Moulson A.J., Herbert J.M. Electroceramics: Materials, Properties, Applications

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522 MAGNETIC CERAMICS

Fig. 9.43 Production press for oriented ferrite components. (Courtesy of Philips Technical

Review.)

Table 9.5 Properties of barium ferrites made using diﬀerent processes

Sintered

Calendered with

Anisotropic

Property Unit polymer Isotropic Extruded Wet pressed

Remanence T 0.16 0.20 0.30 0.40

Coercivity kA m

112 140 150 180

(BH)

max

kJ m

5 7 15 30

Density kg m

3400 4800 4800 4800

TEAMFLY

Team-Fly

PREPARATION OF FERRITES 523

Fig. 9.44 Orientation of particles during extrusion.

Fig. 9.45 Orientation of particles during calendering.

calendering, that is by passing a mixture of polymer and ferrite between closely

spaced rollers rotating at diﬀerent speeds. The strong shearing action as the

mixture passes through the nip between the rollers both disperses the powder and

orients the plate-like particles (Fig. 9.45). Some 20–30 passes through a nip 1 mm

wide may be needed to give the maximum eﬀect.

The principal properties obtainable with the various processes are compared in

Table 9.5.

9.4.6 Finishing

Machining the sintered ferrite is expensive, so that all possible control over shape

and dimensions is concentrated in the pressing operation and the sintering

conditions must be suﬃciently uniform to keep dimensions within speciﬁcation.

However, certain surfaces may have to be improved in smoothness and ﬂatness

so that they can form magnetic circuits by contact with other components with a

minimum air gap. Pot-cores have their mating surfaces lapped, and the E, C and

I cores used in high-frequency transformers have mating surfaces ground ﬂat and

parallel. In many instances hard ferrite magnets are required to ﬁt into metal

housings or onto other components, and some diamond grinding is usually

required to achieve the required dimensional tolerances.

9.5 Applications

9.5.1 Inductors and transformers for small-signal

applications

A major use of high-quality pot-core inductors is in combination with capacitors

in ﬁlter circuits. They were once extensively used in telephone systems but solid

state switched systems have replaced them. The soft MnZn and NiZn ferrite

systems are dominant for pot-core manufacture, although metal ‘dust cores’ are

used for certain applications. The important design principles can be understood

by reference to a simple series LCR circuit to which a sinusoidal voltage U of

angular frequency o is applied (Fig. 9.46). The circuit impedance

Z ¼ R þ jðoL  1=oCÞ is a minimum when oL ¼ 1=oC. Thus the resonant

frequency o

is given by

¼ðLCÞ

1=2

ð9:48Þ

At this frequency the current through the circuit is a maximum and the total

applied voltage U appears across R; the voltages across L and C are out of phase

by p. The current through the circuit is U/R and the voltage across C is

524 MAGNETIC CERAMICS

It therefore follows from this and Eq. (9.48) that



¼ Q ð9:49Þ

where Q is the ‘circuit magniﬁcation factor’ or ‘quality factor’. It can also be

shown that

Q ¼

2do



2df



ð9:50Þ

where do (or df ) is the change in o (or f ) from o

(or f

) required to reduce the

power dissipated in the circuit to half the resonance value. Alternatively, in terms

of voltages, do is the change from o

required to reduce the voltage across C (or

L)to1/

2 of its peak resonance value. The circuit is therefore selective in its

response to signals of diﬀerent frequency, and Q measures selectivity. The

practical aim is usually to maximize the circuit Q, and from Eq. (9.49) this

requires L and R to be maximized and minimized respectively. In order to

achieve a high circuit Q the materials which are used in the circuit components

must be chosen with care.

As discussed in Section 9.3.1, the quality of the ferrite is measured by its loss

factor (tan d)/m

which should be as small as possible, and in the following

discussion it is assumed that this is the case.

The inductance L of the core is given by

L ¼ m

D ð9:51Þ

where m

is the eﬀective relative permeability, n is the number of turns and D is a

constant depending upon core geometry. It follows that, for a given L, a higher

will allow n to be reduced proportionately to m

1=2

. A decrease in the number

APPLICATIONS 525

Fig. 9.46 Series LCR circuit.

of turns results in lower winding-resistance losses (the so-called ‘copper losses’)

and hence higher Q; a high m

also enables the core size to be kept small.

There are two ferrite material properties which were not discussed in Section

9.3.1 but which are important in the inductor context: they are the temperature

and time stabilities of the permeability which, of course, determine the stability

of the inductance. The temperature coeﬃcient of permeability must be low, and

this has been achieved for certain MnZn ferrite formulations as indicated in

Fig. 9.18. A small residual temperature coeﬃcient of inductance can be

compensated by a suitable coeﬃcient of opposite sign in the capacitance of the

resonant combination.

526 MAGNETIC CERAMICS

Fig. 9.47 Change in permeability with time or ‘disaccommodation’.

Fig. 9.48 Pot core: (a) complete unit; (b) schematic diagram of structure. (Courtesy of Philips

Components Ltd.)

A time variation in inductance arises because the permeability diminishes after

the establishment of a fresh magnetic state; this eﬀect is known as

‘disaccommodation’ and is illustrated in Fig. 9.47.

The fall in permeability is roughly proportional to the logarithm of time.

Therefore, if there is a loss of 1.5% between 1 min and 1 week (approximately

min), it will take 10

weeks (about 200 years) for the loss of a further 1.5% to

occur! Disaccommodation is thought to be due to the directional ordering of ion

pairs such as Mn

and Fe

, and it is increased by a high concentration of

metal ion vacancies which favours ionic diﬀusion. The vacancy concentration

can be kept low by minimizing the oxygen in the sintering atmosphere.

The permeability is also aﬀected by stress: the induced change decays

logarithmically with time as a form of disaccommodation. Inductors are usually

made in two parts so that the winding can be introduced on a bobbin; the parts

must then be joined closely together to prevent the permeability from being

aﬀected by an uncontrolled air gap. If a mechanical clamp is used, the force must

not be excessive and must be the same in similar units. Its eﬀect must be allowed

to decay before the inductance value is ﬁnally adjusted.

A typical design of a pot core for an inductor is shown in Fig. 9.48. There is a

gap in the central limb of the core when the surfaces of the outer parts are in

contact. There is also a hole through the centre of the core into which a

magnetizable rod can be inserted. The position of this rod relative to the gap can

be altered so as to adjust the value of the inductance. Apart from allowing this

adjustment, the gap reduces and controls the magnetic losses of the core (Eq.

(9.12)). If m

is the relative permeability without a gap and m

is the relative

permeability with a gap, the losses due to the core (tan d

¼ 1=Q), its

temperature coeﬃcient and changes due to disaccommodation are all reduced by

the factor m

(see Section 9.1.4). In many ﬁlter applications a constant

bandwidth is required over a wide range of frequencies so that the ratio of

bandwidth to centre frequency diminishes as the frequency increases. Q therefore

needs to be higher and tolerance on inductance variations less at higher

frequencies. This can be achieved, without altering either the core design or the

ferrite composition, by increasing the gap width. Cores are manufactured with

diameters ranging from 10 to 45 mm and inductance values ranging from the

order of microhenries to 5 H. Various core geometries are available (Fig. 9.17)

but no new principles are involved. Choice is determined mainly by considera-

tions such as size economy and compatibility with printed-circuit-board

technology.

In the use of ferrites as inductors for tuned circuits, the Q of the materials is of

prime importance. Wide-band transformers are also used extensively in

communications systems, for example to transform signal voltages and to

provide impedance matching and d.c. isolation of one part of a circuit from

another. Pulse transformers are of increasing importance because of the rapidly

growing use of pulsed signals in communications technology. Since a pulse can

APPLICATIONS 527

be synthesized from its Fourier components, a pulse transformer needs to be, in

eﬀect, a wide-band transformer. An analysis of the equivalent circuit for a

transformer shows that core losses have little eﬀect on the transformer’s

eﬃciency, provided that they are acceptable at the lower end of the frequency

band to be transmitted. For example, an MnZn ferrite is a perfectly acceptable

material for a wide-band transformer for the frequency range 100 kHz to

50 MHz. The reason for this is that as the frequency increases the core losses

(equivalent to a resistance shunting the transformer’s mutual inductance)

become less signiﬁcant compared with the impedance of the transformer. For

wide-band transformers it is the high initial permeability of the MnZn ferrites

coupled with an acceptably low loss which makes them the favoured material.

Because mating surfaces must inevitably lead to a reduction in eﬀective

permeability, the transformer cores are available in toroid as well as pot-core

forms.

An important application of ferrites is for shielding sensitive equipment (e.g.

data-processing, telecommunications and audio-visual equipment) from electro-

magnetic interference (EMI). Both NiZn- and MZn-based ferrites components

are capable of suppressing interference up to the GHz frequency range by virtue

of the high impedance they present to high frequency currents. The ferrite parts

are made in a variety of shapes to enclose the leads to be shielded, as shown in

Fig. 9.17.

Multilayer technology is exploited just as for multilayer capacitors (see Section

5.4.3) to EIA size speciﬁcations, and inductor chips can be bandoliered ready for

surface mounting, typical inductance values lying in the range 1 nH to about

20 mH. They ﬁnd important applications as EMI suppressors as well as for a wide

range of applications as a lumped circuit component in equipment of all types –

communications, ‘entertainment’, computers, etc. (see Fig. 9.17).

9.5.2 Transformers for power applications

There are many high-frequency (typically 1 kHz to 1 MHz) applications where a

high saturation ﬂux density is the prime requirement. Examples are power

transformers to transmit a single frequency, those required to transmit over a

narrow frequency band, as in the power unit of an ultrasonic generator, and

wide-band matching transformers to feed transmitting aerials. Television line

output transformers are, commercially speaking, important examples of power

transformers and, although not a transformer, the beam deﬂection yoke

(Fig. 9.17) falls into the same category.

The saturation magnetization of ferrites (about 0.5 T) is too low for them to

compete with Si–Fe laminations (about 2.0 T) at power frequencies. At higher

frequencies eddy current losses preclude the use of metallic ferromagnets, and

ferrites are widely used.

528 MAGNETIC CERAMICS

The growth in the demand for switch mode power supplies has led to a

corresponding demand for high-frequency ferrite-cored power transformers. The

switch-mode principle is not new, and it is the availability of suitable power-

switching transistors, rectiﬁers, capacitors and ferrite cores which has enabled

full advantage to be taken of the small size and inherent eﬃciency of the type of

supply. In a typical unit the mains supply is rectiﬁed, smoothed and chopped at a

high frequency, usually in the range 25–100 kHz, by a power transistor. This

chopped voltage is transformed to the desired voltage by a ferrite-cored

transformer and ﬁnally rectiﬁed and smoothed. Transformers capable of

handling up to 2 kW are readily available.

As far as material properties are concerned, the general requirements of

ferrites for power applications are similar to those for pot cores, but the

permeability can be allowed to vary more widely. As high ﬁelds are likely to be

applied, the hysteresis losses will be important. They can be minimized by

keeping the crystalline anisotropy to a low level, for instance by substituting

cobalt for about 1% of the nickel in (Ni,Zn)Fe

(cf. Table 9.1). The internal

shape anisotropy due to inhomogeneities and porosity can be minimized by

ensuring that mixing, pressing, and sintering conditions are such as to yield a

homogeneous high-density body.

As expected, the NiZn ferrite system is available for the higher frequencies (up

to approximately 5 MHz), whereas for frequencies up to about 100 kHz the

MnZn ferrites are favoured because of their higher permeabilities.

The shapes used are mostly simple E or C cores and I bars (Fig. 9.49). These

allow simple high-speed winding machines to be used either to put windings

directly on the ferrites or to wind bobbins which can be slipped onto the

accessible limbs. The C and E cores must have their magnetic circuits completed

by securing I cores across the appropriate limbs. The mating surfaces must be

ground so that the air gap is minimal. Alternatively, cores can be fabricated as

closed magnetic circuits and fractured into parts onto which windings can be

ﬁtted. The ceramic texture must be such that the two parts can then be clamped

together without any damage to the mating surfaces. The process of fracturing is

assisted by pressing grooves into the ‘green’ shape and can be achieved either

mechanically or through thermal stress by the local application of a ﬂame or a

hot wire. Careful production control is needed to give a good yield of suitable

fractures.

APPLICATIONS 529

Fig. 9.49 Transformer core shapes.

Ferrites having a square hysteresis loop (e.g. (Mg, Mn, Zn) Fe

), developed

for the now outdated computer core memories, have found applications in the

form of a toroidal ‘saturable inductor’ for regulating the output currents in

switched-mode power supplies.

9.5.3 Antennas

Small antennas comprising a suitable winding on a ferrite rod are needed for

radios, pagers and for RF identiﬁcation transponders. In the case of a

transponder information is stored in a tag (an application for ferroelectric

memories – see Section 5.7.5), which can be read by a signal from an

interrogating unit. The cylindrical rods (Fig. 9.17) are precisely dimensioned

with sizes down to 0.76 mm diam. by 4.82 mm. The tag carries no battery,

suﬃcient power to transmit the stored information being derived from the

interrogating signal. Applications include car key identiﬁcation so that if the

correct code is not detected then the steering wheel and fuel supply are blocked,

airport baggage checks, control of access to buidings and traceability in food

chains.

A short winding of n turns of area A will develop an e.m.f. of amplitude U if

placed in an alternating magnetic ﬁeld of angular frequency o and amplitude H,

where

U ¼ m

oHAn ð9:52Þ

If a long rod of eﬀective relative permeability m

is inserted in the coil the e.m.f.

becomes

U ¼ m

oHAn ð9:53Þ

Because the magnitudes of the electric and magnetic vectors of an electro-

magnetic wave are related by H ¼ðe

1=2

E and the wave velocity in vacuo is

given by c ¼ðe

1=2

, it follows that

U ¼ m

A ﬁgure of merit for an antenna is the eﬀective height h

, where

¼ U=E ð9:54Þ

and, since c ¼ðo=2pÞl where l is the wavelength,

¼ 2pm

ð9:55Þ

Therefore h

will increase at shorter wavelengths and with increased m

, which is

related to the material permeability m

by Eq. (9.9). Values of h

for two materials

530 MAGNETIC CERAMICS

are given in Table 9.6. The h

values are very small compared with, for example,

those for a correctly designed dipole interacting with the E vector of the

electromagnetic ﬁeld. By comparison with a dipole the ferrite-cored antenna is

very ineﬃcient, but very much more compact!

The signal power available to the ﬁrst stage of a receiver is proportional to

, where Q

is the inverse of the loss tangent for the rod and coil combination

together with any metal objects that may absorb or distort the radiation. It is

therefore important that the ferrite should have low losses in the frequency range

for which the antenna is designed. (Ni,Zn)Fe

is used at frequencies above

1 MHz since its losses are less than those of (Mn,Zn)Fe

. Figure 9.29 gives the

permeability and loss for some compositions of the former type as a function of

frequency and for a range of zinc contents.

Since the ferrite is required in rod form it is usually made by extrusion. A

simple circular section is sometimes replaced by one having ribs parallel to the

axis of a central cylinder. This structure is intended to avoid the eﬀects of

dimensional resonance (see Section 9.3.1) which would cause the antenna to have

poor response over a small part of its total frequency range. The eﬀect of a

ribbed structure is that only a fraction of the material will have a resonant

dimension at any particular frequency so that, compared with an unribbed rod,

there will be a minor drop in eﬀective height over a wider frequency band. The

relatively high losses at megahertz frequencies usually damp the resonance and

their eﬀects can be largely eliminated by suitable design.

9.5.4 Information storage and optical signal processing

Information storage

The continuously evolving technologies concerned with information storage are

many and complex and involve metals, ceramics and polymers in active roles.

The following discussion is concerned only with those aspects which involve

ceramics and is therefore very restricted. Comprehensive descriptions of the

APPLICATIONS 531

Table 9.6 Antenna rod dimensions and properties

Length/mm Diameter/mm

Demagnetizing

factor N

/mm

175 200 9.5 0.0043 100 5.9

175 150 12.7 0.0112 59 6.3

500 200 9.5 0.0045 154 9.1

500 150 9.5 0.0073 108 6.4

Short central winding of 40 turns; 1 MHz ( ¼ 300 m).