IEC/IEEE 62704-4:2020

IEC/IEEE 62704-4 ®
Edition 1.0 2020-10
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Determining the peak spatial-average specific absorption rate (SAR) in the
human body from wireless communication devices, 30 MHz to 6 GHz –
Part 4: General requirements for using the finite element method for SAR
calculations
Détermination du débit d’absorption spécifique (DAS) maximal moyenné
dans le corps humain, produit par les dispositifs de communications sans fil,
30 MHz à 6 GHz –
Partie 4: Exigences générales d'utilisation de la méthode des éléments finis
pour les calculs du DAS
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IEC/IEEE 62704-4 ®
Edition 1.0 2020-10
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
colour
inside
Determining the peak spatial-average specific absorption rate (SAR) in the

human body from wireless communication devices, 30 MHz to 6 GHz –

Part 4: General requirements for using the finite element method for SAR

calculations
Détermination du débit d’absorption spécifique (DAS) maximal moyenné

dans le corps humain, produit par les dispositifs de communications sans fil,

30 MHz à 6 GHz –
Partie 4: Exigences générales d'utilisation de la méthode des éléments finis

pour les calculs du DAS
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.20 ISBN 978-2-8322-8535-0

– 2 – IEC/IEEE 62704-4:2020 © IEC/IEEE 2020
CONTENTS
FOREWORD . 5
INTRODUCTION . 7
1 Scope . 8
2 Normative references . 8
3 Terms and definitions . 8
4 Abbreviated terms . 9
5 Finite element method – basic description . 9
6 SAR calculation and averaging . 10
6.1 General . 10
6.2 SAR averaging . 11
6.2.1 General . 11
6.2.2 Evaluation of psSAR with an FEM mesh . 11
6.3 Power scaling . 12
7 Considerations for the uncertainty evaluation . 12
7.1 General . 12
7.2 Uncertainty due to device positioning, mesh density, and simulation
parameters . 13
7.2.1 General . 13
7.2.2 Mesh convergence. 14
7.2.3 Open boundary conditions . 14
7.2.4 Power budget . 14
7.2.5 Convergence of psSAR sampling . 14
7.2.6 Dielectric parameters of the phantom or body model . 15
7.3 Uncertainty and validation of the developed numerical model of the DUT . 15
7.3.1 General . 15
7.3.2 Uncertainty of the DUT model (d ≥ λ/2 or d ≥ 200 mm) . 16
7.3.3 Uncertainty of the DUT model (d < λ/2 and d < 200 mm) . 17
7.3.4 Phantom uncertainty (d < λ/2 and d < 200 mm) . 18
7.3.5 Model validation . 19
7.4 Uncertainty budget . 19
8 Code verification. 20
8.1 General . 20
8.1.1 Rationale . 20
8.1.2 Code performance verification . 21
8.1.3 Canonical benchmarks . 21
8.2 Code performance verification . 21
8.2.1 Propagation in a rectangular waveguide . 21
8.2.2 Planar dielectric boundaries . 26
8.2.3 Open boundary conditions . 28
8.3 Weak patch test . 28
8.3.1 General . 28
8.3.2 Free-space weak patch test . 29
8.3.3 Dielectric-layer weak patch test . 33
8.4 Verification of the psSAR calculation . 36
8.5 Canonical benchmarks . 36
8.5.1 Mie sphere . 36

8.5.2 Generic dipole . 37
8.5.3 Microstrip terminated with open boundary conditions . 38
8.5.4 psSAR calculation SAM phantom / generic phone . 39
8.5.5 Setup for system performance check . 39
Annex A (informative) Fundamentals of the finite element method . 41
A.1 General . 41
A.2 Model boundary value problem . 41
A.3 Galerkin weak form . 42
A.4 Finite element approximation . 42
A.5 Considerations for using FEM . 43
Annex B (informative) File format for field and SAR data. 44
Annex C (informative) Analytical solution for error calculation in weak patch-test
problems . 45
C.1 Generation of control mesh and FEM field values . 45
C.2 Free-space weak patch test . 45
C.3 Dielectric-layer weak patch test . 45
Bibliography . 48

Figure 1 – Waveguide filled half with free-space (green) and half with dielectric (blue) . 24
Figure 2 – Aligned rectangular waveguide and locations of the sample points E , E ,
01 10
E , E and E at which the E components are recorded . 25
11 12 21 x
Figure 3 – Weak patch test arrangement: a free-space cube with edge length L
illuminated by a plane wave . 29
Figure 4 – Dielectric-layer weak patch test arrangement . 33
Figure 5 – Geometry of the microstrip line . 38
Figure 6 – Geometry of the setup for the system performance check according to [21] . 40

Table 1 – Budget of the uncertainty contributions of the numerical algorithm and of the
rendering of the test-setup or simulation-setup . 13
Table 2 – Budget of the uncertainty of the developed model of the DUT. 17
Table 3 – Overall assessment uncertainty budget for the numerical simulation results . 20
Table 4 – Results of the evaluation of the numerical dispersion characteristics to be
reported for each mesh axis and each orientation of the waveguide for at least three
increasing numbers of DoF . 25
Table 5 – Results of the evaluation of the numerical reflection coefficient to be
reported; frequency range is indicated for each value to be reported . 27
Table 6 – Guiding parameters for coarse and fine mesh generation for the weak patch test . 30
Table 7 – Results of the evaluation of the error measures on the control mesh for the
weak patch test for the lowest order . 32
Table 8 – Results of the evaluation of the error measures on the control mesh for the
weak patch test for the second lowest order . 32
Table 9 – Results of the evaluation of the error measures on the control mesh for the
weak patch test for the third lowest order . 33
Table 10 – Guiding parameters for coarse and fine mesh generation for the dielectric-
layered weak patch test . 34
Table 11 – Results of the evaluation of error measures on the control mesh for the
dielectric-layered weak patch test for the lowest order . 35

– 4 – IEC/IEEE 62704-4:2020 © IEC/IEEE 2020
Table 12 – Results of the evaluation of error measures on the control mesh for the
dielectric-layered weak patch test for the second lowest order . 35
Table 13 – Results of the evaluation of error measures on the control mesh for the

dielectric-layered weak patch test for the third lowest order . 36
Table 14 – Results of the SAR evaluation of the Mie sphere . 37
Table 15 – Results of the dipole evaluation . 38
Table 16 – Results of the microstrip evaluation . 39
Table 17 – 1 g and 10 g psSAR for the SAM phantom exposed to the generic phone for
1 W accepted power as specified in [19] . 39
Table 18 – Dielectric parameters of the setup (Table 1 of [21]) . 40
Table 19 – Mechanical parameters of the setup (Tables 1 and 2 of [21]) . 40
Table 20 – 1 g and 10 g psSAR normalized to 1 W accepted power and feed-point
impedance (Table 3 and Table 4 of [21]) . 40

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
DETERMINING THE PEAK SPATIAL-AVERAGE SPECIFIC ABSORPTION
RATE (SAR) IN THE HUMAN BODY FROM WIRELESS
COMMUNICATION DEVICES, 30 MHZ TO 6 GHZ –

Part 4: General requirements for using the
finite element method for SAR calculations

FOREWORD
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indispensable for the correct application of this publication.

– 6 – IEC/IEEE 62704-4:2020 © IEC/IEEE 2020
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International Standard IEC/IEEE 62704-4 has been prepared by IEC technical committee
TC 106: Methods for the assessment of electric, magnetic and electromagnetic fields
associated with human exposure, in cooperation with International Committee on
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This publication is published as an IEC/IEEE Dual Logo standard.
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Directives, Part 2.
A list of all parts in the IEC/IEEE 62704 series, published under the general title Determining
the peak spatial-average specific absorption rate (SAR) in the human body from wireless
communications devices, 30 MHz to 6 GHz, can be found on the IEC website.
The IEC technical committee and IEEE technical committee have decided that the contents of
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INTRODUCTION
Finite element methods have reached a level of maturity that allows their application in
specific absorption rate (SAR) assessments of professional-use and consumer-use wireless
communication devices. In the recent past, SAR compliance assessments for small
transmitters were performed almost exclusively using measurements. 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. US Federal
Communications Commission) encourage the development of consensus standards and
encouraged the establishment of the ICES Technical Committee 34 Subcommittee 2. The
benefits to the users and the regulators include standardized and accepted protocols,
verification and validation techniques, benchmark data, reporting format and means for
estimating the overall assessment uncertainty in order to produce valid, repeatable, and
reproducible data.
The purpose of this document is to specify numerical techniques and models to determine
peak spatial-average specific absorption rates (SAR). SAR will be determined by applying
finite element method simulations of the electromagnetic field conditions produced by wireless
communication devices in models of the human anatomy. Intended users of this document are
(but are not limited to) wireless communication device manufacturers, service providers for
wireless communication that are required to certify that their products comply with the
applicable SAR limits, and government agencies.
Several methods described in this document are based on techniques specified in
IEC/IEEE 62704-1:2017.
– 8 – IEC/IEEE 62704-4:2020 © IEC/IEEE 2020
DETERMINING THE PEAK SPATIAL-AVERAGE SPECIFIC ABSORPTION
RATE (SAR) IN THE HUMAN BODY FROM WIRELESS
COMMUNICATION DEVICES, 30 MHZ TO 6 GHZ –

Part 4: General requirements for using the
finite element method for SAR calculations

1 Scope
This part of IEC/IEEE 62704 describes the concepts, techniques, and limitations of the finite
element method (FEM) and specifies models and procedures for verification, validation and
uncertainty assessment for the FEM when used for determining the peak spatial-average
specific absorption rate (psSAR) in phantoms or anatomical models. It recommends and
provides guidance on the modelling of wireless communication devices, and provides
benchmark data for simulating the SAR in such phantoms or models.
This document does not recommend specific SAR limits because these are found elsewhere
(e.g. in IEEE Std C95.1 [1] or in the guidelines published by the International Commission on
Non-Ionizing Radiation Protection (ICNIRP) [2]).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their
content constitutes requirements of this document. For dated references, only the edition
cited applies. For undated references, the latest edition of the referenced document (including
any amendments) applies.
IEC 62209-1, Measurement procedure for the assessment of specific absorption rate of
human exposure to radio frequency fields from hand-held and body-mounted wireless
communication devices – Part 1: Devices used next to the ear (Frequency range of 300 MHz
to 6 GHz)
IEC/IEEE 62704-1:2017, Determining the peak spatial-average specific absorption rate (SAR)
in the human body from wireless communications devices, 30 MHz to 6 GHz – Part 1: General
requirements for using the finite-difference time-domain (FDTD) method for SAR calculations
IEEE Std 1528, IEEE Recommended Practice for Determining the Peak Spatial-Average
Specific Absorption Rate (SAR) in the Human Head From Wireless Communications Devices:
Measurement Techniques
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO, IEC, and IEEE maintain terminological databases for use in standardization at the
following addresses:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp
• IEEE Dictionary Online: available at http://dictionary.ieee.org
___________
Numbers in square brackets refer to the Bibliography.

3.1
mesh
discrete representation of the simulation model as a
set of voxels in a regular three-dimensional Cartesian arrangement
Note 1 to entry: In the scientific literature, the mesh is often referred to as a "grid."
[SOURCE: IEC/IEEE 62704-1:2017, 3.21, modified – The specific context " time-domain method>" has been added.]
3.2
mesh
discrete representation of the simulation model as a set of
tetrahedral elements in an irregularly three-dimensional arrangement
Note 1 to entry: In the scientific literature, the mesh is often referred to as a "grid."
3.3
element
smallest three-dimensional part of a mesh
EXAMPLE A voxel or a tetrahedron.
3.4
subregion
spatially limited three-dimensional region within a computational domain
3.5
accepted power
power delivered to a load by a source
4 Abbreviated terms
ASCII American Standard Code for Information Interchange
BVP Boundary Value Problem
DoF Degrees of Freedom
DUT Device Under Test
FDTD Finite-Difference Time-Domain
FEM Finite Element Method
PDE Partial Differential Equation
PEC Perfect Electric Conductor
PMC Perfect Magnetic Conductor
psSAR peak spatial-average Specific Absorption Rate
SAR Specific Absorption Rate
SI International System of Units
TVFE Tangential Vector Finite Elements
5 Finite element method – basic description
This document describes applications of the finite element method (FEM) to calculate the
specific absorption rate (SAR). Reasons for using FEM include its proven track record in a
broad range of electromagnetic applications, and its ability to use an unstructured, usually
tetrahedral, mesh that conforms to complicated geometries, employing arbitrarily small
elements where needed and larger elements elsewhere.

– 10 – IEC/IEEE 62704-4:2020 © IEC/IEEE 2020
Multiple ways exist to solve Maxwell’s equations with FEM. Implementations can be based on
field quantities or on potential quantities, and may be formulated using either the weighted
residual method or the variational method [3], [4]. The weighted residual method starts
directly from the partial differential equation (PDE) of the boundary value problem, whereas
the variational method starts from the variational representation of the boundary value
problem. All implementations have the following in common:
a) They are based on PDEs, not on integral equations. The PDEs are derived from Maxwell’s
equations augmented by proper boundary conditions in order to frame a well-defined
boundary value problem on a finite computational domain.
b) The size of the computational domain is finite. Radiation towards infinity is implemented
through an open boundary condition on its outer boundaries. Radiated fields outside the
domain can be computed by integrating over a boundary that encloses the radiating
structure.
c) After applying excitations and boundary conditions and discretizing the computational
domain into a mesh, the derived PDE is transformed into a matrix equation in which the
matrix is large, sparse, and banded. "Large" is a consequence of having a large number of
unknowns, several per element on a large mesh. "Sparse" and "banded" are
consequences of the fact that all interactions are formulated as local interactions.
d) In the limit of infinitesimally small elements, the solution approaches the exact solution of
the PDE.
Annex A contains more information on FEM, along with references to literature and a
discussion of its limitations. Clause 8 describes a set of tests is described that shall be used
to determine whether a particular implementation of FEM is correct and sufficiently accurate
to be used for SAR calculations.
This document refers to Nédélec elements of the first kind, which are polynomially exact up to
(curl) or edge elements) as lowest order; up to order 1 (H (curl) elements) as
order 0 (H
0 1
second lowest order; and up to order 2 (H (curl) elements) as third lowest order [5]. If an
implementation of the FEM is applied with one of these orders, the respective parts of the
code verification shall be executed with this order.
6 SAR calculation and averaging
6.1 General
The local specific absorption rate (SAR) in a location in tissue is given in Equation (1):
σE
SAR = (1)
2ρ
where ρ is the mass density of the tissue, E is the magnitude of the electric field vector, and σ
is the electric conductivity. Since the local SAR can vary strongly with position, the quantity of
interest is often the peak spatial-average SAR. Contemporary safety standards and guidelines
specify time-averaged whole-body-averaged SAR limits and psSAR limits, neither of which
should be exceeded. The spatial-average SAR is averaged over a specified mass with a
specified volume, e.g. 1 g or 10 g of tissue in the shape of a cube [1], [2].
NOTE Cubical averaging volumes are applied in all existing standards for the measurement of psSAR, and are
also recommended by [1], [2] and [6]. Other averaging volumes have been proposed, e.g. in [2], and might be
included in future revisions of this document.

6.2 SAR averaging
6.2.1 General
The objective of the methods to evaluate the psSAR described here is to yield results that
correspond to the methods and definitions of Clause 6 of IEC/IEEE 62704-1:2017, which
describes how to compute psSAR on a rectangular mesh. The same algorithm shall be
applied to calculate psSAR for FEM simulations within this document. Since the algorithm of
Clause 6 of IEC/IEEE 62704-1:2017 is specified on rectilinear meshes with varying mesh step,
the vector components of the electric fields, the conductivity, and the mass density of the
finite element mesh shall be resampled on a Cartesian mesh. The resampling is carried out
with increasingly fine mesh steps until convergence of the dissipated power is reached in the
subregions where local SAR maxima are located. In order to reduce the computation time for
the iterative resampling and SAR averaging, subregions with local SAR maxima are identified
in a pre-scan. In these subregions, the psSAR is then calculated according to Clause 6 of
IEC/IEEE 62704-1:2017. The maximum psSAR of all subregions shall be reported as the
psSAR maximum together with its interpolation uncertainty. The details of the steps of the
algorithm are provided in 6.2.2.
6.2.2 Evaluation of psSAR with an FEM mesh
6.2.2.1 General
The following steps shall be carried out to resample the geometry and the power density in a
set of subregions around local SAR maxima for the application of the SAR averaging
algorithm of IEC/IEEE 62704-1:2017.
a) Specify an orientation of a rectilinear mesh relative to the coordinate system of the FEM
mesh considering the relevant features of the model; this orientation shall align with
surface planes or conducting planes of the phantom or of the DUT.
b) Iteratively resample the geometry and local SAR distribution in the rectilinear mesh and
evaluate psSAR at each iteration until convergence is achieved (see 6.2.2.2).
c) Report the highest psSAR of all subregions together with its interpolation uncertainty.
6.2.2.2 Calculation of the psSAR on an iteratively refined rectangular mesh
The psSAR shall be evaluated on a rectilinear mesh that encompasses a subregion around a
local SAR maximum with individual equidistant mesh steps for each axis. Each mesh cell is
assigned the local distribution of the dissipated power, the conductivity, and the mass density.
a) The mass density for each mesh cell shall be assigned by nearest-neighbour interpolation
of the mass density distribution of the tetrahedral mesh.
b) The conductivity for each mesh cell shall be assigned by nearest-neighbour interpolation
of the mass density distribution of the tetrahedral mesh.
c) In the mesh cells that have a mass density different from zero, the dissipated power
density is calculated by evaluating the electric field of the finite element mesh in the
centre of the mesh cell of the rectilinear mesh.
d) The initial mesh step length Δ for each axis of the rectilinear mesh shall be calculated in
accordance with Equation (2):
m
Δ ≤ 3 (2)
ρ
max
where
m is the averaging mass of the target volume;
ρ is the maximum mass density of the geometry in the computational domain.
max
– 12 – IEC/IEEE 62704-4:2020 © IEC/IEEE 2020
e) The psSAR for the subregion under evaluation shall be calculated on the initial mesh
according to the procedure specified in IEC/IEEE 62704-1:2017. Then the subregion shall
be resampled on a rectilinear mesh with a reduced mesh step size Δ = 0,5 Δ . This
i+1 i
procedure shall be repeated until the difference in psSAR from the previous iteration to the
present iteration is less than 1 %.
6.3 Power scaling
In FEM simulations, the accepted power is generally delivered to the device by means of a
port with known characteristic impedance. Depending on the input impedance of the device, a
specific power level is accepted by the antenna or load. The simulation results, including SAR,
will be relative to this accepted power. To obtain the SAR for a different accepted power level,
such as the target accepted power, the SAR results shall be adjusted by scaling using
Equation (3):
P
acc,target
(3)
SAR = SAR
scaled scaled
P
acc,computed
where
P is the target accepted power;
acc,target
P is the accepted power computed by the FEM simulation.
acc,computed
For these calculations, P is the power delivered to the load by the simulation,
acc,computed
which is found from the complex voltage and current at the feed-point of the FEM mesh in
accordance with Equation (4):
∗
P = Re UI (4)
acc,computed { }
where U and I are complex quantities, and the asterisk indicates complex conjugate.
If an incident plane wave source is applied, SAR can be scaled based on the incident power
density. The incident power density can be computed using Equation (5):
∗
P Re EH× (5)
{ }
inc inc inc
where E and H represent the incident electric field and magnetic field from the plane
inc inc
wave. The computed incident power density can then be used to scale the SAR in the same
manner as the accepted power.
Changes in SAR due to performance variations in radio frequency (RF) components that
affect P (due to thermal, electrical, or other tolerances) shall be determined during
acc,target
experimental validation of the numerical model of the DUT (see 7.3). It shall be considered
either by choosing the maximum possible value for P or by adding the performance
acc,target
variation in the uncertainty budget (see 7.4).
7 Considerations for the uncertainty evaluation
7.1 General
Assuming the FEM code has been implemented correctly, which shall be determined with the
tests described in Clause 8, some uncertainties remain. This Clause 7 shows how they shall
=
be evaluated to obtain a measure of overall assessment uncertainty. It follows the
computational uncertainty scheme of Clause 7 in IEC/IEEE 62704-1:2017, with modifications
appropriate to FEM. As stated in the cited clause, the computational uncertainties are divided
into the following three categories:
a) discretization accuracy and uncertainty due to mesh density,
b) numerical accuracy of the specific FEM implementation,
c) accuracy of the numerical representation of the actual DUT.
Subclauses 7.2 through 7.4 specify general procedures for the evaluation of the uncertainty.
When applied to device or application-specific FEM-based SAR simulation standards, there
might be modifications appropriate to those applications. Further information can be found in
Clause 7 of IEC/IEEE 62704-1:2017 and in [7], [8].
7.2 Uncertainty due to device positioning, mesh density, and simulation parameters
7.2.1 General
A representative model of the test configuration shall be used to determine the uncertainties
due to mesh density, open boundary conditions, and other associated simulation parameters.
For FEM, the contributions to the uncertainty due to device and phantom positioning are
considered small because the mesh adapts to the surface of arbitrarily shaped objects. The
remaining uncertainties are assumed to be covered in the evaluation of the uncertainty of the
mesh density. Table 1 shows an example template for the quantification of the numerical
uncertainty due to contributions described in 7.2.2 through 7.2.6.
Table 1 – Budget of the uncertainty contributions of the numerical algorithm
and of the rendering of the test-setup or simulation-setup
a b c d e f g h
Uncertainty Tolerance Probability Divisor Uncertainty v or
i
Subclause c
i
component (%) distribution f(d, h) (%) v
eff
Mesh convergence 7.2.2 N 1 1
Open boundary
7.2.3 N 1 1
conditions
Power budget 7.2.4 N 1 1
Convergence of
7.2.5 R 1,73 1
psSAR sampling
Phantom dielectrics 7.2.6 R 1,73 1
Combined std. uncertainty (k = 1)
NOTE 1 Column headings a to h are given for reference.
NOTE 2 Columns c, g, and h are filled in based on the results of the DUT simulations.
NOTE 3 Abbreviations used in Table 1:
N, R, U – normal, rectangular, U-shaped probability distributions
Divisor – divisor used to get standard uncertainty
NOTE 4 The divisor is a function of the probability distribution and degrees of freedom (v and v ).
i eff
NOTE 5 c is the sensitivity coefficient that is applied to convert the variability of the uncertainty
i
component into a variability of psSAR.

– 14 – IEC/IEEE 62704-4:2020 © IEC/IEEE 2020
7.2.2 Mesh convergence
The mesh convergence has a major impact on the accuracy of the results; therefore, psSAR
results produced with a specific initial mesh M need to be compared with psSAR results
produced with a denser mesh M′. Either of the following two strategies shall be applied
depending on whether the FEM code used for the psSAR evaluation employs adaptive mesh
refinement or not.
a) If the applied FEM code does not employ adaptive mesh refinement, the number of
elements per wavelength used for the initial mesh M shall be increased by at least 50 %
considering the respective wavelengths in the dielectrics.
b) If the applied FEM code uses
...