Magnetic Amplifiers


Magnetic Amplifiers


The magnetic amplifier enjoyed its maximum prominence in power control

and low frequency signal-processing electronics from about 1947 to 1957.

By 1957 junction transistors were readily available. Development rapidly

shifted away from magnetic amplifiers toward transistor and semi-conductor

switch equivalents, combined magnetic/transistor amplifiers, and the host

of new devices made possible by the joint use of square-loop cores and

transistors. Complex magnetic-amplifier designs developed in this period

must be looked on as an interim technology. Many magnetic amplifiers in

present use and manufacture are the result of early design commitments

which have not yet been replaced.

There are a few areas , however, in which magnetic amplifiers continue to

excel. In power control , they tolerate extreme environmental and overload

conditions that would be fatal to semi-conductors. They may also generate

less noise because of the slower switching saturable reactors. Perhaps

most important, they permit the summing of a number of input signals that

must remain electrically isolated. In instrumentation amplifiers,

magnetic-amplifier circuits still offer high , drift-free gain with this summing

feature. The development of magnetic-core transistor oscillators makes it

possible to supply ac power of practically any desired frequency for these

amplifiers, making them much smaller than they would be with

power-frequency excitation. Similar circuits have come into increasing use

in magnetometry where the unique direct transducing capability of the

magnetic amplifier puts it in a class by itself.

The magnetic-core transistor oscillator, which is capable of inverting dc to

ac up to about 100 kilohertz and by rectification can convert a single

primary dc power source at high efficiency to several independent

conductively isolated dc voltage supplies, today has all of the engineering

prominence that magnetic amplifiers once enjoyed. Many of these newer

circuits are, in fact, regulated and timed by magnetic-amplifier principles.

The history and present state of the art in magnetic amplifiers is

documented in the proceedings of the Conference on Non-linear

Magnetics and Magnetic Amplifiers, and the more recent IEEE

Transactions on Magnetics.

November 21, 2020 7:06 PM


Principle of the Magnetic Amplifier


The elementary principle of magnetic amplification can be conveniently

represented in terms of a flux-actuated switch in series with a load.

The magnetic material is characterized by the nearly rectangular

hysteresis loop of Fig.1 . In this figure, the narrow hysteresis loop

corresponds to the loop measured at dc and the wider loop is that

measured at the power supply frequency. It should be noted that this

dynamic loop widens with increasing frequency. Fig.2 shows the dc

hysteresis loops corresponding to the three of the materials listed in

Table 1.

Figure 3 shows a winding on a core in series with a resistor representing

the load . At the beginning of a positive half-cycle of the supply voltage,

the core is in some initial flux state Φ0. Essentially all of the supply

voltage is impressed on the core winding until the flux in the core reaches

saturation. In saturation, the core becomes a very low impedance and

practically all of the supply voltage appears across the resistor. This

situation is diagrammed in Fig. 4A for a sinusoidal supply voltage and in

Fig. 4B for a square-wave supply voltage. The lower portions of the

diagrams show that the switching of the supply voltage from the core to

the resistor becomes perfect when the width of the hysteresis loop is zero.

In practical designs, the choice of power supply voltage and frequency ,

core size, winding , and load impedance is subject to the constraints of the

problem. To approximate the above-mentioned ideal conditions is often the

main object of the design.

Fig.5 shows integrals of portions of the supply-voltage integral in analytical

form. It is clear from the figure that the average voltage applied to the load

is a function of the switching angle a, which in turn depends on the initial

flux Φ0. The half-cycle average of the load voltage is expressed

in terms of Φ0 for the sine-wave and square-wave cases as follows :

Sine Wave :


Vr = (2/T) (E8/w)

   X (1+cosa)

(E8/w) ( 1 - cosa) = (E8/w) - NΦ0

cosa = Φ0m

Vr = (2/T) (E8/w)

   X [ 1 + (Φ0m) ]

Square Wave :


Vr = E8 [1 - (a/π)]

(T/2)E8(a/π) = N( Φm - Φ0)

a/π = 1/2 [ 1 - ( Φ0/ Φm) ]

Vr = E8/2 [ 1 + ( Φ0/ Φm ]

It is further obvious that in order for there to be no output, and no excess

flux capacity in the core (normal excitation), the flux linkage capacity of the

core must be set equal to the volt-second capacity of the power supply.

This results in the simple equations

E8 = BmAwN       (Sine Wave)

E8 = (2/π)Bm AwN   (Square Wave)

resulting the peak value of the supply voltage, the maximum flux density of

the core (in webers/meter2), the material cross-section (in meters2), the

angular frequency, and the number of turns..

Correspondingly, the exciting cu""ent for a given coercive force Fe in

ampere-turns is ix = Fe/N = Hel/N, where He is in ampere-turns/meter

and l is the mean length of the magnetic path in the core in meters.

These equations in CGS units become

E8 = BmAwN X 10-8      (Sine Wave)

E8 = (2/π)BmAwN X 10-8  (Square Wave)

where Bm -gauss, A = cm2, E8 = volts (peak), and N = turns.

Im = 0.794Hel/N

where He = oersteds, l -em, and I = amperes.

Although the above discussion contains most of the ideas basic to magnetic

amplifiers, no mention has been made of how Φ0 is related to the control signal.

Further , note that at the end of the half-cycle, Φ0 is at saturation. Thus the

core must be reset to Φ0 in the second half-cycle . If a similar voltage is to be

applied to the load in the second half-cycle, a second core must be included

in the circuit. Such resetting and output problems are responsible for the

variety of amplifier circuit configuration that have been used.

November 21, 2020 7:08 PM


Amplifier Configurations


The amplifier configuration is arranged with two considerations in mind.

One is the method of control, and the other is the type of output desired.

As seen from the discussion above, a core that is brought to saturation

and is gating power to a load on a positive half-cycle must be reset to its

initial state if it is to repeat this function on the next positive half-cycle.

On the other hand it is usually desirable to deliver power to the load on

both half-cycles. Thus a second core will be gating power to the load

during the half-cycle in which the first core is being reset. Since the

increment in flux linkage in the two cores is equal in the steady state, the

core driven from the power supply can be used to reset the second core

by transformer action through the control circuit. In single-phase circuits

the roles of the cores interchange during alternate half-cycles. The use of

one core to reset the other is fundamental to most amplifier configurations.

Several of the most common configurations are shown in Fig. 6. Figure 6A is

the series-connected amplifier, sometimes called the transductor. It has been

extensively analyzed [3, 9, 10] and is commonly used to measure large direct

currents in electro-chemical and power applications [ 11] . The details of the

circuit operation are complicated but, in essence, at most one core is

saturated at a time, gating power to the load. During this interval, the second

(unsaturated) core, which has a very small coercive force, must therefore

maintain the condition NLiL - Ncic = Fc, the dynamic coercive

force of the unsaturated core. The control current ic has the same waveform

as the load current iL but has the same polarity on each half-cycle. Thus,

the rectified average values of the load current and the control current IL and Ic

are related by the turns ratio.

     IL = (Nc/NL)Ic + (1/NL)Fc

a linear function with a constant offset as shown in Fig. 7A. In practice, the

linearity of this function can be kept within about 0.1 percent, which makes

it very useful for instrumentation.

The circuit in Fig. 6B is characterized by parallel-connected saturable reactors,

so that the load current does not have to flow through an unsaturated core.

Thus, since the resetting core is primarily transformer driven through the

control circuit by the power-gating core, only the exciting current for the

resetting core must be carried in the control circuit. In the steady state, the

flux linkages coming from the winding on the gating core must equal the flux

linkages delivered to the resetting core. With zero control voltage, the two

flux linkages will differ by the integral of icrc over the half cycle.

The function of the control voltage is to offset this voltage drop to make the

two flux linkages equal at the desired output level. The diodes decouple the

cores from the power supply during their resetting half-cycles.

When the amplifier is delivering full output, there is essentially no flux excursion

in the gating core. It therefore does not drive the resetting core. Since the

resetting core must not be reset under these conditions, the control current

must be just below the coercive direct current for the core. At zero output, the

gating core drives the resetting core at normal power voltage, resulting in a

control current equal to the normal power-frequency coercive current. Full control

of the amplifier is obtained over a control-current range equal to the widening of

the hysteresis loop from dc to the power-frequency loop, divided of course by the

control-winding turns. The resulting control characteristic is shown in Fig. 7B, with

reference to Fig. 1. Again, there is a minimum output corresponding to the exciting

current for the gating core. Also, the control current and voltage are automatically

rectified because of the half-cycle symmetry of the circuit as seen from the control

terminals. The modification shown in Fig. 6C delivers dc to the load.

A fourth configuration (Fig. 6D) used for very small-signal amplifiers and

magnetometers [12, 13 ] takes advantage of transformer coupling of the

output to eliminate the residual exciting-current component found in the

other circuits. The fundamental component of the induced voltage is

canceled out and, at input currents other than zero, there is a

second-harmonic component in the output proportional to the input current.

The phase of this output reverses with the input-current polarity. Other

examples of high-sensitivity amplifiers can be found in the literature [14].

For many power applications, 3-phase amplifiers are preferred for the usual

reasons. The output is much easier to filter when dc is required [15].

Examples of parametric amplifiers and microwave magnetic amplifiers can

be found in the literature.

November 21, 2020 7:09 PM


Multi-stage Amplifiers


Because of the bilateral characteristics of magnetic amplifiers, multi-stage

amplifiers are difficult to analyze . In addition, their properties as measured

experimentally are technically unattractive and they are difficult to design

even by empirical techniques except when the coupling-circuit impedance

isolates the circuits. In this case, gain and frequency response are usually

sacrificed . With the advent of a highly developed transistor technology, it

is rarely necessary to design multi-stage amplifiers. When it is necessary,

the problem is treated as though the first stage were driving any other

R-L or R-L-C isolated dc load. If this approach does not yield adequate

performance, the designer must resort to less well documented techniques

or initiate a new approach to solving the problem.

November 21, 2020 7:09 PM


Bias and Feedback


Bias and feedback windings look and act exactly like the control

windings shown in Fig. 6. Problems in design arise because these

windings couple induced voltages from the cores into the bias and

feedback circuits. Thus, the circuits are not simply unilateral and

passive [16]. If these circuits are isolated by suitable R-L networks,

then the currents can be treated as though they were additive.

In that case, the bias winding simply translates the origin of the

control current in the direction of the bias.

The output current or voltage can be rectified and passed through simple

R, R-L, or R-L-C networks and the derived current put into a feedback

winding. In such a case, feedback is treated as it is in any other amplifier.

It can linearize the amplifier successfully if the range of output is lowered.

If the amplifier is used as a power device and its range of output is fixed

by performance specifications , feedback is of no help unless compensating

non-linearity can be inserted in other amplifying stages. Feedback in such

cases is useful primarily to lower output or impedance of the amplifier.

November 21, 2020 7:10 PM


Frequency Response


Analysis has shown that the voltage-gain bandwidth procut [17] is :

  Gv (bw) = 4f/N  (series-connected amplifier, Fig. 6A)

  Gv (bw) = 2f/N  (self-saturating amplifier, Fig. 6B)

when f is thee frequency and N is the turns ration Nc/Ng. These relations

show again the advantage of high-frequency power supplies. They also suggest

that if a design is adjusted to increase gain, the bandwidth (frequency response)

will be reduced unless the turns ratios are adjusted to raise the gain-bandwidth

product. High-gain amplifiers can be expected to have a bandwidth of about

one-tenth of the carrier frequency, which is frequently sufficient in instrumentation

applications. In signal-processing applications, it is preferable to use several

stages of low-gain wide-band amplification since the gains multiply and the

bandwidths go down more or less additively. It is in this area that magnetic

amplifiers have been largely replaced by semiconductor circuits.

November 21, 2020 7:11 PM


Choice of Core Materials (Part I)


A variety of core materials can be chosen for magnetic amplifiers.

They can be obtained in the form of tape-wound cores, laminations,

and encapsulated tape cores cut into tow mating C-shaped pieces.

The latter configurations permit the use of simple inexpensive

lathe-wound windings which can be assembled on the core. The

cut-C core configuration maintains the rolling direction of the tape

along the primary magnetic path. The laminations are stamped out

of continuous strip such that part of the magnetic path is along the

direction of rolling and part is perpendicular to it. Since most

good-quality strip is anisotropic, the resulting characteristics of the

core are not as good as they would be in the tape-wound

configuration, which has the best magnetic qualities. As a result,

only the lower-cost lower-quality magnetic materials are widely

used in other than the tape-wound configuration. In addition to

differences in processing and in the cost of raw materials, the

above manufacturing considerations significantly contribute to the

economic basis for choosing core materials. Cost is the dominant

consideration in most amplifier designs. There are, however,

extreme cases where only the highest-quality material can meet

the technical specifications.

In general, the large, heavy, power-control applications make use of

the least expensive materials in the least expensive configuration. In

one important sense, they are sometimes technically superior as well.

First, because of low remanence of the core, using these materials in

a self-saturating configuration (Fig. 6B, 6C) results in a control

characteristic which crosses the control-current axis as shown dotted

in Fig. 7B. This automatically biases the amplifier near the desired

operating point. In addition, the lack of squareness also causes fairly

slow switching at the firing time of the power-gating core. The result

is much less noise than found in the more objectionable gas tubes,

semiconductors, and square-loop core circuits.

November 21, 2020 7:11 PM


Choice of Core Materials (Part 2)


Table 1 lists the core materials available in tape-wound cores from most

of the core manufacturers, plus a guide to their principal applications. An

approximate cost ratio is given for 2-mil tape in a core of about 3 inches

in diameter. This indicates the economic advantage of using materials no

better than necessary . In lamination form, the cost per pound of the

material is lower by about a factor of 5.

Table 2 summarizes the technical properties of these materials. Note that

many of their properties are given in terms of the IEEE standard referenced

in AIEE Standards paper II-432 [18]. The use of these standards in circuit

design and component specification is highly recommended.

The control-current range for self-saturating amplifiers, as indicated in Fig. 7B,

can be estimated by referring to the difference between the dc and 400-hertz

coercive-force columns in Table 2. This value must be multiplied by about 0.8

times the mean magnetic path length of the core in centimeters to obtain

control ampere-turns. The values are for 400 hertz and must be corrected

experimentally for other frequencies. Studies of the properties of materials

and their influence on circuits covering a wide range of frequencies,

temperatures, and materials can be found in the published literature [19, 20].

For more-specific and detailed design information, the designer should use the

referenced literature. Also, several core-materials manufacturers have prepared

excellent booklets containing all the essential tables and nomo-grams for

designing magnetic-core circuits.

November 21, 2020 7:12 PM


Other Design Considerations


The basic design calculations , as discussed above, pick the core size and

number of turns to fit the frequency and voltage. For a given magnetic

material, a larger core requires fewer turns to support a given voltage at

a given frequency. The number of turns varies as the inverse of the

cross-section. From this fact alone, exciting current rises linearly with

cross-section. There is also a linear relation between the exciting current

and the mean magnetic path length for a fixed H. Thus, the exciting

current is proportional to the volume of the material.

As the frequency rises, it is possible to use a smaller core for a fixed

voltage. Comparing a 400-hertz design with a 60-hertz design, for

example, the cores in the 400-hertz unit would be smaller by about

a factor of 7. Since this is true for transformers and inductors as well,

high-frequency power supplies are commonly found on aircraft where

space and weight are important. The higher supply frequency also

puts the carrier farther above the modulation-signal frequency

spectrum, making it easier to recover the signal.

Since in many small-signal applications it is not necessary to have a

large supply voltage, it is common to change available dc signals to

square-wave ac voltages in the range from 5 to 25 kHz and higher.

This means very small cores and very compact, sensitive amplifiers,

a combination that often yields better performance in low-noise

low-signal applications than semiconductor circuits.

November 21, 2020 7:13 PM


Tables and Figures


November 21, 2020 7:13 PM


References and Literature plus Websites' Links


Literature :


[ 01 ] : Institute of Electrical and Electronics Engineers, 345 East 47th Street ,

      New York , New York 10017, before 1965. Many papers published in

      Communication and Electronics as well.

[ 02 ] : IEEE Transactions on Magnetics, Vol. MAG-1, No.1; March 1965.

[ 03 ] : H.F. Storm, "Magnetic Amplifiers", John Wiley & Sons, Inc., New York; 1955.

[ 04 ] : G.E. Lynn, T.J. Pula, J.F. Ringelman, and F.G. Timmel, "Self-Saturating

      Magnetic Amplifier Analysis", McGraw-Hill Book Co., Inc., New York; 1960.

[ 05 ] : D.L. Lafuze, "Magnetic Amplifier Analysis", John Wiley & Sons , Inc.,

      New York; 1962.

[ 06 ] : W.A. Geyger, "Magnetic Amplifier Circuits", McGraw-Hill Book Co., Inc.,

      New York; 1957.

[ 07 ] : R.C. Barker, "Non-linear Magnetics", Electro-Technology, Science and

      Engineering Series 51; March 1963.

[ 08 ] : Each proceedings is published as a special issue of the Journal of

      Applied Physics in the spring of each year.

[ 09 ] : R.C. Barker, "The Series Magnetic Amplifier, Parts I and II",

      Communication and Electronics, pp. 819--831; January 1957.

[ 10 ] : A.G. Milnes, "Transductors and Magnetic Amplifiers", Macmillan Co., Ltd.,

      London ; 1957.

[ 11 ] : A.B. Rosensyein, "1600 000-Ampere High-Speed Magnetic-Amplifier

      Design", AIEE Transactions, Vol. 74, Part I, pp. 90--97; 1955.

[ 12 ] : D.I. Gordon, R.H. Lundsten, and R.A. Chiarodo, "Factors Affecting the

      Sensitivity of Gamma-Level Ring-Core Magnetometers", IEEE

      Transactions on Magnetics, Vol. MAG-1, No. 4, pp. 330--337;

      December 1965.

[ 13 ] : R.C. Barker, "On the Analysis of Second-Harmonic Modulators", IEEE

      Transactions on Magnetics, Vol. MAG-1, No.4, pp. 337--341;

      December 1965. See also S. Ohteru and H. Kobayashi, "A New Type

      Magnetic Modulator", IEEE Transactions on Magnetics, Vol. MAG-1,

      No. 1, pp. 56--62; March 1965.

[ 14 ] : H.E. Darling, "New Magnetic Amplifier Improves EMF to Current Converter",

      IEEE Transactions on Magnetics, Vol. MAG-3, No. 3, pp. 365--369;

      September 1967.

[ 15 ] : H.C. Bourne , Jr., and T. Kusuda, "A Three-Phase Magnetic Amplifier : Part II

      Experimental Results", IEEE Transactions on Magnetics, Vol. MAG-3,

      No. 1, pp. 17--22; March 1967.

[ 16 ] : L.A. Finzi and J.J. Suozzi, "On the Feedback in Magnetic Amplifiers : Part II ,

      Combined Magnetic and Electric Feedbacks", AIEE Transactions, Vol. 78,

      Part I , pp. 136--141; 1959.

[ 17 ] : R.C. Barker and G.M. Northrop, "Some Frequency Response Measurements

      on Magnetic Amplifiers", Proceedings of the National Electronics Conference,

      Vol. 12, pp. 444---453; 1956.

[ 18 ] : AIEE Standards Paper No. 432, obtainable from IEEE Headquarters [1].

[ 19 ] : M. Pasnak and R. Lundsten, "effects of Ultra-high Temperature on Magnetic

      Properties of Core Materials", AIEE Transactions, Vol. 78, Part I,

      pp. 1033--1039; 1959.

[ 20 ] : C.E. Ward and M.F. Littman, "Relation of D-C Magnetic Properties of Oriented

      48-Percent Nickel-Iron to Magnetic-Amplifier Performance", AIEE Transactions,

      Vol. 74, Part I, pp. 422--427; 1955.

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