The Winding Capacitances in Magnetic

Amplifiers

INGE JOHANSEN ASSOCIATE MEMBER AIEE

THE INFLUENCE of winding capaci-tance upon the performance of mag-

netic amplifiers is a matter of some con-cern. Although no systematic investiga-tion has appeared in the literature, it is generally accepted in the art that such capacitances may be responsible for cer-tain peculiarities in the transfer character-istic of the self-saturating magnetic ampli-fier. In this paper a lumped equivalent winding capacitance, connected across the winding terminals, is defined. An approximate, empirical formula is given for it for toroidal core windings. The concept of this equivalent capacitance is shown to be of some value in explaining the experimentally observed behavior of certain types of magnetic amplifiers.

The Equivalent Winding Capacitance

I t is not obvious that the distributed capacitances of a winding can be replaced by an equivalent, lumped capacitance. In most cases the capacitance between turns within one winding is the most im-portant term. The capacitances between different windings and from winding to ground or to the core will be treated later.

To start the analysis, a winding with uniform distributed turn-to-turn capaci-tance is considered. In Fig. 1 (A) each turn has the same capacitance to its two adjacent turns, but no capacitive interac-tion with other turns. When a voltage is induced in such a core winding, it is ob-vious that both the inductive network and the capacitive network separately will

Paper 59-776, recommended by the AIEE Magnetic Amplifiers Committee and approved by the AIEE Technical Operations Department for presentation at the AIEE Summer and Pacific General Meeting and Air Transportation Conference, Seattle, Wash., June 21-26, 1959. Manuscript submitted Novem-ber 3, 1958; made available for printing April 9, 1959. INGE JOHANSBN is with the Technical University of Norway, Trondheim, Norway. This work has been supported in part by the U. S· Office of Naval Research, and was performed while the author was a visiting lecturer at the Carnegie Institute of Technology, Pittsburgh, Pa., on a grant from the Technical University of Norway. The author wishes to acknowledge the help of R. W. Roberts of the Westinghouse Electric Corporation in providing many of the wound cores tested, and the guidance and useful suggestions of Prof. L. A. Finzi.

give the same linear voltage distribution along the winding. The networks can then be separated as shown in Fig. 1(B). This is easily justified by the fact that there is no voltage difference between the points A' and A " and it is accordingly of no importance whether these points are connected or not. I t is then possible to define a lumped capacitance that is equivalent to this idealized internal wind-ing capacitance. This statement is valid whenever the capacitive network yields a linear voltage distribution.

Actually, the capacitive network of toroidal windings is not so simple, and it is unlikely to give a linear voltage dis-tribution in itself. However, in magnetic amplifiers, the voltage distribution is dictated essentially by the magnetic flux, which approximately induces the same voltage in all turns. The winding capaci-tance, important as it may be, is a second order effect as far as the voltage distri-bution is concerned, and the assumption of a linear voltage distribution remains ac-cordingly acceptable for further purposes in this paper. The equivalent winding capacitance for such a voltage distribution is defined here as a lumped capacitance across the terminals of the winding, affect-ing the core mmf (magnetomotive force) in an identical way as the actual dis-tributed turn-to-turn capacitances do.

In Fig. 2 some of the turn-to-turn capacitances are indicated. Between the turns n and m there is a capacitance Cn,m

and a voltage e(n—m)/N, where N is the total number of turns, and e is the voltage across the terminals. If the terminal voltage varies by an amount Ae in the time interval Ä/, the elementary capaci-tance Cn,m causes a contribution to the core mmf, which is expressed by

A(AF) = (n-m)Cn,m n—m Ae

(1) N At

The contribution of the capacitances of all the turns to the turn n is

1 Ae V ^ AF==ÄTT<? An-m)*Cn.m (2)

Finally, the total mmf, F, contributed by the turn-to-turn capacitances of the whole winding, is obtained by extending

the same consideratinn to all the turns, that is, summing n from 1 to N. In this process all the turn-to-turn capacitances are counted twice, and the final expression for the mmf is

1 ÄÝ?×~^ F= > (n-m)2Cn,i

2N AiL^T (3)

A lumped capacitance, Ceq> across the winding terminals will have the same effect if

'=ÜÓ(*-m)2Cn,m (4)

From equation 4 theoretical values of Ceq could be obtained if the values of Cn,m were known. For common toroidal windings this is not the case. Even if the turns were wound in an orderly way, the capacitance Cn,m would be a rather com-plicated function of wire and core dimen-sions, and of m and n. In addition, the turns are wound randomly, and there-fore equation 4 is not useful in obtaining a quantitative expression. Nevertheless, some interesting conclusions can be drawn, as shown in the following.

As a theoretical example, the case of a constant value for Cnm for all values of n and m is considered first. For this case equation 4 shows that Ceq will increase approximately proportional to the num-ber of turns in the winding. As another extreme, the case when each turn has a capacitance only to its two adjacent turns is considered. Here the use of equation 4 shows that Ceq is inversely proportional to the number of turns. In the actual case of randomly wound turns, Ceq is likely

CO

Fig. 1 . W i n d i n g with uniform distributed capacitance

Fig. 2 . Elementary capacitances in a winding

702 Johansen—Winding Capacitances in Magnetic Amplifiers N O V E M B E R 1959

Fig. 4. The measured equivalent capacitance versus the inner surface

of the winding

pp\-

' 3 4

Fig. 3. Fundamental capacitances between two windings on the core

to be between those two theoretical ex-tremes. Hence it is not surprising that actual measurements yield values of Ceg

that are practically independent of the total number of turns.

It can be shown from equation 4 that Ceg is also equivalent to the distributed capacitances in terms of storage of energy. This is a more general property than the one implied by the original definition based on identities of core mmf's.

Equation 4 has been developed under the assumption that the winding has open terminals, but it is recognized that the same equivalent capacitance exists when an impedance is connected across the terminals. In this case the voltage dis-tribution may become less linear, but experiments show that the assumption remains adequate for practical purposes. One interesting conclusion can be drawn at this point. The influence of the winding capacitance upon the core mmf will decrease with decreasing impedance connected at its terminals.

The foregoing discussion has been con-cerned with cores with one winding only. In practical magnetic amplifier circuitry, the influence of the other windings has to be considered. In Fig. 3 there are two windings on the core and the funda-mental winding capacitances are shown. The presence of the second winding has influence in more than one way. To some extent it increases the turn-to-turn capacitances of the original winding, I of Fig. 3, in the same way as a metallic screen would do. The situation is com-plicated further by the fact that a volt-age change in the windings will cause a current to flow through parts of both windings over the capacitances Cn and C24. The mmf which results is due to currents in both of the windings. Thus, it is not enough to ascribe an equivalent capacitance to each winding, but the inter-winding capacitances should also be con-sidered. For the sake of obtaining useful results the analysis is limited to the case where winding I has many more turns than winding II. In that case the mmf contribution due to the current between 3 and 4, i.e., the part of the current flow-

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ing over G3 and C24, can be neglected. The capacitance between two turns, C34, will next be considered. Let N\ be the number of turns between 1 and 2, and N2 the number of turns between 3 and 4. The capacitance C34 will appear to be k (N2/NI)2CM in parallel with G2, as it will be transformed to winding I with the square of the ratio of the number of turns. The factor k depends on the mutual inductance between the windings. With the restriction N2«NU the term k(N2/-NI)2CM may be neglected in comparison to C12. Thus, the main influence of wind-ing II is the same as that of a metallic screen, and the equivalent capacitance of winding I depends only on its own de-sign and on the location of the second winding. It should also be clear that the measured capacitance of a winding with few turns depends more on the other windings on the core than on its own design.

In the following only cases where Í2«Í÷ are considered. In the cases when the winding capacitance is impor-tant this will very often be true and the restriction will not limit the practical value of the derived results.

I t will now be clearly shown that the winding with many turns is the important one. The empirical formula equation 6, presented later, shows that the value of Ceq for a given core is fairly independent of the number of turns. Ascribing the same capacitance Cto two different wind-ings 1 and 2 on the same core with number of turns respectively N\ and N2, it is easily shown that the contribution to the mmf from the capacitances is respectively CNJde'/dt and CN2

2de'/dt, where e' is the voltage per turn. Thus the quantity CN2 is the significant one, and only the winding with the larger number of turns has to be considered.

A simple criterion can be suggested a t this point to determine whether the wind-

ing capacitance is important or not in a practical design. Evidently this is the case when the mmf caused by Ceg is of the same order of magnitude as the change of signal ampere-turns, NAic, required to control the amplifier over its whole range of operation. In order to make a rough estimate of the mmf caused by Ceq, it is evaluated as the product of the turns, N, times the current that flows in Ceq with the gate-voltage impressed on it. This implies that this current is discharged through the winding and the mmf thus produced will be added to the control-ampere turns. If the frequency is ù and the amplitude of the voltage per turn is E, then the maximum value of the capaci-tive ampere-turns is ùÏÍ2Å. If the ratio (uCN2E/NAic is about 1 or larger, the consideration of the influence of the winding capacitance is justified.

Now it is noticed that the quantity CE/coNAic can be regarded as fairly con-stant for a given core, and thus

<*CN*E CE NAic caNAic

(ùÍ)* = Ê-(ùÍ)2 (5)

This shows that the influence of winding capacitance increases roughly with the square of the product of the gate-volt-age frequency and the number of turns in a given circuit.

Hitherto, the analysis has been con-cerned with the "internal" capacitance. The presence of other windings has been regarded to be of importance only to the extent that they increase the capacitance in the winding under consideration. However, the interwinding capacitances may also be of importance. This is so because each winding is connected to external networks, and current can flow in a circuit consisting of the inter-winding capacitance, the windings them-selves, and the external networks. A fur-ther discussion of this point is omitted here.

N O V E M B E R 1959 Johansen—Winding Capacitances in Magnetic Amplifiers 703

Fig. 5. Amplifier circuits that are examined

A—The half-wave amplifier B—The doubler circuit C—The bridge circuit

An Empirical Formula for the Equivalent Winding Capacitance

It has been stated already that an analytic expression for the equivalent winding capacitance is difficult to derive, and that its usefulness is doubtful. Therefore, attempts have been made to obtain an empirical expression. This has met reasonable success, when the accuracy requirements were not too high.

The measurements leading to the em-pirical expression were performed accord-ing to a method given by Terman.* With this method the condition of linear volt-age distribution is preserved. The capacitance was measured with the core present, and the core was driven into saturation by an additional d-c source or it was short-circuited.

The empirical formula derived is based on measurements on windings with cores having inner diameter from 0.5 inch up to 2 inches. The wire was double enamel insulated, and the range of wire size was from No. 30 to No. 42, Awg (American wire gage) size. The formula is valid within the given range when the other windings have few turns, i.e., up to 20% to 30% of the turns of the winding con-sidered. The radial thicknesses were at least equal to 25% of the available window space. A number of measurements yielded the astonishing simple relation that the capacitance is proportional to the inner surface of the winding, and is fairly independent of the number of turns and of the thickness of the wire. In Fig. 4 the equivalent winding capacitance Ceq is plotted versus the inner surface of the winding. I t is seen that this capaci-tance may be expressed as

Ceq = a · A ìì/ (micromicrofarad) (6)

where A is the inner surface of the winding in cm2, and a is a constant within the range of 3.2 to 5.8. Hence, the equation has a certain ambiguity of ±30%, but

this is quite good considering the fact that the windings in question were wound randomly.

Some comments can be made on the use of equation 6. In some cases the winding is wound randomly, but without overlapping. That means that there is a spacing between the beginning and the end of the winding. This reduces the capacitance somewhat. Either case is within the limit of equation 6, but account of this effect might be taken by choosing the value of the constant a within the over-all range stated, so that an accuracy better than =±=30% can be achieved.

I t is stated above that the winding has to be of a certain radial thickness. This is especially important when thin wires are used, as, No. 37 to No. 42. In such cases the winding capacitance will increase with decreasing thickness of the winding, and perhaps a better empirical expression should be sought that also accounts for radial thickness. In this work the number of measurements was too small to justify an attempt in this direc-tion, but this effect should also be considered when choosing a within the range. On the other hand the position of the winding (outer or inner winding) has small effect on a.

The surprisingly simple equation 6 needs some analytical justification. The fact that Ceg is approximately independent of the number of turns has been discussed already. The fact that the wire size is un-important can be explained in part by the fact that the ratio between net copper diameter and total diameter varies within narrow limits, between 0.7 and 0.8 for double enamel insulated copper wire in the range considered. Also, it can be understood qualitatively that the capaci-tance is proportional to some surface of the winding. This surface is equal to the length of a turn multiplied by the mean length of the winding. I t is evident that the winding capacitance is proportional to the length of a turn, and an increase in the mean length of the winding will un-doubtedly increase the capacitive inter-action between the turns, which means an increase in the winding capacitance.

Special Types of Windings

Only randomly wound windings have been discussed above. In some cases special windings are used to minimize voltages between adjacent layers and also to reduce the winding capacitance. The section winding is a type of such windings. Here the winding is divided in sections that follow progressively along the core, while each section is wound randomly.

0 2 4 6 CONTROL AMPERE-TURNS

Fig. 6. Transfer characteristics for the half-wave ampli-fier. Eg = 35 volts, f = 3.6 kc. I:NC = 5,000 turns; Rc = 5.25 megohms; CeqMOO/i/if. ll:Nc = 500 turns; Rc = 52.5 kilohms; Ceq = 100Mjuf. llhNc = 500 turns; Rc = 52.5 kilohms; C =

10,000 μμί

704 Johansen—Winding Capacitances in Magnetic Amplifiers N O V E M B E R 1959

a. b. c. d. CWINDING TERMINALS} .GATEWINDING

-CONTROL WINDINGS

Fig. 7. Cross section of the core and windings

Equation 6 can be used for each section. The resultant capacitance may be ob-tained as the series connection of the capacitances of the various sections. Hence, it appears that Ceq decreases in-versely to the square of the number of sections. This is an approximate reason-ing, however, because the capacitive inter-action between the different sections has not been taken into account. The pres-ence of the core and neighboring windings will mainly provide this coupling, and when the winding is divided into many sections, this will be the dominating factor. For this reason dividing the wind-ing into more than 4 to 6 sections is of no value. If further decrease in the capaci-tance is desired, it is necessary to increase the distance of this winding from the core and from the other windings, at the same time as the number of sections is in-creased.

Experiments on Magnetic Amplifiers

The purpose of this section is to show that the distributed winding capacitance can be replaced by an equivalent lumped capacitance, as defined in the first section, in the study of magnetic amplifier be-havior. The experiments are based on the fact that two magnetic amplifiers that are identical in other respects, will be-have in the same way when the product CN2 is the same. If the concept of an equivalent capacitance is applicable, this will be the case regardless of whether the winding has distributed capacitance (C= CeQ) or whether it has little or no capaci-tance of its own, but is shunted by a capacitor at its terminals. Transfer characteristics of a magnetic amplifier circuit have been measured, where the winding capacitance was significant. This transfer characteristic is later re-ferred to as characteristic I. The equiv-alent winding capacitance, Ceqh was measured, and the product, CeffiiVi2, was calculated. Then the same amplifier cir-cuit was duplicated with a winding having a fewer number of turns, N2) so low that its equivalent capacitance (Ceg2= Cegi) had a negligible effect on the transfer char-

acteristic. The corresponding character-istic is referred to later as transfer char-acteristic II . Finally an external capaci-tance, C, was connected across the termi-nals of this second amplifier, and its value was chosen such that CN2

2=CeqNi2. The corresponding transfer characteristic is called characteristic III . Now if the predictions made in this paper are valid, transfer characteristics I and III should be fairly equal.

The influence of the winding capaci-tance, actual or simulated, upon the amplifier behavior can be seen by com-paring I or I I I to II . In all cases the control winding was chosen as the wind-ing which gives rise to the capacitive effects, since the number of turns could be changed easily without affecting the other parameters in the circuit.

Transfer characteristics I, II, and III were measured for a number of cases. The types of magnetic amplifier circuits that are examined are the half-wave amplifier, the doubler, and the bridge cir-cuit; see Fig. 5. Fig. 6 shows the trans-fer characteristics I, II, and III for the half-wave amplifier. In this case it was difficult to obtain a truly smooth control current. However, care was taken to use the same value of Rc/Nc

2 in all meas-urements. It is seen that there is a good agreement between I and III, as pre-dicted, and that the winding capacitance has a marked influence, as shown by the large difference between I and II. The winding capacitance causes a decrease in

the slope of the transfer characteristic and a shift to the right. Some care was re-quired in order to obtain good agreement between I and III on Fig. 6. Fig. 7 shows a cross section of the core and indicates the location of the two windings. When the control winding is randomly wound, as in this case, the turns with about the same potential as the terminal c will be distributed around the outer surface of the winding, and thus form a screen against the gate winding. When terminal c is connected to the grounded terminal of the signal source a capacitive interaction be-tween the two windings is essentially avoided. The way the gate winding is connected is not very important, because the rate of change of the voltage is small compared to that in the control winding. The influence of the interwinding capaci-tance may be seen by interchanging the terminals c and d. This influence is by no means unimportant but can in many cases be eliminated.

Fig. 8 shows the transfer characteristics I, II, and III of the bridge circuit with low constraint. To- obtain good agree-ment between I and III, the terminals A and B in Fig. 5(C) had to correspond to winding terminal c in Fig. 7. Good re-sults are obtained since in the low con-straint case both terminals have a con-stant potential in comparison to the in-duced voltages in the control windings. Transfer characteristic IV in Fig. 8 demonstrates the importance of the inter-winding capacitance. In this case the

Fig. 8. Transfer characteristics for the bridge circuit. Eg = 35 volts, f = 3.6 kc. I:NC = 5,000 turns; Rc^O; Ceq = 100ììß. ll:Nc = 500 turns; Re—0; Ceq = 100 ììß. lll:Nc = 500 turns; Rc~0 ;

C = 10,000 μμ\. IV: Identical to I, but the terminals on the control winding

are interchanged

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N O V E M B E R 1959 Johansen—Winding Capacitances in Magnetic Amplifiers 705

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Fig. 9. Transfer characteristics of the doubler circuit, as for Fig. 6

The same data Fig. 10. Transfer characteristics of the bridge circuit, as for Fig. 6

The same data

terminals were interchanged for both control windings. The transfer char-acteristics of the doubler and the center tap are quite similar to that of bridge cir-cuit for the low constraint case.

Figs. 9 and 10 show the transfer char-acteristics I, II, and II I of the doubler

and of the bridge circuit for a high con-straint case. In all cases Rc/Nc

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have a constant potential in the high constraint case, and to avoid interwinding capacitive interaction a constant potential on each of the control windings would be required. However, in spite of the in-fluence of interwinding capacitances, it seems that the internal winding capaci-tance is basically the most important. Figs. 9 and 10 show that the character-istics I and III have the same general be-havior, although the quantitative agree-ment is not good. The center-tap circuit

-0 .6 -0 .4 -0.2 0 0.2 0 4 0.6 CONTROL AMPERE-TURNS

Fig. 11. Transfer characteristics for a doubler circuit where the control winding links both cores. l:Nc=30,000 turns, Rc=0, Ceq = 120 ììß. ll:Nc = 1,000 turns, Rc = 0,

Ceq = 120/Zjuf

Fig. 12. The load voltage er and the core voltage Nd^/dt in a half-wave amplifier

A—No influence from the winding capaci-tance

B—The winding capacitance has an important influence

706 Johansen—Winding Capacitances in Magnetic Amplifiers NOVEMBER 1959

has a transfer characteristic similar to that of the bridge circuit.

Fig. 11 shows the transfer character-istics I and II of a doubler circuit with a control winding linking both cores. The characteristics in this case are almost identical, and the winding capacitances have accordingly no influence. This is in agreement with the predictions made since the capacitance is connected across the signal source directly. Experiments show that the winding capacitance has no influence regardless of the impedance of the control circuit. The bridge, the doubler, and the center-tap circuits behave almost identically, provided the number of control turns is large.

No experimentation has been performed to check on the validity of the "equivalent capacitance" concept during transients. Really, the steady state in itself is a succession of transients and the use of the equivalent capacitance, at least in "slow transients," seems justifiable.

I t is not within the scope of this paper to describe why the winding capaci-tance has an influence on the behavior of magnetic amplifier circuits. Each cir-cuit has several modes of operation. Un-symmetrical and subharmonic modes have been found which are not easily understood. Only the operation of the half-wave amplifier is examined in the following.

Fig. 12 shows the voltage er across the load and the induced voltage ÍÜö/dt. In Fig. 12(A) the winding capacitance is of

minor importance, while it has a larger influence in Fig. 12(B). In case a the be-havior can be understood by the descrip-tion in reference 2. For case b the anal-ysis is started as the flux is descending from positive saturation. Limiting the case to resistive loads, the current in the gate-winding will be positive, and the voltage induced in the winding is slightly larger than the impressed voltage. Up to point a, where the gate-voltage is equal to the induced voltage in the gate winding, the winding capacitance is charged nega-tively from the gate voltage. At point a the rectifier blocks. Instead of following the path ab, which indicates the induced voltage in the core under constant mmf, as in Fig. 12(A), the core voltage will follow ac, as the winding capacitance will dis-charge and supply the core with addi-tional negative mmf. The area abc can simply be regarded as the contribution of the winding capacitance to the reset of the core. I t is noticed that the winding capacitance in this case causes a larger reset. The contribution from the capaci-tance is, however, dependent on the firing angle and of the induced core voltage under the corresponding constant mmf. A shift to the right and a change in the slope of the transfer characteristic, as ob-served in Fig. 6, may then be understood.

This explanation gives the key to the understanding of the bridge and the centertap circuit. The doubler behaves in an entirely different way, due to the un-blocking of the rectifiers during the reset

period. In amplifier circuits with low constraint the foregoing reasoning is not valid. Here it is surprising that the slope is almost constant regardless of the wind-ing capacitance, and the only influence is a shift in the transfer characteristic. No attempt has been made to explain this fact. I t suggests, however, that a lumped capacitance across one of the windings could replace a separate bias winding.

Conclusions

In this paper a lumped equivalent wind-ing capacitance Ceq has been defined. This definition has been limited to cases where the winding under consideration has a much larger number of turns than any other winding on the core. An empirical expression has been proposed for the winding capacitance which yields results accurate within ±30% or better.

Experiments show that in a number of cases the distributed capacitance has the same effect as an external shunt capaci-tance at the winding terminals. This en-hances the practical usefulness of the concept of Ceq.

References

1. RADIO ENGINEERS' HANDBOOK (book), F. E. Terman. McGraw-Hill Book Company, Inc., New York, N. Y., first edition, 1943, pp. 84-85, 922-23. 2. DYNAMIC CORE BEHAVIOR AND MAGNETIC AMPLIFIER PERFORMANCE, L. A. Finzi, D. L. Critchlow. AIEE Transactions, pt. I (Com-munication and Electronics), vol. 76, May 1957, pp. 229-40.

Capacitively Coupled Magnetic Amplifiers

H. WILLIAM COLLINS ASSOCIATE MEMBER AIEE

AMPLIFICATION of a-c signals with magnetic amplifiers is gen-

erally more difficult than d-camplification. The conventional full-wave circuits, such as the doubler circuit and the bridge cir-cuit, can yield high performance only by demodulating a-c signals and amplifying the resultant direct current. These cir-cuits remain, in effect, d-c amplifiers and suffer from several shortcomings. For example, the sensitivity is limited by the forward voltage drops of the demodulat-ing elements, the output is affected by d-c drifts of the control characteristics, and the component duplication and in-effeciencies of push-pull circuitry must be used to obtain phase sensitivity. The

work of Ramey has led to the develop-ment in recent years of a number of high-speed magnetic amplifiers of the half-wave type. These circuits can amplify a-c signals without demodulation, but they also have certain shortcomings. The power gain per stage is generally less than the gain of full-wave circuits, the amplifiers remain subject to the effect of zero drift caused by unbalance of com-ponent characteristics, and low-level sensitivity is particularly difficult to obtain. Geyger has shown that the effect of amplifier zero drift on a-c servomotors (or other frequency discriminating output elements) can be eliminated by operating half-wave circuits at a carrier frequency

several times the signal frequency.1

None of these circuits, though, entirely achieves the advantages relative to d-c amplification techniques which are asso-ciated with true a-c amplifiers.

If a magnetic amplifier is operated at a high-carrier frequency, its frequency re-sponse is extended so that it can amplify relatively low-frequency a-c signals with-out demodulation. After filtering the carrier-frequency pulses, the signal-fre-quency modulation can be capacitiviely coupled to the load. This magnetic-amplifier technique realizes the ad-vantages of a true a-c amplifier, namely:

Paper 59-785, recommended by the AIEE Mag-netic Amplifiers Committee and approved by the AIEE Technical Operations Department for presentation at the AIEE Summer and Pacific General Meeting and Air Transportation 'Confer-ence, Seattle, Wash., June 21-26, 1959. Manu-script submitted August 31, 1956; made available for printing April 14, 1959. H. WILLIAM COLLINS is with Crydom Laboratories, Inc., Garden Grove, Calif.

N O V E M B E R 1959 Collins—Capacitively Coupled Magnetic Amplifiers 707