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.
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 = Φ0/Φm
Vr = (2/T) (E8/w)
X [ 1 + (Φ0/Φm) ]
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.
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.
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.
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.
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.
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.
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.
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.
References and Literature plus Websites' Links
=======================================================
https://en.wikipedia.org/wiki/List_of_electromagnetism_equations
https://en.wikipedia.org/wiki/Magnetic_flux
https://en.wikipedia.org/wiki/Magnetic_amplifier
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.