Ferrites: Their Properties and Applications

FERRITES: THEIR PROPERTIES AND APPLICATIONS J. M. Haspers N. V. Philips' Gloeilampenfabrieken, ICOMA Department, Eindhoven, Holland

I. Introduction A. Soft and Hard Magnetic Ferrites II. Properties of Soft Magnetic Ferrites A. Crystal Structure, Ferrimagnetism, Saturation B. Anisotropy and Permeability C. Losses and Related Properties D . Spin Precession E. Magnetostriction F . Permittivity and Dimensional Resonance G. Mechanical Properties H. Commercially Available Soft Ferrites III. Properties of Hard Magnetic Ferrites A. Crystal Structure, Saturation, Remanence B. Coercivity, Wall Shifts and Rotations, Particle Size . . . . C. Oriented Hard Magnetic Ferrites D . Mechanical Properties IV. Applications of Soft Magnetic Ferrites A. Applications Requiring High μ and Low Loss at High Frequencies . B. Applications Based on the Sensitivity of μ to Premagnetization . C. Applications Based on Nonlinear Characteristics D . Applications Based on Magnetostriction E. Applications Based on Mechanical Properties F . Applications Based on Spin Precession V. Applications of Hard Magnetic Ferrites A. Comparison with Steel Magnets B. Loudspeakers C. Telephones D. Television E. Magnetrons F . Premagnetizing of Soft Magnetic Cores G. Pickup Systems H. Generators and Motors I. Couplings and Retarders J. Bearings K. Ultrahigh-Frequency Applications L. Sticking Magnets M. Miscellaneous Applications VI. Special Ferrites A. Ferroxplana References 259

Page 260 260 262 262 265 270 273 276 277 278 280 280 280 283 285 287 287 288 302 306 312 315 317 322 322 323 324 325 326 327 328 329 332 334 334 334 335 336 336 337

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J. M. HASPERS

I. Introduction Ferromagnetism is caused by minor "currents" in the atoms or ions of a substance, originating in the rotation of the electrons in their orbits and around their own axis (spin). If, by some cause inside the atom or ion, an orientation of the magnetic moments from these "currents" takes place, an outside magnetic moment will result. This phenomenon is called "ferromagnetism." On subjection of a ferromagnetic substance to a magnetic field, H, a magnetization, I/cm 3 , occurs, where κ = I/H is considerably larger than 1. "Ferrites" is a general name for a class of nonmetallic magnetic materials which have become important during the last fifteen years. As in metal magnets, the magnetism of ferrites is bound mainly to the elements iron, cobalt, nickel, and manganese; these elements are not present as metals, however, but are bound to oxygen as oxides or oxide compounds. These materials combine a high magnetic with a low electric conductivity, which enables the magnetic conductivity to be used also for high-frequency magnetic fields without being hampered by the simultaneous electric field. In this property lies the key to the practical usefulness of soft magnetic ferrites. Ferrites are manufactured by a ceramic technique, a process which generally involves the pressing or extrusion of a powder and subsequent sintering; the resulting piece is brittle and difficult to machine. Soft magnetic ferrites (those which do not remain magnetized when the magnetic field has been removed) have many uses in the high-frequency range (where they are superior to metal because of their high resistivity) in electrical devices, such as transformers, coils of various kinds, aerials, dynamos, motors, modulators, amplifiers, and tuners; and in electronic devices, such as those used in radio, television, and computers. Hard magnetic ferrites also are used in electrical and electronic devices requiring permanent magnets, the cost of the complete mechanical construction usually being the decisive factor as to whether metal or ferrite magnets are employed. A. SOFT AND HARD MAGNETIC FERRITES

If a ferromagnetic medium is subjected to a magnetic field, H, an additional magnetization flux, 4ΈΙ, occurs, resulting in a total induction, B = H + 4πΙ = μΗ, where μ is the permeability of the material. However, B is not a single-valued but a double-valued function of H; for a decreasing value of H, the value of B is different from that for the same increasing value of H. When the magnet is subjected to an

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a-c field, B lags behind ff, giving rise to the well-known hysteresis loop

(Fig. 1).

IB

FIG. 1. Hysteresis loop.

If H is increased, 4πΙ increases too, until all spinning electrons are oriented parallel; the material is saturated and shows a saturation magnetization 4TTIS, and a corresponding saturation induction, Bs. If H is decreased starting from this saturation point, the parallel orientation is maintained; for H = 0, the induction has remained partly at a certain value BR < Bs, the "rémanent induction" or "remanence" of the material. If the decrease of H is continued by making it negative, it must have a value — Hc before B again equals zero; Hc is the "coercivity" of the material ( I ) . For a certain piece of magnetic material the induction and the field form the "working point." For a fully closed magnetic circuit—a ring without any interruption, through which no current flows (H = 0 ) — the induction has exactly the remanence value, BR; in all other cases the magnet has outside poles, giving a demagnetizing field and a negative value of H inside the material. For a closed magnetic circuit with an air gap, from the continuity of the magnetic flux and the fact that the circular integral of H must be zero (if no outward current is present), it follows that (always on the assumption that no current flows) _ BM _ HM

y, Ap AM

y

IM

IG

Here BM and HM are the B and H in the magnet; AG and AM are the respective cross sections of gap and magnet; l0 and lM are their respec-

262

J. M. HASPERS

tive lengths; and σ is a correction factor for the stray field. All factors on the right-hand side depend only on the dimensions of the magnet and of the circuit in which it is used, so that: (1) The ratio B/H is negative, which means that the working point lies in the second (or fourth) quadrant. (2) The working point is the intersection point of the BH curve of the material with a straight line through the origin with a slope —σ X (AG/AM) X (IM/IG) (working line). For straight rod magnets or for any other shape outside a circuit the same reasoning applies, although then σ, lG, and AG are rather indefinite, so that an exact working line cannot be found. However, the working point still lies on the BH loop in the second quadrant, and the higher the ratio lM/AM of the magnet, the closer the working point approaches the remanence point, BR (2). With ferrites, BR usually varies between 1000 and 4000 gauss at room temperature (for special purposes, BR can be made lower; see Section IV. F ) whereas Hc has a much larger range, from approximately 0.1 to 3000 oersteds. For practical applications, two types of material can be distinguished on the basis of their Hc value: 1. Materials with low Hc. Here the working point lies so low on the BH curve that hardly any induction remains in the absence of an outside magnetic field (unless, as in memory cores, a fully closed magnetic circuit is used), but the induction orients itself very quickly and easily into the direction of an outside field (high permeability), and the material is appropriate for increasing the inductance of a coil, giving a low reluctance path for a magnetic flux, etc. (soft magnetic ferrites) (3). 2. Materials with high Hc. These materials have a low μ and do not easily orient themselves into the direction of an outside field, but they have a high remanence, and produce a field themselves, which can be changed only by very high counter fields (hard magnetic ferrites). Because these two classes are quite different in their applications and in the characteristics and properties essential for those applications, they will be treated separately in the following sections.

II. Properties of Soft Magnetic Ferrites A. CRYSTAL STRUCTURE, FERRIMAGNETISM, SATURATION

The general formula of soft magnetic ferrites is MeFe 2 0 4 or MeO # Fe 2 0 3 , where Me is a bivalent metal. These ferrites all crystallize in a cubic crystal lattice, the so-called "spinel" structure, like the mineral spinel (MgAl 2 0 4 ). This spinel structure shows a close cubic packing of the large oxygen ions (plane-centered cube) with the smaller metal ions placed between, in the interstices (see Fig. 2).

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FIG. 2. "Spinel" structure lattice.

Now it can be seen that two different interstitial sites exist: (1) in the center of the oxygen cube and in the middle of its edges, where each metal atom is surrounded by 6 oxygen ions (octahedral position); and (2) on one-fourth of its cube diagonals, where each metal atom is surrounded by 4 oxygen ions (tetrahedral position). Each cube, containing (8 X y 8 ) + (6 X %) = 4 oxygen ions, possesses 1 + (12 X %) = 4 octahedral sites; 2 are occupied with metal ions. Of the 8 tetrahedral sites, 1 is occupied by a metal ion, giving a total of 3 metal ions on 4 oxygen ions, which is in accordance with the formula MeFe 2 0 4 . In the following discussion, we shall mention the tetrahedral sites "A" and the octahedral sites "B." The type of Me ion determines whether it is placed on an "A" site (normal spinel structure) or on a Ί Γ site (inverted spinel structure). If Me is Zn or Cd, the ferrite has the normal structure and is antiferromagnetic; if Me is Fe++, Mn, Co, Ni, Cu, or Mg, the ferrite has the inverted structure and is ferromagnetic (4). This behavior can be explained by the already-mentioned negative interaction between the spins by superexchange or "double exchange" via the intermediate oxygen ion. In this case, three different interactions exist: A-A, B-B, and A-B. Of these three, the interaction A-B is much stronger than the others, because here the angle A-oxygen-B is more favorable. This means that all spins on A sites orient themselves antiparallel to all spins on B sites, so that all spins on A sites stand parallel, and all B spins too, but in the opposite direction. As there are twice as

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J. M. HASPERS

many ions at B sites as at A sites, a resulting moment in the B direction remains. This is called uncompensated antiferromagnetism or ferrimagnetism, first described by Néel ( 5 ) . In Zn or Cd ferrite, the A sites are taken by the nonmagnetic Zn or Cd ions; consequently the A-A and A-B interactions do not exist, and the negative B-B interaction makes the material antiferromagnetic. It can be advantageous, however, to replace part of the bivalent metal in an inverted ferrite by Zn or Cd. This Zn or Cd settles itself on the A site, so that the total A-B interaction is weakened. Still, as long as the A-B interaction is stronger than the B-B interaction, the parallel orientation of all B spins opposed to the A spins remains; and, because the total A moment diminishes if part of the A site is occupied by the non magnetic Zn or Cd, the resulting moment is increased. If too much Zn is added, the moment decreases again, because then the B-B interaction becomes stronger than the A-B interaction. For Ni ferrite, the optimum is reached if approximately 50% of the Ni is replaced by Zn (4, 6, 7). From the nature of ferrimagnetism it follows that the saturation of the ferrites will be low in comparison with that of ferromagnetic metals because the total moment partly "cancels itself." The maximum saturation obtainable with ferrites at room temperature is about 5500 gauss, against 22,000 gauss for Permendur (50:50 Fe-Co). This is a fundamental drawback of ferrites, especially for power applications at low frequency. The normal behavior of the saturation magnetization of a ferrimagnetic ferrite on temperature increase is a slight decrease until at a certain "Curie temperature" it drops rapidly toward zero. This rapid dropping occurs because at the temperature in question the heat energy kT equals the A-B exchange energy, so that the antiparallel orientation of both lattices vanishes. For practical ferrites, this temperature can vary between room temperature and 600°C; there are other ferrites or similar materials with still lower Curie points, but they have no practical value. A typical example of the behavior of saturation versus temperature is given in Fig. 3 for a Mn-Zn ferrite, in which 40% of the Mn is replaced by Zn. From the above discussion it is clear that addition of Zn or Cd to ferrites with inverted structure increases the saturation, but at the same time decreases the Curie point, because the A-B exchange energy is lowered (8). Figure 4 shows the saturation at 0°C and at the Curie point as a function of Zn content for Ni ferrites in which part of the Ni is replaced by Zn, and in Fig. 3 pure Mn ferrite and a 60:40 Mn-Zn ferrite can be compared. One can see that at temperatures below —10°C the mixed Mn-Zn ferrite has a higher saturation because of the higher residual moment, but at higher temperatures the saturation of

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265

8000

-► T (°C)

FIG. 3. Saturation of Mn ferrite and Mn-Zn ferrite with varying temperature. 6000 r

-.600

5000

H500

400 _ p 300 I 200 IOOOl·

100

50% Ni 50% Zn

IO%Ni 90%Zn

FIG. 4. Saturation at 0°C and Curie temperature for Ni-Zn ferrites as a function of composition.

pure Mn ferrite is higher, because here the high exchange energy is less sensitive to temperature increase (3, p. 158). B. ANISOTROPY AND PERMEABILITY

If a magnetic material is in an unmagnetized state, it is divided into a large number of small domains with parallel spins (Weiss domains). Because these Weiss domains are oriented in all possible directions, the

266

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resulting moment is zero. Between two adjacent Weiss domains a thin transition zone exists in which the orientation gradually changes from that of the first to that of the second Weiss domain. Such a transition zone is called a Bloch wall. If an outside magnetic field of sufficient strength is applied, all Weiss domains are oriented in the direction of this field. This orientation can take place by two mechanisms (3, 7, 9 ) : (1) rotation, in which the spin direction of a whole Weiss domain is turned along with the external field; and (2) wall displacement, in which the domains with a favorable spin orientation are enlarged at the expense of their neighbors by moving of the Bloch walls between them. As regards the occurrence of these mechanisms, a typical difference exists between metal magnets and ferrites. In metals, at a low field only wall displacements take place, until at a certain induction all domains are oriented in that preferential direction (see below) which is nearest to the field. From there by the rotation process a further parallel alignment with the outward field can be obtained. In ferrites the Bloch walls are more fixed and more difficult to move than in metals, perhaps because of the effects of voids in the material. Here μι (see below) is caused merely by rotation, and a higher H is needed before the wall displacements start to contribute. If the permeability, μ = dB/dH, is plotted as a function of H, for H = 0 it is called the initial permeability, μ*; with increasing H it increases to a maximum value, jumax, and then decreases again to a value of 1 at saturation. For soft magnetic metals, the ratio μΧΆΛΧ/μ.ι is usually about 10; for ferrites, it is 2 to 4. For a static small field, metals can reach a /x» of the order of 100,000 (permalloy); the maximum μ\ for ferrites is approximately 10,000. If the static field is replaced by an alternating field of increased frequency, however, the μι of metals decreases because of eddy current losses; but for ferrites μι remains constant into the high frequencies, so that from approximately 1 kc/sec to 50 Mc/sec ferrites have a much higher μι than metals, which leads to many applications in this region. However, /xmax decreases with frequency and asymptotically approaches μι because the walls are inclined to "freeze" in the material and can no longer follow the alternating field (relaxation). This absence of wall displacements leads, for high frequencies, to a μ which up to saturation is rather independent of H, resulting in a low distortion. For high-μ Mn-Zn ferrites, this decrease in distortion becomes noticeable at 20 kc/sec, and at 600 kc/sec the distortion at low induction is practically zero (10). The rotation processes, which are responsible for the μι of ferrites, will take place easily if the material is fully isotropic so that no prefer-

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ence for a certain spin direction exists; in this case a high μι can be expected. There are, however, three important sources of anisotropy in ferromagnetic matter, described below. In order to obtain a high μ, these sources should be made as small as possible (4, 6, 7). 1. Crystal

Anisotropy

The ease of orienting the spins in a certain direction depends on the position with respect to the erystallographic axis. For a cubic spinel lattice, the energy of a certain orientation, Ec, can be given as Ec = K (οί12α22 + αι2α32 -f- a22a32), where aly a2, and a3 are the angles of the orientation with the erystallographic axes. For all cubic ferrites (with the exception of CoFe 2 0 4 , which is not a soft magnetic ferrite) the crystal anisotropy, K, is negative, so that Ec is a minimum for the cubediagonal direction where a± = a2 — «3. This crystal anisotropy can be considered as an anisotropy of the exchange energy in the various crystal directions. This exchange energy is lowered by addition of Zn ferrite (see above), which at the same time lowers the Curie point. Consequently, the highest μι for a ferrite is obtained not far below the Curie point; if one comes too near, however, μι drops again, because Is drops. As an illustration, in Fig. 5 the Curie temperature and μι are given for the Ni-Zn ferrites of Fig. 3 as a function of the ratio of Ni ferrite to Zn ferrite.

40 - ♦ % Zn-ferrite

FIG. 5. Permeability and Curie temperature for Ni-Zn ferrites as a function of composition.

268 2. Stress

J. M. HASPERS

Anisotropy

Stress anisotropy is related to the phenomenon of magnetostriction, which indicates a change in mechanical shape of a magnetic material on magnetization, or, inversely, a magnetization caused by changes in shape, e.g., by an internal stress. This preferred direction of magnetization in the stress direction (or perpendicular to it, depending on the sign of the magnetostriction) of course lowers the permeability. As some internal stresses are unavoidable in a polycrystalline sintered material, care should be taken to make both these stresses and the magnetostriction as small as possible. Internal stresses can be minimized by the use of cubic ferrites, which have an isotropic heat expansion; and magnetostriction can be lessened by making mixed crystals of a ferrite with a negative and a ferrite with a positive magnetostriction. (All ferrites MeFe 2 0 4 have a negative magnetostriction except Fe 3 0 4 , which has a strongly positive one.) For Mn or Mn-Zn ferrite where a high permeability is usually desired, a magnetostriction of nearly zero often is obtained by using a certain amount of excess Fe 2 0 3 , which on firing gives Fe 3 0 4 . However, the presence of both bivalent and trivalent Fe ions in one crystal causes a high electron conductivity and a low resistivity, which in Mn or Mn-Zn ferrites leads to an increase in losses above a frequency of 1 to 1.5 Mc/sec (eddy current loss) and to a very high apparent permittivity, especially at low frequencies. 3. Shape

Anisotropy

As already remarked in Section I, a magnetic circuit that is not fully closed is subject to a demagnetizing field of a value depending on the shape of the circuit. This applies to the outer shape as well as to the "inner" one—that is, to the presence of internal voids filled with air or with a nonmagnetic second phase. Especially if these voids are nonspherical, a preferred orientation occurs in the direction of the smallest demagnetizing field, lowering the permeability. In order to overcome this, voids should be eliminated as much as possible, and any that are still present should be spherical. If these three kinds of anisotropy are made as small as possible, high values of μι, up to 10,000, can be obtained. As will be seen in the next paragraph, however, the higher the μ\ of a ferrite, the lower is the frequency where the ferrite in question becomes unsuitable for many practical applications, because of a sudden increase in losses followed by a gradual decrease in μ. Hence, the frequency determines how much the μι of a suitable ferrite for some application will be. Because of the direct relation between μι and anisotropy, the presence of a premagnetizing field considerably reduces the value of /x, this

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reduction depending on the strength of the bias field and on its angle to the a-c field, by which μ is measured. The higher the μι, the greater is the decrease for a certain bias. Figure 6 gives the dependence of μ% on a

\ \ \ \ \\

> \ ^\ \\ \\

~*>•»^

"ΚΛ X N

X*

—

—

—}

^

"V

'

"*v «s^V

.-^

o^**

• ^ ^ »»^

100 /oNi -fer rite

"***-«, ^

: 0

5 <

10

15

H n r (Oersteds)

FIG. 6. Initial permeability of various Ni-Zn ferrites as a function of d-c bias 64% Zn-36% Ni; 50% Zn-50% Ni; 34% Zn-66% field. KEY: Ni; 20% Zn-80ß Ni.

d-c bias field parallel to the a-c field for a number of Ni-Zn ferrites. For some applications (modulators, particle accelerators), this dependence of μ on a biasing field is rather important. On temperature increase, the exchange energy, the crystal anisotropy, and the internal stress are all lowered, so that it will be clear that μ\ increases. As the Curie temperature for ferrites is much lower than for soft magnetic metals, the TC (temperature coefficient) of μ is usually higher. However, with the high μ of ferrites in the high-frequency region, it is often possible to introduce an air gap in the circuit (shearing). This

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J. M. HASPERS

lowers the initial permeability, μι, to an equivalent permeability, μβ (this can be considered as the μι of an imaginary material which as a closed ring gives the same inductance to a certain coil as the sheared circuit of the original material), which is still higher than the μχ of a high-frequency powdered metal core, while the TC (and the losses in the core) decreases in a ratio μϋ/μι. The TC of the μ\ of a ferrite is therefore usually expressed as Αμ/μ2 AT, because this figure is independent of the air gap. The actual TC in a practical case is obtained by multiplying Αμ/μ2 AT by the equivalent permeability μβ. This Αμ/μ2 AT can vary between —1 X 10"6 and + 5 χ 10Λ To a certain extent, this can be kept in hand by the manufacturing method. For Ni-Zn ferrites a Αμ/μ2 AT between + 5 X 10~6 and + 1 5 χ 10~6 is usual; all values apply to the temperature range of approximately 0° to 70°C (11). Another important point is the instability of μι with time (disaccommodation) probably caused by "freezing" of 180° Bloch walls. This also can, if necessary, be kept low by suitable manufacturing methods, or by introduction of an air gap into the circuit. C. LOSSES AND RELATED PROPERTIES

The losses in a soft magnetic material under certain conditions can be defined as the amount of energy from a high-frequency magnetic field converted into heat in the material. Usually, the losses are expressed in a different way for weak and strong magnetic fields. For weak magnetic fields, the losses are usually expressed as either a series resistance, Rs, or a parallel resistance, Rp, so that the energy loss is expressed as either i2Rs or V2/Rp ( i = current, V = voltage ). This can be indicated by giving the permeability a complex shape μ = // + ///', where ,//'/// = RS/<»L = tan 8, the loss factor. The inverse of this loss factor is the quality, Q. Like the TC of μι, it is possible to reduce the losses in the core by introducing an air gap with a ratio μ€/μ%; therefore, usually the ratio tan δ/μ, at a certain frequency is indicated, because this is independent of the air gap. The losses in a magnetic material are usually divided into three groups: (1) eddy current loss, (2) hysteresis loss, and (3) residual losses. The eddy current loss factor is proportional to ( d2 X f2 ) /p, where d is the smallest dimension of the part in question, / the frequency, and p the resistivity. In metals, this is usually the biggest loss source, so that lowering of d is tried by laminating or powdering, but then μ is reduced too. In ferrites, the eddy current loss is usually negligible because of the high p, which is about 1012 times that for metals. Only for Mn-Zn ferrites containing ferrous ions (see Section II, B) is the resistivity lower, and here in the neighborhood of 0.5 to 1 Mc/sec the losses can no longer be neglected. The hysteresis loss

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factor is proportional to the product i-f (at least for weak fields). On the one hand, this dependence on the current complicates matters because it becomes difficult to speak of a constant hysteresis series resistance; on the other hand, the hysteresis loss can be easily determined by measuring a Q with two different currents under further identical conditions. The real hysteresis loss per cycle is proportional to the surface of the BH loop. If this BH loop is defined by the mathematical expression of Rayleigh, B = (μι + 2vE)H + V(H* — H2), where v is a material constant, and H is the maximum H value, it follows that the total watt loss is equal to %vH* X / X V X 1 0 7 watt, where / = frequency, and V = volume. If this loss is considered as the watt loss, i2Rs, in a series resistance, this resistance, RS) is equal to h χ (ni/l) X (//800) X L, where L is the coil inductance, and 1 is the average magnetic circuit length. On introduction of an air gap, both the self-inductance, L, and the field, ni/l, inside the ferrite are reduced by a factor μβ/μ%, so that Rs is reduced by a factor (μβ/μι)2· Therefore, a constant h/μ2 is usually given for a certain ferrite, being a material constant, independent of the air gap. The hysteresis loss resistance, Rs, is then equal to R8 = (h/μ2) X (ni/l) X (//800) X L X μβ2. Sometimes, instead of h/μ2 a constant 72(24-100) is used, originating from the loading coil technique. This can give no trouble if the conversion factor is known: (h/μ2) X 106 = 548^2(24-100) (12). For commercially available ferrites, h/μ2 lies between 0.4 χ 1 0 3 and 10 X 1 0 3 ohms/H 3 / 2 X ma. From the relaxation effects described under Section II.B it will be clear that a fixed value of h/μ2 can be given only for very low inductions, where μ is still equal to μ%. At higher inductions μ is both induction- and frequency-dependent. Moreover, the ferrites certainly do not fully follow the Rayleigh equation, and with higher induction the differences become more significant. The residual losses, not caused by eddy currents or by hysteresis, are usually negligible for metallic core materials. For ferrites, where at low fields both eddy current losses and hysteresis losses are extremely small, they constitute the major part of the tan Β/μ. Moreover, one of the residual losses is the loss by spin resonance, which at a certain frequency causes an enormous increase in tan δ/μ,, as will be described in the next paragraph. The values of tan 8/μ as a function of frequency for a polycrystalline ferrite depend greatly on the purity and the manufacturing process, so that no fixed values for certain ferrites can be given. As an example, in Fig. 7 some curves are given: A is a normal Mn-Zn ferrite, B and C are special low-loss Mn-Zn ferrites, D is a normal Ni-Zn ferrite, E is a

10" I0 £

10"

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10'

10°

=^f 10*

-.*

—*■ c / s

I0 3

ml /

1 m«-* _

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St=3

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FIG. 7. Loss factor tan δ/μ as a function of frequency for various ferrites.

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272 J. M. HASPERS

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FERRITES

special low-loss Ni-Zn-Co-Mn ferrite, and F is a pure Ni ferrite (4, 13, 14). At strong magnetic fields and high inductions the hysteresis losses become preponderant, so that the losses cannot be defined as a simple series resistance, because this would vary with too many uncontrollable parameters (induction, temperature, etc.). In this case usually the total losses are given in watts per cubic centimeter as a function of frequency, with the maximum occurring induction as a parameter, as given, for example, in Fig. 8 for some Mn-Zn ferrites. This different way of ex-

0.1

2

5

I

2

5

10

2

kc/sec

5 100 2

5 1000

FIG. 8. Total loss in watts per cubic centimeter in Mn-Zn ferrite cores as a function of frequency for different values of peak induction.

pressing losses at weak and strong fields is perfectly logical; for low-field applications usually the losses should be low to ensure a high Q, which is equal to IÛL/R8, so that defining Rs or tan δ = 1./Ç is logical; for highfield applications, not the Q, but the heat development in the core, is usually the important thing, and this can be connected only with the total losses. D. SPIN PRECESSION

If the permeability, μι, of a ferrite is written as μι = μ! -f- / V ( see Section II.C), and both // and / / ' are plotted as a function of frequency on a double logarithmic scale (see Fig. 9, for Ni-Zn ferrites), it is found

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J. M. HASPERS

0.1

2

5

1 2

5

10

2

5

I0 2

2

5

f in mc/sec

FIG. 9. μ and μ." as a function of frequency for various Ni-Zn ferrite compositions. KEY: A = 36% Ni, 64% Zn; B = 50% Ni, 50% Zn; C = 65% Ni, 34% Zn; D = 80% Ni, 20% Zn; E = 100% Ni.

that for every grade μ' first remains constant, then slightly increases, and at still higher frequencies starts to decrease. At a frequency slightly above this decreasing point //' reaches a maximum, so it is clear that in this neighborhood tan Β/μ = μ"/μ'2 sharply increases too (15). This increase in loss can be explained by realizing that the spinning electrons which cause ferromagnetism have both a magnetic moment and an angular spin moment. If they are oriented in an outside field, Hz, and afterward a second field, Hi} is applied perpendicular to Hz, the electrons will start a precession movement (like a spinning top) around their former equilibrium position with a typical angular frequency, ωτ = γΗζ. Here Hz is the original field ( in oersteds ), and γ is equal to g X (e/20ra), where e/m is the charge-to-mass ratio of the electron, expressed as 1.77 X 108 coulombs/gm. The term g is the socalled Lande factor, the ratio between magnetic moment and impulse moment of the ions of a ferromagnetic. If, as stated above, only the electron spins contribute to the ferromagnetism, g is exactly 2; if there

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is still an orbital contribution for the elements of the second half of the third transition series (where the orbital moment and the spin moment are parallel), g is slightly greater than 2. It should be noticed that <ûr = 2π/> is independent of the perpendicular field, Hi. However, if Hi is an alternating field of a frequency equal to the typical frequency, fr, of the precessing system, the precession begins to resonate and to take up energy from the alternating field which finally is converted into heat by damping of the increased precession. This means a steep increase in losses (16, 17). If no static outside field is present, it is replaced by the internal orientation due to crystal anisotropy. For a negative crystal anisotropy constant, K (see Section II.B), the anisotropy field is equal to —%(K/IS) (Is = saturation magnetization in gauss per square centimeter), whereas as long as only rotation processes occur, K is equal to —2πΙ82/(μί — 1). It follows that the frequency, fr, is determined by ίτ{μι — 1) = %γίβ> so that a high μ^ gives a low fr, and vice versa. This is perfectly understandable, because a high μ means a low anisotropy field, and the frequency, fr (usually called the gyromagnetic resonance frequency), is proportional to this anisotropy field. For the vast majority of ferrite applications, being based on the constancy of // and the low tan δ, their gyromagnetic resonance frequency, fr, constitutes an upper limit to the useful frequency range. At higher frequencies, another ferrite with a higher fr, which means a lower μϊ} should be chosen. From the above discussion one would expect a sharp resonance peak in tan δ, which at frequencies above fr would fall oflF again. In fact, this is not true; the losses stay high also for frequencies above / r . This is due in the first place to damping by interaction with other orbits, which for many spins gives an increase in the anisotropy field due to steric hindrance. In the second place, the relation o>r = yHz is valid only for a sphere; for nonspherical shapes the demagnetizing fields cause complications. According to Polder and Smit (17) for an ellipsoid with walls in the yz plane and an a-c field parallel to these walls, the maximum stiffness is not the anisotropy field, HA, but HA -\- 4πΙ8. This means that the maximum angular resonance frequency, ωτ, is equal to γ ( HA + 4πΙ θ ), or for high μ ferrites, where HA is small,
276

J. M. HASPERS

an a-c field perpendicular to it, the magnetization direction will start a precession around HZ9 the direction of this precession depending on the sign of Hz. If the a-c field is caused by a polarized wave passing through the ferrite, it can be considered as a superposition of two circularly polarized fields of opposite rotation senses. One of these senses will correspond to that of the precession, and the other will be opposite. It can be shown that for the former wave the susceptibility, κ, will be IS/(H -\- ω/γ); for the latter, Ia/(H — ω/γ). As μ = 1 + 4™, and the propagation velocity, Ό, of a wave in a medium is c/^/7ß, where c is the light velocity and c the permittivity, it is clear that one of the circularly polarized components of an a-c wave passing through a magnetized ferrite in the magnetization direction will have a higher propagation velocity than the other, so that finally the polarization plane of the wave is rotated (Faraday rotation) (18). Section IV.F will describe how this gyromagnetic resonance and Faraday rotation can lead to some interesting applications of ferrites in the microwave range, in spite of the low permeability of the ferrites in this region. E.

MAGNETOSTRICTION

As already mentioned in Section ILB, magnetostriction is an elastic change in the shape of a magnetic body on magnetization. If the length increases in the direction of the magnetization, the magnetostriction is positive; if it decreases, the magnetostriction is negative. On increase of the field, the magnetostriction, like the magnetization, arrives at a saturation value. This specific change in length at saturation is negative for all cubic ferrites (Mn ferrites, —2 X 10"6; Ni ferrite, —27 X 10"6) with the exception of ferrous ferrite, Fe 3 0 4 , where it is 40 X 10Λ As described in Section II.B, mixed crystals of Fe 3 0 4 and other ferrites can be made in order to obtain a low λ, giving a high μ. If the ferrite is subjected to an a-c field, it starts a mechanical vibration. Because the change in length is independent of the sign of magnetization for an unbiased ferrite, the mechanical vibration will have double the frequency of the a-c field, but for a sufficiently biased ferrite it will have the same frequency. In practice, the opposite phenomenon of magnetostriction occurs, too, and a mechanical stress or strain provides an easy magnetization direction. This means that the mechanical vibration of a biased magnetic ferrite can be transferred back again into an a-c voltage of current of the same frequency. From thermodynamic considerations it follows that only a part of the applied electric energy for the a-c field can be transferred via mechanical energy back into electrical energy. This part is defined as k2, where k is the so-called electromechanical coupling coefficient, which for special ferrites can

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reach a maximum of 0.4. This is a most important constant for magnetostrictive application of ferrites. It should be emphasized, however, that k is not a measure of the electromechanical efficiency, because the electromagnetic energy not converted into mechanical energy is not lost (19). F. PERMITTIVITY AND DIMENSIONAL RESONANCE

As mentioned in Section II.B, in Mn-Zn ferrites frequently some mixed crystals with a little ferrous ferrite are made in order to obtain a low magnetostriction and a high μ. This leads to a low resistivity, of the order of 1 ohm-cm. There remain, however, some very thin boundary layers between crystallites which resist electron movement and where the p retains its original value of the order of 106 ohm-cm. The permittivity, e, of all ferrite materials, independent of their resistivity, lies between 10 and 15, with 13 as a reasonable average figure. In ferrites of low p, still containing some thin layers with high p, however (Fig. 9A), complications occur. If Rx and C± are the resistance and capacitance of a piece of normal ferrite, and R2 and C 2 those of an adjoining boundary layer, which is thinner than the first part by a factor of about 104, it will be clear that in spite of this R2 will be approximately 100 times as large as Ru and C 2 will be about 104 times as large as Ci. For low frequencies, the small capacity, Cl9 has so much impedance that its conductivity can be neglected against Rlt The total resistance measured is that of Rx + R2, which is approximately lOORi, so that the apparent p will be about 100 times as large as the p of the crystallite, but smaller than the p of the walls by a factor of 104. The total capacitance measured is that of C 2 . If this is assumed to exist over the whole thickness of both layers, the apparent e will be very high, in this case of the order of 130,000. This is found only for ferrites of low p; otherwise Ri is too high, and Cx cannot be neglected. For high frequencies Cx is no longer negligible against Ru but now R2 becomes negligible against C 2 . This means that the real p of the crystallites is measured. The total capacitance measured will be the series connection of C± and C2, which is practically equal to d; this will give a normal c of 10 to 15. Consequently, with increasing frequency a considerable drop both in resistivity and in permittivity is to be expected for these ferrites. This is confirmed by actual measurements on a Mn-Zn ferrite, as given in Fig. 10. For comparison the curves for a Ni-Zn ferrite are also given. This shows the same phenomenon, but much less pronounced, and £ is reduced to its normal value at much lower frequencies because of the much higher p of Ni-Zn ferrites. Another complication caused by this high e is the so-called dimensional resonance

278

J. M. HASPERS

ιο 8

106

\

'S

;v

^_ **»V .

"*

P

*' A I04

•^

\

I0 2

\

\ \

\\

\

\

\, v.

€

I I0"2

\ I

\

I02 )0 4 > f in kc/s

FIG. 10. Permittivity and resistivity of Mn-Zn ( ferrites as a function of frequency.

I06 ) and Ni-Zn (

)

loss (20). The wavelength of a wave in a ferrite is equal to v/f or to c/f^/Tjl, where c is the light velocity (3 X 1010 cm/sec). For a ferrite with μ = 103 and c = 105 at 1 Mc/sec, the half-wavelength is 1.5 cm. If one of the dimensions of the ferrite is equal to such a half-wavelength, a resonance can occur, giving considerable additional losses. If a smaller piece cannot be chosen, the only way to overcome this is to select a ferrite with lower c or μ. G. MECHANICAL PROPERTIES

Ferrites are manufactured by a technique similar to that of ceramics; the raw materials are milled, mixed, and prepared to a certain starting

279

FERRITES

mass; from this mass the product is formed by pressing or extrusion and afterward fired at high temperature in a suitable atmosphere. On firing, a linear shrinkage of 18 to 22% occurs. As it is difficult to control this shrinkage, a tolerance of 1 to 3% should be allowed on mechanical dimensions. Of course, for flat or round sides this tolerance can be corrected by grinding afterward, but this means an appreciable price increase and should be done only if absolutely necessary. For pressing, a die is necessary, which should be of hardened steel or, for larger quantities, of tungsten carbide, because of the abrasive properties of the material. In order to facilitate the manufacture of such a die, the shape of the required product should be kept as simple as possible. Slots, holes, and bevels can be provided if they run parallel to the direction of pressing and if they do not reduce the local thickness to less than 1.5 mm, which would make the product mechanically unsound. Moreover, the total height of a pressed product should be no more than three to four times the diameter or wall thickness of a piece; otherwise the loosening of the die will give trouble. These limitations are not absolute laws and can often be overcome by special measures; but special treatment usually causes high prices, so that for economical reasons these limitations should be respected if possible. For extruded parts the length can be much larger than the section, but the section must remain always exactly the same, and not be too complicated. Moreover, the magnetic properties of an extruded part are always slightly inferior to a pressed part of the same material, owing to the higher porosity. Mechanically, the sintered ferrites are similar to ceramics, very hard and rather brittle. The crushing strength is considerably higher than the tensile strength, because the latter is determined mainly by voids in the material, which can never be completely eliminated. Table I gives some average values of mechanical properties for commercial ferrites. Chemically, ferrites are very inert. They are attacked by strong mineral acids but are resistant against weaker acids, halogens, organic TABLE

I

AVERAGE VALUES OF MECHANICAL P R O P E R T I E S FOR COMMERCIAL F E R R I T E S

Young's modulus Linear expansion coefficient Tensile strength Crushing strength Specific heat Thermal conductivity

15,000 k g / m m 2 10~ 5 /°C 2.5 kg/mm2 7.5 k g / m m 2 0-17 c a l / g m / ° C / m 8-14 cal/cm/sec/°C

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J. M. HASPERS

liquids, alkalis, etc. They are unaffected by humidity and other atmospheric conditions and neither attract nor repel water. Machining of ferrites is difficult, owing to their hardness. Grinding and cutting is possible with tools of diamond or silicon carbide. H. COMMERCIALLY AVAILABLE SOFT FERRITES

The commercially available soft magnetic ferrites can be roughly grouped as "general-purpose" and "special-purpose" ferrites. The first category serves for all those purposes where a high inductance or a low reluctance is required with low losses at higher frequencies. Here two groups are available: the Mn or Mn-Zn ferrites, and the Ni or Ni-Zn ferrites. Both groups show many variations but still definitely form one category. The Cu or Mg ferrites can be considered obsolete and are definitely inferior to the Mn or Ni ferrites. The Mn or Mn-Zn ferrites have a high permeability ( ^ = 500 to 5000) and high saturation (>3000 gauss at room temperature), but low Curie points (<250°C) and low resistivity (<1000 ohm-cm). The temperature stability is good, and the stability with time can be made good. The losses are low up to the region of 0.5 to 1.5 Mc/sec, when both high eddy current and gyromagnetic resonance losses occur. Up to these frequencies a Mn or Mn-Zn ferrite is the best general-purpose material. At higher frequencies the Ni or Ni-Zn ferrites should be used. They have lower permeabilities (μι = 10 to 1000) and Curie temperatures between 100° and 600°C. Their temperature coefficient is higher, and their resistivity is also ( > 106 ohm-cm ). The losses are low up to the gyromagnetic frequency, which lies at approximately 1 Mc/sec for /xi = 1000 and at approximately 100 Mc/sec μι — 10. The special-purpose ferrites are usually intended for one kind of application, for which particular properties are wanted. They are usually mixed ferrites and, with the exception of Ni or Mn, contain certain amounts of other metals, such as Cu, Mg, Co, Cr, Al, Fe++, or Cd. They will be mentioned with the corresponding applications. III. Properties of Hard Magnetic Ferrites A. CRYSTAL STRUCTURE, SATURATION, REMANENCE

The general formula of the hard magnetic ferrite materials is MeFei 2 0 1 9 or MeFe 18 0 27 . Here Me is usually Ba, although this may be wholly or partially replaced by Sr or Pb. The commercial product is mainly BaFe 12 Oi 9 , with a small quantity of BaFei 8 0 27 . These materials differ from the soft magnetic ferrites mainly in their crystal structure, which is not cubic, but hexagonal. It consists of a maximum density

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281

packing of oxygen ions, with a number of parallel planes containing 4 oxygen ions each in each unit cell. In each fifth plane one oxygen ion is replaced by Ba, with the iron ions located at interstitial sites between. In the spinels two different kinds of interstitial site exist (see Section ILA), and in the same way five nonequivalent sites exist in the hexagonal structure of BaFei 2 Oi 9 , which in the same way as described in Section ILA give rise to fifteen different interactions. It would be difficult to make an exact calculation for all those superexchange interactions, but on applying the rule of thumb that an interaction is stronger if the distances Me-O decrease and if the angle Me-O-Me deviates more from 90°, a fairly plausible prediction can be made about the mutual positions of the electron spins of the various iron atoms (see Fig. 11). From this it follows that in the unit shown, containing 2 molecules of BaFei 2 0 19 , 16 spins are pointing parallel in one direction, while the other 8 are opposed to those, so that a total of 8 spins remains. For BaFei 8 0 2 7 a similar structure exists, except that here in each seventh oxygen layer one oxygen ion is replaced by Ba. Moreover, 2 ferrous ions and 16 ferric ions are present. Considering the various interactions in a two-molecule cell (see Fig. 12), one can be fairly sure that the spins of the 4 Fe ++ ions and the 20 Fe+++ ions are all parallel, whereas those of the other 12 Fe+++ ions are opposite. From this, saturation magnetic moments at 0°K of 100.5 gauss X cmVgm and 99.6 gauss X cmVgm can be calculated for BaFei 2 0 1 9 and BaFei 8 0 2 7 , respectively. As the Curie point of these hard magnetic ferrites lies at approximately 450°C (723°K), and the saturation depends fairly linearly on temperature, this would mean at room temperature a saturation of 59.2 gauss χ cmVgm, which is in reasonable agreement with the experimental figure of 70 gauss X cmVgm, or 4400 gauss for a specific gravity of 5.0 gm/cm 3 . This saturation is very low in comparison with that of metal magnets, which can go up to 13,000 to 14,000 gauss at room temperature. The reasons are the same as for the soft magnetic ferrites: (1) "dilution" of magnetic ions by oxygen, and (2) the presence of ferrimagnetism, which causes a considerable loss in final moment due to internal compensation of opposed spins. In contrast to the soft magnetic ferrites, where all anisotropy is made low on purpose in order to achieve a high permeability, the hard magnetic ferrites have one preferential direction of orientation along the hexagonal axis with a very high positive crystal anisotropy constant, K (see Section II.B). For soft magnetic ferrites, for example, Ni ferrite, K is about —6 X 104; for Ba ferrite it is approximately 3 χ 10e. Under these circumstances it can be shown that for a random orientation the rémanent magnetization is one half of the saturation, so that at room temperature it should be approximately 2200 gauss. For

FIG. 11. Positions of spins of ions in BaFe12Oi9 lattice.

282 J. M. HASPERS

FERRITES

283

FIG. 12. Positions of spins of ions in BaFei 8 0 2 7 lattice.

the maximum theoretical X-ray density of 5.3 it should be 2330 gauss, but in practice these values can be reached only at the expense of such a drop in coercivity (see below) that the material can hardly be called hard magnetic any longer. For commercially available hard magnetic ferrites with random spin orientation, the rémanent induction, BR, lies between 1900 and 2200 gauss. Of course, things become different if the material is oriented, because then in one direction the remanence can be much more than half the saturation (see Section III.C). From the picture given above about the linear decrease of saturation (and remanence) from very low temperatures to the Curie temperature, it follows that both have a fairly high negative temperature coefficient. For the temperature range between —50° and -f-100°C, this can be given with good approximation as —0.18% per degree centigrade—that is, about ten times as high as the value for metal magnets. B. COERCIVITY, W A L L SHIFTS AND ROTATIONS, PARTICLE SIZE

As mentioned in the Introduction, the most essential quality for a hard magnetic material is a high value for the coercivity, Hc, which

284

J. M. HASPERS

defines the negative field for which the induction becomes zero. If a ferromagnetic material is subjected to a field H, a magnetization 4πί occurs; the induction, B, is equal to H -f- 4πΖ. At remanence (H = 0 ) , 4πΖ is equal to BR. If a negative field is applied, first B will become zero or a field BHC; at a higher negative field IHC, 4πί will become zero itself. Consequently, each magnetic material has a B coercivity and an I coercivity, of which the former is the smaller. For most materials, hardly any difference exists between BHC and IHC> but the hard magnetic ferrites are an exception here, owing to their low remanence and high coercivity. For unoriented Ba ferrite, BHC is approximately 1700 oersteds and IHC is approximately 3000 oersteds. If in the following discussion mention is made of coercivity without further indication, the B coercivity is meant (BHC). At the remanence point 4πΙ is equal to BR. If a negative field is applied, 4ΤΓΓ will certainly not increase, but may remain constant in the most favorable case. In this case BHC = BR, and the BH curve in the second quadrant is a straight line making a 45° angle with the axis. The (BH)maX product (as will be seen later, this is a measure for the volume of material required to obtain a certain field in a volume of given dimensions) is then equal to 0.25BÄ2. This is, however, a theoretical value seldom reached in practice, because lower negative fields cause reduction in 4πί. The orientation of the spins of a Weiss domain into the direction of an outside field can take place in two ways (see Section II.B)—by rotation and by wall displacement. Because of the very high crystal anisotropy of the Ba ferrites, a rotation away from the preferred direction requires a very strong field, so that on applying an increasing field the first orientation is due to wall displacements, whereas rotations do not play any role before the field is much higher. Consequently, if a high coercivity is aimed at for a permanent magnet material, care should be taken that no wall displacements can occur, but only rotations. This can be achieved if all particles in the material consist only of one Weiss domain and if no walls are present. Now from theoretical considerations it is known that for decreasing dimensions of a ferromagnetic particle the ratio between exchange energy and anisotropy energy is changing until at a certain critical diameter, d0, the formation of a wall no longer gives any energetic advantage (22). For BaFei 2 0 1 9 , d0 has a value of 1.3 microns, against 0.03 micron for metallic iron and 0.24 micron for metallic cobalt. Consequently, it is much easier technologically to stay below the critical particle size for ferrites than it is for Fe or for Co, although nowadays this is possible for these metals too.

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285

If all particles lie below d0, in considering the coercive force only rotations should be taken into account. For a material with crystal anisotropy K (other anisotropies for Ba ferrite are certainly not zero but can be neglected here) and magnetization 4πί θ , it can be calculated that the field, H, required to turn the magnetization by 180° is equal to 2K/IS. For random orientation this field, which is the IHC, is 0.96K/ZS. On calculating this for unoriented Ba ferrite, at room temperature, where 4πΙ3 — approximately 4400 gauss and K = 3.1 X 106 ergs/cm 3 , a value of approximately 7300 oersteds is found. However, under practical sintering conditions it is impossible to obtain both a high density and the absence of particles with a diameter below d0, so a compromise should be chosen. A practical value for such a compromise in unoriented Ba ferrite lies at BR = 2100 gauss, IHC = 3000 oersteds, and BHC = 1800 oersteds, giving a (BH)M product of approximately 0.95 X 106 gauss oersted. For a properly made and homogeneous Ba ferrite the magnetization, 4πΙ, remains fairly constant as a function of a negative field, Hs, until it drops suddenly at a value slightly below IHC. The corresponding BH curves then decrease with increasing (negative) H under an angle of approximately 45° with the axis, until for the same field value they also drop steeply. As seen above, for unoriented Ba ferrite usually IHC is appreciably higher than BR. This means that at the field where 4πΙ starts to go down strongly B is already negative, so that the corresponding point on the BH curve lies not in the second but in the third quadrant. As will be seen below, for an oriented Ba ferrite this is different, and this difference has important consequences for the application possibilities of oriented and unoriented hard magnetic ferrites. C. ORIENTED HARD MAGNETIC FERRITES

The permanent magnetism of hard magnetic ferrites is caused by the strong preferred orientation of the spins along the hexagonal axis of the crystals. This means, however, that if an outside field is applied the contribution of each Weiss domain (which means of each small crystal, because no walls are present) to the rémanent magnetization is proportional only to the cosine of the angle between the directions of its hexagonal axis and of the outside field. For a random orientation it can be calculated statistically that this leads to a remanence value equal to half the saturation. The situation becomes quite different, however, if it is possible to orient the crystals in the material before, so that they are more or less aligned. In this case a gain in remanence with a factor 2 as a maximum can be obtained, provided the magnetization occurs in the direction of the oriented

286

J. M. HASPERS

crystal axes; the material has become anisotropic also on a macroscopic scale (23, 24). Figure 13 gives an example of two BH loops of the same

4000

_ 3000 In =3 A

ΐ

2000

1000

0

5000

10000 > H (Oersteds)

15000

FIG. 13. Hysteresis loops of anisotropic ferrite magnets in the preferred direction and perpendicular to it.

anisotropic material in the preferred direction and perpendicular to it. Technologically, this orientation can be realized in various ways. The most favorable method is probably to start from unoriented material, which is ground very fine, so that each particle contains only one crystal, and then orient the still freely movable crystals in an outside magnetic field. In this way, a BR value up to 4000 gauss can be obtained in the preferred direction, against a value of less than 1000 gauss perpendicular to it. As in the isotropic material, some practical compromise should be chosen between high density and uniform low crystal size without walls; this means between remanence and high coercivity. Two realizable combinations are a BR of 4000 gauss with a BHC of 1800 oersteds, and a BR of 3400 gauss with a BHC of 2500 oersteds, giving (BH)max values of about 3.5 χ 106 and 2.6 X 106 gauss oersteds, respectively. The application determines which of these types will be preferred. For an oriented Ba ferrite, the coercive force of the magnetization (IHC) will be smaller than for an unoriented material. This is related to the fact that the energy required to form a Bloch wall in the material is a minimum if the direction of the outside field coincides with the

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287

preferred crystal orientation [see Kittel (22)], so that it is more difficult to avoid the formation of Bloch walls completely. In practice, a value of 3000 for IHC is obtainable, but the necessary compromise with BR usually leads to value of 1600 to 3000 oersteds, as mentioned above. In contrast to unoriented Ba ferrite, here BR > IHC. This means that, for a good material, where 4πΙ remains almost constant with negative H and then suddenly drops, the value of BHC (where B = 0 or 4πΖ = —H) is only slightly different from IHC. Consequently the BHC values for oriented and unoriented hard magnetic ferrite are approximately the same, although the IHC value for the unoriented material is higher. The drop in 4πΖ at a certain negative value of H is caused by irreversible wall shifts; this steep part of the 4πΙΗ or BH curve can be passed only in one direction. Consequently the "working point" (see Section LA) should not lie on this steep part of the BH curve; otherwise an irreversible demagnetization could easily occur. For unoriented Ba ferrite this danger does not exist, because BR < IHC, so that the "knee" in the BH curve lies in the third quadrant and the working point is always above it. For oriented Ba ferrite, however, BR > IHC and the knee of the BH curve lies in the second quadrant. Consequently the magnet system or the length-to-diameter ratio of the magnet should always be designed in such a way that the working point lies above the knee. This is complicated even more by the fact that at temperatures near the Curie temperature the critical diameter, d0, for Ba ferrite has a positive temperature coefficient, so that the coercive force increases with temperature too, but decreases at low temperatures. The remanence, BR, has a negative TC and increases at low temperatures. This means that the slope of the working line should not lie below that of the line from the origin to the "knee" in the BH curve at the lowest working temperature; otherwise at low temperatures demagnetization might still occur. Unoriented Ba ferrite can never demagnetize by cooling and can, moreover, be demagnetized below its own coercivity and still come back reversibly on removal of the field. This is most important for some applications (25). D. MECHANICAL PROPERTIES

In this respect no difference exists between soft magnetic and hard magnetic ferrites. We therefore refer to Section ILG and to Table I, as they apply equally well to hard ferrites. IV. Applications of Soft Magnetic Ferrites After the review of properties of soft magnetic ferrites, given in Section II, the question arises whether these properties make possible

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J. M. HASPERS

a better technical or a more economical solution than an existing one with metal cores (26, 27). If the soft magnetic ferrites are compared with solid or lamellated cores of soft magnetic metals, two general drawbacks of ferrites can be noticed: (1) The much lower saturation magnetization. This is fundamental because of the nature of ferrimagnetism. (2) The difficulty of making narrow tolerances and complicated shapes. This is due to the ceramic technique of manufacturing and to the ceramic nature of the ferrites (hard and brittle), which makes machining very difficult. Although some improvement is certainly possible, ferrites will stay inferior to metals in this respect. For a considerable number of applications, however, other ferrite properties offer so many advantages that these drawbacks are more than compensated for. The first of these properties is the very high resistivity ( 108 to 1013 times that of metals ). This makes the eddy current losses at high frequencies negligible, and the high-frequency loss (up to the gyromagnetic resonance frequency) very small. Because of this small loss, no absorption of high-frequency energy in the outer skin of the ferrite is possible, and the initial permeability remains constant even above the gyromagnetic resonance frequency, and only then slowly decreases with increasing frequency. This combination of high μι and low loss at high frequencies is the basis for all applications of soft magnetic ferrites. In the following discussion we shall first deal with the applications based only on this combination; later, applications in which other ferrite properties also play a role will be treated. A.

APPLICATIONS REQUIRING ONLY HIGH

μ

AND L O W

Loss

AT HIGH FREQUENCIES

1. High-Frequency

Transformers

(11)

In all transformers, a certain minimum mutual inductance should be obtained at the lowest frequency to be transmitted, in a volume and with a number of turns as small as possible. This means, in the first place, that a high μ is important. If the mutual inductance, M, is high (expressed by the coupling coefficient k = MI^J*LxL2y where Lx and L 2 are the inductances of primary and secondary winding), the loss in the core is less critical, being proportional to the square of the current required for magnetizing the core, which for high k is only a small fraction of the actual primary current. The lower limit of the frequency range for applying ferrite depends on the alternative metallic core material being considered and the form

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289

in which it is used, for example, the thickness of the laminations or the spiral strip. With a high-quality nickel-iron toroidal core made of a 1.5-mil spiral strip, the frequency limit would be about 60 kc/sec for a 1-db loss. However, when cost, availability, and convenience of winding are taken into account, this limit (for low-power transformers) may fall back into the upper audio range. For the audio-frequency band (300 to 3400 kc/sec) many ferrite transformers have been designed and used successfully, although with respect to permeability the nickel-iron cores are superior to the existing ferrites. With newer, improved ferrites, this difference is becoming smaller and smaller. These low-power high-frequency transformers may be used for telecommunication purposes, both as audio transformers and for carrier telephony (modulator transformers). Because losses are not important, for broad-band transformers ferrites can be used at frequencies well above their gyromagnetic resonance frequency. The most suitable type of ferrite for these transformers may be given approximately as follows: Up to 1-2 Mc/sec: high-/* Mn-Zn ferrite (μ > 2000) Up to 5-8 Mc/sec: high-/* Ni-Zn ferrite (μ > 700) Above 8 Mc/sec: medium-μ Ni-Zn ferrite ( μ ~ 2 5 0 )

For methods of calculating inductances, numbers of turns, etc., reference is made to handbooks and publications of ferrite manufacturers. Because of the required high permeability, usually a closed core is employed. A ring core is excellent, but difficult to wind. In many cases the best solutions will be given by a "pot core," an Έ " core, or a socalled "cross" core, which is an intermediate shape between the first two. If some d-c premagnetization is present ( transformers in the anode circuit of an amplifier), a small air gap is advantageous, and an optimum design can be determined by means of Hanna curves (28), which can also be found in the above-mentioned handbooks for commercially available core types. For power transformers the situation is becoming different. Here the low saturation is a serious drawback for ferrites, and the frequency limit at which ferrites are preferable to metal lies much higher, usually around 10 kc/sec. Usually the bottleneck for core size here is not the mutual induction, but insulation problems or the maximum temperature permissible for the core, which is heated by the losses. These highinduction losses are mainly hysteresis losses and depend strongly both on frequency and on induction. An elegant method of designing ferrite power transformers for high frequency is described in reference (29). High-frequency high-power transformers may be used, for example, for transmitters, ultrasound generators, and carrier wave generators. A

290

J. M. HASPERS

special case is the television flyback transformer, which will be discussed later. For speaker transformers in radio sets the frequency band is low (below 12 kc/sec) and the required power level high; moreover, direct current is present, which is unfavorable for ferrite too, because μ rapidly goes down with premagnetization. Here metal cores are more suitable. For high fidelity, where a frequency response up to 20 kc/sec or higher is required, ferrite might have a chance, but a more radical solution is to use a high-impedance speaker and to leave out the transformer altogether. A recent application is in d-c to a-c converters, for example, TL lighting in combination with transistors. Here the frequency is fairly low too (1.5 to 2 kc/sec in the United States, up to 8 kc/sec in Europe), but no direct current is present, and the power is usually limited by the available transistors. It seems as if pot cores or E cores of a special Mn ferrite with high saturation are going to replace metal cores in this area, also because a high efficiency (low core loss) is important. Sometimes the low saturation of the ferrite is an advantage, because it acts as a safety measure to protect the transistors, without a base current adjustment being necessary (30). 2. Fulse

Transformers

Here the same requirements are valid as for normal transformers, but an additional factor is the distortion of the output pulse, which may have different causes (losses, real distortion, μ too low, saturation too low, etc.). For high-energy pulse transformers (radar) the use of ferrite is becoming advantageous at pulse lengths below approximately 10 jusec. A high-μ, high-saturation material should be chosen here. For unidirectional pulses, as is usual, the low effective induction range of ferrite can be doubled in practice by biasing with hard magnetic ferrite (see Section V.F) (31, 32). For low-energy pulse transformers (computers) the requirements depend on pulse shape and duration. For long pulses with low rise time a high μι and a low hysteresis loss are preferable, in order to keep the droop as low as possible; for short pulses (below 0.1 //,sec with a rise time of the order of 0.01 /xsec or less) a material suitable for very high frequencies, even with a low μ, is often preferable, because in order to preserve the steepness of the edge the higher harmonics must be able to pass without much attenuation (33). At durations below 10 to 100 /xsec, ferrite is useful for pulse transformers; below 1 to 2 /xsec, it is a "must."

FERRITES

3. Television Flyback

291

Transformers

The flyback transformer is a special kind of power transformer with d-c bias. It acts at the same time as an EHT generator, but for the core this does not make much difference. The frequency is fairly low (10 to 20 kc/sec, or a maximum of 40 to 80 kc/sec during flyback). Although it is possible to suppress the direct current ( desaturation circuit), this is not customary because it requires extra components. The presence of bias makes a small air gap advantageous which can be calculated according to the above-mentioned Hanna curves. The common ferrite shape here is a U core; in the course of years the leg section has progressed from square to octagonal to round, because of higher coupling factor and easier mounting. The first requirement is to pass as much energy as possible in a small and cheap core. This requires a material with low total loss, high saturation, and high amplitude permeability, in most cases a Mn ferrite or Mn-Zn with not too much Zn; the initial permeability is of no importance. The future trend toward higher deflection energies and smaller cabinets necessitates smaller transformers with higher energy and will demand more and higher requirements of the ferrite core material. However, the position of ferrite with regard to other core materials will remain absolutely unassailable (34, 35). The "direct drive" system, which eliminates most of the ferrite by making the deflection coil itself part of the flyback, is possible only for very low energies and cannot be reproduced easily. 4. Deflection Coils In deflection coils for television or for radar, a ferrite yoke ring serves as a low reluctance back path for the flux of the alternating deflection field. Although for existing television line frequencies (10 to 20 kc/sec) the necessity of using ferrite (especially for higher deflection angles where a high energy-efficiency is required) is indisputable, the electrical requirements for the ferrite are less critical than, for example, in transformer or filter cores, because of the presence of a "sheared" magnetic circuit with a big air gap. On the other hand, in order to obtain a good picture quality, the deflection coils must be sufficiently reproducible, which sets high requirements for the mechanical precision of the yoke rings. Moreover, for high deflection angles complicated shapes of yoke rings are necessary to construct coils that can be put as far forward on the cathode-ray tube as possible, in order to give a high

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deflection sensitivity without corner cutting; and these complicated shapes still demand a high mechanical precision (34). On the yoke ring, two types of coil are to be mounted, the line coils (for 10 to 20 kc/sec) and the frame coils (for 50 or 60 cps). For the line coils, the impedance is mainly inductive, and the ohmic part of it can practically be neglected. The pre-shaped saddle-type coils, which are put to the inner side of the yoke ring and show a big outward flare on the front side in order to increase the sensitivity, are generally used. For the frame coil, however, the impedance is mainly ohmic; in order to avoid heating up and bad efficiency the ohmic resistance should be kept as small as possible, which can be done by winding the frame coils toroidally on the yoke rings. This takes full advantage of the low reluctance of the ferrite material and with suitable winding methods leads to a very high copper space factor of the winding, making it possible to choose a small inner diameter for the yoke ring. In this way a high sensitivity can be obtained, which may lead to a saving on the frame output valve and transformer, but the winding technique is more difficult. For 90° deflection, cylindrical yoke rings are customary, cracked into two halves or in quarter sections. With saddle frame coils both types can be used; with toroidal frame coils the two half-rings are preferable. For 110° the risk of cornercutting has increased so much that "flared" yoke rings must be used, enabling the coils to be put further on the neck of the cathode-ray tube. It is probable that the flared quarter-section yoke ring is too difficult to make and will vanish. For toroidal frame coils, the center of the frame deflection always lies exactly in the middle of the yoke ring, whereas for saddle frame coils this center can be shifted further forward by using flared coils. Consequently in the first case a longer flare of the yoke ring is required. A quite different winding technique for deflection coils is the socalled "castellated" one. This uses hand-wound coils in the holes of a slotted yoke ring. The coil sensitivity is very good, and no big winding machines are required. On the other hand, the yoke ring is more expensive, and the method is less suitable for bulk production. For 70° this technique is still frequently used with an eight-slot yoke ring; for 90° an expensive sixteen-slot yoke is required for good picture quality, which makes the method less attractive; for 110°, castellation is out of the question, because the ring cannot be castellated and flared at the same time for a reasonable price. 5. Aerkils (36, 37, 38) Two advantages of the inductive radio receiving aerial over the

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"classical" capacitive antenna are the directional sensitivity and the dropping of the earth connection. Such an inductive loop aerial can be miniaturized and built into the receiving set as a small coil on a rod or plate made of ferrite material. The small core area is compensated for by the "concentration factor," μΐ0ά which indicates the ratio of flux through a small coil in the middle of a ferrite rod or plate compared with the flu through the same coil at the same place without ferrite. This factor μτοά depends only on the μ\ of the ferrite and on the length-to-diameter ratio of the rod or plate; for a graph, see Fig. 14.

0

10

20

30

40

50

trod rod

d

FIG. 14. Concentration factor μΓΟά for ferrite aerial rods as a function of length : diameter ratio for various values of material permeability.

More gain can be obtained by making the inductive aerial part of a tunable circuit covering the desired wave band; this gain in output is a factor Qf, where Q' is the quality of the tuned aerial circuit which largely depends on the Q of the rod. Of course the length-to-diameter ratio of a rod should be chosen as high as possible with regard to mounting and technology. Too long a rod requires a long cabinet; moreover, either the complete set or the rod should be turnable in order to profit from the direction sensitivity; too thin a rod easily breaks, and furthermore the output is also proportional to the section of the rod. For more gain, a high μ and a high Q are necessary. However, as is known from the material properties, these two are to a certain extent contradictory, so that a compromise should be made. This compromise should first aim at a maximum output

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in the frequency band in question with the available materials, but some other considerations may play a part, such as the band width and the signal-to-noise ratio. The relative band width, Af/f, is equal to 1/Q'. For reasons of quality of sound, temperature drift, and padding trouble, this band width should not lie below approximately 4 kc/sec. This means that for the long wave band (150 to 300 kc/sec) Ç' should not lie above approximately 50, and for the lower part of the medium wave band (500 to 1600 kc/sec) it should not lie above approximately 150, so that, unless too much damping is introduced by careless mounting, a high Q of the rod or plate has little value, and the compromise can better be sought in the direction of higher μ. In addition, in many cases with modern tubes or transistors amplification is not a problem; more important is a high signal-to-noise ratio, because this makes possible a high amplification. As far as atmospheric noise is concerned (the most important source of noise, especially for weak signals), this signal-to-noise ratio is proportional to μ2Γ0<ι@', whereas the signal output itself is proportional tO /XrodÇ'·

This trend of considering high μ more important than high Q for long and medium wave reception is confirmed by the latest European development in this respect, where a Ni-Zn ferrite (/Ai ^ 2 0 0 ) is gradually replaced by a Mn-Zn ferrite (μ\ ^ 5 0 0 ) in spite of the fact that the Q of this latter material is rapidly dropping at a rate of 1.5 Mc/sec and must be kept high by special measures (making longitudinal slots 2 to 3 mm in depth over the whole length of the rod) in order to keep the eddy current loss down. For short-wave reception, up to 20 to 30 Mc/sec, and for the higher part of the medium wave band, things are different; here a high Q can never spoil the band width, and special Ni-Mn-Co-Zn ferrites with high Q (see Fig. 7) are preferable. At higher frequencies the merits of ferrite for aerials become very doubtful. In spite of much research, a technically and economically acceptable solution for a television aerial with ferrite has not yet been found, and it seems rather doubtful that it ever will be, even with recent improved high-frequency ferrites ( Ferroxplana, constricted loop materials). The main trouble is that a built-in television aerial will always give bad reception because of interference, reflections, etc., unless quite close to the transmitter, and in this case a built-in antenna needs no ferrite. Also the shortening of a tuned dipole by surrounding it with ferrite does not succeed. The theoretically expected shortening by a factor -\/€μ is not achieved unless very big ferrite bricks are used, which are far too expensive; moreover, the band width of the

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295

aerial decreases with dimensions, independent of the medium. A better possibility for ferrites in television aerials may be an inductive tuning of a broad-band aerial, to which we shall refer below. Except for broadcast, ferrites are interesting for big receiving aerials for marine warfare; usually the frequencies are lower here, of the order of 20 to 40 kc/sec. Another possibility is offered by directional finders, in which the directional sensitivity of ferrite makes it useful up to the high megacycle range. 6. Inductive Heating

Concentration

For local heating of metal parts by generating eddy current loss in them, the flux should be concentrated on the exact spot to be heated. The required frequency depends here on the desired penetration depth of the flux into the metal but usually lies between 5 and 100 kc/sec. In this case, the advantage of ferrite for concentrating the flux is evident. Usually the transformer from the generator has a ferrite core too. 7. Screening

Applications

Here the ferrite prevents the occurrence of stray fields which may give unwanted couplings. For high frequencies ferrite is advantageous because of its high μ; low loss is not important. A typical example is given in Fig. 15. Here both coils of an intermediate-frequency band filter are mounted on a ferrite rod, and each is surrounded by four or five similar rods in a parallel position. In this way 90% of the stray field of each coil is absorbed, and undesired coupling is prevented (11)» The same result would be obtained by surrounding the coils with a ferrite cup core, but the rods are less expensive. The pot cores, where the coil is completely surrounded by the core, are a similar example ( of course, here the losses must be low because the screening is a part of the magnetic circuit). For other screening applications the ferrite should not be rigid but in a flexible shape. This can be achieved by putting a paste of ferrite powder with plastifier on a tape, but in this case the μ decreases to 7 to 10. A similar tape already exists for trimming the old types of pot core. A special example of such a tape is recording tape, which usually contains y-Fe 2 0 3 , but ferrite powder could be used instead. The required coercivity of about 250 oersteds (600 oersteds for television recording) could be realized in ferrite. From a technological point of view, however, y-Fe 2 0 3 is probably easier than ferrites. 8. Chokes In principle, by "choke" every inductance can be indicated that does not belong to a transformer or to a tuned circuit. A division can

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J. M. HASPERS

FIG. 15. Miniature IF-bandfilter with ferrite cores and ferrite screening rods.

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297

be made between chokes with low losses, and chokes where losses may be high. The first category is used, for example, for rectification of alternating current, as coupling coils in valve amplifiers for audio or carrier telephony, for equalizing networks, and in measuring gear. It will be clear that ferrites are very useful here for high-frequency applications because of their high permeability and low losses. Chokes with high losses are used for eliminating undesired coupling or feedback, as in a feed line for the filaments in a series-fed television or frequency-modulated receiver, in the lead-outs of ignition coils to prevent them from acting as transmitting aerials for television interference, as interference suppressors for small motors, etc. Here a high μ is still required, but high losses are not only harmless but even desirable because they absorb the unwanted high-frequency signals. In Section II.D it was mentioned that at the gyromagnetic resonance frequency the losses of ferrite materials sharply increase, while the permeability as a function of / remains constant, until at some higher frequency it begins to decrease slightly. For these chokes a ferrite should be chosen such that the unwanted frequency lies between those two frequencies, so that a combination of high permeability and high losses occurs, giving both maximum choking and maximum damping. The simplest form of choke is a bead of ferrite threaded on the lead; for higher choking or damping, ferrite chokes with more turns should be chosen (39, 40). 9. Coib for Tuned

Circuits

A coil for tuned circuits should resonate with a capacitor at a sharply defined frequency or, together with other similar elements, form a filter for an exactly defined band. Consequently, a sharp resonance (high Q) is wanted. Moreover, the inductance should always be the same and not change with temperature or time. Finally, the volume should be as small as possible, not only for the coils, but for the whole assembly of coils and capacitors together, so that the coils (which usually require more volume than the capacitors) can be mounted close together without unwanted coupling by stray fields (11). It will be clear that for frequencies above approximately 1 kc/sec the use of a ferrite core is preferred, both for its high permeability and for its low loss. The ideal shape to meet with the above requirements is the pot core, shown in Fig. 16. Here a nearly closed magnetic circuit surrounds the coil, with a small adjustable air gap on the inside, while to the outside the coil is fully screened (except for a few small holes for the terminals of the coil). By changing the length of the air gap, the equivalent permeability, μβ, can be varied within wide limits ( see Section

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J. M. HASPERS

FIG. 16. Ferrite pot-core construction.

II.B). As mentioned there, the variations of the inductance with both time and temperature are proportional to μβ/μί, so that from the given material characteristics of the ferrite and the permissible variation in the design the maximum allowable μβ can be found. The same applies to distortion and core loss. The total loss in the coil is the sum of core loss and copper loss; the first is proportional to μβ, and the second is inversely proportional to μβ (because for a high μβ only a few turns are needed to obtain the required inductance). Hence: 1

(tan ô)tot = Q = Αμ€ -\

7?

From this it follows that Q is a maximum for Αμ6 — Β/μβ or μβ = y/B/A. The constants A and B depend on material characteristics and pot core dimensions and are usually given by the core manufacturers (12, 41, 42, 43). In this way it is possible to adjust the air gap for maximum Q in a given case (provided of course that a lower μβ is not needed for TC or distortion requirements). The adjustment of μβ can be done in various ways. The original method was to grind down the center slug with emery paper to the right value; this is an excellent way, but requires some labor; as a more recent development, "preadjusted" pot cores are available in which a certain μβ is guaranteed within narrow tolerances. If a very exact value of self-inductance is required, it is possible to trim this inductance after mounting the core by more or less shunting

FERRITES

299

the air gap and thus changing the μβ. This can be done either with an adjustable slug in a hole of the center core or by pulling a trimmer strip with a ferrite paste of variable thickness through the air gap. It is one of the biggest advantages of ferrite pot cores that such an adjustment after mounting is possible without the trouble of changing the number of turns. For coils of high Q between 1 kc/sec and 1 Mc/sec, ferrite pot cores are the ideal construction for carrier telephony equipment (filters), for measuring equipment in intermediate-frequency coils for radio sets (especially for transistorized pocket sets, where small volume and high Q are important), for equalizing coils, for navigational apparatus, for electronic bookkeeping machines, etc. Sometimes ferrite pot cores are used at even lower frequencies as in 500-cps filters, because of their good screening. Although developed in the first place for tuned circuit coils, they are also used for transformers (e.g., with ring modulators), for carrier telephony, for chokes (e.g., in TL lighting), and for loading coils. At higher frequencies the use of pot cores is limited by their fairly high stray capacitance, which can, however, be reduced by special winding techniques. With the existing trend (especially in Europe) of extending carrier telephony toward higher frequencies, it is to be expected that pot cores in ferrite materials will be used at frequencies up to 10-20 Mc/sec. For intermediate-frequency coils, antenna coils, or oscillator coils in radio sets, pot cores are usually too expensive, but ferrite rods or tubes are sometimes used together with a "palisade" construction (see Section IV.F) for screening; for transistorized pocket sets, however, where small volume and high Q are important, a closed magnetic circuit is used again, either a pot-type or a window-type construction. For intermediate-frequency coils at higher frequencies—for example, television intercarrier sound (5.5 Mc/sec) or frequency modulation (10.7 Mc/sec)—either ferrite or powdered iron cores can be used. Ferrite gives a slightly higher Q, but powdered iron has a lower TC and can be made in complicated shapes (e.g., screw cores) at less expense. For the same reason, at the present state of technique powder cores are superior to ferrite for intermediate-frequency video (approximately 40 Mc/sec). For coils in transmitters the situation is different from all other tuned coils mentioned above because of the high power involved and the consequent high induction in the ferrite. Here the Ç is determined by the hysteresis loss, and the stability by the maximum temperature occurring. For the higher frequencies (above approximately 2 Mc/sec) it makes little sense to introduce in the usual air coil a big and expen-

300

J. M. HASPERS

sive ferrite core, which moreover gives distortion. At lower frequencies in some cases a ferrite core may be advantageous, because it provides an easy method of frequency modulation by permeability tuning. 10. Delay Lines For high-frequency delay lines ferrite can increase considerably the delay time per unit length, giving an appreciable saving in volume. Artificial delay cables built up from LC sections are in fact low-pass filters and usually contain normal ferrite pot core coils. Another system is to put ferrite rings over a coaxial delay cable; this should be combined with miniaturization of the capacitors. Delay lines are used: 1. For memories; here the delay system will hardly be able to maintain itself against drum or matrix systems in the future. 2. In telephone or telegraph exchanges, for multiplex quantum modulation; here the LC sections can be applied very well (44). 3. In color television; here LC sections are too large and too expensive; normally a "delay cable" is used containing some powdered iron compound. It might be possible to construct a cable with both ferrite and a high-e titanate in such a way that the characteristic impedance (proportional y/L/C) remains the same but the delay time (proportional \/LC) per unit length is much increased. In this case the requirement of flexibility for the cable might possibly be dropped because of the very short length required. An alternate solution is provided by an acoustic-delay line, but ferrite would also be used for the electroacoustic transducers. 11. Loading Coils (45, 46, 47) Loading coils are connected into audio telephone cables in order to prevent the "blind" current that passes through the divided capacitance of the cable from giving ohmic losses on its path through the cable. Although the best solution would be to increase the self-inductance of the cable continuously, for reasons of economy separate coils are connected into the cable at a certain distance from each other. These coils should have a high Q, be well "balanced" between forward and backward coupling (good screening required), and have low distortion; otherwise, in particular in so-called "phantom circuits," crosstalk would occur, and the secrecy of telephone conversations would no longer be guaranteed. Although the frequency range (0.3 to 4 kc/sec, and sometimes even 0.3 to 2.7 kc/sec) is fairly low for ferrites, the other requirements lead to the use of ferrite pot cores, usually made of a special

301

FERRITES

Mn-Zn ferrite with a low hysteresis factor, h/μ2, because of the distortion requirement. 12. Ignition Coils (48) Ignition coils serve both for energy storage and as pulse transformer, for a repetition frequency of 10 to 100 kc/sec, so that the use of ferrite seems attractive, for both low losses and high μ. A drawback is the low saturation which limits the "energy storage capacity/' This can be increased by biasing the ferrite core in the opposite direction with hard magnetic ferrite, although this means the introduction of an air gap. Nevertheless, with ferrite it is possible to obtain a saving in copper and in cost of mounting and either a more powerful spark or a reduction in current consumption. Moreover, at low speed too high a voltage is prevented by saturation of the core. A drawback of ferrite, compared to iron plate, is the considerably higher price, which makes the economy of the ferrite construction doubtful for the actual conditions. However, the existing trend in the car industry toward higher compression ratios and a higher number of revolutions requires an ignition coil which can supply more energy with higher frequency. This can be met more easily with a ferrite coil than with the "classical" construction, unless the latter is made heavier and more expensive. Apart from this, a similar ignition coil may offer chances for photographic flashlights or for electrical fences for cattle, although in these cases the repetition frequency is of course lower. 13. Small Dynamos and Motors For high-speed low-power dynamos or for motors where low loss is important (servomechanisms, automatic gear, high-speed centrifuges), it may be advantageous to use a ferrite stator—for example, a slotted yoke ring of the "castellated" type. On the other hand, in many cases laminated iron will be preferred because of the higher saturation and because it is easier to make complicated shapes and to achieve narrow tolerance. 14. Permeability

Tuning by Mechanical Movement

of a Core

(49)

If in a high-frequency coil a cylindrical ferrite core is used, this core can be moved by mechanical means into and out of the coil, thus changing its inductance. For a core and coil with high length-todiameter ratio, a change in inductance by a factor of 30 is quite possible. Usually the Q will undergo some change too, but this can be reduced by special measures.

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J. M. HASPERS

In principle this permeability tuning can be applied in each radio set, but usually the variable capacitor offers a more economical solution. As this variable capacitor is a fairly big component (however, it is being miniaturized, too), permeability tuning is preferred when space is limited (car radios, portables). Of course, the adjustment of ferrite rods in intermediate-frequency filters is in fact permeability tuning, also. In television sets the width control is manipulated by means of permeability tuning with a ferrite rod. It might be possible to apply a similar inductive tuning with ferrite for a broad-band television antenna, although of course capacitive tuning can also be done. B. APPLICATIONS BASED ON THE SENSITIVITY OF μ TO PREMAGNETIZATION

As already remarked in Section ILA, the low-amplitude permeability μ — dB/dH is dependent on H. For H = 0 it is equal to μ^ as H increases, μ first attains a maximum value, μτηΆΧ, and then decreases until at saturation μ = 1. For some ferrites (square-loop ferrites) this decrease is rather sudden, but for most of them it is a gradual one. This means that the self-inductance of a coil with a ferrite core can be strongly influenced by d-c bias; ferrite is much more sensitive than powdered iron here. Although this property is certainly not always favorable, some useful applications may be based on it. In this discussion those applications are dealt with in which a sharp decrease in μ ( a square loop ), although perhaps desirable, is not essential; those cases in which it is really essential are dealt with later. Figure 6 gives some curves of μ = dB/dH as a function of H for various types of ferrites. 1. Modulators The first application of this variable μ is, of course, modulation. If a core is subjected to a low-frequency a-c bias instead of a d-c bias, the impedance and consequently a d-c or a-c voltage over it will be amplitude-modulated. A frequency modulation is obtained even more easily by low-frequency biasing of the oscillator core. For frequencies exceeding 0.5 to 1 kc/sec, the low losses in ferrites together with their d-c sensitivity make them the most suitable material for these purposes (50, 51). These ferrite modulators can be used for transmitters, especially for low power (military communication equipment) and for measuring gear (e.g., sweep generators). For carrier telephony the ring modulator is used, which does not contain ferrite (only ferrite pot cores in its transformers) and which has the advantage that the carrier frequency itself is not passed on, but only the side bands.

FERRITES

303

Special ferrite modulators are used in the centimeter-wave range, where in fact not the μ but the losses in the ferrite, are influenced by low-frequency biasing. 2. Magnetic Amplifiers and Saturable Reactors With a ferrite modulator, by appropriate choice of carrier, bias, and impedances, the energy of the modulation in the modulated signal can be made considerably higher than that of the original low-frequency bias; the core is acting as a magnetic amplifier. Again, it is advantageous to use ferrite cores if the frequency lies above 0.5 to 1 kc/sec. Magnetic amplifiers are robust and stable, do not require any filament current, and can handle fairly high power. Their drawbacks are the fairly complicated construction and the necessity of a high-frequency source. The amplification factor can go up to approximately 102, with positive feedback up to 106, the latter only at the cost of an appreciable delay time. The major applications of magnetic amplifiers lie in the field of measuring gear, servomechanisms, etc., which usually operate at 400 cps or lower with special metal materials which in this frequency range are superior to ferrites. Higher frequencies, where ferrite is superior, would make possible smaller transformers and a shorter delay time but would require an extra high-frequency source, which usually is a considerable drawback. In the future this drawback may be less important in those cases in which many magnetic amplifiers can be fed with one highfrequency source, as in telephone exchanges or in computers and counters. A typical example of magnetic amplifier-like circuits in computers is the so-called parametron circuit, which is described in Japanese literature and can be used for all kinds of steering and logical functions. This circuit sets lower requirement for the ferrite than the equivalent circuitry and is consequently more complicated and less adaptable to miniaturization. Once a ferrite material with specific intrinsic properties for large computers becomes available at a low price (i.e., square-loop ferrite), it will be preferable to ordinary material, in which special properties are introduced only by a complicated circuitry. The ideal ferrite for magnetic amplifiers should have no BH loop and no hysteresis at all, its curve being only a straight line through the origin. Such a ferrite does not exist yet; for low-induction magnetic amplifiers, which are not driven into saturation, probably the best alternative is a high-μ, ferrite with very narrow loop and low hysteresis loss but without a sharp "knee." If the amplifier core is driven into saturation (saturable reactor), a square-loop core with a coercivity as low as possible is often preferable.

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3. Automatic-Frequency

Control

It is possible to make use of the variable μ of ferrite for stabilizing the frequency of frequency-modulated link transmitters or of diathermy apparatus (strongly variable load). Another possibility is stabilizing the frequency in a very-high-frequency tuner for television by biasing a ferrite core, which forms part of the oscillator circuit with a feedback discriminator signal. With improved stability of the tuner this application has become obsolete; it may, however, come up again for ultrahigh frequency in the future. 4. Permeability

Tuning

By biasing a core, the inductance of a tuned circuit coil can be varied by a factor of 100 or more, giving a corresponding variation in resonance frequency (52). It might be used for radio or television tuning, but here a variable capacitor usually gives a simpler solution, or sometimes permeability tuning is realized by mechanical movement. A more common use is for linearity control in television receivers, where a core is more or less biased by varying the distance to a permanent magnet. A popular version of such a tuning device is the rotoroid coil, a ring coil biased in one direction by a permanent rod magnet, with a second magnet that is tunable and can either double or compensate the bias, with all possibilities in between, thus permitting a large variation of inductance (53). For frequencies above 1 kc/sec a combination of soft and hard ferrites gives the best results here. Applications are possible for variable filters, oscillators, measuring gear, etc. 5. Accelerating Machines (49, 54, 55) In nuclear research use is made of particles (electrons, protons, neutrons) with very high kinetic energies. As far as particles with an electric charge (electrons, protons) are concerned, these high energies can be obtained by repeated accelerations in an electric field. For reasons of economy it is desirable to carry out this repeated acceleration with one or at most a limited number of fields. This makes it necessary to deflect the particles by a perpendicular magnetic field so that they describe a circular orbit and are carried back into the acceleration. The value, B, of this magnetic field is determined by B = mv/eR, where m and e are mass and charge of the particles in question, υ is their velocity, and R is the radius of their orbit. During acceleration, v increases; if R is kept constant (fixed orbit), B must increase, which can

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305

be achieved by the use of electromagnets with increasing current. At the same time, the frequency of the electric field in the accelerator must increase synchronously with the speed of the particles, so that on the arrival of the particles in the accelerator, which is localized at one or more distinct points in the orbit, the field has the correct phase. This means that, for example, for a proton accelerator, in which during 1 second the energy of the protons is increased from 3.5 Mev to 3000 Mev in an orbit of 11-meter radius, during this same second the frequency should increase from 350 kc/sec to 4 Mc/sec. The easiest and in fact the only practical way to achieve this is by tuning the inductance of a ferrite coil with a variable bias. It can be executed in two ways: 1. A normal radio-frequency oscillator with a small ferrite core, which is biased synchronously with the particle speed, in order to obtain the right frequency from the oscillator. The signal of the oscillator is amplified in a power amplifier and carried to the "primary" of a "transformer" which is formed by a coil in the anode circuit of this amplifier. The secondary is the single-turn particle orbit itself, and both are coupled by a large ferrite core, usually built from smaller blocks. In this case, the oscillatory coil must preferably have a high sensitivity to d-c bias; for the transformer core this is not necessary, but it should have as high a μ and Q as possible for the considered frequency range. As this range lies usually at 0.5 Mc/sec or higher, ferrites are definitely superior to laminated or powdered metals. Because of the size of the parts, it is necessary to use Ni-Zn ferrites, as with Mn-Zn ferrites dimensional resonance effects (see Section II.F) may be expected. 2. A tuned resonating cavity, with its resonance frequency continuously changing in accordance with the particle velocity. This can be obtained by using cavities with d-c biased ferrite cores. These ferrite cores must fulfill rather severe requirements: a high sensitivity of μ for d-c bias (which means μ should be as high as possible), a fairly high Q over the whole frequency range, low temperature dependence, etc. Moreover, it is technologically difficult to make heavy ferrite parts (rings up to 50 cm in outer diameter and 3 cm in height) without cracking and to achieve a glueing bond which is strong enough. Again, Ni or Ni-Zn ferrites must be used in the megacycle range, as Mn-Zn ferrites give dimensional resonance loss. The old 3-Gev proton accelerator at Brookhaven and the accelerator at Harwell (Great Britain) follow the first principle; the new 30-Gev Brookhaven accelerator and the 25-Gev proton accelerator of CERN at Geneva are so-called strong focusing machines, which follow the second principle for the accelerator.

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C. APPLICATIONS BASED ON NONLINEAR CHARACTERISTICS

I. Magnetic Memories

(56-59)

In soft magnetic ferrites with low coercivity, usually little rémanent magnetism is noticed, because any air gap, however small, leads to a considerable demagnetization. An exception is formed by fully closed circuits, such as ring cores. After removal of a magnetizing current these stay in their true remanence point for an infinite time, without any energy being required. Since the closed circuit forms a complete hysteresis loop having two remanence points, it is possible to use such a ring as a binary memory to store information. By combining the information of a number of these binary memories according to an agreed code, very specific and complicated information can be stored in such a ferrite memory. In order to "read" the information present in a core, it is necessary to apply a current pulse of known polarity, driving it into saturation, and to measure the voltage induced in a second winding around the core. This voltage will be much larger if the pulse and the original remanence had different polarity (signal pulse) than if they had the same polarity (parasite), so that from the magnitude of this voltage the original remanence position can be determined (one or zero). In this way every core in a memory would require two separate wires (it is customary to use small rings with a wire through them giving a "one-turn" winding), both with their driving and their amplifying systems, which would be rather costly. However, by using a special ferrite with square loop the simpler and more efficient "coincidence system" is possible. In this system a number of ring cores are threaded together to a matrix, according to the principle of Fig. 17, and arranged in a number of rows and columns. Through all cores in a row, X wires are threaded, through all cores in a column, Y wires. By the special shape of the BH loop of these ferrites, it is possible to pass a current of a certain value (half-pulse) through an X wire and a Y wire without affecting the remanence state of the core on these wires, while the core at the intersection of the X and Y wires in question is exposed to the double current (full pulse) and is fully switched into the corresponding remanence state. In this way the information is written. For reading, a diagonal winding is wound through all the cores; if a certain core should be read, a half-pulse is carried through the corresponding X and Y wires; if the core switches, a large output is obtained on the read winding; if it was already in the desired polarity, hardly any output is

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FIG. 17. Basic construction of coincident-current ferrite memory matrix.

obtained. Because of the diagonal winding, the parasitic outputs of all other cores cancel each other. From the described system, it will be clear that the ferrite must meet the following requirements: 1. The parasitic outputs should be as small as possible, so that the difiFerence in B value between saturation and remanence on one side and remanence and opposed half-pulse value on the other side must be as small as possible. This requires a very flat upper part of the BH curve (in practice BR/BS = 0.95 and B(— y2H)/B8 = 0.85 have been obtained). 2. On the other hand, for a full pulse the core should switch completely so that for values larger than a half-pulse the BH curve should fall steeply down. These two requirements make necessary a square hysteresis loop of the material in question. Other conditions are: 3. Performance for complicated manipulations should be rapid. This implies the use of short current pulses (of the order of 1 jusec in duration) which should give no high losses and should cause a quick re-

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sponse from the core flux. In both these respects, ferrites are far superior to metal cores for short pulses. 4. Coercivity should be low so that the current required is as small as possible and can easily be supplied by transistors. 5. The temperature dependability of the cores should be as small as possible. 6. The rémanent magnetization should be as high as possible, giving a high output. Various kinds of ferrites which meet these requirements have been developed. In practice, usually either Mg-Mn or Cu-Mn ferrites are used, both with a minor BH loop, because this shows a higher rectangularity than the saturation loop. The squareness ratio B(—1/2H)/B8> is a maximum for a field of approximately 0.7HS, where H8 is the field required for saturation. The field for maximum rectangularity, H max , decreases with increasing temperature; in some cases temperature compensation must be used, by regulating the write and read current with the aid of a thermistor. To a certain extent, the requirements for low coercivity (which means a low H max ) and a quick response (low switching time) are contradictory; for most materials the product of H max and τ (switching time) is about the same, so that a quick material requires a high current, and a material of low current is fairly slow. This can be partly overcome by reducing the core size, so that the same Hmax can be reached with a lower current. It has recently been done by reducing the standard core size from 80 X 50 mils to 50 X 30 mils; but a limit to this miniaturization is set by the trouble and cost of winding the matrices. As an example of the characteristics reached by recent square-loop ferrites, Table II lists some values for a Cu-Mn ferrite in a ring of 50 X 30 mils and 15 mils in height. The permissible temperature range is 20° to 45°C without current compensation, and 0° to 85°C with current compensation. The undisturbed output is greater than 45 mv for a TABLE II VALUES FOR A C U — M N FERRITE

(50 X 30 mils, 15 mils in height) BR/BS ratio, at 40°C Squareness ratio, at 40°C Optimum full current, at 40 °C Optimum half-current, at 40°C Permissible current tolerance Switching time, at 40°C

>0.9 >0.8 505 ma 252 ma ±10% 1.35 μββο

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pulse with 0.2 /xsec rise time. Instead of memory rings, sometimes ferrite plates with holes are used, connected with printed wiring (see 60). Although the plates are simpler and cheaper to thread than the memory rings, the rings are technically superior because of better signal-to-parasite ratio and are thus preferable, provided the threading can be done cheaply enough. Another problem is the so-called nondestructive reading, that is, sensing the available information in a core without destroying it, or rewriting it immediately afterward. This can be done by special circuitry methods (inhibit wire, for example, the so-called "Cambridge system") (61) or by using a special core shape with more than one hole (transfluxor). Ferrite memories are used in all kinds of equipment: computers, telephone exchanges, juke boxes, booking machines, etc. In many cases special requirements will be established for a certain project. 2. Shifting Registers and Driving Cores Shifting registers consist of a certain number of cores in square-loop material connected in series. The rings are fed alternately by one of two impulse windings, and when a pulse is applied the information is passed on from one core to the next on the same winding. Diodes are placed in between to prevent the information from going in the wrong direction. This is the so-called Wang type (62). Greater economy can be achieved by using only one row of cores and one pulse winding and by putting capacitors in between as intermediate stores (Woo type, see 63). Large matrix memories can be driven by tubes, but this becomes fairly expensive. Therefore, an intermediate solution is sometimes chosen by introducing a matrix from large switching cores in square-loop material, which is driven by tubes and itself drives the memory matrix. In this way, for a square memory matrix of n X n cores, the number of tubes (or transistors) can be reduced from 2n to 2 \ / 2 n . The requirements to be met by a ferrite material for shifting registers or for driving cores are somewhat less severe than those for memory cores, because no coincidence is applied here, so that the squareness ratio is unimportant. On the other hand, a high saturation, giving a high output, is desirable (64). For short pulses a competition exists between square-loop ferrites and very thin laminations (y8 mil) of square-loop metal. The laminations are more expensive but have a higher saturation and lower coercivity. 3. Logic Circuits Square-loop ferrite cores not only serve as memories, but in com-

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bination with specific circuitry or with diodes or transistors they can perform all kinds of "logic" operations so that a certain pulse is blocked or can pass (gate circuits). Some of these elementary gate circuits are shown in Fig. 18, the "and," "or," and "inhibit" circuits. Here A and B

A

JL

0 1 0

0 - 1 0 -I I -I

H 0 0 0

1

I

I

JL

- I

If the inhibit i is omitted, the'and" circuit becomes an "or" circuit, with A 0 1 0 I

B 0 0 1 1

INHIBIT:

y

AB-

J-L

ïu

xUh +E

A. 0 1 1

0

b j3 0 0 1

τθ

7777777

0 I 0

FIG. 18. Some logic circuits with square-loop ferrite rings.

are the "write" pulses, i is the "inhibit," and Y is the "read" pulse, which, in case the core was driven to " 1 " by the preceding pulses, drives it back to zero, at the same time triggering the transistor. These elementary gates can be combined to form more complicated ones—inhibit-inhibits, half-adders, full-adders, etc. [see, for example, Richards (65, 66 and 67)]. The ferrite requirements are about the same as for switching registers. A very high saturation is not so essential, because the signal is amplified anyhow.

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4. Transfluxors In general, transfluxors may be described as pieces of square-loop ferrite with more than one hole. By using transfluxors with holes of different dimensions and adapting pulse amplitudes to geometric dimensions, it is possible to block or pass a pulse by a control pulse elsewhere on the transfluxor to obtain part of the piece in the " 1 " and another part in the "zero" position, to obtain magnetic amplification, etc. (see, e.g., 68 and 69). In this way, part of the function of logic circuitry is taken over by one special piece of material. Transfluxors can be used for (1) memories for nondestructive reading, (2) logic circuits, and (3) magnetic amplifiers. In most of these applications the price determines whether a transfluxor or an alternative solution will be chosen. It seems, however, that the transfluxor has a fairly good chance in those cases where it can replace a transistor. 5. Dynamic Magnetic

Flipflops

In contrast to the magnetic memories described above, which can store information for an infinite time without energy consumption, dynamic flipflops can store information only if they are fed with energy. Against this drawback, however, they have the advantages of being able to pass on the amplified information directly to the next stage; of not giving any difficulty in reading and writing, so that the requirements for the ferrite core are not critical; and of having no critical requirements for shape and size of the pulses (70). In view of the existence of square-loop ferrites with good performance and of the trend toward miniaturization which is based on a volume and a heat development as small as possible, it seems fairly sure that the static memory will replace the dynamic one in the future. This is a confirmation of the general trend to replace "general-purpose" ferrites by "special-purpose" ferrites for specific applications. For magnetostrictive and microwave ferrites the same trend will be noticed. 6. Blocking Oscillators and Pulse-Forming

Networks

Blocking oscillators and pulse-forming networks are used mainly in computers and for navigational purposes (radar). A competitor is the multivibrator, which, however, needs tubes. For smaller pulses (10 jusec or smaller) and high repetition frequencies, the high μ, low losses, and low saturation (the "knee" is soon reached) make ferrite the obvious core material. The requirements are not very critical here. For the television line oscillator a normal sine wave oscillator works satisfactorily so that the more expensive blocking oscillator can be avoided.

312 7. Harmonic

J. M. HASPERS

Generators

Harmonie generators are found in carrier telephony, where many carrier frequencies are used, all of which are a multiple of 4 kc/sec and should, moreover, match exactly. They are generated by saturating a ferrite core with a 4-kc/sec sine wave, and filtering out and amplifying the occurring harmonics. With a single generator, only odd harmonics are obtained; with two generators, even harmonics can also be obtained (71). The advantage of ferrite is obvious here, but the greatest amount of this ferrite is used in the filters, whereas in the generator only a small piece is needed. The requirements are not critical (for the generator); practically all kinds of ferrite will do. D. APPLICATIONS BASED ON MAGNETOSTRICTION

If ferrites of high permeability are desired, magnetostriction is an unwanted property, because it increases the stress anisotropy and thus decreases permeability. In Mn or Mn-Zn ferrites, magnetostriction is reduced as much as possible on purpose. On the other hand, if appreciable magnetostriction is present in a ferrite, special applications are possible, based on the conversion of electrical into mechanical vibrations, and vice versa. A competitor will always be the electrostrictive (or piezoelectric) material, which can do the same. Because magnetostriction is a quadratic effect, and the change in length is independent of the sign of the field, for frequency reproduction a bias is necessary, either by direct current or by permanent magnets, which must be higher than the a-c amplitude. 1. Accelerometers and Pickups With accelerometers and pickups, mechanical vibrations are converted into alternating current over a wide frequency range. This wide frequency range indicates that the material must be used far from its mechanical resonance frequency in order to have a constant frequency response. Consequently, the mechanical resonance and the Q factor are unimportant here, but a high sensitivity to vibrations is required, and in the case of accelerometers a high crushing strength also. The sensitivity is proportional to the coupling coefficient, k, which can be defined as the square root of the fractional conversion of stored magnetic energy (in the coil and core) to stored elastic energy (in the vibrator). This k2 refers to the stored energies, and not to the mechanoelectric (or electromechanic) efficiency, which fortunately is much higher (see, e.g., 72).

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Whereas for normal ferrites k is of the order of 0.10 to 0.15 for special Ni-Co ferrites, it can increase to approximately 0.3 or even 0.35. However, for some piezoelectric titanates it can be higher, above 0.6. Moreover, for the small pieces usually required for this application, titantes have the advantage of needing no coil, only two silvered surfaces. For this reason, although ferrite could be used for these nonresonance applications, piezoelectric materials usually are preferred. 2. Mechanical

Filters

For mechanical filters the mechanical resonance of the vibrating ferrite is used. A ferrite rod in longitudinal vibration is in resonance at a frequency equal to v/2l, where I is the rod length, and v is the wave propagation velocity in ferrite, which (for nonporous ferrite) is approximately 5600 m/sec. For an extensional ring vibrator with radius R, the resonance frequency is equal to O/2UR. A resonating mechanical vibrator in vacuum or in air (low attenuation, no mechanical load) can be considered as a parallel LC circuit in series with an extra L, dimensioned in such a way that the frequency of series resonance (fA) lies slightly higher than that of parallel resonance (fR), so that (fA — JR)/JA — %fc2 for the ring vibrator and 4&2/π2 for the longitudinal vibrator. This series resonance at fA gives for the ferrites a very sharp peak with a mechanical Q /actor of 6000 to 8000, much higher than obtainable with a normal LC filter. Thus it is possible to use these small and simple mechanical filters with good result for telecommunication purposes, especially for pass filters where steep edges are required. In these cases it is possible to replace some sections in a multisection filter by mechanical filter sections at equal performance. Apart from the high mechanical Q of the ferrite, the k must be as high as possible, and the TC must be low. With special Ni-Co ferrites, a change in fA below 0.05% at temperatures between 20° and 50°C can be obtained. A good description of narrow-band magnetostriction filters is given by references (73) and (74). 3. Electromechanical

Generators for Ultrasound

Here again the ferrite is used at its mechanical resonance frequency, but, contrary to the filter application, as much power as possible should be transferred from the coil through the vibrating ferrite to a surrounding liquid medium or to a wall to which it is coupled. Of course, here the mechanical Ç is damped down. Ultrasound generation is used for a multitude of purposes: for cleaning apparatus, for underwater signaling and echo sounding, for

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drilling, emulsifying, welding, mixing, void detection, etc. The frequency usually lies between 20 and 40 kc/sec; here the required power for cleaning and drilling and the attenuation on propagation in water are much lower than at higher frequencies. Only for special requirements (detection of voids, cleaning of narrow holes) is it necessary to use a higher frequency, of the order of 1 Mc/sec. The requirements for the vibrator are high electroacoustic efficiency, high energy transfer, and good stability with time and temperature (for generators under sea water or a large amount of cleaning liquid, the latter is not necessary). The electroacoustic efficiency depends on frequency and on load and reaches a maximum for certain values of both (see van der Bürgt, Philips Matronics 15, September 1958). For vibrators working at frequencies between 10 and 100 kc/sec, some special Ni-Co-Cu ferrites have recently been developed. These show a k of 0.21 to 0.30, which is about the same as for the customary nickel stacks. However, the magnetic Q of the ferrite transducer is of the order of 300, compared to 3 to 6 for nickel, because of the absence of eddy current loss. Moreover, the unloaded mechanical Q for a suitably wound and mounted ferrite transducer is about 1000, for nickel approximately 100, because of friction between the laminations. This means that with ferrite an a of 0.01 can be obtained, giving an efficiency of over 98%, where for nickel a is 0.2 to 0.5, giving an efficiency of 40 to 50%. This high efficiency is reached at an optimum d-c bias which for ferrite lies at approximately two-thirds the saturation flux, that is, about 2000 gauss (75). Strictly speaking, these figures are valid only for low-power applications, such as hydrophones (see below), and not for generators. Yet at high power, the difference remains; in practice the efficiency of nickel is of the order of 40%, whereas with ferrite it is 80 to 85%. For ferrite vibrators, the permissible power is limited by the vibrating amplitude; if the increase in length exceeds about 10~4 (for special ferrites), the danger of mechanical breakage or fatigue occurs. This amplitude is inversely proportional to the damped mechanical Q. For the optimum load, with QmeCh about 20, a generated power of the order of 8 watts/cm 2 can be realized with ferrite. With nickel, this figure is about double; the limit is determined by saturation or by fatigue, not by breaking. When the above factors are considered, the stability with time and temperature, both for ferrite and for nickel, is satisfactory. Consequently nickel is preferable if very high intensities are to be used for long periods (drilling); in most other cases, the higher efficiency

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(making possible a cheaper and smaller high-frequency generator) and the lower price of the ferrite itself will probably lead to the use of ferrite in the future. 4.

Hydrophones

Hydrophones are microphones for underwater detection of ultrasound waves, by transferring them into electric currents. Usually some directional sensitivity is wanted, which can be obtained by using a hollow cylindrical shape. If only a single frequency is received, the mechanical resonance of the hydrophone should be made equal to that frequency. Since no power is required, the advantage of ferrite is evident from the efficiency considerations given in Section IV.D.3. If a broad frequency band is to be detected, the resonance frequency is laid above that band, in order to make the response independent of frequency. In this case the hydrophones can be compared with the accelerometers or pickups mentioned in Section IV.D.l. The most important factor is the coupling coefficient, k, which both for nickel and for ferrites is of the order of 0.25 to 0.3. A third possibility is titanate, which can reach a slightly higher k but has other drawbacks (stability). Because of the low amplitude, no permanent bias is required in ferrite hydrophones. Once the ferrite is polarized, it operates at remanence. Under these conditions, k is of the order of 0.25 (19). 5. Frequency

Stabilizers

In principle it is possible to use a piezomagnetic resonator for frequency stabilizing, for example, in oscillators. Quartz crystals, although more expensive, are more stable and simpler, however, and need no bias. Because of these advantages quartz is usually chosen (76). E. APPLICATIONS BASED ON MECHANICAL PROPERTIES

Compared with metals, the most characteristic mechanical properties of ferrites are their hardness and brittleness. In many cases these are a drawback, because they make machining after firing very difficult, so that narrow tolerances and complicated forms cannot easily be obtained. One application in which, besides the electric and magnetic ferrite properties of ferrite, hardness and brittleness play a role too, partly favorable and partly unfavorable, is in heads for magnetic registration. These consist of a ring or related type of closed soft magnetic core, interrupted by an air gap (or sometimes two air gaps near each other). The registration medium (tape, wire, or a drum surface) passes in front of the gap. A coil is wound around the core.

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J. M. HASPERS

A magnetic recording head has three functions; recording, reproducing, or erasing. In the first and third functions, a current is passed through the coil, exciting a flux in the core and in the air gap. The magnetic registration medium traverses the stray field of the air gap. For reproducing, a flux originates from the registration medium; if this medium passes in front of the gap, the head offers a low reluctance path for this flux compared with the gap (77). For recording, the flux density in the magnetic head should be as high as possible, thus requiring a material with a high saturation. In sound recording, a high-frequency bias is superimposed on the signal, in order to obtain a linear relation between input and output. This bias has so high a frequency (usually 40 to 50 kc/sec) that it is not recorded itself, but it must pass the head well, so that the eddy current loss should be small and the inductance not too high. The latter requirement necessitates a high reluctance of the gap. Since the gap length is limited by the tape velocity and the highest frequency to be recorded (for a tape velocity of 9.5 cm/sec and a frequency of 15 kc/sec, the maximum permissible gap length is 6 microns), this high reluctance can be found only by a low gap height. The gap height is limited by the wearing of the head in contact with the tape, giving at low height too low a lifetime and too much change in reluctance during this lifetime. The walls of the gap should be straight and parallel and should not show any chipping. For reproducing, in the first place the reluctance of the "back circuit" should be low compared with that of the gap. This means that there is a requirement for a high permeability of the core material as well as one for a high gap reluctance. The gap length and height are again limited by frequency and lifetime conditions and the gap walls should be parallel. When ferrite is compared with nickel-iron alloys as core material for recording-reproducing heads (both functions are usually combined in one head) the alloys have a much higher saturation and a somewhat higher permeability. On the other hand, the eddy current loss is much lower in the ferrite, and, moreover, due to its hardness, the ferrite is practically never worn out by the contact with the tape, so that a gap height of approximately 0.15 mm can be chosen, compared to at least 0.4 mm for nickel-iron. The decisive drawback for the ferrites has been their brittleness, which makes it impossible to maintain a 6-micron gap sufficiently parallel and, moreover, causes breaking out of small chips when in contact with the tape. For higher gap lengths, as in professional apparatus, where the tape speed is 76 or 38 cm/sec instead of 9.5 cm/sec, or in computer registration apparatus, where no linearity

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and less sharp definition are required, it is possible to use ferrite heads, because here the influence of chipping and irregularities of the gap walls is much less. On the other hand, the high gap length gives a low reluctance, so that a low gap height is not necessary. For magnetic drum computer heads there is actually no contact between drum and head. Still, ferrite is widely used, because of the large gap and the high pulse repetition frequency to be recorded (usually 100 kc/sec or higher). This makes the absence of eddy currents in the ferrite most important (78, 79). For erasing heads a high gap length can be used and is even desirable in order to obtain good erasing over the whole depth of some tapes. Moreover, erasing is usually done at a fairly high frequency (50-100 kc/sec) where the absence of eddy current loss in ferrites greatly reduces the required power (in some cases with ferrite heads only 10 to 20% of the power required with metal heads is necessary). Consequently, ferrite heads are widely used for erasing but only in special cases ( drum or tape computer memories) for recording and reproducing (80). Recently, however, by means of special techniques it has become possible to manufacture ferrite heads with smooth and parallel gaps of lengths down to 1 or 2 microns, which do not chip off in contact with a tape. These heads are not widely available yet, but they will probably permit ferrite to be used for recording and reproducing heads and moreover will further the solution of the problem of television recording, where the frequencies to be recorded (up to 5 Mc/sec) make the use of ferrite almost obligatory, although a very short gap is needed. F. APPLICATIONS BASED ON SPIN PRECESSION

In Section II.D, the gyromagnetic resonance of ferrites was described, and also the critical frequency, fr, which constitutes the upper frequency limit for the use of a ferrite in the applications mentioned so far. Exceptions are those applications in which only μ is important and not the loss (broad-band transformers, screening applications, damping chokes), but at frequencies above / r , μι soon begins to decrease too, making ferrite unattractive for these applications also. As mentioned in Section II.D, there is an upper frequency limit for the gyromagnetic loss, given by ω = y χ 4πΙ8, where γ = 8.85g, if ω is expressed in megacycles per second and 4TTIS in gauss. The Lande factor, g, is usually about 2, and slightly higher for some ferrites. However, at higher frequencies /xi of the ferrite is about 1, so that for all applications described above it has no value. Nevertheless, in this ultrahigh-frequency range, at frequencies above 1 kMc/sec some most interesting applications exist, for which the use

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J. M. HASPERS

of ferrite is essential; the applications do not work at lower frequencies first because of the losses and second because the phenomena in question are proportional to the frequency and would be too weak to be practical below the gyromagnetic loss zone (81, 82, 83). 1. Isofotors In principle, an isolator is a nonreciprocal network element, which in one direction gives a considerably higher damping than in the opposite direction. In the kilo megacycle per second range these elements, of course, consist of wave guide or coaxial cable sections. In telecommunication transmitters and receivers for these ultrahighfrequency bands in radar equipment, in measuring gear, etc., it is always necessary to have the impedance of all parts of an apparatus (such as generators, wave guides, amplifiers) exactly matched; otherwise reflections may occur which cause interference by forming standing waves, etc. This exact matching is difficult and may not always be quite constant with temperature or time. Consequently, in many cases the introduction of an isolator, having low attenuation for the desired transmission but damping away the reflections, provides a favorable solution. An isolator for the ultrahigh-frequency band can be based on three different principles: 1. Faraday rotation (84, 85, 86). This has already been described in Section II.D. If a linear polarized wave is passing through a piece of ferrite, saturated in the direction of propagation of the wave, the plane of polarization rotates, the direction of rotation being independent of the direction of propagation, and the angle of rotation for a certain ferrite and a fixed diameter being proportional to the length of the piece. By choosing the length of the ferrite piece (usually a round rod), a rotation of 45° can be realized; then a reflection, if any, on its return again turns 45° in the same direction, so that afterward it has rotated 90° with respect to the original wave and can be absorbed easily by a direction sensitive absorber, which does not influence the original wave. The specific rotation of a ferrite rod increases with increasing thickness, but the relation is not linear. However, thick rods should preferably be tapered at the ends, in order to avoid reflections. The advantage of this method is the low biasing field necessary for all frequencies. A field of 50 to 60 oersteds which can be easily realized by passing one or two Ba ferrite rings on the rod, will do. Moreover, a very low forward damping can be obtained (0.2 db, compared to 30 db backward), because the heat absorption does not take place in the ferrite itself, but in the absorber (usually a polarization wedge). Draw-

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backs of Faraday rotation are the expensive mechanical construction (a rectangular wave guide should gradually go over into a round one and, after the ferrite, again into a rectangular one which has turned over 45° ) and its unsuitability for very high power. The choice of ferrite depends on the frequency. In any case it must have a low porosity (to avoid internal distortion), a high resistivity, and low dielectric losses. The saturation should be as high as possible (because the rotation is proportional to it) but low enough to remain at the operating frequency above the gyromagnetic resonance loss region. For 4000 Mc/sec, for example, a ferrite with g = 2.05 should have a saturation value below (2π X 4000)/(2.05 X 8.85) gauss, or 1380 gauss. This low saturation can be realized by addition of chromium or aluminum to Ni-Cu or Mn-Mg ferrites. In this way, microwave ferrites with saturation values of 300 to 4000 gauss are made available. 2. Gyromagnetic resonance (87, 88). Inside a rectangular wave guide a traveling TE01 wave is elliptically polarized. Near the side walls the long axis of this ellipse lies in a longitudinal direction, and in the middle of the wave guide it lies in a transversal direction, so that somewhere between the polarization it is not elliptical but circular. If at this spot a slab of ferrite is placed with its largest dimension in longitudinal direction and is magnetized perpendicular to the plane of polarization of the wave, for one direction of propagation the sense of circular polarization will coincide with that of the spin precession in the ferrite, whereas for the other direction it will be opposite. As mentioned in Section II.D, such a spin precession has a typical angular frequency, ωτ, which is equal to yHz, where Hz is the total field ( internal + external ) inside the ferrite. If the outside field is adjusted in such a way that ωτ is equal to the angular frequency of the wave, a resonance will occur for that direction of propagation where the sense of polarization and spin precession coincide, so that a wave in this direction will be heavily attenuated. An important point here is the band width of the resonance curve. Being a pure resonance curve, this band width is inversely proportional to the damping peak height. Because of the relation ωΓ = yHz, the relative field band width, ΔΗΖ/ΗΖ, is equal to the relative frequency band width, Αωτ/ωτ. Too high a band width gives a bad ratio of forward to backward damping; too low a band width reduces the useful frequency band of the isolator. If necessary, this band can be increased by using a slightly inhomogeneous bias field. This bias field can be provided by an electromagnet, a steel magnet, or a ferrite magnet. With an electromagnet the field can be easily adjusted, which is an advantage if the isolator should function only occasionally [for example, an isolator

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between receiver and TR (transmitter-receiver) box of a radar equipment as an extra protection for the receiver which however should function only during emission of a transmitting pulse] but it consumes current and gives additional heating. A steel magnet is stable with temperature, but can demagnetize if short circuited; a ferrite magnet is safe against short circuiting, but has a certain temperature drift. The resonance isolator is simple and can be used for high-power applications, provided suitable cooling exists. However, the heat is dissipated in the ferrite itself, so that the damping ratio forward to backward is lower than for the rotator (1 db forward compared to 30 db backward), and for higher frequencies very high bias fields are required. The ferrite requirements are identical to those for the Faraday rotator, with the exception of the saturation limit, which does not exist here because the material is subjected to a high magnetizing field (89). For transversally magnetized slabs in a resonance isolator, no high saturation limit exists. 3. Field disphcement (90, 91). In Section II.D is also mentioned the fact that, when two opposite circularly polarized waves are applied through a transversally magnetized ferrite, for one of them the susceptibility, K, is IS/(H + ω/γ), and for the other it is IS/(H — ω/γ). The permeability, μ, in these cases is, respectively, 1 + ( 4 π ί β ) / (H -f- ω/γ) and 1 + (4TTIS)/(H — ω/γ). If a ferrite is chosen for which 4πΙ8 < ω/γ (this is necessary for the absence of resonance losses), there can always be chosen a field, H, for which the permeability of a piece of ferrite is either greater or less than 1, depending on the sense of polarization of a wave. This means that, for a circularly polarized wave (and to a somewhat smaller extent also for an elliptically polarized wave) for one direction of propagation, energy is sucked into a transversally biased ferrite, whereas for the opposite direction energy is driven out of the ferrite. If on the surface of the ferrite an absorbing strip covered with, for example, metallic titanium, is glued, this absorbs only one of the waves; because of the opposite wave no energy is present there. In this way a unidirectional attenuation is obtained, with a high forward to backward damping ratio (0.2 to 30 db) and a simple mechanical construction. A drawback is that until now no field displacement isolator for high power has been used. The ferrite requirements here are almost identical with those of the rotator: 4TTIS should be as high as possible, however <ω/γ, low porosity, high resistivity, and low dielectric loss. The resonance band width, H, should be small, so that at the H value required here the / / ' lies well out-

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side the resonance peak. For low frequencies, where ω/γ is small, this is more critical than for higher ones. 2. Phase Shifters (Gyrators)

(92, 93)

Both the Faraday rotation and the transversal magnetization can also be used to obtain a 180° phase shift in waves. If the rotator is designed for 90° rotation instead of 45°, a wave and its reflection obtain a phase difference of 180°. In the same way use can be made of the different propagation velocity (v = c/^yiji; see Section II.D) in order to obtain a phase difference for opposite wave directions. If a phase shift of 90° is obtained, in principle by introducing a 90° junction in the wave guide at the right spot, it might be possible to construct a TR box (if necessary, with a time-synchronized isolator in the receiver connection; see Section V.F.I) or a hybrid circuit for ultrahigh-frequency carrier telephony. This will, however, set rather severe requirements for the ferrites with regard to losses, power dissipation, etc. 3. Circulators

(94)

Circulators represent somewhat more universal application of the same principle as the phase shifter. In Fig. 19, one of the possible exe-

FIG. 19. Circulator.

cutions is indicated. A wave entering at A divides itself over I and II; after these branches both half-waves have a phase difference of 180°, and all energy vanishes at B. In the same way B-> C, C —> D, and D-> A. This principle can also be used for TR boxes. 4. Switches

(93)

Switches can be obtained by making an isolator with electromagnetic

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bias. When the current is switched on, the isolator constitutes a blocking for a wave in backward direction. 5. Modulation (95, 96, 97) This If the quency, passing

is an extension of the last paragraph in Section IV.B.l. switch is opened and closed according to some low frethe losses vary and the low frequency is modulated on the high-frequency wave.

6. Radar Beam Scanning

(98)

From the relation μ = 1 + ( 4 π ί β ) / ( Η — ω/γ) it follows that by varying H with a low frequency, μ of a ferrite piece can be varied with the same frequency. If a radar beam passes through a ferrite-filled wave guide and leaves through a number of holes on the sides along the length of the guide, the waves between two neighboring holes have a phase shift and will cooperate only for these directions, where they are still in phase owing to their different path lengths. If the phase shift is periodically changed by low-frequency biasing of the ferrite, the beam moves to and fro with the same frequency (98a), This may be important for heavy radar antennas which need only to cover a restricted angle. 7. Radiation

(99)

Finally, ferrite rods may be used as radiating antennas at ultrahigh frequencies. The advantages are a good directivity and an easy possibility of phase shift or modulation. In order to avoid reflections, tapering of the ferrite is usually necessary. For all these ultrahigh-frequency applications, the ferrite requirements are about the same as those already mentioned for the rotation isolator. V. Applications of Hard Magnetic Ferrites A. COMPARISON WITH STEEL MAGNETS

The preceding paragraphs have made it clear that the applications of soft magnetic ferrites occur mostly in the high-frequency range, where these ferrites are definitely superior to laminated or powdered metal because of their high resistivity and that they have some applications for which metal would not work at all. On the other hand, for low-frequency applications metals are superior owing to their higher saturation and permeability. Consequently, metals and ferrites here are more or less complementary, each with their own applications (100,101). For permanent magnets the application situation is not so clear. Of

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course, the hard magnetic ferrites have a high resistivity too and are consequently preferable for high-frequency applications. Unfortunately the field of high-frequency applications for permanent magnets is small, much smaller than for soft magnetic material so that the bulk of hard magnetic ferrite applications lies in direct competition with metal magnets. The differences in their properties can often be largely compensated for by adapting the magnet shapes, so that in these cases the choice of ferrites or metals becomes a matter of price. Although hard magnetic ferrites are intrinsically cheaper than metal magnets due to their cheap raw materials, this is not a decisive factor. As opposed to soft ferrites, which find their main applications in electronic circuitry where the mounting can be adapted relatively easily to the ferrite shape, the main applications of permanent magnets require an expensive mechanical construction which should be modified on shifting from metal to ferrite. It is not the cost of the magnet that is decisive, but the cost of this whole mechanical construction (at equal performance). As this may vary considerably from case to case and from customer to customer, for such applications it is not possible to indicate whether steel or ferrite will be preferable. The following discussion will offer some comparison of the relative merits of both materials, but it should be kept in mind that the choice is often less obvious here than for soft materials. B. LOUDSPEAKERS {102,

103,

104)

For loudspeakers, a constant magnetic field is maintained in a narrow gap, in which a speech coil is vibrating. The gap height, coil dimensions, and required field are determined in the first place by the acoustical requirements of the speaker. The required fields can be realized both with ferrites and with steel, but the magnet system has to be modified: because of its low BR and high Hc the ferrite requires a larger area, but the system can be flatter. This is important for car radios and small pocket sets, where the larger area is not so important because for the cone a large area is required anyhow. Here ferrite is preferable. A special grade of steel with high coercivity (Ticonal X) can do the same, but is still too expensive. For normal broadcast speakers, record players, tape recorders, etc., both ferrite and steel can be used. The larger area of the ferrite magnet requires somewhat larger pole pieces, which to a certain extent compensates for the magnet price. For small speakers, steel is often preferred because of the smaller volume; for bigger speakers, where the lower price of raw material for the ferrite is more important, the ferrite is probably preferable. For television sets, especially with short neck

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tubes, the questions of available mounting depth and stray field are becoming important. With steel magnets, it is possible to make a center pole construction with a brace around it. This brace gives a partial screening of the stray field, so that this will interfere less with the tube picture. With ferrite magnets such a construction is not possible because the low BR requires too large an area; hence their stray field is some what larger. On the other hand, with the same mounting space available, the magnet of the flatter ferrite speaker stays somewhat further away from the cathode-ray tube. Both the ferrite and the steel speakers can, of course, be completely screened with an iron cap, but this considerably increases the cost price of the speaker. If the available space for mounting becomes more restricted, ferrite has an advantage (provided the stray field is still acceptable) because the ferrite speaker is flatter. On further reduction of the mounting depth an inverted so-called "wafer construction" is necessary, with the magnet system mounted on the front side of the coils. Here the speaker depth is again much lower and the stray field can be partly screened by a soft iron cone-bearer, while the acoustical drawbacks of a wafer speaker can be avoided by special construction. In these wafer constructions ferrite again has the advantage of a flat magnet system which does not protrude from the cone on the front side. However, if in addition to the reduction in depth the area of the mounting space is reduced also, such that a 6 inch or smaller speaker must be used, then a wafer construction with ferrite cannot be used because of the area it requires, and in spite of the high price Ticonal X has to be used. To conclude, it can be said that for some special types of speakers the ferrite is superior, whereas for some other special types steel is superior. For the majority however, the question "ferrite or steel" is first a matter of price. C. TELEPHONES

In magnetic telephones a membrane is brought into vibration by the current in a speech coil. A permanent magnet is used to provide a bias and to obtain a linear characteristic. The magnet requirements are not very critical, either ferrite or unoriented steel can be used. With ferrite a flat construction can be made, which is attractive, provided the construction is adapted to the flat magnet. The price will be decisive here also. For old-fashioned hand-operated telephone equipment, permanent magnets are still used in the ringing generator, usually bipolar steel magnets. These could be replaced by ferrite, if at the same time the num-

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ber of poles was increased and the construction changed. However, this is hardly worth while for a vanishing item. Another possible application is in electrodynamic microphones. These are robust, but less sensitive than the carbon microphone, so that their use is restricted. A fourth magnet application in telephones is the ringer, in which the bell is operating on alternating current, the armature being polarized by the magnet. For all these applications, cheapness of cost and accuracy of shape as well as holes and grooves are more important than magnetic performance. Either a cheap steel magnet (unoriented) or an unoriented ferrite magnet can be used. In many cases powdered magnets with plastic binder will stand a good chance too, because these can be made easily in any shape. D. TELEVISION

Originally, the largest magnet application in television sets was for permanent magnetic focusing of the electron beam in order to obtain a sufficiently small and distinct spot on the screen. For this application, ferrites are definitely superior to steel because shorter magnets can be used due to the high coercivity; these take less space on the tube neck. Moreover by changing the mutual distance in a two-ring system the focusing strength can easily be adjusted (see Fig. 20) (105, 106). At present, permanent magnetic focusing has been abandoned in favor of electrostatic focusing by means of two focusing electrodes built in the tube. This is not better, neither technically nor economically, but it is easier for the manufacturer of the set, because he can leave his focusing problems to the tube manufacturer, and, moreover, a rather bulky object on the tube neck is eliminated. With ferrite it might be possible to obtain an internal magnetic focusing, also inside the tube, which could be adjusted with a soft iron ring outside. With magnetic focusing, the centering of the picture on the screen can be easily done by a movement of the focusing rings perpendicular to the tube axis. With static focusing a separate centering device may be necessary. One solution is a round ferrite magnet clamped to the tube neck diametrically magnetized, with two ring pole shoes around. In this way, two independent movements are possible: the direction of the adjusting field can be changed by turning the whole device around the tube neck and its strength can be adjusted by turning the diametrically magnetized magnet inside the pole shoes. A similar system can be adopted for the ion trap magnet, if this is still necessary for 110° straight gun tubes. A last television application

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J. M. HASPERS 200hxl0 3 0e 2 cm

6

8 d in mm

10

FIG. 20. Value of fHx?dx (a measure for focusing power) in a two-ring Baferrite focusing system with varying ring distance.

for magnets (for loudspeakers refer to Section V.B) are magnets for pincushion correction. If a deflection coil is made so as to give a minimum deflection defocusing (good picture brightness also in the corners), considerable pin-cushion distortion occurs, which can be compensated with two diametrically magnetized cylindrical ferrite magnets besides the flare of the deflection coil. By turning the magnets, the compensation can be adjusted until an optimum picture quality is obtained. E.

MAGNETRONS

Until now steel magnets have always been preferred for magnetrons. The required field for the usual 3-cm magnetrons (10,000 gauss or more) was too high for ferrite magnets; moreover, the high temperature coefficient (which may cause up to 10% variation in output) was and is prohibitive for radar magnetrons. There is, however, a trend toward the use of cheap and small magnetrons for industrial and domestic purposes (e.g. for cooking and for

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quickly heating up lunches in snack bars). Here the required fields are smaller, of the order of 5000-6000 gauss, and the output variation is not critical. A 2 kilowatt magnetron for 2400 Mc/sec, intended for industrial and household applications, was equipped with ring magnets in oriented Ba ferrite giving considerable savings in cost compared with the cast steel magnet used previously. Also the performance of the magnetron was not affected at all (107). F. PREMAGNETIZING OF SOFT MAGNETIC CORES

Premagnetizing is usually done in order to change the permeability or to increase the induction range of soft magnetic cores. Especially in high-frequency circuits where soft magnetic ferrite is used with a high sensitivity of its μ for bias (see Section IV.B), this can be advantageous. In this case ferrite magnets must be used. A disadvantage compared with d-c bias is that a permanent magnet requires an air gap in the circuit. If such an air gap is not present, it has to be introduced, giving an increase in reluctance. This permanent magnet biasing can have the following purposes (108): Increasing the induction range for cores with an asymmetric load. The "classical" examples of this case are the impulse transformer (31) and the ignition coil with a soft ferrite core (see Sections IV.A.2 and IV.A.12). For these applications the induction in the ferrite, and in the magnet too, goes through zero. This means that the magnet must be exposed to a demagnetizing field stronger than its own coercivity and still not demagnetize permanently! This is only possible with unoriented Ba ferrite (see Section III) and not with oriented ferrite or with steel. 2. Changing the inductance of a ferrite core. This has already been mentioned in Section IV.B.4, e.g. for rotoroid coils and for linearity control in television sets. Another example is a local biasing of an aerial rod in ferrite by placing short ferrite magnets on both sides of the short antenna coil. In this way, for the same inductance the number of turns of the coil can be increased while the actual concentration factor of the transmitter flux is hardly affected by the magnet. In this way the aerial output can be increased by about 23%, but the antenna device becomes more complicated. 3. Compensation of a direct current flux in transformer cores. In transformers in the anode circuit of a tube the primary winding usually carries direct current, thus reducing the core permeability and the coupling factor of the transformer (communication amplifier transformers, speaker transformers, television flyback transformers, etc.). Frequently, these transformers already have an air gap in their magnetic

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J. M. HASPERS

circuit which is the most favorable solution for transformers carrying direct current (see 28). If this air gap is large enough to put a magnet into it (at least 1 mm), it is advantageous to do so (then a short ferrite magnet is the only solution); if the optimum air gap is not large enough, then it would be better to omit the magnet altogether. 4. Premagnetizing in order to reach a linear characteristic. An example of this is the telephone magnet mentioned in Section V.C. When the a-c field of the speech coil is superimposed on the constant field of a magnet the membrane vibrates with the voice frequency, whereas without bias double frequency together with higher harmonics occurs. A similar case is discussed in Section IV.D, where for the same reasons a permanent magnetic bias of magnetostrictive ferrites in filters and ultrasound generators is necessary. For these frequencies the advantage of ferrite over steel magnets is evident. 5. Biasing of soft magnetic ferrite which works in its saturation. This occurs in ultrahigh-frequency applications, such as isolators and phase shifters. Three different cases are given below: (a) The magnetic field should not exist permanently, but only at certain times (switches, synchronized isolators). In this case, an electromagnet is to be used. (b) The magnetic field is permanent and must have exactly the same value within a certain temperature range (resonance isolator). In this case a steel magnet should be chosen, ferrite being prohibitive because of its high temperature coefficient, and precautions should be taken to avoid an accidental magnetic short-circuit of the steel magnets, which might cause demagnetization, (c) The magnetic field is permanent and not critical as long as the soft ferrite remains saturated (rotators; to a certain extent also field displacement isolators). Here ferrite magnets can offer the advantage of their high stabihty provided the working line lies so high, that also at the lowest ambient temperature the "knee" in the BH curve is not passed. G. PICKUP SYSTEMS

For pickup systems mechanical energy of a defined frequency is converted into electrical energy in order to amplify it with constant frequency and if necessary convert it back into mechanical energy. This can be done by moving a magnet or a part of a biased circuit with the required frequency and "picking up" the occurring flux changes with a coil. A good example is a high-fidelity magnetic pickup, where the mechanical vibrations of a gramophone needle are converted into rotational vibrations of a diametrically magnetized rod in Ba ferrite, picked up with a coil and amplified. Although an extra amplifier is necessary,

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the reproduction quality herewith is better than for a piezo-electric pickup. Another possible application is in electronic music instruments, for example, guitars, mandolins, also pianos and Hammond organs. Here a magnet is used in a circuit which is more or less closed by a vibrating string (or a ferromagnetic element attached to it) so that the flux changes can be picked up in a coil and amplified. If desired, the string can be kept vibrating by means of feedback. Here the advantages of ferrite magnets are their stability, the absence of eddy current losses, and the possibility of using short magnets, which cause less increase in the reluctance of the circuit. The use of ferrite magnets in a study piano for protection of the strings against too strong beating is in fact a magnetic coupling. The above-mentioned possibility of bringing a magnet system into vibration with a certain frequency, picking up the flux variation, amplifying it, and keeping the system in constant vibration at the same frequency by feedback can also be used for time measurement, e.g., electronic watches. In order to supply the required energy with only a small battery it is necessary to use for the amplification a transistor with a small leakage current. Other possible industrial applications are, e.g. counting the number of strokes of a press or pump, detecting iron in paper or textile bands. H. GENERATORS AND MOTORS

Like pickups, generators convert mechanical energy into electrical energy, but here the electrical energy as such is important and not the frequency. This means that distortion is no problem, but the requirements for efficiency, power capacity, mechanical construction, etc., are severe. For field energizing, two methods are possible here: electromagnets and permanent magnets. Electromagnets give higher fields and permit easy regulation of the obtained voltage, but they consume current and are slightly less sure in operation. For high power, electromagnets are usually preferred, because the required permanent magnets would be very expensive and would make the mechanical construction heavy and bulky. For small power, electromagnets become relatively expensive and complicated, and often no space is available for the winding. Unless a very exact regulation is necessary, permanent magnets are preferable (109). It is difficult to indicate generally whether steel magnets or ferrite magnets should be used. The latter are more stable, and can be magnetized in their short direction too, but the obtainable flux density is lower, unless rather bulky and expensive pole pieces are introduced.

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Unoriented ferrite magnets have the lowest flux density but have the advantage that they can be magnetized with many poles (as a rule of thumb, one can say the maximum possible number of poles for radial magnetization of a rotor is about equal to the diameter in millimeters). Oriented ferrites have higher flux density, but it is still difBcult and expensive, though not impossible, to make them with radial magnetization. If flux densities of more than 4000 gauss are required, steel is usually preferable; for lower fields the price of the complete construction, adapted to the magnet used, should be considered from case to case. The higher the number of poles, the better usually are the chances of (unoriented) ferrite as compared to steel. Some specific types of generators, for which ferrite magnets are considered are the following: 1. Bicycle dynamos. For rotors with four poles or more, ferrite magnets are technically and economically preferable to (unoriented) steel magnets, even if used in a steel construction. For dipole systems steel is preferable; in view of the distinct advantage of ferrite in multipole systems, a certain trend does exist toward their use. 2. Car dynamos. In spite of their inefficiency and the necessity of a commutator, until now d-c dynamos have been used in cars, because a cheap rectifier of high efficiency and able to withstand 75°-80°C did not exist. Permanent magnets can be used in the d-c dynamo, but because of the difficult regulation an electromagnet is usually chosen. This situation is changing as a result of the availability of silicon rectifiers of high efficiency, which can easily withstand temperatures up to 100°-120°C. Their price is still high, but in the coming years a drop can be expected. With these rectifiers it is possible to use an a-c generator (alternator) instead of the d-c dynamo. Such an alternator does not require a commutator and also has the following advantages: (1) small volume and low weight; (2) high efficiency (up to 75% against 40% for the d-c dynamo); and (3) sufficient loading at low speed without overloading at high speed. Because of the advantages of small volume and high efficiency the use of permanent magnets becomes very attractive here, especially ferrite magnets because of their high stability and the absence of eddy current losses. The only problem is that of regulation. It seems now that this can be solved in various ways, for example, by a relay driven by the amount of gas developed, or by continuous variation by means of conical pulleys or by saturating chokes (see 110 and 111). Therefore, this seems one of the most promising applications for ferrite magnets. 3. Gasoline sets for field work, etc. These sets usually work on higher voltage than car dynamos and have no accumulator so that exact voltage regulation is not necessary. Moreover, for these sets, which are frequently

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used for military purposes or in deserted regions, a high security is desirable. All these conditions favor the use of permanent magnets for these sets, either steel or ferrite. If the required induction is not too high, their better stability favors the ferrite magnets. 4. Small dynamos for servomechanisms, etc. For servomechanisms a small lightweight piece of apparatus is needed, which can easily be realized by working at higher frequencies, above 1 kc/sec. This makes the use of ferrite magnets attractive, provided the TC does not interfere and the required tolerances can be met. 5. Telephone generators. For the customary 2-pole generators, steel magnets are preferable. This is a vanishing item anyhow, because of the advance of automatic telephony (see Section V.C). 6. Magnetos. Although every generator with a permanent magnet may be called a magneto, here the term is applied mainly to explosion motors which generate their own electrical energy, which is carried from the generator directly to the spark plugs. When explosion motors for cars were developed this system was tried, but it failed because the available magnets were not stable enough and gave too much eddy current loss. Thus the advantages of ferrite magnets are re-emphasized here. The big advantage of this system is that the powerful spark needed at higher speed is easily obtained. For motor cycles and scooters where a flywheel is available for speed stabilization anyhow, these magnetos are used on a large scale by building permanent magnets in the flywheel houses. Because of the possibility of using short ferrite magnets magnetized in their short direction (which eliminates the use of pole shoes) and because of their high stability and the absence of eddy current loss, ferrite magnets are preferable here. The only drawback is that they cannot be cased together with the flywheel housing; if this must be done, steel is required. For a mechanical construction, however, ferrite offers the advantage. In motors, electrical energy is transferred into mechanical energy, the opposite of what occurs in generators. It is evident that permanent magnets can be considered only if a constant field is required, as in d-c motors, or in synchronous motors. In d-c motors, like d-c generators, for high powers or for those cases where an exact speed regulation is required, electromagnets are preferred, whereas for small power and low voltage permanent magnets are more desirable. This is, in particular, the case for motors running on an accumulator, e.g. for servomechanisms, toys, car applications. The choice between steel or ferrite magnets is again governed by various factors such as required induction, efficiency. In a car window cleaner

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J. M. HASPERS

motor a torque of 21 kg-cm was required at approximately 15 turns per minute. With electromagnets the required torque was reached at a current consumption of 2.3 amp. With unoriented ferrite magnets the torque could not be obtained because the field was too weak; however with oriented ferrite the required torque was already reached with a current consumption of 1.6 amp. The two ferrite magnets used had a length of 2 cm and a rectangular area of 1.9 X 2.4 cm, and were used with plate iron pole shoes. In a car heater motor of 1 kg-cm the efficiency was increased from 37 to 62% by replacing the electromagnets with semicircular segments of unoriented Ba ferrite, with the rotor turning inside. The advantages of the ferrite magnets were twofold: In the first place, the ferrite magnets could cover almost the whole circumference ( 2 χ 1 8 0 ° ) without excessive stray-field loss, and for this reason the pole shoes of the electromagnet could not be made longer than 2 X 120°; in the second place the ferrite magnet, with a reversible permeability of about 1, largely increased the air gap "seen" by the rotor reaction, so that this had little influence, considerably less than with pole pieces made of soft iron of high permeability (112). These two examples may illustrate the advantages of ferrite magnets for some kinds of d-c motor. Synchronous motors are usually very small, with a speed coupled to the driving frequency; only for small motors can the problem of starting be easily solved. The main applications are for clocks or watches. Ferrite magnets have the advantages of stability, the possibility of multipole magnetization, and the absence of eddy current loss. To summarize, generators and motors seem to offer good chances for permanent magnets in fields of lower power, but for a comparison between steel and ferrite the cost of the whole construction should be compared which may be different for each case. I. COUPLINGS AND RETARDERS

(113)

A torque can be transferred from one axis to another by means of magnetic forces, either electromagnetic or permanent magnets. The electromagnetic coupling provides good regulation but is complicated and hardly used. The permanent magnetic coupling is used much more frequently. It has the following advantages: (1) simple construction; (2) strict aligning of the axes is not necessary; (3) simple mounting and demounting; (4) possibility of coupling through a wall (provided this wall is not ferromagnetic); (5) no friction; (6) automatic

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safety against overloading; and (7) separation of vibrations of both axes. The permanent magnetic couplings can be divided into synchronous couplings, where the number of revolutions of both axes is exactly the same and the coupling occurs by mere magnetic attraction, and eddy current couplings, where a certain slip occurs between both axes; then the occurring eddy current losses are more or less responsible for the coupling. For both types of coupling, ferrite magnets have an advantage over steel magnets, because they can be applied as flat magnets in a simple construction, which is completely resistant to the fairly high demagnetizing forces. Application of magnetic couplings is found in particular if one of the advantages numbered 4, 6, or 7 is important—for example, in pumps for corrosive liquids, water meters, gas meters, chemical agitators or vacuum agitators, protection of cog wheels. If, in an eddy current coupling, one of the axes is fixed, or if between two coupled rotors, each consisting of a number of magnets of alternating polarity, a metal ring is brought which cannot rotate, 100% slip occurs, and the fixed ring strongly retards the rotor, because the kinetic energy is converted via eddy current loss into heat. Thus a retarder without mechanical contacts is obtained causing little wear and with a braking force proportional to speed (up to a certain limit, when the slip angle becomes of the order of half the distance between two adjacent poles), making it very suitable for quick braking of heavy trucks in mountain regions. Because the retarder force is very low at lower speed the eddy current brake should be combined with a normal brake. The extra cost of the retarder is compensated for by better and quicker braking at high speed, and longer lifetime of the normal brake and of the tires, which are not blocked so that the risk of skidding is less. A major problem of the eddy current brake is the removal of the dissipated heat. Both water cooling and air cooling are possible. Water cooling requires a more complicated construction, but the brake can be kept smaller and the temperature is kept lower, so that the air gap between rings can also be smaller (less thermal expansion of the metal parts), giving a more efficient braking. On the other hand, air cooling is simpler and allows a much higher temperature limit. For air-cooled systems steel magnets may be superior because of their higher Curie point, although the maximum working temperature for ferrite magnets (400°C) is usually not reached. For water-cooled systems, ferrite magnets are preferable because of the high demagnetizing field that occurs.

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In addition to its uses for trucks or railway wagons, an eddy current retarder may also be useful for cables running off a crane or winch. J. BEARINGS

In a manner analogous to that of a magnetic coupling, it is possible for a ferrite disk magnet (or a number of disk magnets glued together) to rotate within a ring magnet with the same inner polarity as the outer polarity of the inner cylinder. In this way a frictionless bearing is obtained with good radial stability (in order to have a linear bearing characteristic the length of the magnet in axial direction should be at least three times the gap length). For a horizontal axis it is possible to compensate for the gravitational force by removing part of the outer ring. The only trouble is, however, the occurrence of forces in the axial direction. According to a theorem by Earnshaw (see, e.g., 113a) SL magnet cannot be in a fully stable equilibrium in the field of other magnets, so that a radially stable bearing is not stable in the axial direction and needs a mechanical support there. Still, the friction of this support can be kept low. Magnetic bearings should find applications in small precision instruments which must move lightly, such as indication meters and counters. Because of the high demagnetizing forces, ferrites are here superior to steel magnets. K. ULTRAHIGH-FREQUENCY APPLICATIONS

In Section IV.F the microwave applications of soft magnetic ferrites were discussed. However, hard magnetic ferrites also show Faraday rotation and gyromagnetic resonance. Ba ferrite can be used in a rémanent state and then act as its own premagnetizing agent. However, this ferrite is active only at very high frequencies; a resonance isolator using Ba ferrite at remanence can operate only at 48 kMc/sec. With modified Ba ferrites this frequency can be brought down or increased further, up to 100 kMc and higher. L. STICKING MAGNETS

Sticking to a ferromagnetic material is more or less the first property of a magnet observed in daily life. Whereas practically all magnet applications mentioned so far have been for industrial purposes, in this area household applications are becoming important. Usually the magnetic requirements are not very severe, and only a certain minimum sticking force of the magnet or system (for high forces a pole shoe system is recommendable) is required. This force strongly depends on the air gap between the magnet and the wall, so that the

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smoothness of the wall surface may be critical unless a discrete air gap exists. A second requirement is sufficient stability, which can always be met by suitable designing, although in this respect ferrite magnets give rise to fewer problems than do steel magnets. Usually, various alternative solutions to a sticking magnet exist, so that the price of the magnet or the system is an important point. Sticking magnets can be divided into the following main groups: 1. Magnetic separators. These remove undesired ferromagnetic parts from other media, for example, from oil, where ferrite magnets are used for carter filters in cars, or from fiber materials, as in textile or paper mills, where pieces of iron resulting from the emballage of the raw materials (cotton, straw, cellulose) are removed by a permanent magnet installation before entering the transport band where they could do much harm. Another example is the magnet in a cow's stomachs to protect against perforation by iron particles in the food. Ferrite, steel, or electromagnets all can be used here; usually the required size and the price of the complete construction are the deciding factors. 2. Magnets for handling iron parts. These usually involve rather big magnet systems, used in mechanical industry, such as lifting magnets on cranes or winches or chucks for machine tools. Usually high forces are required, which can be obtained most easily by electromagnets. However, electromagnets have the serious drawback that a sudden falling out of the current may cause heavy damage to machinery or even to people. Permanent magnet systems are safer but require a separate loosening system, which can be obtained by shifting two halves of the system in such a way that they short circuit each other, or by sideways displacement of the magnets by ridges, etc. 3. Magnets for temporary fixing of small articles. These magnets have many household and domestic uses, because easy fixation on all kinds of places is possible only for smaller and lighter articles. Some examples are magnets for lamps (trouble light), soap holders, curtain rods, door latches (for example, in iceboxes), ashtrays, service trays, tools, calendars, and planning boards. Cheap, short, stable magnets are needed, thus providing good possibilities for unoriented ferrite. M. MISCELLANEOUS APPLICATIONS

A broad field for cheap magnets, not yet mentioned, is the toy industry. With cheap, stable magnets, the number of applications is as unlimited as human imagination. Magnetic football games, chess boards, dart throwing games, etc., have already been developed. A final application for permanent magnets is for tubes or valves in

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water pipes which can be operated through the pipe wall. This may be more or less considered as a coupling through a wall. VI. Special Ferrites A. FERROXPLANA (114,

115)

In Section III, in the discussion of the structure and properties of the hard magnetic Ba ferrites, it was mentioned that the main component is BaFei 2 0 1 9 or BaO-6Fe 2 0 3 , being a hexagonal structure with one Ba ion in each of five layers. It also contains another oxide, BaFei 8 0 2 7 or BaFei 2 0 19 , plus two molecules of ferrous ferrite, FeO-Fe 2 0 3 . These two molecules of usually cubic material are incorporated in the hexagonal structure so that every seventh layer contains a Ba ion. All these compounds are hexagonal and have a strong positive crystal anisotropy— i.e., a preferred direction of orientation of the magnetization along the hexagonal axis. The same is the case if in BaFei 8 0 2 7 the two ferrous ions are replaced by other bivalent ions, MeO. From BaO, MeO, and Fe 2 0 3 , other components can be formed, having, for example, the structure Ba 2 Me 2 Fe 12 0 22 (Y) or Ba 3 Me 2 Fe 24 04i (Z). All these compounds are hexagonal, but the Y compound and the Z compound, if cobalt is taken for Me, have no positive but a negative crystal anisotropy. This means the preferred orientation is no longer in the direction of the hexagonal axis, but in the plane perpendicular to that direction. Inside this plane the magnetization can easily turn, giving a fairly high permeability, but the magnetization strongly resists being turned out of this plane, giving a very low permeability of almost 1 in that direction. This combination of rather high permeability inside the plane, but difficult turning (and difficult precession) outside it, leads to die precession formula given in Section II.D, jr(^% — 1) = %yls being no longer valid. To the second member a factor p should be added, being of the order of 4 to 5. This means that for such a material, usually called Ferroxplana, the frequency limit for low losses lies four to five times as high as for the corresponding soft ferrite with equal permeability, or, inversely, for a fixed frequency limit the Ferroxplana material has a permeability four or five times as high as that of the corresponding ferrite. For instance, a nickel ferrite with μι Ä 17 has a frequency limit at 50 Mc/sec, whereas for a Ferroxplana with μι τζ, 17 this limit lies at about 210 Mc/sec. On a macroscopic scale, for the crystals in a polycrystalline, permeability is equal in all directions. For those materials a maximum permeability in various directions on a macroscopic scale can be obtained by

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orienting the Ferroxplana so that, as in oriented Ba ferrite, the hexagonal axes of all crystals are in parallel orientation. In this way, the preferred direction a μ» of maximum about 60 can be realized with low losses up to 200 Mc/sec, or a μι of 20 with low losses up to 600 Mc/sec. Ferroxplana is a very recent development, so that it is still difficult to say what properties will be obtainable and for what purposes it will be suitable. Some possible applications are: 1. Tuner transformers for television in the 200-Mc/sec band; in the future, also for the 500-Mc/sec band. 2. Video intermediate-frequency coils, provided the stability with time and temperature can be made sufficiently high. 3. Modulation for frequency-modulated transmitter or for ultrahighfrequency telecommunication. 4. Generators or transformers for short impulses. A good transformer has been developed for 40 nanoseconds pulses with a rise time of 5 nanoseconds. This is not possible for classical ferrites, because the higher harmonics are attenuated too much and the short rise time cannot be maintained. The possibility of using Ferroxplana for television aerials seems doubtful for the reasons given in Section IV.A.5. REFERENCES

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