Automotive EMC Analysis Using the Hybrid Finite

Element Boundary Integral Approach J.F. Mologni

#1, M. Kopp

#, C.L.R. Siqueira

#, A. Colin

*2 and A. Nogueira

*

# Electronic Design Automation Department, ESSS / ANSYS

423 Rocio Street, Office 1001, São Paulo, Brazil 1 juliano@esss.com.br

*Electromagnetic Compatibility Department, FIAT

3455 Contorno Avenue, Betim, Brazil 2 arnaud.colin@fiat.com.br

Abstract—The majority of innovative trends in automotive

industry today relies on electronic systems. Understanding the

electromagnetic behavior of the electronic control units (ECUs)

in a vehicle has become an ever increasing concern of automotive

manufacturers. Computational Electromagnetic Modeling

(CEM) is a cost effective approach that has being adopted by the

automotive industry to address electromagnetic compatibility

(EMC) problems. Automotive structures are electrically large in

nature and the systems required for a complete EMC analysis

can be fairly complex. For this reason, there is no single

numerical technique that can be used to address all automotive

EMC problems. This paper shows how the automotive standard

ISO11452-2 can be solved using the hybrid Finite Element

Boundary Integral (FEBI) approach. A comparative study

indicates that FEBI is faster and requires less computational

effort than the Finite Element Method (FEM) for this particular

analysis. Recent technology advances on FEBI are also presented

showing the great potential of this technique to address

automotive EMC problems.

I. INTRODUCTION

Automotive EMC studies are of great concern today due to

the widespread use of electronics and wireless technologies

that can lead to electromagnetic interference (EMI), affecting

the performance of the automotive electronic systems. Several

EMI issues were already reported on automotive and

aerospace industry [1-6], and the use of wireless devices, such

as cell phones, ground positioning systems (GPS) and

Bluetooth devices, which are brought into the vehicles,

increases this concern. There are EMC automotive standards

aiming to reduce the potential EMI in vehicles. One of the

most important standards in automotive is the ISO 11451-2,

which is applied to road vehicles and describes a vehicle test

method for electrical disturbances from narrowband radiated

electromagnetic energy. The test determines the immunity of

passenger cars and commercial vehicles to electrical

disturbances from off-vehicle radiation sources, regardless of

the vehicle propulsion system [7]. The test should be

performed in an absorber-lined shielded enclosure, aiming to

create an indoor electromagnetic compatibility testing facility

that simulates open field testing. Typically, the floor is not

covered with absorbing material, but such covering is allowed.

An example of a rectangular shielded enclosure is shown in

Fig. 1.

Fig. 1. ISO 11451-2 test apparatus; adapted from [7]. The equipments shown

are 1) absorber-lined shielded enclosure; 2) RF absorber material; 3) vehicle dynamometer on turntable; 4) antenna; 5) amplifier room; 6) control room.

This experiment is very time consuming and requires a

physical prototype of the vehicle. Hence, numerical

simulation becomes a very attractive approach.

A complete electromagnetic numerical simulation of a

model representing ISO 11451-2 was only possible using the

FEM due to the introduction of domain decomposition method

(DDM), which became commercially available in ANSYS

HFSS [8] in 2009. DDM increases simulation capacity by

parallelizing the entire computational domain into sub

domains that are solved on different cores or computers

connected to a network [9-15]. FEM models require a mesh to

be created on air region, increasing the size of the problem.

The air region can be removed from the simulation through

the use of the Method of Moments (MoM) technique. The

MoM is a numerical approach that uses the Green’s function

considering Sommerfeld’s radiation condition at infinity and

no air region needs to be modelled [16-17]. On the other hand,

the MoM is not very efficient when modelling non conductive

materials [16], which are very often used in vehicles. In order

to overcome this issue, the hybrid finite element boundary

integral technique was developed. FEBI is a numerical

method that uses the MoM solution as a truncation boundary

for the FEM solution and hence combines the best of FEM

and MoM methods increasing the simulation speed and

reducing computational effort [18-19]. A full vehicle

simulation according to ISO 11451-2 standard using the FEBI

technique is presented detailing the EMI on electronic

embedded subsystems. The results are compared to a FEM

simulation in order to demonstrate the accuracy of the results

using FEBI.

II. ELECTROMAGNETIC NUMERICAL TECHNIQUES

A. Finite Element Method

The FEM subdivides a 3D model into a finite number of

smaller subsections called elements. The elements can be of

any shape, but tetrahedra usually conforms better to arbitrary

geometries [20], and for that reason is the element shape used

by HFSS. The whole group of elements is named the mesh. A

solution is found for the fields within the finite elements, and

these fields are interrelated so that Maxwell’s equations are

satisfied over inter-element boundaries, yielding a field

solution for the original 3D model. Once the field solution has

been solved, the generalized scattering matrix (S-Matrix)

solution can be calculated. HFSS solves eq. 1, also known as

wave equation, for each element on the model [8]:

(1)

where k = ω/c is the wave number of free-space; c is the

speed of light; ω=2πf is the angular frequency; µr(x,y) is the

complex relative permeability and εr(x,y) is the complex

relative permittivity. By solving eq.1, the electric field mode

pattern Em (x,y) and the propagation constant γm are both calculated for all the modes specified. The magnetic field is

calculated according to eq. 2:

(2)

Eq. 2 implies that HFSS solve equations in terms of electric

and magnetic fields and not voltages and currents. FEM

requires an air box surrounding the geometries so eq. 1 and eq.

2 are used for radiation patterns calculation. The size of this

air box depends on the frequency and needs to be placed at

least λ/4 when using an absorbing boundary condition (ABC). Fig. 2 shows the electric field distribution and the antenna

radiation far field pattern at 1GHz according to ISO 11451-2.

For simplification, the model in Fig. 1 only considers the

chassis, tire and glasses. All ECUs and wiring harness were

removed. A broad band horn antenna was used in this model.

The air region was modelled for the entire room including the

absorber elements on the side and top walls. The absorber

elements could be removed from the model by using

absorbing boundary conditions or a perfectly matched layer

(PML) applied to the outer faces of the air box. For this

particular simulation 78% of the total number of elements was

used to model the air.

Fig. 2. Full 3D FEM model showing a cross sectional electric field plot (a.u.)

in the air region and on the chassis of the vehicle at 1GHz. Antenna far field

pattern is also shown.

B. Method of Moments

The FEM solves partial ordinary equations and the MoM,

solves integral equation (IE). MoM models do not require an

air region to be modelled. The radiated electric field is

calculated from the induced surface current through eq. 3:

(3)

where J(r´) is the unknown surface current density on the

surface S of the model (r ϵ S) and E(r) is the incident electric

field. Harmonic time dependence of the form jωµ is

suppressed in frequency domain. One can eliminate the

dependence of E(r) by enforcing the boundary conditions on

the tangential electric field leading to eq. 4:

(4)

where n(r) is the outward unit normal from the surface S.

Rewriting the above equation in terms of the known incident

electric field E(r) yields:

(5)

Eq. 5 is known as the electric field integral equation (EFIE)

for a perfectly conducting surface, where ∇´S is the surface divergence [21]. Once solved for the unknown current J(r) the

radiated field on any spatial coordinate can be calculated

using Sommerfeld’s radiation condition at infinity.

0),(),(1 22

2 =−

×∇×∇ −− mm eyxEkeyxE mrm

r

γγ εµ

),(1

yxEH m

r

×∇=ωµ

´)(´´1

)()()(2

drrJk

rJrrGjrES

r

′∇∇+′′−−= ∫∫ωµ

´´),(´´)(´

´),(´)()()()(

2

0

drrrGrJS

rrGrJkjrnrErn

S

∫

∇⋅∇

−×=×ωε

0)()()()( =×−=× rErnrErn

Fig. 3. Comparison between FEM, IE and FEBI models.

C. Finite Element Boundary Integral

FEM is a general purpose numerical technique that solves

for volumetric electric. The air region surrounding the model

must be included and terminated with an ABC. MoM solves

directly for currents on object surfaces not requiring a

surrounding air volume. To take advantage of both MoM and

FEM, FEBI was developed. Fig. 3 shows the model of the

broadband antenna used in our simulations for these three

different methods. The air box in FEBI is very conformal to

the geometry and its offset distance to the antenna itself can

be as close as possible, being only limited by numerical errors.

Therefore, the air region is dramatically reduced which leads

to a faster solution. All three numerical techniques in HFSS

use the adaptive mesh algorithm that yields very accurate

results. The accuracy can also be observed in Fig. 4 where the

reflection coefficient of the antenna models for FEM, MoM

and FEBI shows virtually no difference. The inset in Fig. 4

shows the far field pattern of the antenna, which is also the

same for the three mathematical procedures.

The FEBI solver used in HFSS considers two different

domains for a single problem. It starts by partitioning the

original problem domain Ω into two non-overlapping sub-

domains Ω1 and Ω2, as shown in Fig. 5 [18].

(6)

The interface between Ω1 and Ω2 is denoted as ∂Ω1 in the

FEM domain and ∂Ω2 in the IE domain. This distinction is

required because the present formulation allows non

conformal coupling between two domains. This means that

the mesh, the basis function and basis order, the matrix

assembling and solution process can be treated independently

for each domain. The ability to handle different basis orders in

a modular approach for each domain is crucial for a robust

FEBI solver because higher order IE solvers are still in

development [18]. Based on DDM, the final system matrix

can be written as:

(7)

where AFE and ABI represent the system matrices of FEM and

boundary integral (BI) domains, respectively, and C is the

coupling matrix between them. The coupling is calculated

based only on the electric and magnetic currents at the

interface; hence, it is extremely sparse. The solution of eq. 7 is

accomplished iteratively via splitting:

(8)

where n is the total number of domains. Simplifying eq. 8

results on eq. 9:

(9)

The advantages of using DDM are apparent from (9). Both

FEM and BI domains are decoupled so parallelization

becomes trivial. The above mathematical procedure shows

that BI can be used as an exact termination condition in FEM.

Φ=ΩΩΩ=Ω=

II 21

2,1

,i

i

1−

−

=

n

BI

FE

TBI

FE

n

BI

FE

BI

FE

X

X

C

C

Y

Y

X

X

A

A

1

1

−

−

×−=×

×−=×n

FEBI

n

BIBI

n

BIFE

n

FEFE

CYA

CYA

Fig. 4. Reflection Coefficient of the broadband horn antenna.

=

BI

FE

BI

FE

BI

T

FE

Y

Y

X

X

AC

CA

Fig. 5. Domain decomposition of the full model into FEM and IE domains.

Due to the implementation’s modularity, state-of-the-art

FEM and IE solvers are easily employed in a hybrid way.

Another great advantage of FEBI is that different domains can

be simulated in different computers using DDM. Moreover, if

the dimension of one of the domains is electrically large,

DDM technique can be employed once again to solve the

FEM domain.

III. ISO 11451-2 EMC ANALYSIS OF A ECU CONNECTED TO

AN ENGINE WIRING HARNESS

In order to demonstrate the benefits of FEBI, the same

simulation of Fig. 2 using FEM was duplicated and solved

with FEBI. The air box that comprises the whole model when

using FEM was replaced by two air box very conformal

whose surfaces are now extremely close to the antenna and the

vehicle. The absorber elements are not modelled in this

simulation and they were replaced by a PML in FEM and the

BI boundary in FEBI The electric field distribution plot is

shown for the entire domain in Fig. 6 for both FEM and FEBI.

As observed, the size of the air box when using FEBI is

extremely smaller which leads to a faster simulation. The total

solving time was 310 minutes for FEM and 28 minutes for

FEBI. The total amount of RAM required for FEM and FEBI

was 75 GB and 6.8 GB, respectively. So both solving time and

computational effort were reduced by over 10 times just by

using FEBI instead of FEM. The accuracy of the results can

be observed in Fig. 6 where the electric field on the surface of

the vehicle is very similar. Fig. 7 shows the far field pattern of

the antenna including the whole mode, indicating a very good

agreement as well.

Since FEBI uses only a moderate amount of RAM, the

complexity of the model can be increased so additional ECUs

and wiring harnesses can be added to model. A radiated

immunity analysis according to ISO 11451-2 is then

performed on a wiring harness that sends on board diagnostics

(OBD) data from the engine to an ECU. Fig. 8a shows the

routing of the wiring harness that connects the engine to the

ECU. The wiring harness end is attached to the red four-way

connector shown in Fig 8b. The pin on the connector that is

attached to the wiring harness is soldered to a trace that is

connected to a microcontroller.

Because conductors with any given length can act as a

radiation source, the wiring harness plays a vital role in EMI.

To better understand the effect of the wiring harness, two

simulations were performed. The first simulation contains all

the above mentioned geometry as well as the car and source

antenna. The OBD signal is applied at the engine end of the

wiring harness. For the second simulation the wiring harness

is removed and the OBD signal is applied directly into the

Fig. 6. Electric field plot (a.u.) for FEM and FEBI models at 1GHz.

Fig. 7. Antenna Far Field pattern at ϕ=90o comprising the whole model.

Fig. 8. Electric field plot on the wiring harness (a.u.) at 4GHz. a) Details of the

routing from the engine to the PCB and b) the wiring harness attachment to the

PCB on the red four-way connector.

a)

b)

four way connector on the ECU. For both simulations the

antenna excitation was set to a constant 150V sinusoidal

signal with a frequency sweep varying from 10 to 500MHz.

Fig 9 shows the eye diagram of the OBD signal at the

microcontroller when the antenna radiates at 145MHz. The

EMI is most pronounced when the ECU is connected to the

wiring harness, which works as a receiving antenna at

145MHz. The interference causes distortion to the OBD signal,

and as a consequence the eye height decreases when

compared to the case without wiring harness, as observed on

Fig. 9a and 9b. This is undesirable effect that could lead to

signal integrity problems.

IV. EVOLUTION OF HYBRID SOLVERS

Regular FEBI approach needs an air volume enclosing all

objects of the model, as shown in Fig. 6. Recent advances in

FEM-IE solvers permit to directly solve conducting objects

with an IE solution applied to the surface without the need of

an air region around the object. The example of Fig. 10

shows that the antenna and the motor objects are enclosed by

a yellow air region and they are solved using the FEM solver.

The red chassis is an IE Region, and it is solved directly using

IE formulation, which includes the coupling between all

domains through radiated near and far fields via boundary

integral. This advancement improves even more simulation

time and computational effort.

The two FEM domains and the IE region in Fig. 10 are

physically separated as the coupling using IE formulation is

done through radiated fields. Today’s state of the art hybrid

FEM-IE solvers allows IE Regions to be in physical contact

with FEM domains, so the coupling is also made through

conductors. Fig. 11a shows an automotive example of this

application where a door is an IE Region that has a part inside

the FEM domain, enclosed by a yellow air region, and a part

on the exterior of the FEM domain. The complex geometries

(the speaker, twisted pair cable, grommets and connectors) are

solved using the FEM as well as a part of the door. The door

on the outside of the FEM domain is solved using the IE

solver and the coupling between the FEM and IE domains is

made, in this case, through a single conductor which is the

metallic door. The resulted current density is shown in Fig.

11b, where a smooth plot is observed even in the borders

where FEM and IE are connected.

V. CONCLUSION

With the introduction of the hybrid solver FEBI that

presents an order of magnitude improvement in simulation

speed and reduction in computational effort, simulation of a

full vehicle according to EMC standards is feasible. A

passenger vehicle was virtually tested under ISO 14451-2

standard showing the EMI from a broadband horn antenna in a

digital OBD digital line for two cases: when an ECU that

reads the OBD data inside the vehicle is connected to the

engine wiring harness and when the same ECU is simulated

unconnected to the wiring harness. An undesirable distortion

on the OBD signal was observed when the antenna radiates at

145MHz and the ECU is connected to the wiring harness. This

Fig. 9. Eye diagrams of the OBD signal at the microcontroller with the antenna

radiating at 145MHz: a) with wiring harness and b) without wiring harness.

Fig. 10. 3D Model showing the chassis as an IE Region.

a)

b)

was due to the fact that the wiring harness was acting as an

antenna for this particular frequency due to its physical length.

Recent advances on hybrid FEM-IE solvers were also

addressed. Today’s state of the art technology includes the

coupling between FEM and IE domains through radiated near

and far fields and conductors, where the two domains can be

in physical contact.

The importance of electromagnetic numerical simulation

implies not only on cost reduction and lowering time to

market, but also on the safety of vehicles and passengers that

are relying to a greater extent on electronic systems.

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