32 IRE TRANSACTIONS ON COMPONENT PARTS

Permanent Magnets in. Audio Ckvices* R. J. PARKERf

March

Summary-The permanent magnet is considered as a component for changing the form of energy, and a brief review of the basic physics of the permanent magnet is included with emphasis.on the nature of the magnetization process and how the permanent magnet functions in establishing external magnetic field energy.

Presently availabIe characteristics of permanent magnets and future possibilities for improving the efficiency of the permanent magnet are discussed as well as the relationships between audio device performance and the unit properties of permanent magnets.

In using the permanent magnet, the choice of unit properties, volume, geometry, and magnetic circuit arrangement greatly in- fluence the end performance and efficiency of audio devices. As an aid in exploiting the optimum combination of these variables an electrical analog system u;sing lumped constants is introduced. Data on leakage permeance are presented for the more widely used permanent magnet arrangements in audio work. The analog tech- nique is of general interest from the viewpoint of understanding the energy relationships involved in the efficient application of the permanent magnet and as an aid in predicting permanent magnet performance on a firm engineering basis.

INTRODUCTION

P

ERMANENT magnets find wide application in audio devices in which a magnetic field serves as the medium of energy transformation in the

transformation of electrical energy to mechanical energy and also iu changing; mechanical energy to electrical energy. As a key component in these devices the permanent magnet influences the efficiency, physical size, and cost. It is the purpose of this paper to describe the permanent magnet as a basic system for establishing field energy and to show how permanent magnet properties influence audio device performance. Presently available permanent magnet materials and future possibilities are discussed as well as an electric,81 analog approach to permanent magnet design problems.

BASIC PHYSICS OF THE PERMANENT MAGNET

The permanent magnet can be conveniently thought of as a grouping of elementary magnetic volumes or domains, a domain being the smallest region in which the atoms have their magnetic moments held parallel and thus act as a sin@;l.e elementary magnet which may be controlled by man-m.ade external fields. In a ferro- magnetic material the :&e and orientation of the domains are-influenced by three potential energies:

1) The potential energy due to the interaction existing between neighbor.ing atoms,

2) The potential energy associated with the directional dependence of magnetization commonly called anisotropy energy,

* Manuscript received by the PGCP, September 17, 1957; re- vised manuscript received, November 18, 1957. This pa er was presented at the National EXectronics Conference held in 8. hrcago, Ill. on October 7-9,. 1957.

t General Electrrc Co., Fdmore, Mich.

3) Magnetostatic energy or the external field energy associated with the domain.

The size, shape, and orientation of the system of element,ary magnet volumes in a given clondition are in a state of balance so that minimum total potential energy is involved. In a demap;netized condition the domains shift so that closed paths for the flux exist and the mag- netostatic energy is a minimum.

Any field which mart can produce serves only as a control in changing the magnetostatic energy and thus the balance of the total influence on the domains. Magneti- zation curves and hysteresis loops show the .change in induction due to domain .boundaries shif’ting and due to the rotation of the magnetization vectors as the external field is increased. The shapes of the curves result from the fact that some domains are more favorably oriented with respect to the applied field direction than others. In many materials attempkj are made to order the system and increase the percentage of domains having this preferred axis aligned with the direction of ultimative magnetization and use.

In general, the principle action in low coercive force magnet materials is a shifting of the domain boundaries. In the early steel magnets coercive force is generally explained on the basis of producing strain in the crystal lattice which impeded the movement of domain bound- aries. In the Alnico family the action is onle of domain wall movement with IOW values of applied field, and as the field is increased, the magnetization vectors of the domains are actually rotated against the forces of anisotropy. In other words, if the domains have a preferred direction of magnetization with respect to the crystal lattice or with respect to their shape, external energy is necessary to rotate the magnetization vector into the direction of the applied fields.

Perma.nent magnets have been made from part.icles of single domain size. In such a system there are no domain walls since from the viewpoint of the potential energy associated with the domain there is a critical size below which domain boundaries cannot exist. In. such a magnet the external field directly opposes the forces of anisotropy.

Recent advances1 make it possible to control the shape of these single domain volumes and when properly aligned and spaced in a composite magnet, volume properties as good as those of the Alnico family can be obtained with promise of vastly superior permanent magnets as this new technology is developed.

IT. 0. Paine, L. I. Mendelsohn, and F. E. Luborsky, “Fine particle magnets,” AI%E Trun:~., vol. 76, pp. 851-857; October, 1957.

1958 Parker: Permanent Magnets in Audio Devices

Fundamentally the properties of permanent magnets appear to be governed by the following:

(a) m-+ 33 6

---L H l‘,

2)

3)

4)

Saturation induction of the domain (chemical composition),

Shape of the domains,

Spacing of the domains,

Orientation or ordering of the domain system.

Ability to control and change the unit building blocks and their arrangement offers tremendous possibilities in the designing of permanent magnet devices.

The mechanism of using the permanent magnet to establish external field energy is shown pictorially in Fig. 1. In Fig. l(a) the external observation is of a demagne- tized volume because the domains, although each are fully magnetized, satisfy the minimum energy requirements by taking position to form closed magnetic circuits within the material. In Fig. l(b) under the influence of a high external field the domains are rotated against .t,he forces of anisotropy into the direction of the field. In terms of the hysteresis loop, area OAB, represents the work done or energy extracted from the magnetizing source for a unit volume. In Fig. l(c), as the field is reduced to zero, a residual flux remains representing a new minimum energy balance point. As the size and orientation of the domains has shifted, a new balance among the three potential energies occurs after the external field influence is removed. Area OAB, represents the energy returned from the magnet to the electrical circuit. In Fig. l(d) a gap is introduced at each end of the magnet and the domains near the ends change their orientation due to the unbalance created by the gap and take up a position essentially 180’ from the original direction in Fig. 1 (c) . It is this influence that gives rise to the negative magneto- motive force OH. Area ODT is proportional to potential energy in the external gap on a unit volume basis. To move the operating point from Br to D requires additional energy input. In this case it was the mechanical energy necessary to introduce the gaps in the system. Area ODBr is proportional to the total potential energy increase of of the magnet and its external field. Area ODT is pro- portional to the potential energy stored in the external field, and area BrDT represents the potential stored energy within the magnet itself. With reference to Fig. l(e), suppose the poles are allowed to contact the magnet faces reducing the gap to zero. Mechanical work will have been done and the operating point will move from D to S. The domains near the poles will revert back to nearly their same orientation. The potential energy in the external field and in the internal magnet system will be reduced and mechanical work will have been done. As the magnet cycles back and forth, a minor hysteresis loop will be traced. In this service the magnet and its external field act as a system for alternately storing and releasing energy as the demagnetizing influence of the poles is changed.

(bl

CC) BL+

(e)

Fig. l-Pictorial description of basic physics of the permanent magnet.

SELECTINGTHEPERMANENTMAGNETMATERIAL

Fig. 2 shows demagnetization and external energy product contours for widely used permanent magnets. Generally speaking, in audio considerations the energy product is the most significant criterion of a permanent magnet. In order to improve the fullness of the demagnet- ization curve, ordering of the elementary magnet volumes has been used in many of the present-day magnets. Fig. 3 compares the crystal structure of conventional and directional grain Alnico 5. In this instance, by controlling the flow of heat during casting, the crystal structure is ’ oriented. Crystal edges are parallel over a large per cent of the magnet volume. During heat treatment an ex- ternal field applied in the same direction as the parallel crystal edges is influential in aligning the domains in the same axis. The demagnetization curve of a highly ordered system of domains is essentially rectangular, and with reference to Fig. l(d) area ODT is a high per cent of the area ODBr which means that, as the self- demagnetization influence of the poles is encountered nearly all of the increase in potential energy of the system exists in the external field. This results in maximum volumetric efficiency for fixed gap devices.

34 IRE TRANSACTIONS ON

DEMAChETlZlNG CCEFFKIENT SlDPE B/H

COMPONENT PARTS II/f arch

25 30 sp ‘FtOl&JCTj3dljdXIO’

4pc 11

IO

Fig. 2-Demagnetization and energy product curves.

.Fig. 3-Oriented crystal structure of Alnico 5 directional grain.

In applications involving the storing and releasing of potential field energy over an operating cycle (variable gap or external demagnetizing influence), linear de- magnetization curves in which area ODBr Fig. l(d) is large in respect to area ODT offer the most efficient arrangement. In such a systeni the external energy product is not necessarily a significant criterion of permanent magnet performance.

RELATING PERNIANENT MAGNET PROPERTIES TO AUDIO DEVICE PERFORMANCE

Mouing Coil Dynamils 8ystems

Moving coil dynamic systems constitute the largest category of usage of the permanent magnet in audio devices. The dynamic speaker is the largest volume application of permanent magnets in this country, and essentially all loudspeakers use a permanent magnet. The advantage of no power consumption, reduced hum, and lower installatilm costs are widely recognized ad- vantages of the permanent magnet over electromagnetic excitation in speakers. Consider Fig. 4(a) which shows the arrangement of a. typical permanent magnet and return path used in the loudspeaker and Fig. 4(b) which shows the demagnetizing curve of the permanent magnet material. In order to relate speaker performance to the magnet properties, consider the fundamental design

Fig. 4-The magnetic structure of the dynamic speaker.

equations of the permanent magnet in which bhe rise of magnetic potential is equated to the drop across the gap and the total flux in the magnet is equated to the flux in external space.

where Lm = Lg = Hg = Hd ‘=

where Am = Bd = Ag = Bg = F =

Bg =

LmHd = LgHg

magnet length (cm), gap length (cm), gap potential/cm, magnet potential/cm.

(1)

AmBd = AgBgF (2)

magnet area square cm, magnet flux density, gap area, gap den&y, leakage factor = total permeance/useful permeance, Hg (numerically in air gap).

Multiplying (1) and (2) we have LmAmBdHd = LgAgBg2F or

VmBdHd = VgBg2F

where Vm (magnet volume) = LmAm volume) = LgAg and

Bg = \/VmRdHd/F?.

(3)

and Vg (gap

(4)

The sound pressure output of a speaker is proportional to Bg and in comparing sound pressure differences the decibel is commonly used. For a given configuration the change in sound pressure is related to gap density, magnet volume, and energy prod.uct by the following expression:

decibel (dbj = 20 log,, Bgl Bg,

= 10 log,, (Bdhd)J(BdHd), = 10 logl,, VI/V,. (5)

From (3) the gap enerp;y is proportional to the volume of the magnet and its external energy product, and in- versely proportional to F. The design problem in speakers is primarily one of arranging the magnetic circuit so that maximum total available energy is established for a given volume and then arranging the exposed surfaces and circuit configuration to keep F to a minimum so that a high percent)age of the total external en.ergy exists in the gap. E:ach permanent magnet material has an optimum

1958 Parker: Permanent Magnets in Audio Devices 35

ratio of Bd/Hd (demagnetization coefficient). The selec- tion of this ratio can be made from an inspection of Fig. 2. A line through the origin having a slope so that it intersects the demagnetization curve of a given material at the point of maximum BH product, as indicated by the energy contour lines, will represent the optimum Bd/Hd.

High gap densities are desirable in the speaker since the conversion efficiency of the speaker is a direct function of gap density. With the extreme case of zero gap density all the power input would be dissipated as heat in the voice coil and no sound power output would result. With a high value of gap density the voice coil moves as current flows in it, and a counter electromotive force is established limiting the energy loss in the voice ‘coil and allowing mechanical or acoustic output. Present-day magnetic materials limit the gap density to about 15,000 Gauss. In Table I, performance data on commonly used magnet configurations for speakers are listed. Magnet weight, gap density, gap energy, expressed in ergs, and magnetic efficiency of each magnet are listed for each standard voice coil group. Gap energy (ergs) = Bg2Vg/8s and magnetic efficiency, a performance criterion expressing the percentage of total magnetic flux existing in the useful air gap, is equal to l/F X 100.

Four basic arrangements are used:

1) Pole stem permanent magnet material extending into top plate,

2) Standard RETMA magnets with stepped pole piece, 3) High-efficiency cylindrical pole piece arrangement, 4) Ring magnets.

The design arrangement chosen depends primarily on the magnitude of gap density required. Pole stem and high-efficiency arrangements allow limited concentration of the flux near the gap, and the present operating densities of commercially available magnets yield gap densities of the order of 5000-7000 Gauss.

The standard magnet series, while laid out to cover a range gap density 6000-10,000 Gauss, finds widest appli- cation in the higher gap density requirements. The ring structure allows the magnet area to be independent of the voice coil diameter and allows considerable flux concentration in the top plate, and gap densities of the order of 15,000 Gauss are obtainable. The circuit efficiency is lowest in the ring arrangement due to the placement of the magnet with respect to the gap.

Magnet weight is to a large extent widely accepted as a criterion of speaker performance. As new permanent magnet materials and arrangements appear, the necessity to have a more realistic measure of performance is felt. The gap energy values are a more fundamental index of performance and undoubtedly will be accepted in specify- ing the magnetic structure of a speaker.

Moving Armature Systems

Fig. 5(a) illustrates the usage of the permanent magnet in moving armature systems, another broad category of

TABLE I LOUDSPEANGR MAGNETIC STRUCTURE DATA

72 u 0.134 o.mlo6 o.40xlo6 REnu FmnA 2 3 1.00 1.17

I- ‘19 n lzzzl 0 0.x0 C.LOxl& Rigb 1.0 ElliciencJ

&a 54

nm 5oz

91m 50s

6500 65s

t

74m 5a

w.c.3 54

10300 5w

7600 652

7600 501

8900 54

loBoo 54

Br

Bc

&I

(4 (b) Fig. 5-The moving armature system.

audio devices employing the permanent magnet. In this arrangement a thin ferromagnetic diaphragm is placed over the poles of the magnet. On the poles are coils. The diaphragm is supported a few thousandths of an inch from the magnet and experiences an attractive force. When current flows through the coils in such a direction as to add to the magnet flux the diaphragm moves closer to the poles. When the current is reversed the pull is reduced. When an alternating current of audio frequency is applied to the coils the diaphragm motion results in sound power output.

To link the permanent magnet properties with device performance, reference is made to Fig. 5(b). The de-

HC Hd 0 EC Ed (a) (b)

Fig. B-The basic electrical analog of the permanent magnet.

magnetization curve and its air gap characteristic line shows the basic electrical analogy of the permanent

are shown. With no signal applied the magnet con- magnet.

figuration ,and gap between poles and diaphragm result In the interest of simplicity a linear demagnetization

in magnet operation at point (D). If the current allows curve for a single cubic centimeter of permanent magnet

the magnetomotive force contributed by the magnet to material is shown in Fig. 6(a) with the assumption that

decrease, then the flux density in the magnet will increase all th.e circuit permeance is in the air gap. Fig. 6(b)

from (D) to (R). The l.ocation of (R) depends on the pro- shows the electrical network representing this arrange-

duct of current and turns involved and the slope of the ment.

minor hysteresis loop. The force on the diaphragm will be Since the demagnetization characteristic was assumed

proportional to the sum of the flux density originally to be a straight line, it may be represented by a linear

contributed by the permanent magnet and the increase resistance 12, = EC/J,. In this case EC represents the

due to the current squared. Mathematically the deflection coercive force and J, represents the residual flux density.

change may be expressed as follows: The electrical analog of perrneance is conductance (G) and is expressed as A/Lp where p is the resistivity. As

(d) deflection = K (Bd + Ci)” = KBd2 convenient quantities one volt may represent 1000 oersteds and one ampere 10G lines of flux, so that the

where K is a constant, (6) resistivity of space becomes 1000 ohm/c.m3 and permeance d = deflection of diaphragm, values may be converted into values of resistance, the C = slope of minor hysteresis loop, reciprocal of conductance, by the relationship R = l/G = i = current. l/P x 1000.

In order to have a useful analog sy,stem one must be Rewriting the above expression for deflection able to set up nonlinear B-H relations.hips. Fig. 7 shows

how three constant voltage sources and linear resistances d = KB,Ci + KC%’ = KCi (Bd + Ci). (7) are used with predetermined switching to allow the

simulation of any permanent magnet material. R, is

Since B, is large compared with Ci, the approximate tangent to the curve at Br and Rm is tangent at the deflection charge may be written d = KCB,i. maximum energy point with Rc tangent at the coercive

The contribution of the permanent magnet in terms of force point. Contact making relays smibch from one deflection is apparent since without, it the deflection element to the next as controlled by the current in the would be only due to C’L In selecting a permanent magnet network. Fig. S(a) and S(b) shows how a speaker magnet for this usage, magnets with high values of residual (Br) structure is zoned and the leakage permeance lumped to are popular. Since, due to the nature of the permanent simulate magnet operation. Meters calibrated in terms of magnet, high values’ of C are somewhat in conflict with B and H allow the metering of gap density, leakage flux high Br, the best criterion is perhaps the product of Br for each zone, and the flux density at ealch zone inside the and C. Another aspect, of this problem is that to operate magnet. Easily changed electrical components allow the magnet at high induction usually requires appreciable rapid change of unit properties and geometry. The zoning length of permanent magnet, and for a given amount of of the magnet and its l.eakage field allows considerable ampere turns, the change in magnet magnetomotive accuracy since the effective magnetomotive force is force as plotted on the demagnetization curve will vary associated with each zone, and an accurate integration of inverselv with the magnet length. ” .J magnetomotive force around the circuit results. Fig.

IRE TRANSACTIONS ON COMPONENT PARTS March ~----- ------~~~-~~~~~

;~?J/j$~~

- EM EC (Unit Fbtemtia~

I. ----- ------- ---------- 2 EO

(a) (b) Fig. ‘?--The electrical .snalog of the demagn8tization curve.

THE ELECTRICAL ANALOG OF THE PEIRMSNENT MAGNE:T

Permanent rnagnet circuit analysis ‘by’ its very nature is cut and try, and considerable time and effort is involved in optimizing a permanent magnet configuration. As an aid in exploiting new permanent magnet materials and circuits arrangements and utilizing them most effectively, an electrical analog approach has been. developed. Fig. 6

1968 Rand: A New Concept in Temperature-Rise Measurement of Transformers 37

(a) (b) Cc) Fig. S-Equivalent electrical network of the dynamic speaker structure.

8(c) shows the mathematical expressions’ for permeance for the zones involved. For commonly encountered dimen- sions the leakage permeance or equivalent resistance can be plotted as a function of geometry. Once the network representing a particular permanent magnet and its external field is set up, the influence of external fields and interior loop operation can be conveniently studied by applying a voltage representing the magnitude of the influence.

Perhaps the greatest value of this analog approach is that it represents an orderly system of organizing per- formance data calculated or measured as a result of

r F. G. Spreadbury, “Permanent Magnets,” Sir Isaac Pitman and Sons, Inc., London, Eng., ch. 4, 5; 1949.

experience. These data are broken into increments which can be assembled in various ways to predict the per- formance of new permanent magnet systems.

CONCLUSION

The permanent magnet and its external field represent a unique system for changing the state of energy. Specific relationships between the external field and the induction for a given application service are desirable. Ability to isolate and control the nature of the elementary building blocks of the permanent magnet promises to make available superior permanent magnets with unlimited design possibilities. As an aid in understanding and predicting the performance of a given permanent magnet in a magnetic circuit the use of electrical analogs offers great convenience and flexibility.

A New Concept in Temperature-Wise Measurement of Transformers*

ABRAHAM RANDt

Summary-Present methods of measuring transformer temper- ature rise require instrumentation with a high degree of accuracy, expensive temperature-control chambers, and relatively skilled operators. A new approach and method is described which provides equal or better accuracy while employing less accurate instruments, a lesser degree of operator skill, and without resorting to temper- ature-controlled test chambers.

This paper describes a bridge test circuit which utilizes a cali- brated temperature-rise “standard” which acts as a reference in evaluating a test unit. The bridge circuit provides a measure of

* Manuscript received by the PGCP, October 9, 1957; revised manuscript received, November 22, 1957. This paper was presented at the National Electronics Conference held in Chicago, Ill. on October 7-9, 1957.

t U. S. Army Signal Eng. Labs., Fort Monmouth, N. J.

compensation for varying electrical and ambient conditions. Data and curves are presented which indicate that the constant-temper- ature chamber could be dispensed with, except for the purpose of calibrating reference “standards.”

T

0 a great ext,ent, the life expectancy and reliability of a transformer depends upon insulation hot-spot temperature. Because it is not feasible to insert

thermocouples deep into the winding of a sealed, cased unit, in present methods the next best thing is done: the average winding temperature is measured in terms of copper resistance and a linearized temperature co- efficient of resistance.