of Ferrite Chokes

8/12/2019 of Ferrite Chokes

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II. MODEL FOR FERRITE MATERIAL PARAMETERSThe equivalent circuit parameters (resistance, inductance

and capacitance) for a ferrite choke can be extracted from its

measured and numerically simulated input impedance as

shown below.

A. Complex Permittivity and PermeabilitySoft ferrites used as common-mode chokes in the VHF and

UHF ranges demonstrate mainly non-resonance frequencybehavior for both permittivity and permeability. Their

permittivity and permeability can be approximated by one or

multiple Debye terms as [9]:

1

;1

nSi

i eij

=

= +

+ %

1

11

1

nSi

i mij

=

= +

+ % (1)

whereei

andmi

are the electric and magnetic Debye

relaxation times. Measured frequency characteristics of

and of ferrite chokes can be curve-fitted using (1) with an

accuracy that depends on the number of terms. Typically, five

terms are considered sufficient for material frequencydependencies of ferrites [9, 10]. Curve-fitting using genetic

algorithms works well [11], though any accurate curve-fittingtechnique may be applied.

Fig.2. Picture of the ferrite choke under study

Fig. 2 shows a picture of the ferrite choke studied in thiswork. The choke is made of a soft spinel-type Ni-Cu-Mg-Zn

ferrite. Its measured and curve-fitted characteristics are shown

in Figs. 3 and 4. The frequency dependence of permeability is

approximated using two and five Debye terms in Fig. 3.Five

terms were used in the plot labeled curve fit and two terms

in the plot labeled CST, as CST Microwave Studio is only

able to use two Debye terms to represent frequency

dependence. As is seen from Fig. 3, five Debye terms

approximate the dependencies much better that two. The five

Debye terms, related to the thin dashed curves in Fig.3, have

static permeability values ofs

= 117.5226; 213.3247;

161.8502; 116.3565, and 141.0182, respectively. The

corresponding relaxation times are m =

4.0327

10

-7

s,1.501810-9s, 3.679710-12 s, 3.722310-16 s, and 2.092910-11s.

The two-term Debye parameters related to the permittivity in

Fig. 4 and used in CST Microwave Studio simulations are the

following: static values are1s

= 24.835 and 2s = 16.75,

high-frequency limit is = 15.271, and the relaxation times

are1e

= 1.04210-7s and 2e = 3.16810-9s.

100

102

0

100

200

300

400

500

600

Frequency [MHz]

Relativerealpartof Ni-Zn measuredNi-Zn CST

Curve Fit

100

102

0

50

100

150

200

Frequency [MHz]

Relativeimaginarypartof Ni-Zn measured

Ni-Zn CST

Curve Fit

Fig.3. Simulated, measured and curve-fitted magnetic permeability for Ni-Cu-Mg-Zn ferrite under test: (a) real part and (b) imaginary part

100

101

102

0

5

10

15

20

25

Frequency [MHz]

Relativep

arts

Real part

Imaginary part

Fig.4. Approximated frequency characteristics of permittivity using Debyecurves

B.Measurement and Numerical Model SetupsThe experimental and corresponding numerical setup is

shown in Fig. 5. It consists of a wire 0.66 mm in diameter and

154 mm in length placed 30 mm above and parallel to the

ground plane. The wire goes through the ferrite choke. The

dimensions of the ferrite choke are indicated in Fig. 2. The

wire should be placed as close to the ground plane as possible

to reduce loop inductance, but the distance between the

ground plane and the wire is limited by the ferrite chokes

dimensions. A time-domain reflectometer (TDR) was used to

determine a matching load impedance to minimize reflectionsfrom the circuit. The TDR was connected to an SMA

connector placed on the board with a 50-ohm coaxial cable as

shown in Fig. 6. The center connector of the SMA was

directly connected to the 0.66-mm diameter wire, used torealize the transmission line between the source (here the

TDR) and the load. The copper ground plane on the board,

used as return path for currents, is directly soldered to the

external part of the SMA connector. The matched load

impedance in the model was set to 295.5 ohms.

Fig.5. Numerical model setup

39.67 mm

25.4 mm

51.31 mm

radius r

(a) (b)

GND

295.5

50S-port

4 mm

30 mm

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Fig.6. Block diagram of TDR measurement

The input impedance of the circuit in Fig. 5 was measured

using a vector network analyzer (VNA) or impedance

analyzer. The VNA was connected to the on-board SMAconnector with the 50-ohm coaxial cable used for the previous

measurement. The outer shield of the SMA was soldered tothe ground plane. The center pin of the SMA was soldered to

the wire. The wire was terminated with a 295.5-ohm axial

resistor.The 50-ohm VNA port used to measure the input

impedance of the circuit was modeled in CST Microwave

Studio as a 50-ohm S-parameter port. The ferrite choke was

placed as close as possible to the source to obtain higher CM

input impedance effect. The ferrite choke was represented

with a cylinder of magneto-dielectric frequency-dispersive

material.

C.Evaluation of Equivalent Permeability of Ferrite Corewith Air Gaps

A ferrite core is often split as shown in Fig. 2. Even when

these parts are tightly clamped together, narrow air gaps may

degrade the magnetic performance of the core. Since direct

numerical modeling of cores containing narrow air gaps maydrastically increase computer memory and simulation time, it

is reasonable prior to numerical simulations to evaluate the

degraded permeability of the equivalent intact core,corresponding to the core with the gap. This equivalent

permeability can then be used in simulating the non-gappedcore. The equivalent permeability can be obtained using the

continuity of reluctance of magnetic circuits [12]. The generalexpression for the reluctance of a magnetic circuit is

( )( )0

r

l

=

,

Ampere turns

Wb

(2)

where ( ) r is the relative frequency-dependent

permeability,0

is the free-space permeability, lis the

length of the magnetic circuit, and is the cross-sectional

area of the magnetic core. The reluctance associated with the

magnetic circuit with gaps is

( )

( )0 0

2 22 , ,

r

r g g Ampere turns

A A Wb

= +

%

(3)

where ( )r is the initial relative complex permeability of

the ferrite choke, as in Fig. 7, r is the distance between the

center of the cylindrical structure and the half-radial-thickness

circumference (Fig. 2), and gis the total thickness of air gaps

between the two ferrite parts. The degraded permeability can

then be found from (2) and (3) as

( )( ) 0

2.

r

r

A

=

%

% (4)

The relative permeability calculated for air gaps of 1.0, 0.1,and 0.01 mm are compared in Fig. 8.

100

102

0

100

200

300

400

Frequency [MHz]

Relativerealpartof

Starting material

0.01 mm gap

0.1 mm gap

1 mm gap

100

101

102

0

50

100

150

200

Frequency [MHz]Relativeimaginary

partof

Starting material

0.01 mm gap

0.1 mm gap

1 mm gap

Fig.7. Equivalent permeability for ferrite core with different sized air gaps: (a)

real parts and (b) imaginary parts.

Fig. 8 shows the magnitude of the input impedance

modeled using the CST Microwave Studio software for two

cases: split ferrite (modeled with a 1-mm air gap), and not

split ferrite (modeled as a core without any gaps, but with the

reduced equivalent permeability as in Fig. 7). Even using the

worst case 1-mm air gap there is a good agreement between

the impedance for both numerically modeled curves. This

result justifies substituting a choke with an air gap by an intact

choke having the reduced equivalent permeability in order to

reduce the required computational resources. In the work

reported here, however, the clamp was tightly closed so that

the gap was ~0.01 mm, and further results were obtained

while neglecting the gap effect.

100

101

102

103

200

300

400

500

600

700

Z11 Magnitude Comparisons - 1 mm gap

Frequency [MHz]

|Zin

|[]

Split ferrite

Not Split ferrite

Fig.8. Input impedance magnitude

D.Effect of Temperature and Magnetic Saturation uponFerrite Choke Permeability

Heating of the ferrite choke and saturation due to strong

(differential) currents may occur in high-power switching

power supplies. Fig. 9 (a) shows the typical behavior of

relative static permeability as a function of temperature for the

Mn-Zn ferrite under test at 100 kHz. There is a drastic drop instatic permeability close to the Curie temperature (which

depends on the type of ferrite). For the particular ferrite under

test, the maximum temperature inside the enclosure, where the

ferrite is placed, due to an 80-A r.m.s. three-phase 60 Hz

functional current, was found to be ~ 800C. This is well below

the Curie temperature for the ferrite under study. Hence, the

temperature effect on magnetic permeability was not further

considered.

(a) (b)

TDR Coaxial

cable

SMA onboard

Shorted

wire

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-50 0 50 100 150 2000

200

400

600

800

Temperature [C]

Relatives

tatic

0 5 10 15

0

100

200

300

400

H [Oe]

Relatives

tatic

Fig.9. Main causes of permeability degradation on ferrite choke under test: (a)

Curie temperature and (b) magnetic saturation effect.

Magnetic permeability of the ferrite may also be reduced

due to magnetic saturation. Relative static permeability as a

function of the applied magnetization field is shown in Fig. 9

(b). This saturation effect is associated with the high-level

differential mode current on the wires. This differential modecurrent is not attenuated by the presence of the ferrite, but it

produces a strong local magnetization field around the wire

and can cause local saturation inside the ferrite choke.

Simulation of this phenomenon was performed using CST EM

Studio 2009.

Fig.101.Magnetic flux density evaluated using CST EM Studio

Fig. 10 shows the peak values of the H field inside the

ferrite choke when the inner wires carry 80-A r.m.s 3-phase

current. Most of the bottom of the ferrite is under saturation

conditions. The highest field magnitude is about 3400 A/m,

which corresponds to ~ 42 Oe (note that 1 Oe is equivalent to

~ 80 A/m). As shown in Fig. 9 (b), there will be a significant

drop in permeability. Saturation cannot be ignored for this

case.

Saturation may be taken into account by degrading the

equivalent permeability of the ferrite, as in the reluctance

approach given in (2)-(4). To improve the overall performance

of the ferrite, it may be reasonable to increase the ferritesouter diameter. Since the H field decreases with the increase

of the distance from the wire (source of the H fields), theincreased thickness of the ferrite choke may reduce the

saturated region. Considering saturation, the choke may be

considered as a combination of different cylinders with

different material properties. The overall reluctance will be

the parallel reluctance between those cylinders, and will be

smaller than the smallest reluctance given by the highest

permeability.

III.RLCEQUIVALENT CIRCUIT MODELAfter developing a good numerical model of the ferrite, an

equivalent circuit lumped-element model with frequency-

dependent parameters related to constitutive parameters of the

ferrite choke, its geometry, and position with respect to the

ground plane was developed as shown below.

A.Assumptions for RLC Equivalent Lumped-CircuitParameter ExtractionThe input impedance of the ferrite choke was

approximately obtained by subtracting the input impedance

looking into a circuit without the ferrite (11 'Z ) from the input

impedance when the ferrite was in place (11

Z ), as is

schematically represented in Fig. 11. The effect of the ferrite

on the input impedance was thus separated from the total input

impedance of the circuit. This approximation only works over

a limited frequency range, however, where distributed circuit

effects may be neglected (i.e. a quasistatic approximation).

Fig.11. Input impedances subtraction

We used a lumped-circuit model for a ferrite chokes as

shown in Fig. 1. In the proposed model, inductance and

resistance are frequency-dependent. The capacitance in

parallel with resistance and inductance is also considered. For

simplicity, capacitance is taken as constant with frequency.

This assumption is reasonable, since it mainly depends on the

ferrites permittivity, which does not vary as much as

permeability in the frequency range of interest, as seen from

Figs. 3 and 4.

B.Equivalent Lumped Circuit Model Parameter ExtractionLumped RLC parameters were obtained using two

methods. The first method used measurements made on the

full-length ferrite choke. The second method used numericalsimulations with a ferrite of one-third the length of the actual

choke. These test cases were chosen to check the effect of the

length of the ferrite on input impedance Zinand on equivalent

RLC parameters. This study will be used to extract an

analytical expression for input impedance components (realand imaginary) of the ferrite as a function of frequency,

geometry, and material properties.

Fig. 12 shows a comparison of Zin components obtainedwith measurement and with simulation. The full-length ferrite

is shown for both cases. The starting material properties

shown in Fig. 7 were used for the simulation.

The extraction of equivalent RLC lumped-circuit

parameters starts from finding a static inductance value. It is

evaluated for the region where inductance is approximately

constant with frequency, as shown in Fig. 13 (a). This

frequency range is characterized by a 20-db/decade increase in

(a)

Curie

Temperature

(b)

Saturation

Minus

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the input impedance magnitude. The static inductance is

found from the imaginary components of input impedance at a

point in this region by using the relation

( )0

Im( ) [H].

2

feZ fL

f= (5)

This static inductance (5), together with the evaluated

resonance frequency (where the imaginary component of

input impedances passes through zero), is used to obtain afrequency-dependent inductance

( )( )

[ ]0 2 H ,1 /

res

LL f

f f=

+ (6)

where0

L is the static inductance value andres

f is the

resonant frequency extracted from the imaginary component

of the input impedance of the ferrite, shown in Fig. 13 (b).

This kind of relation is proposed since inductance is

proportional to the real part of , which is approximated (for

the numerical model) with the real part of a Debye curve.

100

102

100

200

300

400

500

600

Freqeuncy [MHz]

ZinValue

Measured

Simulated

100

102

-400

-300

-200

-100

0

100

Freqeuncy [MHz]

ZinValue

Measured

Simulated

Fig.122. Input impedance comparison between measurement and simulation:(a) real, and (b) imaginary part.

100

101

102

20

30

40

50

Frequency [MHz]

|Zin|[dB

]

Measurem. - Full -length

Num. model - 1/3 length

100

102

-300

-200

-100

0

100

200

Frequency [MHz]

Im

(Zin)[]

Measurem. - Full-length


100

102

0

100

200

300

Frequency [MHz]

Re(Zin)[]

Measurem. - Full -length


Fig.13. Input impedance components: (a) absolute values, (b) imaginarycomponents, and (c) real components

For measurements (solid lines) in Fig. 13, the inductance

can be considered constant in the range of about 8 MHz -

40 MHz. Evaluation was performed using the imaginary

component of the input impedance at 25 MHz.

The initial static L0 inductance values was extracted for

ferrite chokes of two different lengths for the initial length

of 39.7 mm, and for 1/3 of this length (13.23 mm) then the

frequency-dependent L(f) curves were calculated using (6).

The results are shown in Fig. 14. The inductance value for theshorter choke is less than that for the longer one, but is not 1/3

value of the inductance of the whole choke. Since the model

for a ferrite includes not only inductance but also resistance

and capacitance, this result is not entirely unexpected since theseries impedance of three equal-length ferrites is the sum of

the complex impedance of each part which is dependent on

more than just inductance.

The frequency dependent inductances in Fig. 14 (a) have

the same shape as the real part of permeability in Fig. 7 (a).

The shape of the dependencies obtained using Fujiwaras

equation [8], shown in Fig. 14 (b), are close to those in Fig.

14 (a), but the values differ since the equivalent circuit in [8]

is different than the equivalent circuit used here.

100

101

102

0

0.2

0.4

0.6

0.8

1

Frequency [MHz]

Inductan

ce[H]

Full-length

One-third length

100

101

102

0

0.5

1

1.5

2

Frequency [MHz]

Inductan

ce[H]

Full-length

One-third length

Fig.14. Evaluated inductance as a function of frequency: (a) in present work;(b) using Fujiwaras equation [10].

Once the resonance frequency and the inductance, ( )res

L f ,

is known, one can calculate the corresponding capacitance

value by using the well-known relation

( ) ( ) [ ]21

F .2 res res

Cf L f

=

(7)

In the proposed equivalent RLC circuit, this capacitance is

assumed to be constant with frequency within the frequency

range of interest (below 200 MHz). This assumption is

reasonable for a quasi-static approximation and since the

dielectric properties of the ferrite do not vary drastically with

frequency (compared to the variation in magnetic properties),

as shown in Fig. 4. The extracted capacitance values for the

two test cases are shown in Table I.

TABLEI

EVALUATED CAPACITANCE VALUES

fres[MHz]

L(fres)[H]

C [pF]

Measurements Full- length 55 0.45 8.5

Numerical model 1/3 length 59 0.13 2.9

The last parameter to be extracted is the resistance as a

function of frequency. Resistance is dependent on the

imaginary component of magnetic permeability, which

behaves as an imaginary part of a Debye curve. Thus, the

expression for resistance as a function of frequency is

represented by the general equation for the imaginary part of

Debye curves as

(a) (b)

(a) (b)

(a)

(c)

fres

(b)

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6/6

( )( )

[ ]2

2 / ,

1 /

res MAX

res

f f RR f

f f

=

+ (8)

whereMAX

Ris the maximum (resonance) value of resistance

and is evaluated using the resonance expression for the

proposed lumped-circuit model

( )( ) ( )

[ ]Re .resin resMAX

L fZ f

R C

=

(9)

In (9), the term ( )( )Re in resZ f represents the value of the realcomponent of the input impedance for a ferrite on a wire at the

resonance frequency. This term can be found from Fig. 13 (c).

Once MAXR is known, the resistance values as a function of

frequency may be evaluated using (8). The curves obtainedfor the studied cases for the full-length and one-third full-length ferrite choke are shown in Fig. 15.

100

102

0

50

100

150

200

250

Frequency [MHz]

Resistance[]

Full-length

One-third length

Fig.15. Evaluated resistance as a function of frequency

C.Equivalent Circuit Model VerificationThe proposed method for RLC parameter extraction was

verified by substituting the evaluated lumped-circuit RLCparameters into the relations that represent the proposed

equivalent circuit model:

( )( ) ( )

( ) ( )( ) ( ) ( )( )2 22Re ;

1 2 2in

R f

Z ff L f C f R f C

= +

(10)

( )( )( ) ( ) ( ) ( )( )

( ) ( )( ) ( ) ( )( )

2 2 2

2 22

2 2 2Im ,

1 2 2

res

in

f L f C f fZ f

f L f C f R f C

=

+

(11)

and comparing the obtained results with the measured and

numerically simulated results. The measured, simulated, andmodeled input impedance are compared in Fig. 16 (a, b). The

proposed model gives a reasonable approximation of theimpedance up to the resonance frequency. This frequencylimit is due to using a lumped-element approximation ratherthan a distributed circuit when the chokes length becomes

comparable to the wavelength in a ferrite. Since the ferritesunder study are used to suppress CM currents produced byswitching power supplies, and the operating frequencies areon the order of hundreds of kHz, the proposed model will bevalid for this kind of circuit.

100

101

102

0

50

100

150

200

250

300

Frequency [MHz]

Re(Zin)[]

Measured - Full-length

Numerical Model - 1/3 length

From measurem. - Full-length

From num. model - 1/3 length

100

101

102

-300

-200

-100

0

100

200

Frequency [MHz]

Im(Zin)[]

Measured - Full-length

Numerical model - 1/3 length

From measurem. - Full-length

From num. model - 1/3 length

Fig.16. Comparison of the original and modeled ferrites input impedance: (a)real and (b) imaginary components.

IV.CONCLUSIONSRLC lumped-element equivalent circuit parameters for a

ferrite choke on a wire above the ground plane were extractedfrom measurements and numerical simulations using CST

Microwave Studio 2009. A reasonable approximation of inputimpedance was obtained below the quasistatic frequency limit(~100 MHz). This frequency limit is acceptable for analysis ofcommon-mode suppression in comparatively low-frequencyautomotive applications. In the future this frequencylimitation will be extended using a distributed circuit model.

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(a)

(b)

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