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Simulating EMC/EMI Effects for High-Power Inverter Systems

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<strong>Simulating</strong> <strong>EMC</strong>/<strong>EMI</strong> <strong>Effects</strong> <strong>for</strong><br />

<strong>High</strong> <strong>Power</strong> <strong>Inverter</strong> <strong>Systems</strong><br />

Emmanuel Batista<br />

Vincent Delafosse,<br />

Alstom Pearl<br />

Ryan Magargle Ansoft Corporation<br />

emmanuel.batista@transport.alstom.com<br />

vdelafosse@ansoft.com<br />

rmagargle@ansoft.com<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Acknowledgments<br />

This work has been based on the work of<br />

Emmanuel Batista, J.M. Dienot, M. Mermet-Guyennet<br />

Special Thanks:<br />

–<br />

–<br />

–<br />

P. Solomalala (Pearl/Alstom)<br />

O.Roll, X. Legoar, D. Prestaux,<br />

X. Wu, M. Rosu, S. Kher (Ansoft)<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Pearl: <strong>Power</strong> Electronics Associated Research Laboratory<br />

Research<br />

Viability<br />

and Validation of technologies Development<br />

and maintenance<br />

Passive Components<br />

Active Components<br />

Packaging<br />

and validation of prototypes<br />

Models-Simulation-Fabrication<br />

<strong>EMC</strong><br />

Solve multi-domain/temps/structure<br />

Design of methods <strong>for</strong> conception<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Motivation<br />

•<br />

•<br />

•<br />

•<br />

<strong>High</strong> power IGBT based inverter systems have specific <strong>EMC</strong>/<strong>EMI</strong><br />

requirements<br />

The prediction of <strong>EMC</strong>/<strong>EMI</strong> fields is very difficult . Physical prototyping<br />

can result in long design cycles<br />

Simulation tools can help with the use of several techniques<br />

The physical quantities in the inverter that need accurate simulation are:<br />

–<br />

–<br />

–<br />

–<br />

–<br />

Quantity of current going through the conductors<br />

Frequency dependent parasitics (RLC) between conductors<br />

IGBT characterization curves<br />

<strong>Power</strong> dissipation<br />

Emitted fields<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Overview<br />

•<br />

•<br />

•<br />

•<br />

•<br />

•<br />

Introduction to the power study<br />

Static electromagnetic field study<br />

Parasitics extraction<br />

IGBT characterization<br />

System simulation<br />

Emitted fields<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Introduction<br />

•<br />

These<br />

power converters<br />

Pantograph<br />

Traction Supply<br />

Traction<br />

Motor<br />

IGBT Module Top Row<br />

are used<br />

<strong>Inverter</strong><br />

in high<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

AM<br />

3~<br />

speed trains (TGV)<br />

<strong>Inverter</strong> Leg


Introduction<br />

Emitter<br />

Dielectric<br />

Gel<br />

Diode<br />

Chip<br />

IGBT<br />

Chips<br />

6.5kV IGBT Module Characteristics<br />

Baseplate<br />

Ceramic<br />

Substrate<br />

Collector<br />

Packaging<br />

6.5kV-600A<br />

6.5kV 600A<br />

Module<br />

24 IGBT and<br />

12 Diode Chips<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Introduction<br />

6.5kV IGBT Module Analysis<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

•<br />

•<br />

•<br />

•<br />

Include package in IGBT<br />

per<strong>for</strong>mance<br />

Find DC current distribution<br />

Find switching currents <strong>for</strong><br />

power dissipation<br />

Use power dissipation to<br />

determine environmental<br />

electromagnetic fields


Introduction<br />

IGBT Module<br />

Pack 3D<br />

accurate model<br />

Electromagnetic<br />

(EM) study<br />

Model design developed<br />

•<br />

Parameters<br />

Extraction<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

at<br />

Alstom/Pearl<br />

Design and Couplings<br />

Model<br />

IGBT Model<br />

Tridimensional IGBT pack model and EM study<br />

• Parasitic model extraction<br />

• IGBT circuit model<br />

• Far Field Study <strong>for</strong> Electric Field EM<br />

Far Field Study


Introduction<br />

Different<br />

Finite Element Method<br />

Modeling<br />

Boundary Element<br />

Method<br />

•<br />

techniques will<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

be<br />

seen<br />

Tridimensional IGBT pack model and EM study<br />

• Parasitic model extraction<br />

• IGBT circuit model<br />

System Simulation<br />

• Far Field Study <strong>for</strong> Electric Field EM<br />

Finite Element<br />

Method


Overview<br />

•<br />

•<br />

•<br />

•<br />

•<br />

•<br />

Introduction to the power study<br />

Static electromagnetic field study<br />

Parasitics extraction<br />

IGBT characterization<br />

System simulation<br />

Emitted fields<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


ElectroMagnetic Study<br />

•<br />

•<br />

Module layout<br />

verification<br />

The module contains 8 IGBTs in parallel:<br />

does each IGBT receive the same amount of<br />

current?<br />

–<br />

–<br />

If the current flows un-evenly, this will cause<br />

mechanical stress and reliability issues.<br />

Electromagnetic simulation is required. We<br />

use Maxwell3D.<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


ElectroMagnetic Study<br />

•<br />

•<br />

•<br />

•<br />

•<br />

The layout<br />

The DC solver<br />

in imported<br />

is<br />

The input current<br />

The sink<br />

used<br />

from<br />

(600 A) is<br />

(return current<br />

Outputs: conduction path<br />

path) is<br />

the CAD tool<br />

defined<br />

defined<br />

600 A Sink<br />

and current<br />

distribution<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


ElectroMagnetic Study<br />

The structure is meshed<br />

using automatic and<br />

adaptive meshing<br />

Current Distribution<br />

IGBTs on, Diodes off<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


ElectroMagnetic Study<br />

•<br />

•<br />

•<br />

The end IGBTs see less current<br />

than the center ones.<br />

This can cause reliability issues<br />

as the center IGBTs will be<br />

overloaded<br />

An optimization of the copper<br />

tracks can be made in order to<br />

equalize the currents.<br />

Igbt1a and Igbt4a have the<br />

highest quantity of current<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Overview<br />

•<br />

•<br />

•<br />

•<br />

•<br />

•<br />

Introduction to the power study<br />

Near field electromagnetic study<br />

Parasitics extraction<br />

IGBT characterization<br />

System simulation<br />

Emitted fields<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Parasitics Extraction<br />

•<br />

•<br />

•<br />

Once the layout is optimized, the next step is to extract the resistance,<br />

inductance and capacitance (RLC) parameters of the package.<br />

For this<br />

Example<br />

we<br />

use the boundary<br />

<strong>for</strong> two conductors<br />

element<br />

method<br />

in Q3D<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Parasitics Extraction<br />

•<br />

Frequency Dependent <strong>Effects</strong><br />

•<br />

•<br />

•<br />

Integrated power-electronic modules exhibit frequency-dependent<br />

behavior due to eddy current and skin effects.<br />

In these cases, it may not be sufficient to rely on resistance and<br />

inductance extracted at a single operating frequency<br />

For example, coax conductors:<br />

Low Frequency <strong>High</strong> Frequency<br />

Same<br />

geometry<br />

Different<br />

frequency<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

=<br />

Different Parasitics


Parasitics Extraction<br />

•<br />

Gate<br />

Extracting parameters is straight<strong>for</strong>ward as the nets are<br />

automatically assigned.<br />

net<br />

Emitter<br />

Collector net<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

net


Parasitics Extraction<br />

•<br />

•<br />

How do we set up the frequency sweep?<br />

–<br />

–<br />

We<br />

Through Nyquist sampling, we know that to capture a<br />

time step of Ts, we need to obtain frequency domain<br />

in<strong>for</strong>mation up to:<br />

1<br />

Fmax<br />

=<br />

2×<br />

t<br />

For a time domain wave<strong>for</strong>m with a risetime of 80 ns, in<br />

order to capture the ringing in the time domain, we would<br />

want to capture at least 4 samples during this risetime.<br />

This implies a sampling time of 20 ns<br />

need<br />

to solve<br />

s<br />

up to 50 MHz (= 1/20ns)<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Parasitics Extraction<br />

•<br />

The simulation outputs consist of the RLC matrices <strong>for</strong> different frequencies<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Parasitics Extraction<br />

•<br />

•<br />

How do we<br />

Basic methodology:<br />

•<br />

•<br />

•<br />

•<br />

use the parasitics in the circuit simulator?<br />

Compute N-port S parameters (frequency sweep)<br />

Convert this into in<strong>for</strong>mation that circuit simulator understands<br />

Circuit simulator per<strong>for</strong>ms inverse FFT to find impulse response<br />

n<br />

y(<br />

nΔt)<br />

≅ ∑ s((<br />

n − k)<br />

Δt)<br />

x(<br />

kΔt)<br />

k = n−(<br />

N −1)<br />

Convolution is used to produce time-domain results<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

t<br />

∫−∞ Y ( jω<br />

) = S(<br />

jω)<br />

X ( jω)<br />

→ y(<br />

t)<br />

= s(<br />

t)<br />

⊗ x(<br />

t)<br />

= s(<br />

t −τ<br />

) x(<br />

τ ) dτ<br />

Copper shield<br />

Silicon<br />

Polyethylene<br />

Silicon<br />

Copper<br />

Voltage<br />

1.1<br />

1.1<br />

1.1<br />

1.0<br />

950.0m<br />

900.0m<br />

876.5m<br />

Voltage versus Time Using Different 2D Extractor Mode<br />

Damping<br />

VM11.V [V]<br />

VM_Linear_1Hz_Model.V [V]<br />

VM_Linear_1MHz_Model.V [V]<br />

VM_Frequency_Model.V [V]<br />

Phase<br />

17.55u 18.00u 18.50u 19.00u 19.50u<br />

20.00u<br />

Time (Seconds)


Overview<br />

•<br />

•<br />

•<br />

•<br />

•<br />

•<br />

Introduction to the power study<br />

Near field electromagnetic study<br />

Parasitics extraction<br />

IGBT characterization<br />

System simulation<br />

Emitted fields<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


SIMPLORER 8<br />

•<br />

•<br />

Simplorer 8 is a circuit simulation<br />

tool <strong>for</strong> solving multi-domain lumped<br />

circuit problems.<br />

Link projects together to achieve<br />

dynamic linking of multiple<br />

simulations on a single sheet.<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


SIMPLORER 8<br />

•<br />

Modeling<br />

•<br />

•<br />

•<br />

•<br />

New Parametrization<br />

tool <strong>for</strong> IGBT<br />

Enhanced SMPS Library - Over<br />

450 New VHDL-AMS DC/DC<br />

Converter Models in SMPS Digital<br />

Co-simulation<br />

Spice–Pspiceintegration<br />

Enhancements to individual<br />

models …<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


System Integration<br />

•<br />

How do we<br />

import the results<br />

from<br />

•<br />

•<br />

•<br />

•<br />

•<br />

Q3D?: Q3D dynamic link<br />

2 Types of links: Single Frequency or<br />

Frequency dependent<br />

No need<br />

to manually<br />

import output file<br />

Simplorer incorporates directly the Q3D<br />

project<br />

If some results are not available, Simplorer<br />

dynamically launches Q3D<br />

Parameters and variables can be passed<br />

between S8 and Q3D<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


System Simulation<br />

Wattmeter<br />

IGBT<br />

Vc<br />

<strong>Power</strong> Module from Q3D<br />

<strong>for</strong> board parasitics<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

Vg


IGBT Characterization<br />

2 types of models<br />

•<br />

•<br />

•<br />

Basic Dynamic<br />

Accurate models of the semiconductors<br />

are needed to achieve a good circuit<br />

simulation<br />

Simplorer 8 offers a parameterization<br />

tool <strong>for</strong> IGBTs<br />

The user needs to import the data from<br />

the datasheet<br />

are available<br />

and Average Dynamic<br />

in Simplorer 8:<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


IGBT Characterization<br />

Objective Average Basic<br />

Dynamic<br />

DC<br />

characteristics<br />

Electrical<br />

Dynamics<br />

Thermal<br />

Dynamics<br />

Capacitance<br />

Models<br />

-<br />

Transfer characteristic<br />

Advanced Dynamic<br />

Ic(Vge) accurate<br />

- Output characteristic Ic(Vce) accurate in<br />

the regions of voltage and current saturation<br />

- Intrinsic temperature dependency<br />

-<br />

Considered<br />

Partial Fractional or<br />

Continued Fractional<br />

- Default Full access to the<br />

C(V) C(V) characteristics<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


IGBT Characterization<br />

Sub circuit of the basic dynamic IGBT model<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


IGBT Characterization<br />

SheetScan<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


IGBT Characterization<br />

•<br />

•<br />

Once all the curves<br />

The tool<br />

fits<br />

and data are entered, start<br />

the data to the internal<br />

Characterization tool<br />

extraction<br />

Simplorer model using<br />

Genetic<br />

Algorithm<br />

Component dialog<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


IGBT Characterization<br />

Test Circuit<br />

rise time= 40 μs<br />

fall time = 50 μs<br />

Ansoft Corporation Simplorer1<br />

50.00 3000.00<br />

15.00<br />

R2.I [A]<br />

40.00<br />

30.00<br />

20.00<br />

10.00<br />

0.00<br />

-10.00<br />

U1.VCE<br />

2500.00<br />

2000.00<br />

1500.00<br />

1000.00<br />

500.00<br />

0.00<br />

499.90 499.95 500.00 500.05 500.10<br />

Time [us]<br />

500.15 500.20 500.25 500.30<br />

2000.00<br />

1500.00<br />

1000.00<br />

500.00<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

switch_on<br />

TR<br />

TR<br />

TR<br />

Curve Info<br />

Ansoft Corporation Simplorer1<br />

50.00 2500.00<br />

15.00<br />

Curve Info<br />

R2.I [A]<br />

40.00<br />

30.00<br />

20.00<br />

10.00<br />

0.00<br />

-10.00<br />

U1.VCE<br />

Vce<br />

Switch on<br />

Switch off<br />

switch_off<br />

Ic<br />

Vce<br />

0.00<br />

-15.00<br />

999.00 999.50 1000.00 1000.50 1001.00<br />

Time [us]<br />

1001.50 1002.00 1002.50 1003.00<br />

Ic<br />

U1.VCE<br />

VM2.V<br />

R2.I<br />

TR<br />

5.00<br />

0.00<br />

-5.00<br />

10.00<br />

5.00<br />

0.00<br />

-10.00<br />

-5.00<br />

-10.00<br />

-15.00<br />

U1.VCE<br />

VM2.V<br />

TR 10.00<br />

TR<br />

R2.I<br />

VM2.V [V]<br />

VM2.V [V]


System Simulation<br />

2500 Voltage<br />

Source<br />

Line Resistance<br />

and Line Inductance<br />

Vg: Gate Voltage<br />

(+/-15V)<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


System Simulation<br />

•<br />

•<br />

•<br />

Issue:<br />

•<br />

•<br />

Accurate simulation of the switching of the IGBTS requires<br />

very small time steps (hmin = 10ps)<br />

System simulation requires<br />

long time step<br />

(t = 5ms)<br />

Simplorer allows the user to dynamically change hmin and hmax<br />

using State Graphs.<br />

When<br />

the switching<br />

has occured, the time step<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

can<br />

be<br />

increased.<br />

Switching Steady state Switching


System Simulation<br />

-Vge<br />

Vce<br />

Vge<br />

Vce<br />

Ic<br />

Reduce Time Step HMin<br />

Ic<br />

Vge<br />

Vce<br />

Vce, Vge, Ic<br />

over time (Igbt3b)<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

Vge<br />

Vce<br />

Ic<br />

Vge<br />

Ic<br />

g<br />

Vce<br />

c<br />

e<br />

Ic


System Simulation<br />

Vg<br />

Vce<br />

Vge<br />

<strong>Power</strong><br />

The power pulse duration is much smaller than the rise/fall time<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

Ic<br />

of Ic<br />

and Vce


System Simulation<br />

Instantaneous power level through Igbt3a<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


System Simulation<br />

<strong>Power</strong> levels of the full set of IGBT’s on switch on<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


System Simulation<br />

•<br />

•<br />

Igbt1a and Igbt4a receive the highest<br />

power levels.<br />

This is consistent with the DC<br />

Conduction Maxwell3D solution<br />

Igbt1a<br />

Igbt4a<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


System Simulation<br />

The fundamental frequencies of the power range<br />

between 16 and 54 MHz<br />

t @<br />

Pmax<br />

(μs)<br />

t @ P<br />


System Simulation<br />

FTT of the power through Igbt1a<br />

Most of the power level is below 110 MHz<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Emitted Fields<br />

•<br />

•<br />

There is very high power going through the IGBTs (almost 60 000 W in this<br />

study) during a very short period of time (60 ns). This switching can cause<br />

<strong>EMI</strong> issues in the inverter, but also in the surrounding equipment<br />

To be<br />

•<br />

•<br />

answered<br />

using<br />

the finite<br />

Will the module radiate?<br />

Are the field<br />

levels<br />

surrounding<br />

element<br />

method<br />

the module within<br />

in HFSS:<br />

mandated levels?<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Emitted Fields<br />

•<br />

•<br />

•<br />

•<br />

•<br />

The power pulse in the IGBTs have most of the<br />

energy in the 16- 110 MHz range.<br />

The largest<br />

There is<br />

metallic<br />

piece<br />

is<br />

a chance of having<br />

λ<br />

< 4 * L = 600 mm.<br />

This is<br />

By itself, the module will<br />

150 mm in the module<br />

radiation if<br />

<strong>for</strong> a frequency<br />

not radiate.<br />

of 500 MHz.<br />

However, the power module in the train is<br />

surrounded by other metallic objects than can be<br />

fairly large. These objects can cause the radiation<br />

of electric fields during switching.<br />

Maxwell’s Equations<br />

div D = ρ<br />

curl E = -∂B/∂t<br />

div B = 0<br />

curl H = J + ∂D/∂t<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Emitted Fields<br />

Exposure<br />

limits<br />

defined<br />

by European<br />

Community<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

•<br />

•<br />

Regulators impose<br />

maximum levels of<br />

electric fields close to<br />

electric equipment.<br />

In the 10-110 MHz<br />

range:<br />

Emax=61V/m


Emitted Fields<br />

•<br />

•<br />

Each<br />

IGBT pad is<br />

The port lies between<br />

excited<br />

using<br />

the collector<br />

lumped<br />

ports<br />

and emitter pads<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Emitted Fields<br />

•<br />

•<br />

The structure is discretized with adaptive meshing. The meshing<br />

frequency is 100 MHz<br />

The frequency<br />

sweep<br />

ranges from 15MHz to 120 MHz<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Emitted Fields<br />

Spectrum<br />

(MHz)<br />

For each<br />

<strong>Power</strong><br />

(W)<br />

frequency, the power amplitude is<br />

E field at 1m <strong>for</strong> 1000w<br />

(V/m)<br />

E field at 1m<br />

(V/m)<br />

16.52892562 21439.97604 2.6312 56.41286497<br />

33.05785124 8635.09049 2.7994 24.17307232<br />

49.58677686 5579.619715 2.8731 16.0308054<br />

66.11570248 4131.16773 3.063 12.65376676<br />

82.6446281 3276.823585 3.4045 11.15594589<br />

99.17355372 2712.888158 3.8924 10.55964586<br />

115.7024793 2308.359536 4.4861 10.35553171<br />

132.231405 2022.75744 4.905 9.921625241<br />

Spectrum from<br />

Outputs from Simplorer<br />

Inputs <strong>for</strong> HFSS<br />

Simplorer<br />

Outputs From HFSS<br />

(normalized results)<br />

Fields Levels<br />

entered<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary


Emitted Fields<br />

mag<br />

E @ 100 MHz, <strong>Power</strong> = 10 000W<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary<br />

•<br />

•<br />

•<br />

The E field is very localized<br />

close to the module even at<br />

100 MHz<br />

However, the very high<br />

power can lead to large<br />

values of E field even far<br />

from the module<br />

This design is fine at<br />

110MHz.<br />

<strong>Power</strong> E field at 1m<br />

Spectrum (M Hz) (W) (V/ m)<br />

115.7024793 2308.359536 10.35553171


Conclusion<br />

•<br />

•<br />

•<br />

•<br />

We have seen that the combination of several simulation techniques can<br />

give a good approach to <strong>EMC</strong>/<strong>EMI</strong> issues, both in conduction and emission<br />

modes<br />

Accurate prediction requires the use of Finite Element Methods, Boundary<br />

Element Methods, System Simulation along with Accurate Component<br />

Characteristics<br />

Package traces need optimization to balance current distribution<br />

The simulated module does not radiate <strong>for</strong> the given harmonics, and is<br />

within regulated near field field limits.<br />

© 2008 Ansoft, LLC All rights reserved. Ansoft, LLC Proprietary

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