Finite Element Analysis of Electromagnetic Interference Suppression Components

by Benjamin R. Kennedy

Departmental Honors Thesis

The University of Tennessee at Chattanooga Mechanical Engineering

Project Director: Dr. Ron Goulet Examination Date: April 3rd, 2007

Dr. James Hiestand Dr. Virgil Thomason

Dr. David Levine

Examining Committee Signatures:

Project Director

Department Examiner

Department Examiner

Liaison, Departmental Honors Committee

Chairperson, University Departmental Honors Committee

TABLE OF CONTENTS Abstract 1

1. Introduction 2

1.1. Problem Definition 2

1.2. Background 2

1.2.1. Soft Ferrite Magnetism 2

1.2.2. Resonance in Soft Ferrite Material 3

1.2.3. Soft Ferrite in EMI Suppression 4

1.2.4. Finite Element Analysis 5

1.2.5. FEA in Ferrite Component Design 7

2. Theory 8

2.1. Electromagnetics 8

2.2. FEMM Equations 11

3. Methodology 14

3.1. Specimen Selection 14

3.2. Electrical and Physical Testing 15

3.3. 2-D Model Construction 16

3.4. Problem Definition 17

3.5. Meshing 18

3.6. Post Processing 19

4. Results 20

4.1. Nickel Zinc Components 20

4.2. Manganese Zinc Components 23

5. Discussion 27

5.1. Planar Geometry Assumption 27

5.2. Wire Placement Assumption 28

5.3. Flux Leakage 29

5.4. Resonance Error 30

6. Conclusions 31

7. Recommendations 32

8. Bibliography 33

9. Appendix 34

1

Abstract Electromagnetic interference (EMI) is the disruption of operation of an

electronic device caused by an electromagnetic field. EMI through input ports can be

reduced by using soft ferrite components that produce high impedance when excited

by the errant electromagnetic field. Development costs associated with the design of

new EMI suppression components is steep because of prototyping, but could be

greatly reduced by modeling the electrical properties of new components from the

known material properties through the use of finite element analysis.

The goal of this project was to validate a 2-D finite element model of

the electrical properties of impedance, resistance, and reactance based on the material

properties acquired from simple toroid cores. The work required to accomplish this

goal includes physical and electrical specimen testing, construction of the 2-D planar

model in FEMM 4.0 or SolidWorks 2006, analysis of the model using FEMM 4.0,

and the validation of the model using the experimental results.

The finite element model accurately predicted the low frequency electrical

properties of the components, but failed to predict properties past the onset of

material resonance. The model also encountered decreased accuracy from geometric

assumptions required for 2-D planar modeling and from flux leakage from

components. The model is invalid for the design of suppression components since

they operate in their resonance range. More exact 3-D modeling techniques might be

able to model the effects of resonance, but the 2-D finite element analysis could be

used in the design of components that operate at frequencies below resonance.

2

1. Introduction

1.1 Problem Definition

The objective of this project is to develop an experimentally validated 2-D

finite element model to approximate the electromagnetic behavior of large or non-

toroidal soft ferrite electromagnetic interference (EMI) suppression components

based on material properties derived from a simple toroid of the same material with

the objective of reducing prototyping costs and design time.

EMI through input ports can be greatly reduced by using soft ferrite

components that produce high impedance when excited by the errant electromagnetic

field. Development costs associated with the design of new EMI suppression

components is steep because of prototyping costs. The cost of prototyping could be

greatly reduced by modeling the electrical properties of new components from the

known material properties through the use of finite element analysis.

1.2 Background

1.2.1 Soft Ferrite Magnetism

Soft ferrite is one of the most diverse magnetic materials used in industry,

finding use primarily as power transformer cores, electromagnetic interference

suppression cores, and signal conditioning cores in computer hardware, and

telecommunications. The wide use of soft ferrite results from the diverse types of

3

materials available, the extensive range of operating frequencies, the versatility of

core shapes, and their low cost.

Soft ferrite is a ferrimagnetic material, and is composed primarily of iron,

typically combined with nickel and zinc (NiZn) or manganese and zinc (MnZn)

though some applications require the use of more expensive metals such as cobalt,

titanium, or silicon.1 The magnetism results from the nature of transition metals;

transition metals have a large quantity of uncompensated electrons which produce a

net magnetic moment. When multiple ions are combined they arrange themselves in

a crystalline structure that lines up some of these uncompensated electrons in planes

of net magnetic charge. If all of the planes of magnetic charge face the same

direction, the material is ferromagnetic. When some of the planes face the opposite

direction with a net magnetic moment still remaining, the material is ferrimagnetic.

Since ferromagnetic materials have all of the small magnetic dipoles facing

the same direction, they have a larger maximum magnetic moment. 2 Ferrimagnetic

materials are more useful in the electronics industry, however, because while the

opposing magnetic moments reduce the maximum magnetic moment of the material,

it also increases resistivity, which reduces energy loss from eddy currents.3

1.2.2 Resonance in Soft Ferrite Materials

Resonance in a soft ferrite material describes the propagation of standing

electromagnetic waves inside the ferrite. Resonance is referred to both as material

resonance and dimensional resonance, since it depends both on the material properties

4

of permeability and permittivity and the dimensions of the component. Dimensions

affect resonance since the fundamental standing wave will set up across the smallest

cross-sectional area of the component while permeability and permittivity affect the

magnitude of the resonance response. Higher permeability and permittivity create a

stronger resonance effect. Both the material properties and the cross-sectional area

factor in to the frequency where resonance occurs. Larger dimensions and conversely

smaller permeability and permittivity create a lower resonance frequency.

When the fundamental standing wave sets up across the smallest cross-

sectional area of a component, the surface magnetic flux applied by the harmonic

current source is cancelled by the generated magnetic flux in the center of the

component. Under these conditions the net reactive flux is zero, creating a large

resistive response. Essentially, all of the energy applied by the current source is

dissipated as heat instead of generating a net magnetic response. Since the electric

and magnetic fields are linked, there is a corresponding standing wave in the electric

flux density. This means that both the observed permeability and permittivity are

zero at the resonance frequency.2

1.2.3 Soft Ferrite in EMI Suppression

Soft ferrite components are often used to suppress unintended signals

traveling through, or being emitted from cables or wires. For example, the plastic

cylinders found on computer monitor cables are EMI suppression cores used to

prevent noise from other instruments interfering with the display. Soft ferrite

5

components suppress unintended signals by acting on the magnetic fields that

surround the cable or wire.

When a signal travels through a conductor, a magnetic field is generated

around that conductor. A soft ferrite component, when placed around the conductor,

interacts with this magnetic field. The applied magnetic field activates the ferrite,

which in response to the magnetic field, imposes an impedance that reduces the

magnitude of the unintended signal. The frequency range where the component has

high impedance is the frequency range it suppresses; frequencies outside this range,

where the impedance is very low, are unimpeded. Thorough definitions of impedance

and relevant material properties are explained in depth later in Section 2.

1.2.4 Finite Element Analysis

Finite element analysis (FEA) is a numerical method that models a region by

dividing it into small discrete elements composed of interconnecting nodes. Finite

element analysis obtains the solution to the model by determining the behavior of

each element separately, then combining the individual effects to predict the behavior

of the entire model. The interconnecting nodes of the elements make the solution of

one element dependent on another, meaning that to reach an accurate solution, FEA

must solve each element several times, possibly thousands of times, to reach a

solution. The accuracy is also dependant upon the number of elements. More

elements will increase the models solution accuracy, but as the number of elements

increase, the solution time increases as well.

6

Finite element analysis can be used with either 2-D or 3-D models. 3-D

models generally offer a more accurate analysis as they include all three planes of the

physical world. A 3-D model is also composed of a great deal more nodes and

elements as well, drastically increasing solution time. For this reason, it is often

desirable to employ a 2-D model to reduce solution time. A 2-D model estimates the

missing third dimension using either axisymmetric or planar geometry.4

Axisymmetric geometry generates a model using cylindrical components x, r, and ,

where is taken as 360. Planar geometry generates a model using Cartesian

components x, y, and z, where z is specified as some constant value for the entire

model.5

The iterative nature of FEA makes the analysis of models impractical by hand

but perfect for computers. Several electromagnetic FEA packages exist, ranging from

fully three dimensional packages such as ANSYS and Maxwell 3D, to simpler 2-D

packages like Maxwell 2D, Quickfield, and FEMM. All FEA computer simulations

consist of three parts; the preprocessor, analysis, and postprocessor. The

preprocessing consists of constructing the model from nodes, curves, and surfaces,

defining boundary conditions and block labels, and generating the mesh. Analysis is

the automated process where the model is solved using the prescribed conditions and

computational procedures. Postprocessing involves the visualization, study, and

analysis of results. In electromagnetic models, this often involves a flux density plot,

and the determination of circuit characteristics such as voltage drop, resistance,

reactance, and inductance.5

7

1.2.5 FEA in Ferrite Component Design

The traditional method of designing a new soft ferrite component involves the

creation of prototypes and physically testing their magnetic properties to determine

the best material composition and concentrations. Even if the composition of the

component is known, the specific concentrations of individual elements in the

material will drastically vary the properties of the ferrite, requiring several

concentrations to be tested. If the part is relatively large, testing could present a large

material cost. If the geometry is new, a new die must be generated to press the part.

Also, the mixing of the large batches of materials, pressing, and firing the prototypes,

and electrical testing all present a large commitment of resources.3

Finite element analysis software can greatly reduce cost, as known material

constants can be evaluated for the new components geometry, modeling the

electrical properties of the component with a much smaller time and monetary

commitment. Several free 2-D FEA electromagnetic packages exist, the most notable

being Finite Element Method Magnetics (FEMM) for its simple interface, lack of

node restrictions, and built in LUA scripting capabilities. Using free 2-D FEA

packages has the obvious advantage of eliminating the cost associated with licensing

expensive 3-D software, but is useful only if it is possible to produce a valid 2-D

model of the frequency response of the component.6

8

2. Theory

2.1 Electromagnetics

The basic circuit properties defining a soft ferrite component are the

impedance, resistance, reactance, and inductance. Impedance measures the

opposition of the ferrite component to an alternating current and consists of both the

resistance and reactance of a component. The magnitude of impedance is given as

equation 2.1

5.022 )(|| XRZ += (2.1) where |Z| is the magnitude of the impedance, R is the resistance, and X is the

reactance, all in the units of ohms. The reactance of a soft ferrite component is

primarily due to its inductance, and relates to the inductance according to equation

2.2

LjX L = (2.2) The inductive reactance contributes to the opposition of an alternating current

because the varying current generates a varying magnetic field; this magnetic field in

turn produces an electromotive force resisting changes in the current. Thus an

inductor resists the alternating current by greater and greater amounts as the

frequency increases. The inductance is a measure of the amount of magnetic flux

produced for a given electric current. This relationship is described in equation 2.3

iL= (2.3)

9

where L is the inductance in henrys, is the flux density in webers, and i is the

current in amperes.7

The electrical properties depend upon both the magnetic properties of the

material and the physical dimensions of the component. The permeability of the

component is purely a function of the material, independent of its size or shape.

Permeability has both a real and imaginary component known as the inductive and

resistive components. The real component measures energy stored in the material,

while the imaginary component describes the energy loss due to material resistance.

The real and imaginary components of permeability relate to inductance and

resistance by equations 2.4 and 2.5

0

'LL= (2.4)

02

"fLR = (2.5)

where and are the inductive and resistive permeability, L is the inductance in

henries, R is the resistance in ohms, f is the frequency in hertz, and L0 is the nominal

inductance based on the mean magnetic path length and area, described by equation

2.6.

e

e

lANL

2

00 = (2.6)

0 is the permeability of free space, 4x10-7 henrys/meter, N is the number of turns of

wire around the component, Ae is the mean magnetic path area in meters2, and le is

the mean magnetic path length in meters. The mean magnetic path length and area

10

vary depending on the component geometry. Closed form values are determined

from equations 2.7 and 2.8.

= ldAlAee (2.7)

= 22 ldAlAee (2.8) Solving equations 2.7 and 2.8 for the case of a toroid with square cross section,

dA=hdr and l=2r, Ae and le are determined to be

21

12

11)/ln(2

rrrrle =

(2.9)

21

122

11)/(ln

rrrrhAe = (2.10)

where h is the height of the toroid, r1 is the inner radius, and r2 is the outer radius.

With these equations, the permeability of a material can be determined from a

toroid for use in modeling the electrical properties of parts with more complex

geometries. Most models do not accept real and imaginary permeability components,

so the magnitude of permeability and hysteresis angle are used instead, described in

equations 2.11 and 2.12.

5.022 )"'(|| += (2.11)

)'"(tan 1 = (2.12)

11

Equations 2.1, 2.4 to 2.6, and 2.9 through 2.12 are all directly used to calculate

inductance, Z, and the inductive and resistive permeability, and , from the

measured and modeled data.3

2.2 FEMM Equations

For time harmonic magnetic problems, FEMM solves a single equation

relating magnetic vector potential to current density derived from three of Maxwells

equations; Gausss law of magnetism, Amperes circuit law, and Faradays law of

induction. Gausss law, Amperes law, and Faradays law are given as equations

2.13, 2.14, and 2.15 respectively,

0= B (2.13)

tDJH += (2.14)

tBE = (2.15)

where B (Wb/m2) is the magnetic flux density, H (A/m) is the magnetic field strength,

J (A/m2) is the current density, E is the electric field intensity, and and are known as the divergence and curl operators respectively, both with units 1/m. The

change in electric flux density with respect to time tD , or displacement current, is

assumed zero form magnetic problems in FEMM. This assumption is valid for

frequencies below the radio range and problems that do not involve coils of wire.

Magnetic flux density B and magnetic field strength H relate to each other by the

12

permeability , while electric field intensity E and current density J are related by the

material conductivity . These relationships are described in equations 2.16 and 2.17.

HBB )(= (2.16) EJ = (2.17) where (B) implies permeability is a function of the magnetic flux density. Equations

2.13, 2.14, and 2.15 can be simplified by solving the electromagnetic field in terms of

magnetic vector potential. The magnetic flux density B relates magnetic vector

potential A by equation 2.18.

AB = (2.18) Substituting equations 2.16 and 2.18 into equation 2.14 yields equation 2.19

JBA =

)( (2.19)

which relates the magnetic vector potential to the known current density and

permeability. Substituting in the magnetic vector potential into Faradays law (eq.

2.18) yields equation 2.20.

AE = (2.20) Integrating this equation and substituting the resulting value of the electric field

intensity E into equation 2.17 yields the relationship given in equation 2.21

VAJ = (2.21) where V is a constant voltage gradient used by FEMM to enforce constraints on the current carried in conductive regions. Substituting equation 2.21 into equation 2.19

yields equation 2.22.

13

VJABA

src +=

)( (2.22)

When the current oscillates at a constant frequency, taking the phasor transform of the

magnetic vector potential A and substituting back into equation 2.22 yields the

equation FEMM employs to solve a specified model, described in equation 2.23

VJajBa

src +=

)( (2.23)

where is the specified current frequency multiplied by 2, a is the complex number

form of the magnetic vector potential, and srcJ is the phasor transform of the applied

current source.5

14

3. Methodology

The goal of this study is to develop an experimentally validated 2-D finite

element model to approximate the electromagnetic behavior of large or non-toroidal

soft ferrite components based on material data gathered from simple toroidal test

cores. The work required to accomplish this goal includes physical and electrical

specimen testing, construction of the 2-D planar model in FEMM 4.0 or SolidWorks

2006, analysis of the model using FEMM 4.0, and the validation of the model using

the experimental results.

3.1 Specimen Selection

Specimens were selected to best explore the capabilities of FEMM 4.0. The

variables explored are material type, size, flux fringing, and eddy current effects due

to sharp corners. To address these variables, five components were selected from two

different material types. The five components are pictured in Figure 2.1. All five

specimens are EMI suppression components. The first two specimens, pictured top

left and top center, are a toroid and ribbon core respectively, constructed of Steward

NiZn material 64. The last three, pictured top right, bottom left, and bottom right, are

a toroid, and two oval cores, denoted number 1 and 2, composed of Steward MnZn

material 28. The size difference between the small NiZn components and the large

MnZn components investigates the possiblility of size dependency on model

accuracy. The ribbon core investigates the capability of FEMM to account for flux

15

fringing from the component due to the close inner walls, while the oval cores test the

sharp corner modeling accuracy.

Figure 2.1: Soft Ferrite Test Components

3.2 Electrical and Physical Testing

All electrical testing was completed on a Hewlett Packard 4396B

Network/Spectrum/Impedance Analyzer mounted with an Agilent 16092A Spring

Clip Fixture. The meter was fully calibrated before testing, and the fixture was

shorted using the testing wire to remove the wires effect on the components

electrical properties before each test. Each of the five components was then tested

three times each for impedance, resistance, reactance, and inductance at 200 points

across the frequency range from 100 kHz to 1.8 GHz. The three runs of each

component are then averaged, and electrical properties are then refined and graphed

16

with Microsoft Excel. The standard deviation in each result was calculated using the

Students T statistic, but since the agreement between each test was so close, they are

not included on any of the graphs. The permeability and phase angle for the MnZn

and NiZn are derived from the inductance and resistance of the toroid cores in Excel,

using equations defined in the theory section. The ferrite core physical dimensions

were measured using digital calipers to ten thousandths of an inch (.0001 inch). Each

measurement was taken in three places along the sample to ensure there were no

physical defects in the component. Figures A.1, A.2, A.3, A.4, and A.5 show the

average measured dimensions of each component.

3.3 2-D Model Construction

The physical model consists of the outer boundary of the solution region, the

component, and the wire. The components were drawn as planar two dimensional

components in SolidWorks to allow for easy dimension modification and uploaded to

FEMM as a .dxf file. The outer boundary and wire were drawn in the FEMM

preprocessor. The outer boundary is simply some expanse of air around the

component, which in the model is defined as a circular region with a radius of 18

inches centered on the component. The wire is a circle placed in the center of the

component with a standard diameter based on the gauge. 18 AWG and 28 AWG wire

were both used, 18 AWG for the large MnZn core and 28 AWG for the small NiZn

core, with standard diameters of 0.0403in and 0.0126in respectively.

17

3.4 Problem Definition

The problem in FEMM is defined by the problem type, units, frequency,

depth, solver precision, and minimum angle. All components are modeled as a planar

problem type, with inch units, and the default solver precision and minimum angles

of 1e-008 significant digits and 30 degrees. The depth is equal to the height of the

component modeled, while the frequency varies between .1 and 100 MHz for each

run. The component is described by the block label Ferrite defined as a linear B-

H material. The properties required to define the material are the relative

permeabilities in the x and y directions, x and y, and the hysteresis angle in the x

and y directions, hx and hy. All components modeled are constructed of isotropic

material so the x and y components are equal.

The wire is defined both by a block label and a circuit element label. The

wire block label is defined from the material library included with FEMM, which has

block labels describing the material and physical characteristics of all copper AWG

wires. The circuit element label simply describes the wire as a current carrying

element, with a specified current and number of turns. For each of the models, the

current is specified as 0.1 amperes and 1 turn. The specification of 0.1 amperes is

somewhat arbitrary; any current inside of the linear permeability range of the material

would be acceptable.

The area between the problem boundary and the component and the wire and

the component is defined by the air block label, which has a relative permeability of

1. The boundary itself is defined as a Dirichlet boundary condition, where the value

18

of magnetic vector potential A is a known value. The value of A for this model is

assumed zero, meaning all flux is contained within the region. This assumption is

valid as long as the boundary is sufficiently far from the component. Another option

would have been to impose a Robin mixed boundary condition, where the magnetic

vector potential A is related to its normal derivative by a constant. This would allow

the boundary to mimic the behavior of an unbounded region. Since the model area is

so large, the Robin mixed boundary condition is unnecessary.

3.5 Meshing

FEMM 4.0 will automatically generate a triangular mesh, but it is fairly

coarse, requiring user defined refinement of the mesh to increase accuracy. Since the

magnetic activity occurs primarily in the ferrite component only its mesh need be

refined, with the exception of the ribbon core, which has a refined mesh for both the

component and the air gap between itself and the wire so that flux leakage into the air

gap is properly modeled. The size of the mesh depends primarily on the size of the

component. A very fine mesh on a large part would create a prohibitively large

number of nodes, drastically increasing solution time. For instance, the NiZn toroid

model has a mesh size of .02 for the component while the NiZn ribbon, with a smaller

surface area, has a mesh size of .008 for the component and .01 for the air gap. All of

the MnZn components have a much larger mesh size of 0.04. Meshes of the NiZn

toroid, NiZn ribbon, and MnZn oval core 1 are in the Appendix as Figures A.6, A.7,

and A.8.

19

3.6 Post Processing

After running the analysis, the electrical properties are determined by selecting

the circuit properties for the current-carrying wire. The resistance and reactance of the

component is simply the voltage divided by the current of the wire, where the

resistance is the real component and the reactance is the imaginary component. The

voltage divided by current for each frequency is copied to a text file, and then opened

in Microsoft Excel using spaces as delimiters in order to separate the resistance and

reactance into individual columns without having to cut and paste directly from the

FEMM postprocessor. Impedance is determined by using equation 2.1 defined in the

theory section. These results are then compared with the measured values of

impedance, resistance and reactance in Microsoft Excel in order to validate the

accuracy of the model.

A flux density plot is also produced in the post processor, which is useful in

visualizing edge effects and flux leakage. Flux density plots of the NiZn toroid, NiZn

ribbon, and MnZn oval core 1 are provided in the appendix as Figures A.9, A.10, and

A.11.

20

4. Results The simulation results obtained from FEMM 4.0 are compared to the

experimental data obtained from electrical testing. The simulation was run for 27

frequencies between .1 and 1000 MHz for the NiZn components and 24 frequencies

between .1 and 200 MHz for the MnZn toroid, and 23 frequencies between .1 and 100

MHz for the two MnZn oval components. The frequency range of the MnZn material

is limited because of the sharp breakdown of the materials magnetic response beyond

its resonance frequency. The results of the simulation and measurement of

impedance, resistance, and reactance are given below in Figures 4.1 through 4.5, with

data tables found in Appendix A as Tables A.1 through A.5. Figures of the inductive

and resistive permeability are also included in Appendix A as Figures A.12 and A.13.

4.1 Nickel Zinc Components

The electrical properties predicted by the model and the measured electrical

properties for the NiZn toroid are described in Figure 4.1. The measured reactance of

the component increases from .33 at .1 MHz to a maximum of 17.75 around 75

MHz before decreasing to .94 at 1000 MHz. The model reactance starts at .33 as

well, but continues to increase with frequency, with a value of 82.41 at 1000 MHz.

The measured and modeled impedance match closely below 10 MHz, but the model

diverges from the measured values with the increase in frequency. The measured and

modeled resistances agree almost perfectly over the entire range of values, with a

maximum difference of only 2.26% between the two curves.

21

The results for the ribbon component are similar to the toroid, with the measured

and modeled electrical properties described by Figure 4.2, but without the close

agreement between the measured and modeled resistance of the toroid. The measured

impedance begins at 1.09 at .1 MHz, with a maximum of 150 at 75 MHz. The

impedance then decreases to 16.44 at 1000 MHz. The measured and modeled

impedance match with less than a 7.5% difference up to 20 MHz, but rapidly diverges

past this point. The model does not predict the rapid increase in resistance and

reactance starting around 10 MHz, producing the divergent behavior.

22

0

10

20

30

40

50

60

70

80

0.1 1 10 100 1000

Frequency (MHz)

ZRX

()

Z ModeledR ModeledX ModeledZ MeasuredR MeasuredX Measured

Figure 4.1 Measured and FEA Model ZRX curves for NiZn Toroid

020

4060

80100120

140160

180200

0.10 1.00 10.00 100.00 1000.00

Frequency (MHz)

ZRX

()

Z ModeledR ModeledX ModeledZ MeasuredR MeasuredX Measured

Figure 4.2 Measured and FEA Model ZRX curves for NiZn Ribbon

23

4.2 Manganese Zinc Components

The electrical properties predicted by the model and the measured electrical

properties for the MnZn toroid are described in Figure 4.3. The model and

experimental impedance, resistance, and reactance all closely match for the MnZn

toroid. The initial values for the measured impedance, resistance, and reactance at .1

MHz are .93 , .14 , and .92 respectively, with corresponding modeled values of

.91 , .15 , and .90 . The impedance has a maximum difference of -3.32% at 200

MHz, with a modeled impedance of 185 and a measured impedance of 179 .

The resistance has several points through the lower frequency range with large

percent difference, with a maximum of -38.34% at 1.63 MHz. The measured

resistance at this frequency is .00116 while the modeled resistance is.00160 .

Due to the very low values for resistance in the low frequency range before the onset

of resonance, these large differences are difficult to see. The reactance of the model

matches very well to the measured values at and below 75 MHz. At 100 and 200

MHz the model predicts an increasing reactance with values of 92 and 95 , while

the true reactance is rapidly decreasing with values of 83.85 and 66.31 .

Figure 4.4 describes the modeled and measured electrical properties of MnZn

oval core 1 over the .1 to 200 MHz frequency range. The modeled electrical

properties of oval

core 1 are accurate for a smaller range of frequencies than the MnZn toroid core. The

percent difference between the model and the measured values of impedance at 10

MHz, 15 MHz, and 20 MHz are -4.79%, -9.48%, and -20.66%, showing the onset of

24

a rapid divergence between the model and measured values. The difference between

the modeled and measured resistance also differs significantly starting at 10 MHz,

with a percent difference of -17.7%, corresponding to values of 33.58 and 28.54 ,

respectively. The modeled and measured reactance at 10 MHz is 52.06 and 51.78

corresponding to a difference of only .5%, with the percent difference reaching -

5.1% around 35 MHz. The modeled reactance continues to increase past this point

while the measured reactance decreases to zero.

The model of MnZn oval core 2 reacts similarly to the model of MnZn oval

core 1 due to their similar geometry. Figure 4.5 gives the modeled and measured

impedance, resistance, and reactance for oval core 2. The shape of the measured

impedance, resistance, and reactance curve are similar to the toroid and oval core 1

curves, but divergence between the impedance begins closer to 15 MHz, resistance

earlier at 5 MHz, and impedance later around 35 MHz. For Impedance, the

difference between impedance at 15 MHz, 20 MHz, and 35 MHz is 4.75%, 16.03%,

and 28.73%, again showing a rapid divergence between modeled and measured

impedance in the high frequency range. The measured reactance decreases from

98.63 at 35 MHz to 66.52 and 24.52 at 75 and 100 MHz. The model predicts a

reactance that continues to increase past 35 MHz, with values of 119.14 and 128.24

at 75 and 100 MHz.

25

0

50

100

150

200

250

300

0.1 1 10 100 1000

Frequency (MHz)

ZRX

()

Z ModeledR ModeledX ModeledZ MeasuredR MeasuredX Measured

Figure 4.3 Measured and FEA Model ZRX curves for MnZn Toroid

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

0.1 1 10 100 1000

Frequency (MHz)

ZRX

()

Z ModeledR ModeledX ModeledZ MeasuredR MeasuredX Measured

Figure 4.4 Measured and FEA Model ZRX curves for MnZn Oval Core 1

26

0

50

100

150

200

250

300

350

400

450

500

0.1 1 10 100 1000

Frequency (MHz)

ZRX

()

Z ModeledR ModeledX ModeledZ MeasuredR MeasuredX Measured

Figure 4.5 Measured and FEA Model ZRX curves for MnZn Oval Core 2

27

5. Discussion

The trends between the FEA model and the experimental results suggest that

the model accurately predicts the electrical properties of EMI components until after

the onset of resonance, when the reactance drastically decreases, and the resistance

rapidly increases. The model at this point predicts a reactance that continues to

increase. Both the ribbon core and the oval cores show errors in resistance earlier in

their frequency range than the toroid cores. The ribbon core model displays lower

resistance than the measured resistance in the resonance but a rapidly increasing

modeled resistance as the measured resistance drops. The oval cores show much

larger resistances beginning around 10 MHz. Deviations in the modeled and

measured values primarily result from the inability of FEMM 4.0 to model the

resonance effect in the material, but three other modeling factors could contribute to

the deviations in the frequency ranges before the onset of resonance, the geometric

assumptions required for a 2-D planar geometry, flux leakage, and wire placement.

5.1 Planar Geometry Assumption

The 2-D planar model of the two oval MnZn components assumes the

geometry of the components is the same as those shown in Figures A.4 and A.5. The

actual oval components have rounded, instead of square edges, as shown in Figure 2.1

in the methodology section. These rounded corners would reduce the effect of eddy

currents that occur on the corners of magnetic components. Since FEMM 4.0

accounts for the eddy current effect of corners in its planar analysis, it should predict

28

a greater resistance in the two oval cores than is actually present. Increase in

resistance due to eddy currents is relatively small at low frequency, but generates the

majority of the resistance of the component at high frequencies. This would explain

why the percent difference in resistance for the oval components is similar to the

MnZn toroid at low frequency, but has much higher errors as the frequency exceeds

15 MHz.

5.2 Wire Placement Assumption

In the FEA model, the current-carrying wire is placed in the center of the

component. In actual testing it was impossible to place the wire directly in the center

of the components. In order to determine the possible effect of the wire placement on

the measurements, the center of the NiZn toroid was filled with Styrofoam to hold the

wire in place. After the Styrofoam was fitted in the NiZn toroid, the wire was simply

threaded through the center of the foam with a needle for the first test, and near the

inner diameter of the toroid for the second test. Figure 5.1 shows that the electrical

measurements are unaffected by the placement of the wire.

29

0

5

10

15

20

25

30

35

40

45

0.1 1 10 100 1000 10000

Frequency (MHz)

ZRX

()

ZcRcXcZoRoXo

Figure 5.1 Effects of Wire Placement on NiZn Toroid Electrical Measurements

Zc, Rc, and Xc are the impedance, resistance, and reactance of the component with

the wire placed in the center, while Zo, Ro, and Xo are the impedance, resistance, and

reactance of the component with the wire located on the inner edge of the toroid.

Since the wire placements have no effect on the measured data, the assumption of a

perfectly centered wire is valid, and would not contribute any error to the

measurements.

5.3 Flux Leakage

Flux leakage is the effect of magnetic flux leaking out of a component into the

surrounding air. The NiZn ribbon core has a large quantity of flux leakage to its inner

air gap due to the small inside width of .03 inches relative to its inside length of .98

inches, as seen in figure A.2 in the Appendix. The flux leakage to the air in the

component center intensifies as frequency increases and causes an increase in

resistance and a decrease in reactance due to the much smaller permeability of air in

30

relation to the ferrite. This effect accounts for the level region in reactance and the

higher levels of resistance before resonance in the ribbon between 20 and 75 MHz.

The model fails to predict the high levels of flux leakage in the ribbon core, resulting

in a lower predicted resistance before resonance and a higher predicted reactance.

5.4 Resonance Error

Resonance in the material generates the greatest error. Looking at Figures 4.1

through 4.5, resonance in the different components occurs at different frequencies.

The resonance of the NiZn toroid occurs around 35 MHz, while resonance in the

ribbon component occurs closer to 50 MHz. The MnZn toroid experiences resonance

at 100 MHz, while both oval components resonate at 35 MHz. FEMM models the

reactance for each of the components accurately at this point, but models the

reactance as continuing to increase past this point, creating large differences in

measured and modeled values. This error is best viewed in the NiZn components,

since the measured reactance remains positive for higher frequencies.

31

6. Conclusions The objective of this project was to develop and experimentally validated 2-D

finite element model to approximate the behavior of EMI suppression components

based on the material properties found from a toroid test sample. The model is valid

for frequencies below the resonance frequency, but fails beyond this point. Physical

and electrical properties of five soft ferrite components from two different materials

were obtained. The permeabilities of the two different material types, MnZn and

NiZn, were derived from the two toroid components, and along with the physical

dimensions of each component, were used to model the electrical properties for the

five different components. The model and measured impedance, resistance, and

reactance were then compared. The models were found to closely estimate the

electrical properties of the components under 10 MHz, with percent differences

between the values of the primary property, impedance, less than 10%.

Above 10 MHz, the error begins to increase because of the onset of resonance

in the material. The model predicts increasing impedance, while the actual

components impedance decreases. Unfortunately, since the frequency region with

high impedence is the region of interest in EMI suppression design, the 2-D model is

not sufficient for their design. Modeling of components where the region of

operation is below the resonance frequency is still possible.

32

7. Recommendations Knowing that the 2-D modeling software cannot accurately predict the

resonance effect in the components, the first step is to use more complete 3-D

modeling software. Both ANSYS 8.0 and Maxwell 3D are reported as being

able to model resonance in magnetic materials. This would also allow for a

more exact modeling of components with rounded edges.

The components modeled are all used in EMI suppression. From these

models it was determined that components functioning at frequencies below

resonance can be modeled accurately. Components designed specifically for

operation in the regions below resonance should be further investigated to

validate this observation.

33

8. Bibliography 1. Soft Ferrites a Users Guide. 5th. Chicago: Magnetic Materials Produces

Association, 1998. 2. Boll, Richard. Soft Magnetic Materials. 1979. London: Heyden & Son Ltd,

London, 1979. 3. Snelling, Eric C.. Soft Ferrites. Cleveland: CRC Press, 1969. 4. Hoole, S. Ratnajeevan H.. Computer-Aided Analysis and Design of

Electromagnetic Devices. New York: Elsevier, 1989. 5. Meeker, David. "Reference Manual." Finite Element Method Magnetics. 08 Jan

2006. Foster-Miller. 28 Mar 2007 .

6. Meeker, David. "Finite Element Method Magnetics and Related Programs." Finite

Element Method Magnetics. 01 Dec 2006. Foster-Miller. 28 Mar 2007 .

7. Bobrow, Leonard S. Fundamentals of Electrical Engineering. 2nd. Oxford:

Oxford University Press, 1996. 8. Plonus, Martin A.. Applied Electromagnetics. New York: McGraw-Hill, Inc.,

1978. 9. Fogiel, M. The Electromagnetics Problem Solver. 3rd. Piscataway NJ: Research

and Education Association, 2000. 10. Adam, J. Douglas, Lionel E. Davis, Gerald F. Dionne, Ernst F. Schloemann, and

Steven N. Stitzer. "Ferrite Devices and Materials." IEEE Transactions on Microwave Theory and Techniques 50(2002): 721-737.

34

9. Appendix

Figure A.1 NiZn Toroid Dimensions

Figure A.2 NiZn Ribbon Dimensions

35

Figure A.3 MnZn Toroid Dimensions

Figure A.4 MnZn Oval Core 1

36

Figure A.5 MnZn Oval Core 2

Figure A.6 Meshed Model for NiZn Toroid

37

Figure A.7 Meshed Model for NiZn Ribbon

Figure A.8 Meshed Model for MnZn Oval Core 1

38

Figure A.9 Flux Density Plot for NiZn Toroid

Figure A.10 Flux Density Plot for NiZn Ribbon

39

Figure A.11 Flux Density Plot for MnZn Oval Core 1

40

41

42

43

44

45

0

100

200

300

400

500

600

700

800

0.1 1 10 100 1000

Frequency (MHz)

Rel

ativ

e Pe

rmea

bilit

y

u'u"

Figure A.12 Inductive and Resistive Permeability of Steward NiZn Material 64

-20

0

20

40

60

80

100

120

140

160

180

0.1 1 10 100 1000

Frequency (MHz)

Rel

ativ

e P

erm

eabi

lity

u'u"

Figure A.13 Inductive and Resistive Permeability of Steward MnZn Material 28