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Computational electromagnetics techniques have reached a level of maturity which allows their use in SAR assessments of professional and consumer wireless communication devices. In the recent past, SAR compliance assessments for small transmitters were performed almost exclusively through measurements.
The increasing cost of assessing product compliance with exposure standards calls for new techniques.
Such techniques should be time efficient and cost effective. Some wireless communication devices are used in situations where experimental SAR assessment is extremely complex or not possible at all. National regulatory bodies, e.g. the U.S. Federal Communications Commission, encourage the development of consensus standards and encouraged the establishment of this subcommittee. The benefits to the users and the regulators include standardized and accepted protocols and standardized anatomical models, validation techniques, benchmark data, reporting format and means for estimating the overall uncertainty in order to produce valid, repeatable, and reproducible data.
The scope of this project is to describe the concepts, techniques, models, validation procedures, uncertainties and limitations of the Finite-Element Method when used for determining the spatial-peak specific absorption rate (SAR) in standardized models exposed to wireless communication devices, in particular vehicle-mounted antennas and personal wireless devices such as handheld mobile phones. It recommends and provides guidance on modeling of wireless devices and provides benchmark data for simulation of such models. It defines model contents, guidance on meshing and test positions at the anatomical models. This document will not recommend specific SAR values since these are found in other documents, e.g., IEEE C95.1-1999.
The purpose of this document is to specify numerical techniques, anatomical models, and models to determine spatial peak specific absorption rates (SAR) in the human body of persons exposed to wireless communication devices, in particular vehicle-mounted antennas and personal wireless devices such as handheld mobile phones. SAR will be determined by applying Finite-Element simulations of the electromagnetic field conditions produced by wireless devices in standardized models of the human anatomy. Intended users of this practice will be (but will not be limited to) wireless communication devices manufacturers, service providers for wireless communication that are required to certify that their products comply with the applicable SAR limits, and government agencies.
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Finite Element Method : This standard applies the Finite-Element Method (FEM) to calculate SAR. The reasons for using FEM include its proven track record in a broad range of electromagnetic applications, and its ability to use a tetrahedral mesh that conforms to complicated geometries, employing arbitrarily small elements where needed and not-very-small elements elsewhere. In order to determine the applicability of this standard, it shall be clear whether a specific numerical solution of Maxwell’s equations qualifies to be considered an implementation of FEM.
This is not entirely straightforward since there are multiple ways to solve Maxwell’s equations with FEM.
Implementations can be based on fields or on potentials, and may involve minimization of an energyrelated functional [B1, B2]. All implementations have the following in common:
• They are based on differential equations, not on integral equations.
• The size of the computational domain is finite. Radiation towards infinity is implemented through an absorbing boundary condition, a Perfectly Matched Layer, or an implementation of the
Boundary Element Method (BEM) on outer boundaries. Radiated fields outside the domain can be computed by integrating over a boundary that encloses the radiating structure.
• After applying excitations and boundary conditions and discretizing the computational domain into a mesh, a matrix equation results in which the matrix is large, sparse, and banded. “Large” is a consequence of having a large number of unknowns, several per mesh element on a large mesh.
“Sparse” and “banded” are consequences of the fact that all interactions are formulated as local interactions.
• In the limit of infinitesimally small mesh elements, the solution approaches the exact solution to
Maxwell’s equations.
Elsewhere in this document a set of tests is described with which one can determine whether a particular implementation of FEM is correct and sufficiently accurate to be used for SAR certification.
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The local specific absorption rate (SAR) in a given location in tissue is defined by where E
SAR = E • J conj
/ (2 ρ ) = σE
is the electric field vector, J conj
2 /(2ρ) (4.1.1) is the conjugate of the volume current density, ρ is the mass density of the tissue, E is the magnitude of the electr ic field vector and σ is the electric conductivity. Since local SAR can vary strongly with position, the quantity of interest is often average SAR. Contemporary safety standards and guidelines specify time-averaged whole-body-averaged SARs and peak spatialaverage SARs, neither of which should be exceeded. The spatial SAR is usually averaged over a specified volume, e.g., 1 g of tissue in most of the body or 10 g of contiguous tissue in an extremity of the body
[B132].
IEEE Std. 1528.1 describes how to compute spatial-average SAR on a rectangular grid. In the finiteelement method, the electric field, and hence the local SAR, is known everywhere, but the rectangular grid is not inherently available. Therefore, the algorithm that computes the spatial-average SAR in finite elements needs to create a rectangular virtual grid overlaying the finite-element mesh. This grid shall consist of points spaced d millimeters in the X, Y and Z directions, where the value of d corresponds to the recommended voxel size for the given application as given in 1528.2 and 1528.3. Each grid point will be the center of a cube of d×d×d mm 3 . These cubes take the role of voxels as described in the SAR-averaging algorithm in 1528.1. The geometry in the model shall be oriented such that the antenna be aligned as much as possible with the grid.
Once this virtual grid has been defined, the algorithm of 1528.1 can be applied to compute spatial-average
SAR.
In FEM simulations, the input power is often delivered to the device by means of a port with a known characteristic impedance. Depending on the input impedance of the device, a certain power level is accepted. The simulation results, including SAR, will be relative to this accepted power. To obtain the SAR for a different accepted-power level, the SAR results can be adjusted by scaling the results:
SAR scaled
= SAR computed
P acc,
P acc, desired computed
(3.3.1) where P acc, desired
is the desired accepted power (e.g. 0.6 W) and P acc, computed by the FEM simulation, e.g. 1 W/(1-|S
11
| 2 ).
is the accepted power computed
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Assuming the Finite-Element code has been implemented correctly, which can be determined with the tests described in the next chapter, some uncertainties remain. This chapter lists the most important ones and shows how they can be combined to obtain a measure of total uncertainty. It follows the chapter on
Computational Uncertainty in IEEE Std. 1528.1 with modifications appropriate to the Finite Element
Method. As stated in that chapter, the computational uncertainties can be divided into the following three categories: a) positioning accuracy and uncertainty due to mesh density, b) accuracy of the numerical method, c) accuracy of the numerical representation of the actual DUT.
This chapter defines general procedures for the evaluation of the uncertainty. In later chapters, when applied to specific applications, there may be modifications appropriate to those applications.
It is recommended to define a standard modeling of the test configuration (e.g., kind and location of the absorbing boundary with respect to the phantom, mesh density, etc.) and to determine the uncertainty parameters for these in a generic global way that are valid for all tests of the particular setup.
4.2.1 Positioning
In the modeling environment, positioning can be done with high accuracy. The finite-element mesh will conform to the surfaces and not change the separation between source and phantom. Therefore, it is to be expected that the uncertainty in the positioning will be small. To quantify the effect of this uncertainty, the distance between the phantom and the source shall be varied by ± 0.1% of a free-space wavelength. The deviation of the target quantity (e.g., peak spatial-average SAR) shall be reported which corresponds to the uncertainty (rectangular distribution).
4.2.2 Mesh density
The mesh density has a major impact on the accuracy of the results. Therefore, SAR results produced with a particular mesh need to be compared with SAR results produced with a denser mesh. If your finiteelement code does not employ adaptive mesh refinement, set the number of mesh elements per wavelength
(material dependent) for the initial mesh first to 1.15 times and then to 1.3 times the default value and both times rerun the entire simulation. This default value shall be at least ten if you are using linear basis and test functions, and be at least three if you are using quadratic basis and test functions, such as H1 curl elements.
If your finite-element code uses adaptive mesh refinement, perform extra adaptive passes until the number of mesh elements has increased by at least 20%. In any case, the maximum SAR deviation shall be reported.
4.2.3 Absorbing boundaries or PMLs
The impact of the absorbing boundaries or PMLs should be determined by moving the boundaries outward by a quarter of a wavelength for several test cases, e.g., dipoles at the extreme locations of the DUT (closest to the phantom and closest to the absorbing boundary). The maximum deviation of the target quantity (e.g., peak spatial-average SAR) shall be reported.
4.2.4 Power budget
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The sum of the absorbed and radiated power should be compared to the power entering the computational domain at the source. Their difference corresponds to the tolerance (normal distribution).
Table 1 Budget of the uncertainty contributions of the positioning, mesh density and the numerical method a
Uncertainty b
Section
Component
Positioning 4.2.1
4.2.2 Mesh density
Absorbing boundary
4.2.3
Power budget
4.2.4
Combined std. uncertainty (k=1) c
Tolerance in dB d
Probability distribution
R
N
N
N e
Divisor f(d,h)
1.73
1
1
1 f c i
1
1
1
1 g
Uncertainty in dB h
(v v i
) eff
2 or
Refer to the corresponding section in IEEE Std. 1528.1 (section 4.3).
The total uncertainty budget is calculated in the same way as in the corresponding section of IEEE Std.
1528.1 (section 4.4.)
Table 2 Numerical uncertainty budget a
Positioning, mesh, method
Numerical representation of the DUT b
4.2
4.3
Combined Std.
Uncertainty (k=1)
Expanded Std. Uncertainty
(k=2) c
d
N
N e
f(d, h)
1
1 f g
i
1
1 h
i
eff
2
This chapter provides procedures for the following two levels of code validation.
Code Performance Validation
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Canonical Benchmarks
An implementation of the Finite Element Method can be validated by the manufacturer according to the benchmarks defined in this chapter. A code that has passed the quality criteria can be labeled as “Compliant with IEEE 1528.4”. This chapter follows the chapter on Code Validation in IEEE Std. 1528.1 with modifications proper to the Finite Element Method. Below, the objectives of the different levels of validation are described.
5.1.1 Code performance validation
The code performance validation provides methods to determine that the finite-element algorithm has been implemented correctly and works accurately within the constraints due to the finite numerical accuracy. It further determines the quality of absorbing boundary conditions and certain parts of the post processing algorithms. All canonical benchmarks can be compared to analytical solutions of the physical problem or its numerical representation. The methods characterize the implementation of the finite-element algorithm in a very general way. They are defined such that it is not possible to tune the implementation for a particular benchmark or application without improving the overall quality of the code.
5.1.2 Canonical benchmarks
The canonical benchmarks assess the cumulative accuracy of a code and its applicability considering the interaction of its different modules, such as mesh generation, computational kernel, representation of sources, data extraction algorithms of the post processor, etc.
5.2.1 Propagation homogeneous medium
A straight rectangular waveguide with ports on both ends is well suited as a first test of an implementation of the Finite-Element Method. The waveguide shall have a width of 20 mm, a height of 10 mm and a length of 300 mm. The waveguide shall be filled homogeneously with a material which, in three separate simulations, shall assume the following properties: i. ε ii. ε r r
= 1, σ = 0 S/m;
= 2, σ = 0 S/m; iii. Re( ε r
) = 2, σ = 0.2.S/m.
To verify that the mesh is independent of orientation, rotate the waveguide such that it is not parallel with
10
mode at 10 GHz. any principal coordinate plane (XY, XZ, YZ). The waveguide is to be driven in the TE
To be reported are the magnitudes of S
21
and S
11
, as well as the values of the real and imaginary parts of the propagation constant γ. T he table below provides the reference values [B17] and criteria for passing this test.
Re( ε r
)
σ
|S
21
| rerefence value
Criterion for |S
|S
11
| reference value
Criterion for |S
21
11
|
|
Re(γ) reference value
Criterion for Re(γ)
Im(γ) reference value
Criterion for Im(γ)
1
0
1
≥ 0.9999
0
≤ 0.
003
0
± 0.1 m
± 2%
-1
138.75 m -1
2
0
1
≥ 0.9999
0
≤ 0.003
0
± 0.1 m
± 2%
-1
251.35 m -1
2
0.2
8.7 × 10
± 5 × 10
0
≤ 0.00
3
31.17 m
± 2%
± 2%
-5
-6
-1
253.28 m -1
Table 3 Criteria for the waveguide evaluation
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The criteria for passing have been chosen such that any correct FEM implementation can pass the test with ease.
An additional benefit of this test is that it can tell the user what, in his FEM implementation, the maximum allowable mesh element size is relative to a wavelength.
5.2.2 Planar dielectric boundary
In order to test the reflection of a plane wave by a dielectric boundary, a rectangular waveguide can again be used. It is well known that the TE
10
mode can be thought of as a superposition of two plane waves
[B17]. Each wave’s direction of propagation makes an angle θ with the axis of the wave guide, given by cos 2 θ = 1 – (c/2af) (5.1) 2 where c is the speed of light, a is the width of the wave guide and f is the frequency.
Assuming the axis of the waveguide is the Z axis and assuming the waveguide is filled with vacuum for
Z>0 and filled with dielectric 1 with complex relative permittivity ε r
for Z<0, Fresnel reflection coefficients for the TE and the TM cases, defined as ratios of electric field strengths, are given by [B18]
R TE = (k
0,z
– k
1,z
) / (k
0,z
+ k k
0,z
1,z
)
+ k
1,z
)
(5.2)
(5.3) R TM = (ε r k
0,z
– k
1,z
) / (ε r where k
0,z and k
1,z denote the z component of the propagation vector of the plane wave in vacuum and in the dielectric, respectively. They can be evaluated through k
0,z cosθ (5.4) k
1,z
= k
= k
0
0
√(ε r
– sin 2 θ)
Finally, ε r
is complex and is given by
(5.5) where Re( ε
ε r
= Re( ε r
) – jσ/(2πfε
0
) (5.6) r
) denotes the real part of the relative permittivity and σ is the conductivity of the medium.
For this test, create a 20 mm × 10 mm waveguide with a length of 60 mm, as shown in Figure 1. Fill the top half with vacuum and the bottom half with dielectric.
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Figure 1 Waveguide filled half with vacuum and half with dielectric
In one copy of the model, all side walls shall be lossless metal, such that the dominant mode is the TE
10 mode with propagation constant 138.75 m -1 at 10 GHz and represents the TE case in the reflection analysis.
In another copy of the model, the side walls that are parallel to the XZ plane shall be perfect magnetic conductor while the other walls be perfect electric conductor, such that the second mode (after a TEM mode which won’t be used in this test) has propagation constant 138.75 m at 10 GHz and represents the
Re(ε r
2
2
2
TM case in the reflection analysis.
Before simulation, rotate the waveguides over an arbitrary angle such that no face is parallel with any coordinate plane. Drive the waveguides with 10 GHz in the proper mode. In doing so, it is good practice to enable all propagating modes, but the coupling between modes is expected to be negligible. Simulations are to be run for the cases of lossless and lossy dielectric as shown in Table 4. For the Finite-Element code to pass the test, results need to be within 2% of the analytical values given in Table 4.
) σ (S/m)
0
0.2
1
R TE
0.4739
0.4755
0.5105
R TM
0.1763
0.1779
0.2121
Table 4 Reflection at a dielectric interface
5.2.3 Absorbing boundary condition (ABC) or Perfectly Matched Layer (PML)
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1
2
A proper implementation of an absorbing boundary condition or a PML should absorb waves that strike it.
However, absorption cannot be perfect, especially when the wave strikes at a large angle from normal incidence. A way to test the boundary condition or the PML is to place it at the end of a rectangular waveguide. Signals propagating in a rectangular waveguide in the TE
10
mode can be thought of as two plane waves bouncing off the sidewalls as they travel down the waveguide. The angle of their propagation directions with the axis of the waveguide is given by Eq. (5.1). What matters for this test is the fact that the angle with the axis is small for high frequencies and tends to 90 degrees as the frequency goes down towards cutoff.
For this test, a 20 mm × 2 mm rectangular waveguide with a length of 60 mm shall be fed with a port on one end and terminated with an absorbing boundary condition or a PML at the other end. A copy of this geometry shall also have a port on one end and an ABC or PML at the other end, while having Perfect
Magnetic Conductor (PMC) boundaries on the 2 mm × 60 mm sides. The latter structure would represent a parallel-plate waveguide and is to be excited with the TEM mode, so the power strikes the ABC or PML
The test is to be repeated with the waveguide filled with homogeneous lossless dielectric with relative permittivity ε
ε r perpendicularly.
The rectangular-waveguide models are to be simulated at 10, 20 and 30 GHz. This frequency sweep will involve a wide range of angles at which the plane waves strike the ABC or PML. The parallel-plate model is to be simulated at 10 GHz. r
=2.
Table 5 presents the valid ranges of S
11
for these tests.
S
11
for TE
10
mode at 10 GHz
< -10 dB
< -15 dB
S
11
for TE
10
mode at 20 GHz
< -20 dB
< -25 dB
S
11
for TE
10
mode at 30 GHz
< -30 dB
< -35 dB
S
11
for TEM mode at 10 GHz
< -40 dB
< -40 dB
Table 5 Valid ranges for S
11
It is expected that any FEM code with a correct implementation of the second-order ABC and/or the PML will produce a result many dB below these limits. They are not intended to be a stress test but to determine whether an FEM code has been implemented correctly.
5.2.4 SAR averaging
Refer to the section “SAR averaging” in IEEE Std. 1528.1 (section 5.2.4. )
5.3.1 Generic dipole antenna
The feed-point impedance and the far-field pattern of a dipole antenna (half-wavelength dipole at 1 GHz) shall be evaluated at 1 GHz. The dipole has a length of 150 mm and a diameter of 4 mm. The feeding gap size is 2 mm. The computational domain shall extend at least 200 mm from the dipole in all directions.
The quantities for evaluation and the maximum permitted error are given in table 6. The power budget is defined as the difference between the radiated power as determined by the far-field evaluation and the
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IEEE P1528.4/D1.0, <month> <year> accepted power as determined from S
11
. Reference results computed with the Method of Moments are provided in a file on the CD that is shipped with this standard.
Table 6 - Results of the dipole evaluation
Quantity
Re(Z) at 1.0 GHz
Im(Z) at 1.0 GHz
Frequency for Im{Z} = 0
Power budget 1.0 GHz
Result Limit
40 Ω < Re{Z} < 140 Ω
30 Ω < Im{Z} < 130 Ω
850 MHz < f < 950 MHz
5%
5.3.2 Microstrip terminated with Absorbing Boundary Condition or Perfectly Matched
Layer.
The propagation constant and wave impedance of a microstrip line and the reflection coefficient for quasi-
TEM operation shall be evaluated.
Figure 2 - Geometry of the micro strip line
The substrate is lossless and has a relative permittivity of 4. The geometry of the micro strip line is given in
Figure 2. The line is to be terminated with an absorbing boundary condition or with a PML. For an impedance close to 50 Ω, the width w of the micro strip and the heigh t h of the substrate shall be 1.0 mm and 0.5 mm, respectively. The thickness of the stripline is negligible with respect to the other dimensions of the geometry. It can therefore be modeled as an infinitely thin sheet.
The propagation constant, the characteristic impedance and the reflection coefficient |S
11
| shall be reported at 1 GHz.
Quantity Reference Limit
Propagation constant
Characteristic impedance (real)
Characteristic impedance (im)
|S
11
|
36.9 m
50.
6 Ω
0
0
-1
Deviation from reference
± 3%
± 5
2 Ω
Ω
-20 dB
Table 7 - Results of the micro-strip evaluation
5.3.3 SAR calculation SAM phantom / generic phone
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The benchmark described in Beard et al. [B19] shall be repeated for the SAM phantom with the generic phone in the “touch” and the “tilted” position as described in IEEE 1528 [B20] at 835 MHz and at 1900
MHz. To be reported are the 1-g and 10-g peak spatial average values for the two positions and frequencies. The SAR results shall be normalized to the feed-point power. They must be within the standard deviation reported by Beard et al. [B19]. Supplemental information on the configuration can be found in Kainz et al [B21].
5.3.4 Setup for system performance check
Refer to the corresponding section in IEEE Std. 1528.1.
As stated in IEEE Std. 1528.2 in the chapter on Test Device Modeling, the two relevant elements that define the exposure condition in vehicular environments are: the communication device(s) antenna(s) and the vehicle body itself. The pavement shall also be included, especially in the case of bystander exposure models, while in passenger exposure models it can be neglected. Refer to the section on test device modeling in 1528.2 for a general introduction into the transceiver, the antenna and the vehicle.
6.1.1 Vehicle modeling
For reliable and repeatable simulations the specific CAD model has been defined and is available. To conduct a successful simulation according to the present document this standard CAD model of the vehicle shall be used. The computational model of the vehicle body will comprise mainly perfect electric conductor
(PEC). It is important that the mesh of the model be inspected to ensure continuity of the metal sheets forming the vehicle body where appropriate. These metal sheets can be modeled as a collection of thin layers, properly interconnected among them; as volumetric PEC objects; or as a combination of thin and volumetric objects.
Modeling of windows glasses is not necessary, as the electromagnetic field scattering by the glass surfaces is a second order effect compared with that produced by PEC. Likewise, the modeling of dielectric parts within the vehicle is not necessary. Certain external parts of the vehicle like front and rear bumpers may also have PEC properties in the model. This can be done only with those parts in the car model. In general it will be allowed to assign PEC properties to dielectric parts if it is believed that the conservative nature of the assessment is enhanced in so doing, but in no circumstance when the resulting metal body alters significantly the electromagnetic energy path to the exposed subject (e.g., if using metal in lieu of window glass in the case of exposure inside the vehicle due to an antenna mounted on the outside of the body).
Rear window defoggers are frequently encountered in practice. Defogging elements are high resistivity conductors that warm up when conducting DC currents. From an electromagnetic point of view they are scatterers that may act adversely to RF energy flow through the window. In most cases they are laid out horizontally following a vertical array pattern, thus will interact more with fields featuring horizontally polarized rather than vertically polarized electric fields. For the purpose of this standard, the effect of defoggers will be neglected.
6.1.2 Communications device modeling
Refer to the section on communications device modeling in IEEE Std. 1528.2, replacing the abbreviation
FDTD by FEM. As stated in that section, because of the linearity of the electromagnetic model, simulations
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The antenna shall be driven by a port. As a consequence, antenna input power, input impedance and return loss are readily available, and the input power can be scaled such that the antenna output power reaches the correct level. In case a matching circuit is to be included, keep the characteristic impedance of the port realvalued and realize reactances through lumped elements near the port.
6.1.3 Exposed subject modeling
Refer to the section on exposed subject modeling in IEEE Std. 1528.2. As stated in that section, the exposed subject can be modeled by the “Visible Human” model discussed there and available with that standard. Developers of FEM software will need to incorporate this “Visible Human” model into the FEM model. Since all objects in the “Visible Human” model consist of cubic cells, a.k.a. voxels, which form approximations of the true shapes of the objects they represent, and since the FEM mesh will consist of tetrahedra, it is appropriate not to represent all the cubes exactly in the FEM model. A typical deviation of half a voxel size between the “Visible Human” and the corresponding objects in the FEM model is acceptable.
6.1.4 Exposure conditions
Refer to the section on exposure conditions in IEEE Std. 1528.2. That section presents and explains the necessary considerations for passengers and bystanders.
6.1.5 Accounting for whole-body average SAR in different-size human bodies
Refer to the section on whole-body resonance in IEEE Std. 1528.2.
Refer to the chapter on validation of the numerical models in IEEE Std. 1528.2, replacing FD-TD by FEM, and replacing the FD-TD grid resolution by the density of the FEM unstructured mesh.
Refer to the chapter on computational uncertainty in IEEE Std. 1528.2 with the following modifications:
The finite-element simulation code is to be validated according to chapter 5 of this document, IEEE
Std. 1528.4
, usually by the software vendor;
The uncertainty of the numerical algorithm shall be evaluated according to chapter 4 of this document,
IEEE Std. 1528.4.
Other than that, the procedure outlined in 1528.2 can be followed to arrive at a total uncertainty budget for exposure simulations with vehicle-mounted antennas and bystander and/or passenger models.
Refer to the chapter titled Benchmark Simulation Models in IEEE Std. 1528.2.
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The following sections present each step that needs to be taken in computing SAR in a head or body phantom from a personal wireless communication device, such as a mobile phone. In the following, this device will be called the Device Under Test (DUT).
7.1.1 Geometry
In the Finite-Element Method, when a mesh consisting of tetrahedra is used, “staircasing” of curved surfaces does not occur. However, the calculation of spatial-average SAR relies on cubical volumes of which the orientation matters. Therefore, the procedure of 1528.3 needs to be followed: the DUT model be aligned in parallel with one of the principal planes of the coordinate system and the SAM head phantom be rotated in order to achieve its proper orientation relative to the DUT.
7.1.1.1 Head and body phantom models
Refer to the sections on head and body phantom models in 1528.3.
7.1.1.2 DUT model
The DUT (mobile phone) model normally contains many different solids, typically more than one hundred, making this model a very complex structure to handle. As a minimum requirement, parts such as: antenna, chassis, printed circuit board (PCB), display, battery, other large metal components and the dielectrics supporting and surrounding the antenna have to be included in the model.
In order to save computational resources it is recommended that components in the DUT model that do not have any impact on the emitted RF fields are removed, for instance components located inside shield-cans.
The most important parts of the DUT model are the metallic components since they have the biggest impact on the RF fields. Particular care must be taken to ensure that electrical connections between metal objects be preserved, so that that artificial floating does not occur.
Usually the PCB is not well represented in the CAD model and it should preferably be represented by few thin metallic layers filled with dielectric material. It is acceptable to model it as one thick solid metal, since doing so is unlikely to lead to under-estimation of the SAR.
The battery can be modeled as a single metal object, connected electrically to other metal objects to avoid artificial floating.
For the source in the Finite Element Method, the same consideration applies as for the FD-TD feed-gap source model: it may be necessary to remove a small part such as a feeding pin from the original CAD model to create room to insert a source. The source will be an electric gap source with a real-valued characteristic impedance. If a source model exists that includes lumped circuit elements, e.g. elements for which the values were obtained from circuit simulation of the final stage of the RF amplifier, then these lumped elements may be included close to the source but still separate from it. See IEEE Std. 1528.3, the section titled “RF Source”, for the required accuracy in computing the antenna driving point impedance.
7.1.1.3 Positioning of the DUT at the phantom
Refer to the corresponding section in 1528.3.
7.1.2 Mesh generation
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In the Finite-Element Method, the mesh will automatically conform to the geometry, adjusting itself to oblique faces and to small details. However, curved surfaces can only be approximated by the mesh, since the mesh elements are tetrahedra with flat faces. For curved surfaces in the mobile phone, it is sufficient if the mesh elements approximate the true surfaces to an accuracy of 0.1 mm. This corresponds to the accuracy recommended in 1528.3 for the FD-TD grid in the phone. As stated in 1528.3, this can be relaxed for parts like the housing far from the touching area. For curved surfaces in the phantom, the mesh near the
DUT should approximate the true surface of the phantom with an accuracy of 0.25 mm, while farther away,
2 mm is sufficient, at least up to 2 GHz. This corresponds to the accuracy recommended in 1528.3 for the
FD-TD grid in the phantom.
In large homogeneous volumes like the inner head and the air, one needs to ensure that the initial mesh be fine enough to have the proper number of elements per wavelength. What this number is depends on the type of basis functions used in the Finite Element method and was determined with the waveguide test in section 5.1 of this IEEE Std. 1528.4.
7.1.3 Simulation Parameters
7.1.3.1 Boundary conditions
On the outer faces of the computational domain, an absorbing boundary condition or a PML will need to be applied. The absorbing boundary should be located at least λ/4 from all objects , where λ denotes the free space wavelength, while the PML can be located as little as λ/10 from all objects. On the side of the phantom away from the phone, the fields are expected to be weak and the boundaries can be brought closer to the phantom.
7.1.3.2 Source signal
In a frequency-domain simulation, the simulation frequency will typically be set to the expected resonance frequency of the antenna in its operating environment. Since the excitation is sinusoidal and steady state, one need not specify an excitation bandwidth or duration.
7.1.4 FEM simulation
The section on mesh generation provided guidelines for the mesh density and accuracy. Still, the initial mesh is rarely of good-enough quality to capture all the field gradients. If the finite-element software doesn’t have automatic adaptive mesh refinement, increase the number of mesh elements per wavelength by 25%, rerun the simulation and re-evaluate the maximum average SAR. Repeat this until the maximum average SAR changes by less than 5% from one iteration to the next. If the finite-element software has automatic adaptive mesh refinement, perform up to five adaptive passes at the expected resonance frequency, allowing a mesh growth of at least 30% per pass. The number of adaptive passes can be fewer than five if S
11
changes by less than 0.02 from one pass to the next while S
11
<0.5, the latter condition indicating that the simulation frequency is close to the resonance.
The resulting fields will be steady-state fields at the chosen frequency. A frequency sweep is necessary for two reasons: (1) To confirm that mesh adaptation has been done close enough to the resonance frequency to include all relevant field effects; and (2) to evaluate SAR at the resonance frequency itself rather than close to it.
Once an FEM simulation has been completed, the coefficients of the basis functions are known explicitly in all the mesh nodes and possibly some special mesh points such as edge and face centers. Since the basis functions are known everywhere inside the mesh elements, the fields are also known everywhere. Then, the
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IEEE P1528.4/D1.0, <month> <year> determination of SAR in a volume simply involves the integration of σ E 2 /(2ρ) over that volume. It is not necessary that that volume coincide with a group of mesh elements. It can be a small cube that cuts through tetrahedral mesh elements.
For the purpose of compliance, a peak value of the SAR averaged over 1 g or 10 g of cube-shaped tissue has been specified. In IEEE Std. 1528.1 a detailed description of an approach for finding spatial average
SAR is given. Chapter 4 of this Recommended Practice details how to apply this in conjunction with the
Finite Element Method.
Refer to the chapter on Benchmark Validation Models in IEEE Std. 1528.3.
Refer to the chapter on Computational Uncertainty in IEEE Std. 1528.3.
[B1] P.P. Silvester and R.L Ferrari, “Finite Elements for Electrical Engineers”, Cambridge University
Press, second edition 1990, ISBN 0 521 37829 X (paperback) 0 521 37219 4 (hardcover)
[B2] Jianming Jin, “The Finite Element Method in Electromagnetics”, John Wiley and Sons, Inc.,
1993, ISBN 0-471-58627-7
[B3] Z.J. Cendes and J. Lee, “The Transfinite Element Method for Modeling MMIC Devices”, IEEE
Transactions on Microwave Theory and Techniques, Vol. 36, No. 12, pp. 1639-1649, December 1988
[B4] J.E. Bracken, D.K. Sun and Z.J. Cendes, “S-Domain Methods for Simultaneous Time and
Frequency Characterization of Electromagnetic Devices”, IEEE Trans. MTT, Vol. 46, No. 9, pp. 1277-
1290, September 1998.
[B5] D.-K. Sun, Z.J. Cendes, J.-F. Lee, “ALPS - A new fast frequency-sweep procedure for microwave devices”, IEEE Trans. MTT, Vol. 49, No. 2, pp. 398 – 402, Feb. 2001.
[B6] O. Ramahi and R. Mittra, “Finite-element analysis of dielectric scatterers using the absorbing boundary condition”, IEEE Trans. Magnetics, Vol. 25, no. 4, pp. 3043-3045, July 1989.
[B7] J.P. Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves”,
Journal of Computational Physics, No. 114, pp. 185-200, 1994.
[B8] J-Y Wu, D.M. Kingsland, J-F Lee and R. Lee, “A Comparison of Anisotropic PML to
Berenger’s PML and Its Application to the Finite-Element Method for EM Scattering”, IEEE Trans. Ant.
Propagat., Vol. 45, no. 1, pp. 40-50, 1995.
[B9] N. Appannagari, I. Bardi, R. Edlinger, J. Manges, M.H. Vogel, Z. Cendes, J. Hadden,
“Modeling phased array antennas in Ansoft HFSS”, Proceedings of the 2000 IEEE International
Conference on Phased Array Systems and Technology, 21-25 May 2000, pp. 323-326.
[B10] P.P. Silvester and G. Pelosi, “Finite Elements for Wave Electromagnetics”, pp. 177-194, IEEE
Press, 1994, ISBN 0-7803-1040-3
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IEEE P1528.4/D1.0, <month> <year>
[B11] M.A. Morgan, C.H. Chen, S.C. Hill and P.W. Barber, “Finite-Element Boundary-Integral
Formulation for Electromagnetic Scattering”, Wave Motion, Vol. 6, pp. 91-103, 1984.
[B12] J.D. Collins, J.L. Volakis, J-M Jin, “A Combined Finite Element – Boundary Integral
Formulation for Solution of Two-Dimensional Scattering Problems via CGFFT”, IEEE Trans. Antennas
Propagat., Vol. 38 no. 11, pp. 1852-1858, Nov. 1990.
[B13] X. Yuan, D.R. Lynch, J. W. Strohbehn, “Coupling of Finite Element and Moment Methods for
Electromagnetic Scattering from Inhomogeneous Objects”, IEEE Trans. Antennas Propagat., Vol. 38, no.
3, pp. 386-393, 1990.
[B14] IEEE Std C95.3-2002, “IEEE Recommended Practice for Measurements and Computations of
Radio Frequency Electromagnetic Fields With Respect to Human Exposure to Such Fields, 100 kHz-300
GHz”
[B15] Vogel, M.H., and Kleihorst, R.P., “Large-Scale Simulations Including a Human-Body Model for MRI”, Proceedings of the IEEE International Microwave Symposium, June 2007.
[B16] Italian National Research Council, Institute for Applied Physics (2005) “Dielectric Properties of
Body Tissue in the Frequency Range 10 Hz – 100 GHz”, Florence, Italy
[http://niremf.ifac.cnr.it/tissprop/]
[B17] Rizzi, P.A.., “Microwave Engineering – Passive Circuits,” Prentice Hall, Inc., 1988.
[B18] Chew, W.C., “Waves and Fields in Inhomogeneous Media,” IEEE Press, 1995, Chapter 2.
[B19] Beard, B.B., Kainz, W., Onishi, T., Iyama, T., Watanabe, S., Fujiwara, O., Wang, J., Bit-Babik,
G., Faraone, A., Wiart, J., Christ, A., Kuster, N., Lee, A., Kroeze, H., Siegbahn, M., Keshvari, J.,
Abrishamkar, H., Simon, W., Manteuffel, D., and Nikoloski, N., “Comparisons of computed mobile phone induced SAR in the SAM phantom to that in anatomically correct models of the human head,”
IEEE Transactions on Electromagnetic Compatibility, Vol. 48 , No. 2, pp. 397-407, 2006.
[B20] IEEE Std 1528™-2003, IEEE Recommended Practice for Determining the Peak Spatial-
Average Specific Absorption Rate (SAR) in the Human Head from Wireless Communications Devices:
Measurement Techniques.
[B21] Kainz, W., Christ, A., Kellom, T., Seidman, S., Nikoloski, N., Beard, B., and Kuster, N.,
“Dosimetric comparison of the specific anthropomorphic mannequin (SAM) to 14 anatomical head models using a novel definition for the mobile phone positioning,” Physics in Medicine and Biology,
Vol. 50, pp.1075-1089, 2005
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IEEE P1528.4/D1.0, <month> <year>
Silvester and Ferrari [B1] and Jin [B2] offer a detailed explanation of how the Finite Element Method is derived from Maxwell’s equations.
Excitations can be implemented through ports, which excite modes on transmission lines. This can be done in such a way that an S (scattering) matrix is produced automatically after solving the matrix equation. This is called the Transfinite Element Method and is discussed by Cendes and Lee in [B3].
Other possible excitations include voltage sources and incident waves. Incident waves are not limited to plane waves, but can also be spherical waves, cylindrical waves, Gaussian beams, and radiated fields produced by a simulation of an antenna in a different location in a separate model.
In the Finite-Element Method, the computational domain is divided into many small volumes, the mesh elements, within which the field is approximated by simple basis functions with initially unknown coefficients. Mesh elements can have multiple shapes, such as bricks, prisms, tetrahedra and general hexahedra.
Brick-shaped elements in FEM have their use in simple geometries only. In the Finite-Difference Time-
Domain Method one can make brick-shaped cells small and numerous enough to approximate a complicated geometry well. Also, techniques exist to compensate for “staircase” approximations of surfaces. In FEM, though, that isn’t the case. Brick-shaped elements in FEM are not appropriate to model real-life wireless devices, their antennas, and human bodies.
Prism-shaped elements in FEM can be useful in layered geometries, such as printed circuit boards. They are not appropriate, though, to model real-life wireless devices, their antennas, and human bodies.
A tetrahedral mesh has the flexibility to combine small elements where needed with larger elements elsewhere is able to conform to any geometry while keeping the total mesh size, and thereby memory and
CPU requirements, acceptable.
General hexahedra can be viewed as deformed bricks, with faces tilted and adjusted in size to conform to geometries in the model. Such elements, especially in an unstructured mesh, also have the necessary flexibility.
Therefore, this standard requires that the Finite Element Method used for SAR calculations employ a tetrahedral mesh or a general hexahedral mesh that has the flexibility to contain small and large elements simultaneously and to conform to the complicated geometries typically found in wireless devices, their antennas, their environment, and human bodies. This standard rejects meshes that are limited to brickshaped or prism-shaped elements.
In regions in the computational domain that have little geometric detail and no large field gradients, the largest possible mesh element size in the Finite-Element method that still provides accurate solutions depends on the choice of the basis functions. If the basis functions are linear, mesh elements need to be smaller than a tenth of the local wavelength in the material. If the basis functions are quadratic, this increases to a third of a wavelength. The loss of accuracy with increasing element size is gradual.
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IEEE P1528.4/D1.0, <month> <year>
In the Finite Element Method, material parameters are defined inside each object. In this method, there is no question which material takes priority on an interface between two objects: fields are computed unambiguously inside mesh elements and satisfy boundary conditions on interfaces between objects.
For electromagnetic simulations of SAR, usually the following material parameters are of interest: relative dielectric permittivity ε magnetic permeability µ r
, bulk electric conductivity σ and mass density ρ. In almost all cases the relative r
equals one.
The permittivity and conductivity tend to be frequency dependent. Since the material parameters don’t exhibit rapid changes in bands encompassing individual antenna resonances, the frequency dependencies can be represented conveniently by data tables. Some software products will have built-in functions to describe frequency dependencies, such as the Debye model, the Lorentz model or the Cole-Cole model.
Frequency-dependent material parameters ensure that the correct materials are used at every frequency.
They have a consequence for the use of frequency sweeps, though. In frequency-domain methods,
•
• sophisticated frequency sweeps based on pole-zero expansions such as AWE or ALPS [B4,B5] may not be able to take frequency-dependent materials into account, and a choice needs to be made:
Perform the frequency sweep by solving explicitly at multiple frequencies and interpolate;
Use a pole-zero expansion for the frequency sweep but assume constant material parameters.
In this application, both are expected to give valid results, provided the material parameters chosen in the second case belong to a frequency point in the antenna resonance curve of interest, and the sweep range does not cover a second antenna resonance.
In SAR simulations, two kinds of boundary conditions tend to be important: boundaries representing conducting metal surfaces and absorbing boundaries.
For any metal, the skin depth at the frequencies of interest will be small relative to other dimensions in the model. For instance, the skin depth of copper at 1 GHz is about 0.002 mm. In a printed-circuit board, copper is used and the thickness of traces and planes is usually at least 0.017 mm and more often 0.035 mm, i.e. many times the skin depth at 1 GHz. To solve inside metals explicitly, mesh elements in the metal would need to be as short as a fraction of a skin depth perpendicular to the surface and would have extreme aspect ratios. For accuracy, many mesh elements would be needed. Therefore, it is very inefficient to try to solve for fields inside the metals explicitly. Instead, metals should be handled through boundary conditions.
The surfaces of the metals should be assigned finite-conductivity boundary conditions. Alternatively, a
PEC boundary condition can be used, which simply enforces zero tangential electric field. In practice, for this application, these two boundary conditions give almost the same results, since metal losses in a communication device are very small compared to other losses and have negligible effect on the fields. If there is any effect, the simulation with PEC will tend to radiate more power and show increased SAR relative to a simulation with finite conductivity boundaries, so there can be no incorrect certification due to the use of PEC boundaries.
Metals in a PCB as well as patch antennas can have aspect ratios of more than a thousand, e.g. be tens of mm long while being only a few hundredths of a mm thick. Mesh elements outside the metal, connecting to the sides of such objects, would also have very large aspect ratios. For accuracy, many mesh elements would be needed. In such a case, it is acceptable to model the metal as a 2D sheet rather than as a 3D object. This is expected to have negligible effect on the fields for this application.
In the Finite Element Method, the outer boundary of the computational domain needs to be terminated with a boundary condition. For SAR simulations, an absorption mechanism is needed that simulates radiation towards infinity, like the walls of an anechoic chamber do in measurements. Most often, a second-order absorbing boundary condition is used for this [B6]. Such a boundary condition has to be placed at least a quarter-wavelength away (more is better) from any objects and be convex. It is most effective when outgoing waves strike it perpendicularly and is not effective for grazing fields. Second-order radiation boundaries are accurate enough for the determination of SAR from wireless communication devices, provided the boundaries are convex and are placed more than a quarter wavelength away from any objects.
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IEEE P1528.4/D1.0, <month> <year>
More accuracy can be obtained with higher-order radiation boundaries, with Perfectly Matched Layers
(PMLs), and with a hybrid FEM-Boundary-Element Method. PMLs are layers of anisotropic absorbing material, first introduced by Berenger [B7, B8]. A recent improvement on them for Finite Elements is the concept of adaptive PMLs [B9], where one layer is sufficient and the mesh is refined adaptively inside. In the hybrid FEM-BEM method, the Finite Element Method is applied to a volume that includes all the objects, while the Method of Moments is applied on the surface of that encompassing volume in order to take care of the radiation [B10-B13]. This eliminates the need for absorbing boundaries or perfectly matched layers in the finite-element method. The matrix for this kind of approach has a sparse part for the
FEM volume and a dense block for the surface of that volume.
Both with radiation boundaries and PMLs, the radiated fields outside the computational domain can be computed by integration over a closed surface inside the domain, e.g. the outer surface of the air volume surrounding all objects.
For calculations of power and efficiency, see 1528.1, Annex A.6. That section contains a general description which does not depend on a particular choice of simulation method.
An antenna in a numerical model can be fed in several ways. One can attach a wave port to a transmission line in order to excite it with an accurate representation of the propagating mode, or one can excite a feed point in a simpler way with the appropriate electric field or voltage between its terminals. In any case, part of the original CAD model has to be removed to give space for the excitation.
For a source model that includes lumped circuit elements the values for the elements are obtained from results of circuit simulation of the final stage of the RF amplifier or design data for the wireless device.
These lumped elements, if included in the model, should be placed close to the RF source but still be a separate entity in the model.
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A computational model of the human anatomy is a mathematical representation of the external envelope of the human body shape together with the boundaries of the internal organs and tissues. The volumes of the organs are filled with a medium assigned with the correct physical properties. The human-body models used by FD-TD codes tend to be difficult to simulate with Finite-Element software, because the large number of FD-TD voxels generates an impractical number of faces in the Finite-Element software. A
Finite-Element-friendly heterogeneous human-body model has been reported in [B15]. This model represents an average adult male. It contains over 300 objects representing organs, muscles and bones.
As stated in the corresponding Annex in IEEE Std. 1528.1, dielectric and conductive properties of the tissue shall be in accordance with the data published by the Italian National Research Council – Institute for
Applied Physics [B16].
Refer to the last section of the corresponding Annex in IEEE Std. 1528.1. That section discusses the SAM
(Specific Anthropomorphic Mannequin) head model as well as body phantoms.
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