Th. Lingel 1

Magnetic Biasing Techniques for Circulators,

Analysis and Design Considerations

Thomas Lingellingel@IEEE.org

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Outline

• Motivation

• Review Units and Magnetic Materials

• Hysteresis & Demagnetization curve of a

Permanent Magnet

• Magnetic Circuit Analysis

• Permanent Magnet Materials

• Temperature Compensation

• Conclusion

This presentation is mainly geared towards biased above ferromagnetic resonance designs for circulators /isolators although concepts are generally applicable to other devices as well.

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Circulator Magnetic Components

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• Establish DC bias field inside the ferrite(s) for proper

RF operation over temperature

• Guaranty operation after exposure to extreme

temperature conditions (storage, reflow, etc.)

• Minimize volume of necessary components while

providing efficient shielding

• Cost efficient designs with the right selection of

materials and dimensions

Motivation

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• Biot-Savart Law and Ampere’s Law

2

00

4 r

rldIBd

rrr ×

=π

µ∫∫ = AdJldH

L

rrrrNI=

Magnetic Term Symbol SI unit CGS unit conversion factor

Magnetic Induction B Tesla (T) Gauss (G) 1 T = 104 G

Magnetic Field Strength H A/m Oersted (Oe) 1 A/m =4π/103 Oe

Magnetization M A/m emu/cm3 1 A/m = 10-3 emu/cm3

Magnetic Moment m Am2, J/T emu 1 Am2 = 103emu

Flux Φ Wb (Vs) or Tm2 Maxwell or Gcm2 1Wb= 10-8 Mx

Permeability offree space

µ0 H/m dimensionless 4πx10-7 H/m = 1 (cgs)

Overview Magneto-Static Analysis

• Two common unit Systems

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Ferromagnetic Elements (“Iron Triad”)

Currie

Temp.[K]

4πMs[G]

@ 20°C

Fe 1043 21580

Co 1388 17900

Ni 627 6084

Note: Magnetic Materials

typically contain one or

more ferromagnetic

Element

Sm2Co17

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H

B

HB 0µ=

B

H

)(0 MHB += µ

Permanent Magnetic Materials

M

H

)(HM

Material Contribution

Soft-Magnetic

Hard-Magnetic

B

H

+ =

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B/µ0M

H

HcHci/HcJ

Br

BHmaxintrinsic

normal

H

HHB rr

rrr

)1(0

0

χµµµµ

+===

)(0 MHBrrr

+= µ

SMHBrrr

π4+=

JHBrrr

+= 0µ

Permanent Magnetic Materials

cgs:

SI: Sommerfeld

SI: Kennely

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0

1000

2000

3000

4000

5000

6000

7000

-40 -20 0 20 40 60 80 100

AlloyFerrite

0

1000

2000

3000

4000

5000

6000

7000

0 100 200 300 400 500

H [Oe]

B [

G]

1500

1600

1700

1800

1900

2000

2100

2200

2300

0 50 100 150 200

H [Oe]

B [

G]

Soft-Magnetic Materials

Properties of Return path

material (typically Steel) will

also have to be included

4πM

s [G

]

Temperature [°C]

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Demagnetizing Field

0=Gl

RBB =

0=H

RB

Gl

RMG BBB <=

B

RMG BBB <=

0=∫ ldHrr

GGMM lHlH −=

MHGH

Gl

N S

Permanent Magnet

Old concept to illustrate that a

closed magnetized toroid does

not have an internal magnetic

field strength; this changes once

an air gap is introduced

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Magnetic Circuit Analysis

0=⋅= ∫ ldNI H

( )M

G

MG H

l

lH −=

0=+ GGMM lHlH

MΘ GΘ

Gl

Ml

GAMA

• Field Strength in Steel Yoke neglected

• Fringing neglected

Permanent

Magnet

Steel Yoke

Air-Gap

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GM Φ=ΦGG HB 0µ= ( )M

G

MG H

l

lH −=

G

G

MMGGMM A

l

lHABAB 0µ−==

GM

MG

M

M

lA

lA

H

B−=

0µ“Load Line” or Permeance Coefficient:

GM

MG

M

M

lA

lA

k

k

H

B

−=

2

1

0µ

Leakage coefficient k1 and Loss

Factor k2 can be used to account

for non-ideal models

Isolated Permanent Magnet, demagnetization factor N

determined by GeometryN

N

H

B

m

M −−=

1

0µ

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Bm

Hm

GM

MG

lA

lA0Pc :Slope µ−=

)(0 MHBM += µOperating point

Scaled B-H curve of the air-gap, mirrored on the B-axis

Permeance Coefficient or Loadline

( )M

G

MG H

l

lH −=

Open

Short

Energy

Bd

Hd

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Intrinsic Permeance coefficient

Additional magneto-motive force (m.m.f.)

GM

MG

M

MM

lA

lA

H

MH−=

+

0

0 )(

µ

µ

MB

Hm

Bm

1+== cci

M

M PPH

M

ml

Ni

Note: Permeance coefficients are usually

defined as positive numbers

/µ0M

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• RF specifications dictate ferrite size and DC bias level

• Magnet size has to be determined and Material selected:

� Bias level must be achieved with margin for tuning

� Magnet Volume is minimized, Operation at a high

Energy level without risking demagnetization at

extreme temperatures

� Magnet is producible (aspect ratios, minimal height)

� Magnet fits all other design constraints

(housing size, cost)

Design Approach

Different concepts are presented: Analytical/load-line approach, graphical solution, equivalent network approach

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Ferrite

Fl

Ml

FAMA

Permanent Magnet

Steel Yoke

Loadline Approach with Ferrite

Bm

Hm

FM

MF

lA

lA0µ−

M

FF

A

AM0µ

0=⋅∫ ldH GM Φ=Φ

Slope:

CP

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0

2000

4000

6000

8000

10000

12000

-12000 -10000 -8000 -6000 -4000 -2000 0

H [Oe]

B[G

]

Source

Load

Example

FerriteDiameter: 20mmHeight: 2mm4πMs: 2000G

HDC: 1000Oe

Magnet SmCo Ceramic

HM [Oe] 5000 2000

BM [G] 5000 2000

Height [mm] 0.4 1

Diameter [mm] 15.49 24.49

Operating point

from Source line

Input

M

FFM

H

lHl −=

M

FFFM

B

AMHA

)(0 +=

µ

Comparison: What size magnet do I need

to achieve 1000Oe internal field strength

for a given ferrite using a SmCo or a

Ceramic magnet, both operated on an

idealized demagnetization curve at

maximum energy output

turns out that energy product times

volume has to be the same!

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B, H and M do not need to

be parallel/anti-parallel to

each other!

Maxwell-2D BOR-model

]Oe[zH

z

z

H

B

0µ

Ceramic

Magnet

Ferrite

Magnet appears effectively

~2mm smaller in diameter

because of fringing fields

This is an FEM model of the

ceramic magnet case from the

previous slide

Fringing is causing the magnet to

look effectively smaller in diameter,

resulting in a steeper loadline and

lower field strength within the

ferrite

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H

B Φ

Θ

Multiply by area

Multiply by height

∫=Θ ldHrr

∫=Φ AdBrr

Graphical Solution with “Magnetic Voltages and Currents”

Graphical solutions can

take nonlinearities into

account

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Magnetic Circuit Analysis

Permanent Magnet

Soft-magnetic Material

A

lRM

µ=

l

APM

µ=

lH cM =ΘA

lRM

µ=

AM SM π4=Φ

Electrical circuit analysis

tools can be an efficient

way to analyze magnetic

circuits

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Scalar Magnetic Potential (Voltage) [A]: ∫=Θ ldHrr

∫=Φ AdBrr

Magnetic Flux (Current) [Wb, Vs]:

Φ

Θ=MRMagnetic Reluctance [A-turn/Wb]:

A

lRM

µ=

Hl=Θ

BA=Φ

Also Magnetomotive Force m.m.f [A-turns]

Permeance [H]

Θ

Φ=P

l

AP

µ=

Θ−∇=⇒=×∇ HHrr

0

Equivalent Networks

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0

Magnet_FluxSource2

Ferrite_FluxSource1

Ma

gn

et_

Re

lucta

nce

Fe

rrite

_R

elu

cta

nce

Airg

ap

_R

elu

cta

nce

V Theta_Magnet

+A

PH

I_M

ag

ne

t

V Theta_Ferrite

ReturnPath_Reluctance

V

+A

V

[Oe] [mG] [Oe] [MGOe] [mG]

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Operating point

H

B

Ferrite is modeled like a permanent magnet, one has to ensure that the operating point is in the saturated area of the First Quadrant of the Hysteresis

• Based on the dimensions of the ideal model a numerical

model can be generated, taking fringing and all material

properties into account

• Energy Product and Permeance Coefficient are

varying within the magnet volume !

This is the trick which was used in the

circuit model on the previous slide

Rather than working with the nonlinear

curve of the softmagnetic ferrite we

assume a linear BH characteristics of a

permanent magnet operated in the first

quadrant

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Demagnetization at Temperature Extremes

Recoil on minor

hysteresis,

irreversible

change

- Temperature +

Note: The higher reluctance of ferrites at elevated temperatures reduces the operating temperature range even further.

Load line is passing the

knee point at elevated

temperature

This leads to

irreversible field loss

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Comparison of Magnetic Materials

NdFeBSmCo

Ceramic

AlNiCo

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Permanent Magnetic Materials

Energy

Prod.

[MGOe]~ ~ Tc[°C] µ-recoil

AlNiCo ~1.4-10 -0.02 +0.01 ~900 grade dependent (~2..5)

Ceramic ~2.7-4 -0.2 +0.27 ~450 ~1.05-1.15

Sm2Co17 ~18-32 -0.035 -0.2 ~820 ~1.05-1.1

NdFeB ~10-48 -0.12 -0.65 ~350 ~1.05-1.1

Numbers shown are only guidelines, many different materials are available.

A Higher Energy Product is usually traded for lower Hci values.

The change of Br and Hci is not linear, therefore numbers are only rough guidelines.

All sintered magnets are brittle, another alternative are bonded magnets which typically

have lower Energy Products.

°∆

∆

CTB

B

r

r %

°∆

∆

CTH

H

ci

ci %α β

Reversible Changes

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Measurement Results of NdFeB at

different Temperatures

25°C

75°C 100°C 130°C

Limit of the Measurement Equipment

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B/µ0M

H

Measured Demagnetization Curve

Tuning

Tuning is necessary in most cases to account for material and mechanical tolerances.

The Operating point in this case will be on a minor hysteresis loop.

Measured Demagnetization

curves at different

demagnetization levels

This is what happens during

calibration “knock-down” of a

circulator, we start at saturation

and find the right minor

hysteresis for the specified

frequency range

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Temperature Compensation Elements

−

=

100

0

0

µκ

κµ

µ j

j

P

t

22

0

01ωω

ωωµ

−+= m

22

0 ωω

ωωκ

−= m

The Bias field needs to be reduced in the above

Resonance operation if the Saturation Magnetization

decreases with increasing temperature, however on-

and off- diagonal elements can not be kept constant

simultaneously by only adjusting the bias level.

Adjustment of µeff can be used as guideline, but the

frequency response has to be the criteria.

Significant change in Br (Ceramic Magnets, NdFeB) make it easier to temperature compensate when biased above resonance. Other materials need more/additional temperature compensation components.

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Temperature

Fre

qu

en

cy

soft magnetic Flux limiting Airgap

Bandwidth

Nickel content

Less More MoreLess

Operation of Temperature Compensation Alloys

)(thicknessf=αSummary on how temperature

compensation elements (typically

disks) in a series configuration work

First knee point is related to when

the temperature compensation

material gets saturated, slope of the

center frequency vs temperature

depends on the thickness, second

knee point relates to the Curie

temperature of the temperature

compensation material

Temperature compensation alloys

are typically binary NiFe alloys with

about 30%-32% Nickel content

This plot is a contour plot of center frequency and upper/lower frequency limit vs temperature, it provides insight on the temperature compensation design and what handles can be adjusted

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Conclusion

• The DC bias design is essential for proper RF

performance

• With increasing material costs the optimization of

magneto-static components becomes more important

• Simple circuit models of the magneto-static problem

help to get a basic understanding and to define

starting structures for numerical simulations

• There is no one-fits-all design. Specific material

selection and geometry are driven by actual RF-

specifications and mechanical constraints.