Aspects of RF Simulation and Analysis Software Methods ... frank zeppenfeldt.pdf · SAR...

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tE

∂∂

−=×∇ BtDJH

∂∂

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Aspects of RF Simulation and Analysis Software Methods

David Carpenter

Remcom

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HF Technology, May 15, 2006

Solving Maxwell’s Equations

Differential, integral and asymptotic approaches

Popular examples:

FEM (finite element method) – normally frequency domain

FDTD (finite difference time domain)BEM (boundary element method)MoM (Method of Moments)

GTD/UTD (Geometrical/uniform theory of diffraction) with SBR (shooting and bouncing rays)PO Physical Optics

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Finite Difference Time Domain Method

Explicitly solves Maxwell’s Equations in time domain

Subdivide geometry into spatial grid

Grid is small compared to wavelength

Grid is small compared to geometry features

Step through time

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FDTD ApplicationsAntennas-impedance, radiation, efficiency, matchingSAR determination for Cell Phones, Pagers, WiFiMRI designFCC Acceptance for Medical Implant Communications Service (MICS)Microwave Circuits, Waveguides, Fiber Optics, S-ParametersEMC/EMI, Shielding, Coupling Scattering, Radar Cross SectionPropagationPhotonicsSpecial Materials, including Nonlinear, Dispersive, Negative Index (NIM) and AnisotropicPlasmas (Exhaust, Re-entry)Lightning, EMP

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FDTD AdvantagesSimplicity: no Green’s functions, no matrices, no asymptotics, no shape functions

Wide frequency bandwidth from one calculation

Wide variety of materials: dielectric/magnetic, frequency-dependent, nonlinear, anisotropic

General geometries (computer memory not dictated by shape)

Scales well so suitable for electrically large problems

Fits well in parallel computer architectures

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FDTD Disadvantages

Moment Method does not need to solve for fields in free space

At very low frequencies the FDTD time step may be very small compared with the period of the sine wave, so many time steps may

be needed.

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Maxwell Curl Equations

Now assume 1-D propagation in z-direction

1-D Curl Equations

Faraday’s Law

Ampere’s Law

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Apply Finite Difference Approximation

Quantize Space and Time

z = k∆z t = n∆tLocate E and H fields centered in time and spaceApply finite differences

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Horn Antenna - Typical Application (1)

Pyramidal Horn AntennaIllustrate some of the capabilities of FDTD The horn geometry could be generated using CAD import, or using sweeping and/or shellingFor this example a built-in horn primitive of XFDTD will be used

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Enter the Horn Parameters for the Horn and Waveguide Feed as shown in the menu

Horn Antenna - Typical Application (2)

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Horn Antenna - Typical Application (3)

FD CAD object and mesh

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Horn Antenna - Typical Application (4)

Near Field display

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Horn Antenna E-Plane Gain Pattern

Antenna Far Zone Gain

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BioEM Applications (1)

FDTD well suited for Bio-EM analysis such as SAR (Specific Absorption Rate)

Usual to start with a model of the human body including all tissue details

FDTD models this well with a small mesh throughout

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BioEM Applications (2)

whereSAR – Specific Absorption Rate (W/kg)

- electrical conductivity (S/m)- magnitude of electric field (V/m)- material density (kg/m3)

z

zz

y

yy

x

xx EEESAR

ρ

σ

ρ

σ

ρ

σ

222

222

++=

zyxE ,,

SAR calculated from the electric fields and tissue characteristics

zyx ,,σ

zyxE ,,

zyx ,,ρ

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BioEM Applications (3)zyxE ,,

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GTD/UTD

General purpose ray-based electromagnetic analysis for radiation, antenna, scattering, propagation and EMC applications

A ray-based EM solver based on the UTD (Uniform Theory of Diffraction)

Evaluate E-fields using UTD with material dependent reflection, transmission and diffraction coefficients

Combine E-fields with antenna patterns to find received power, time and frequency domain E-field, far-zone radiation patterns, path loss, RCS, etc

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Hybrid SBR/GTD Approach

Objects and features are represented by vector dataPositions of Tx/Rx point are requiredFind geometrical ray paths by using a fast ray tracing procedurebased on the Shooting and Bouncing Ray (SBR) methodConstruct the geometrical optics and the edge diffracted paths from geometrical pathsEvaluate E-fields using the Uniform Theory of Diffraction (UTD) and material dependent reflection and transmission coefficientsCombine E-fields with antenna patterns to find signal strength, angle of arrival, etc.

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Line-of-Sight Rays and Reflected Rays

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Diffracted Rays

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Multiple Transmitters and Interactions

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Suitable for electrically large models (1)

Geometric features should be greater than a wavelength

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Suitable for electrically large models (2)

Model size/computation time limited by number of facets, edges and vertices

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May include creeping waves

Creeping wave propagation allows propagation across surfaces andaround cylinders etc.

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May be used for propagation studies (1)

Indoor

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May be used for propagation studies (2)

Outdoor

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May be used for propagation studies (3)

Time of arrival

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May be used for propagation studies (4)

Outdoor - Indoor

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Summary

There are a number of methods for EM simulation

All have strengths and weaknessesSelect the correct method for the application

Most commercial packages are relatively easy to use based on latest GUIs

Graphical images provide an insight into results that hand calculations and simple numerical methods may not.