The RF Module - KESCO | 計測エンジニアリングシステム ... · Formulations per Module COMSOL Multiphysics1 RF Module AC/DC Module Static Electric Currents ... Plasma Module1

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The RF Modulefor High Frequency Electromagnetics Modeling

Electromagnetics in COMSOL Multiphysics is extended by add-on Modules

1) Start Here

2) Add Modules based upon your needs

3) Additional Modules extendthe physics you can address

4) Interface with your CAD data and MATLAB

Types of Electromagnetics Modeling

RF Module

Static Low Frequency Transient High Frequency

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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.

High Frequency Modeling

• Electromagnetic Waves formulation solves for the electric and magnetic fields with Frequency domain and Eigenfrequency (resonant mode) analysis

Rat‐race CouplerMicrostrip Patch Antenna ArraySubstrate Integrated Waveguide

Transient Modeling

Second Harmonic Generation, Electromagnetic Waves, Transient

Coaxial Cable, Electromagnetic Waves, Transient

• Transient electromagnetics solves for nonlinear wave phenomena• For transient phenomena such as signal propagation as a function of time

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

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

Microwave Heating

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

Formulations per Module

COMSOL Multiphysics1 AC/DC Module RF Module

Static Electric CurrentsStatic Joule HeatingElectrostaticsMagnetic Fields2

Electric Currents in SolidsElectric Currents in ShellsJoule HeatingElectrostaticsMagnetic FieldsInduction HeatingMagnetic and Electric FieldsRotating MachineryElectric Circuits

Electromagnetic Waves- Frequency Domain- Time Explicit- Transient

Microwave HeatingTransmission Line EquationsElectrical 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

Wave Optics Module

Electromagnetic Waves- Frequency Domain- Time Explicit- Transient- Beam Envelopes

Laser Heating

Feature Overview: Boundary Conditions

• Voltage source, Current source, & Insulating surfaces• Thick volumes of electrically resistive, or conductive, material• Thin layers of electrically resistive, or conductive, material• Perfectly conducting boundaries• Periodicity conditions• Connections to external circuit models• Lumped, Coaxial, and other Waveguide feeds• Electromagnetic wave excitations• Absorbing (Radiating) boundaries

Feature Overview: Domain Conditions

• Background Field excitation for scattering problems• Perfectly Matched Layer for modeling of free space

Half‐wave dipole antenna, surrounded by Perfectly Matched Layer

PEC Sphere illuminated by a background plane wave

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


Modeling of Conductive Geometries

http://www.comsol.com/showroom/gallery/11742/http://www.comsol.com/showroom/gallery/12621/http://www.comsol.com/showroom/gallery/8715/

• Geometrically very thin, highly conductive, electrically thicker than skin-depth – Perfect Electric Conductor (PEC) Boundary Condition, lossless, non-penetrable

• Geometrically very thin, conductive, and lossy– Transition Boundary Condition, lossy, skin-depth dependent penetration, modeled in 2D

• Conductive, electrically much thicker than skin-depth– Impedance Boundary Condition, lossy, non-penetrable

Thin copper layer modeled as PEC at 1.6 [GHz]

Very thin silver layer modeled via Transition Boundary Condition at 428 [THz]

Copper rod represented by Impedance Boundary Condition

Feature Overview: Material Models

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• 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

• RF Module supports loss tangents and dispersion models– Drude-Lorentz, and Debye dispersion

Feature Overview: Data Extraction

• Impedance, Admittance, and S-parameters• Touchstone file export• Far-field plots for radiation

Far‐Field Radiation Pattern

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Lumped Parameters Touchstone file export

Additional Modules for ElectromagneticsPlasma Module1 MEMS Module2 Particle Tracing Module3

Tunable Cavity FilterMicrowave Plasma Multipactor

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 needed2) Contains the same 3D electrostatic, electric currents in solids, and electric circuits capabilities as the AC/DC Module3) Does not require any other Modules

Additional Modules for Electromagnetics (cont’d)Semiconductor Module1 Wave Optics Module1

MOSFET Mach‐Zehnder Modulator

Solves for the electric potential and electron and hole concentrations in semiconductor materials.

1) Does not require any other Modules

Computes electric and magnetic fields for optical systems where the wavelength is comparable to or much smaller than the studied device or system.

The Optimization Module

• Gradient-Free optimization allows for optimization of geometric parameters, and allows for remeshing of the geometry.

- Nelder-Mead, Coordinate Search, and Monte Carlo algorithms.- Optimize one or more geometric dimensions for a CAD model created directly in COMSOL

Multiphysics or via the LiveLink™ products

• Gradient-Based optimization requires more user interaction to set up a differentiable objective function and a moving mesh, but can handle many more design variables, and can solve much faster.

- Adjoint method is used to compute exact sensitivities

Bowtie Antenna Optimization

Example Models, RF Module

Antennas

Waveguides & Transmission Lines

Scattering Problems

Periodic Problems

Electromagnetic Heating

Resonant Structures

Ferrimagnetic Problems

Passive Devices (Couplers & Filters)

Non-linear Material Modeling

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– Coil Resonance

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Verification of Eigenvalue Solvers


• 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

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


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:

• COMSOL also solves the time-harmonic transmission line equation for the electric potential for electromagnetic wave propagation along one-dimensional transmission lines :

• Typical examples:– Coaxial cable– Waveguides

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Connecting a 3D RF Model to a Circuit Model


• 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

Coaxial Cable to Waveguide Coupling


• A model of a coaxial cable feed that excites a propagating wave inside a rectangular waveguide

• S-parameters for transmission and reflection are computed

SMA connectorized GCPW


• Modeling a grounded coplanar waveguide (GCPW)• Two ways to terminate a CPW using a lumped port and an air-bridge• Excitation from a SMA connector with a coaxial lumped port

Passive Devices Example Models

• Passive devices like couplers, power dividers, and filters can be realized by combining resonant structures and transmission lines. COMSOL calculates the fields distribution, impedance, and S-parameters:

• Typical examples:– 3dB Couplers and Power Dividers– Band-pass Filters

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

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

Waveguide Iris Bandpass Filter


Frequency Selective Surface, CSRR


• One unit cell of the complementary split ring resonator (CSRR) with periodic boundary conditions to simulate an infinite 2D array

• Interior port boundaries combined with perfectly matched layer absorbing higher order modes

Lumped Element Filter


• 5-element maximally low-pass filter on a microstrip line circuit• 0402 surface-mount device (SMD) inductors and capacitors modeled using lumped

element features on 2D boundaries

• 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

Tunable Evanescent Mode Cavity Filter Using a Piezoelectric Device


Electromagnetic and Structural Analysis of a Microwave Filter on a PCB


• 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

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

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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


Vivaldi Antenna


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

Corrugated Circular Horn Antenna


• Designed using a 2D axisymmetric model• Low cross-polarization at the antenna aperture by combining TE mode excited at the

circular waveguide feed and TM mode generated from the corrugated inner surface

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

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Mie Scattering, Radar Cross Section of a Metal Sphere


• 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

User-defined Electric Displacement Example

• COMSOL can generate harmonics via a transient wave simulation, using nonlinear material properties:

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Second Harmonic Generation


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

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– Electromagnetic Band Gap Structures

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

Verification of Fresnel Equations


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

• Higher-order diffraction is captured

Plasmonic Wire Grating


• The 2D model can be easily expanded to 3D using periodic port.

Ferrimagnetic Example Models

• COMSOL can define any material as fully anisotropic. With the user-defined, tensor-formed relative permeability, a ferrite device can be analyzed by solving:

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Lossy Ferrite 3-Port Circulator

• A microwave circulator uses an anisotropic 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/http://www.comsol.com/showroom/gallery/968/

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: – Thermal Drift in a Microwave Filter Cavity– Microwave Ovens– Absorbed Radiation in Living Tissue– Tumor Ablation

Losses

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Absorbed Radiation (SAR) in the Human Brain


• 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

Documents

The RF Module - KESCO | 計測エンジニアリングシステム ... · Formulations per Module COMSOL Multiphysics1 RF Module AC/DC Module Static Electric Currents ... Plasma Module1