network device with 90° phase difference between two coupled ports • The model computes the S-parameters

http://www.comsol.com/showroom/gallery/11727/

Page 72: Comsol Acdc Rf v43a

Rat-Race Coupler (180° Ring Hybrid)

• A four-port network device with 180° phase difference between two ports can be easily fabricated on a PCB board

• The model computes the S-parameters

http://www.comsol.com/showroom/gallery/11739/

Page 73: Comsol Acdc Rf v43a

Substrate Integrated Waveguide

• A waveguide-type structure fabricated on a substrate by adding vias between the microstrip line and ground plane that is easy to fabricate and will act as a high-pass filter

• Sharp cutoff frequency at ~8.6GHz

http://www.comsol.com/showroom/gallery/12127/

Page 74: Comsol Acdc Rf v43a

SMA Connectorized Wilkinson Power Divider

• A Wilkinson power divider is a three-port lossless device and outperforms a T-junction divider and a resistive divider

• Computed S-parameters show good input matching and -3 dB evenly split output

http://www.comsol.com/showroom/gallery/12303/

Page 75: Comsol Acdc Rf v43a

Waveguide Iris Bandpass Filter

• A series of inductive diaphragms in a WR-90 waveguide result in a bandpass frequency response

• Computed S-parameters show good out-of-band rejection

http://www.comsol.com/showroom/gallery/12737/

Page 76: Comsol Acdc Rf v43a

Finding the Impedance of a Coaxial Cable

http://www.comsol.com/showroom/gallery/12351/

• The impedance of a coaxial cable has an analytic solution • A cross-sectional model of a coax cable is used to find the electric and magnetic

fields • The computed impedance agrees with the analytic solution

Page 77: Comsol Acdc Rf v43a

Impedance of a Parallel Wire Transmission Line

http://www.comsol.com/showroom/gallery/12403/

• The impedance of a parallel wire transmission line has an analytic solution • A cross-sectional model is used to find the fields • The transmission line is unshielded, so the fields extend to infinity, associated

modeling issues are addressed • The computed impedance agrees with the analytic solution

Page 78: Comsol Acdc Rf v43a

Connecting a 3D RF Model to a Circuit Model

http://www.comsol.com/showroom/gallery/10833/

• A 3D model of a coaxial cable is connected to a circuit model • The source, and source impedance is modeled by the circuit model, as is the load

on the cable

Page 79: Comsol Acdc Rf v43a

Transient Modeling of a Coaxial Cable

http://www.comsol.com/showroom/gallery/12349/

• A 2D axisymmetric model of a coaxial cable with a transient pulse applied at one end

• The other end has a matched load, open circuit, and short circuit • Transient behavior is computed

Page 80: Comsol Acdc Rf v43a

Rectangular to Elliptical Waveguide Adapter

http://www.comsol.com/showroom/gallery/140/

• A rectangular waveguide has a known, analytic solution for the fields in cross section

• An elliptical waveguide requires that a boundary modes analysis problem be solved to compute the field shapes

• This model shows how to compute waveguide mode shapes, and correctly compute the S-parameters of the adapter

Page 81: Comsol Acdc Rf v43a

Polarized Circular Ports

http://www.comsol.com/showroom/gallery/14043/

• This model illustrates how to align the polarization of degenerate port modes and in particular how to model and excite the TE11 mode of circular waveguides in 3D

Page 82: Comsol Acdc Rf v43a

Photonic Crystal Waveguide Bend

http://www.comsol.com/showroom/gallery/143/

• An array of high-dielectric posts in has a photonic band gaz • Removing one row of posts can create a waveguide • Over certain frequency ranges, good guiding is observed

Page 83: Comsol Acdc Rf v43a

Dielectric Slab Waveguide

http://www.comsol.com/showroom/gallery/12347/

• A slab of dielectric in air acts as an optical waveguide • The computed effective index is compared to analytic solution • The first guided mode is launched into waveguide

Page 84: Comsol Acdc Rf v43a

• Optical fibers are the backbone of the telecommunications infrastructure • This introductory model computes the effective index of several modes

SiO2

SiO2 (doped)

445711 .n =

437812 .n =

Step Index Fiber

http://www.comsol.com/showroom/gallery/145/

Page 85: Comsol Acdc Rf v43a

Electromagnetic and Structural Analysis of a Microwave Filter on a PCB

http://www.comsol.com/showroom/gallery/4461/

• A seventh-pole low-pass Chebyshev filter implemented on a PCB • Geometry is read in from ODB++(X) • Structural deformation of the board under load • Effect of deformation on the S-parameters is solved for

Page 86: Comsol Acdc Rf v43a

Stress-Optical Effects on a Ridge Waveguide

http://www.comsol.com/showroom/gallery/190/

• Structural stresses can result in a change in refractive index • Plane strain structural equations are solved for the stresses • Electromagnetic problem is solved for the effective index

Page 87: Comsol Acdc Rf v43a

Examples of Scattering Problems

• An background electromagnetic field of known shape, such as a plane wave, interacts with various materials and structures. The objective is to find the total field and scattered fields by solving:

• Typical examples: – Mie Scattering – Radar Cross Section (RCS) calculations

( ) ( )scatteredbackgroundtotal

totalrtotal jkEEE

0EE+=

=−−×∇×∇ −0

20

1 ωεσεµ

Page 88: Comsol Acdc Rf v43a

Mie Scattering, Radar Cross Section of a Metal Sphere

http://www.comsol.com/showroom/gallery/10332/

• A sphere of metal is treated as a perfect electric conductor • Plane wave irradiates the sphere • Symmetry reduces the problem size • Second order elements represent the sphere shape to high accuracy • A Perfectly Matched Layer (PML) truncates the modeling domain • Far-field calculation computes the backscattered field • Results agree with analytic solution

Page 89: Comsol Acdc Rf v43a

Radar Cross Section

http://www.comsol.com/showroom/gallery/8613/

• A 2D obloid shape is illuminated by a plane wave from all angles • The scattered field formulation is used to find the RCS

Page 90: Comsol Acdc Rf v43a

Optical Scattering off of a Gold Sphere

http://www.comsol.com/showroom/gallery/12415/

• A gold sphere is illuminated by light of wavelength 400-700nm • Symmetry reduces the problem size • Second order elements represent the sphere shape to high accuracy • A Perfectly Matched Layer (PML) truncates the modeling domain • Gold is modeled as having negative and complex valued permittivity • Far-field calculation computes the scattered fields • Losses within the sphere are computed

Gold sphere

Page 91: Comsol Acdc Rf v43a

Beam Splitter

http://www.comsol.com/showroom/gallery/12729/

• A thin layer of silver is sandwiched between two glass prisms • The thin layer of silver is modeled using the computationally efficient Transition

Boundary Condition • An incoming Gaussian beam gets split into two beams

Page 92: Comsol Acdc Rf v43a

Second Harmonic Generation

http://www.comsol.com/showroom/gallery/956/

• Gaussian beam passing through an optically nonlinear medium • Polarization dependents upon the electric field magnitude • Requires transient non-linear modeling • Frequency doubling is observed

Page 93: Comsol Acdc Rf v43a

Mapped Dielectric Distribution of a Metamaterial Lens

http://www.comsol.com/showroom/gallery/13873/

• Convex lens shape is defined via a known deformation of a rectangular domain • The dielectric distribution is defined on the undeformed, original rectangular domain

and is mapped onto the deformed shape of the lens

Page 94: Comsol Acdc Rf v43a

Examples of Periodic Problems

• Any structure that repeats in one, two, or all three dimensions can be treated as periodic, which allows for the analysis of a single unit cell, with Floquet Periodic boundary conditions:

• Typical examples: – Optical Gratings – Frequency Selective Surfaces

))(exp( ABAB j rrkEE −⋅−=

Page 95: Comsol Acdc Rf v43a

Verification of Fresnel Equations

http://www.comsol.com/showroom/gallery/12407/

• TE- and TM-polarized light incident upon an infinite dielectric slab • 3D model uses Floquet Periodicity • Results agree with analytic solution

Page 96: Comsol Acdc Rf v43a

Plasmonic Wire Grating

• A 2D array of silver cylinders patterned on a substrate is modeled with one unit cell using Floquet periodicity

• Higher-order diffraction is captured

http://www.comsol.com/showroom/gallery/10032/

Page 97: Comsol Acdc Rf v43a

εr = -1 μ r= -1

εr = 1 μ r= 1

http://www.comsol.com/showroom/gallery/12583/

• A bulk material of negative refractive index can be modeled • The relative permittivity and permeability are both set to -1 • The boundary conditions, terminations, and material interfaces require special treatment

Modeling of Negative Refractive Index

Page 98: Comsol Acdc Rf v43a

Electromagnetic Heating Examples

• An electromagnetic wave interacting with any materials will have some loss that leads to rise in temperature over time. Any losses computed from solving the electromagnetic problem can be bi-directionally coupled to the thermal equation:

• Typical examples: – Microwave Ovens – Absorbed Radiation in Living Tissue – Tumor Ablation

( )Losses

neticElectromagp QTktTC =∇⋅∇−

∂∂ρ

Page 99: Comsol Acdc Rf v43a

Heating of a Dielectric Block in a Waveguide

http://www.comsol.com/showroom/gallery/6078/

• Dielectric block inside a waveguide • Waveguide walls coated with copper • There are losses in the block and at the walls of waveguide • Thermal and electrical material properties vary with temperature • The rise in temperature is computed in the block and waveguide structure • Both steady-state thermal solution and transient thermal effects are computed

Page 100: Comsol Acdc Rf v43a

Absorbed Radiation (SAR) in the Human Brain

http://www.comsol.com/showroom/gallery/2190/

• A representative cell phone antenna is placed next to a head • The dielectric properties of the head are from scan data • Absorbed radiation and temperature rise is computed • Pennes Bioheat equation models living tissue

Page 101: Comsol Acdc Rf v43a

Microwave Cancer Therapy

http://www.comsol.com/showroom/gallery/30/

• A coaxial cable with slot is coated with a Teflon sleeve and forms an antenna

• The antenna is inserted into the liver • The radiated power heats the tissue • The Pennes Bioheat equation models

the liver tissue • Model solves for: • The Specific Absorption Rate (SAR) • Temperature field • Radiated fields

Page 102: Comsol Acdc Rf v43a

Potato in a Microwave Oven

http://www.comsol.com/showroom/gallery/1424/

• A half-symmetry model of a potato in a microwave oven • The electromagnetic fields are solved in the frequency domain • The thermal problem is solved transiently