US3262075A - Impedance matching transformer - Google Patents

Description

July 19, 1966 Filed Nov. v. 1961 A. F. PODELL July 19, 1966 A. F. PODELL 3,262,075`

IMPEDANCE MATCHING TRANSFORMER Filed Nov. '7. 1961 3 Sheets-Sheet 2 July 19, 1966 A. F. Pool-:LL 3,262,075

IMPEDANCE MATCHING TRANSFORMER Filed Nov. '7. 1961 3 Sheets-Sheet 3 United States Patent O 3,262,075 IMPEDANCE MATCHING TRANSFRMER Allen F. Podell, Wilton, Conn., assigner to Anzac Electronics, Inc., Cannondale, Conn., a corporation of Connecticut Filed Nov. 7, 1961, Ser. No. 150,697 19 Claims. (Cl. S33-32) The present invention relates to a transformer electrically designed in a novel fashion so as to provide an effective match with the impedances of the input and output circuits between which it is connected, even when those input and output impedances differ greatly.

Impedance matching is greatly desired, particularly in communication circuits and other circuits where a high degree of signal fidelity is required. However, the problem of how to make an effective impedance match, particularly where the impedances differ appreciably from one another, has long plagued the electrical art.

I have discovered that voltage and impedance transformation over awide range as high as the order of :1 can readily be accomplished wit-h a minimum amount of l-oss and circuit complication through the use of one or m-ore aut-otransformers the electrical design of which is novel, particularly insofar as the impedance relationship between adjacent turns of .the transformer is concerned. When that predetermined intenturn impedance relationship is achieved, the Ithus-produced transformer will effectively match input and output mpedances which vary greatly from one another, the transformer will have a very high coupling coefficient, and its distributed capacitance will be effectively zero. When viewed either from its input .or its output, the transformer will look, from an impedance point of View, like a properly electrically designed transmisison line.

Typical of systems where the transformer of the present invention is m-ost valuable, and ills a need not heretofore capable of being filled except Iby very complex circuitry, is a high frequency (4-2000 mega-cycles) communications circuit where filters are employed. The circuit proper may exhibit very high impedances on the order of hundreds of ohms, whereas filters, to exhibit high performance -at the frequencies involved, should have a low impedance, perhaps as low as 2() ohms. Through the use of the .present invention transformers can readily Abe designed which can be inserted into the circuit between the filter and its input and output circuits respectively and which will, in an impedance matching manner, step the high circuit impedance down to the low input impedance of the filter and step the low output impedance of the filter back up to the Ihigh circuit impedance. Another system where the transformer of the present invention is exceptionally effective is one in which the plate circuit output of one distributed amplifier is to be coupled tol the grid circuit input of a second distributed amplifier. The grid andplate circuits of such amplifiers have im-pedances which differ from one another by a factor of two or three. Such a mis-match precludes effective coupling. However, a transformer of the present invention interposed between the two circuits will permit effective and precise coupling thereof.

In accordance with the present invention a'transformer is produced in which the ratio of turns across which the inpu-t and output circuits are connected corresponds to the desired impedancetransformation ratio. The windings themselves are so designed that the impedance between any one turn and an adjacent operative turn conforms to a predetermined impedance relationship, the inter-turn impedances differing from turn to turn in accordance with that relationship. With the input applied across the first turn (at the low impedance end of the transformer) and the output taken across .all of the turns (at the high impedance end of the transformer), and where n is the number of consecutive operative turns in the transformer measured from one end thereof to the other in one rotative direction (m1 voltage transformation ratio), then for proper matching the impedance measured between the end of the last turn (at the high impedance end of the transformer) and the end of the turn which operatively precedes the last `turn should Ibe ZL/n, where ZL is usually the output impedance to be matched. The impedance measured between the next to the last turn and the second from the last turn should be one half of that value, the impedance between the second and third from the last turns should be one-third of that value, and so on. With this impedance relationship the transformer appears, Aboth from its input end and its output end, as a substantially lossless transmission line.

Where the desired voltage transformation is in whole integer multiples, a single autotransfonmer made according to the present invention, having an appropriate number of turns, and with the input applied across a single turn, may be employed. Where the transformation is not of that nature one can either employ a pair of such transformers appropriately connected to one another, or a single transformer can be employed in which the input is .applied across a plurality of turns and the impedance between those turns is appropriately modified to constitute the equivalent of the two appropriately connected singleinput-turn transformers.

There are many ways in which the desired impedance ratio between adjacent Vturns can be achieved. The conductor which defines the winding can itself be configured, as by being of a varying width, to produce the desired results; the spacing between adjacent windings can be appropriately varied to produce that result; or the winding can be produced in whole or in part from a plurality of substantially parallel conductors extending from one end of the transformer to the other, the ends of one or more of those conductor turns being electrically connected to the .beginnings of one or more other conductor turns in an appropriate manner; or combinations of these various approaches can be utilized in a single unit.

To the accomplishment of the above, and to such other objects as may hereinafter appear, the present invention relates to the design land construction of impedance matching transformers as defined in the appended claims and as described in this specification, taken together with the accompanying drawings, in which:

FIG. 1 is a schematic representation of one way in which a transformer may be designed in accordance with the present invention;

FIG. 2 is a semi-pictorial representation of a singleinput-turn transformer having a 3:1 voltage transformation ratio and formed of two turns of a pair of parallel wires;

FIG. 3 is a view similar to FIG. 2, but showing a transformer with a 4:1 voltage transformation ratio formed from three turns of a pair of parallel wires;

FIG. 4 is a view similar to FIG. 2 and showing a transformer having 3:1 voltage transformation ratio formed from three variably spaced consecutive conductor turns;

FIG. 5 is a schematic representation of the transformer of FIG. 4;

FIG. 6 is a View similar to FIG. 2, but showing a transformer having a 3:1 Voltage transformation ratio formed from one turn of four parallel conductors;

FIG. 7 is a schematic representation of the embodiment of FIG. 6;

FIG. 8 is a three-quarter perspective view of a transformer formed from a helically edge-woun-d strip of varying width;

FIG. 9 is a cross sectional view of a transformer formed by winding a conductive strip of varying width about a coil form;

FIG. 10 is a top plan view of a typical conductive strip such as is employed in the embodiment of FIG. 9;

FIGS. 11 and 12 are schematic views indicating the manner in which a pair of single-input-tu-r-n transformers made according to the present invention may be combined and connected to produce an mm voltage transformation ratio, where m/n is not .a whole integer, FIG. l1 showing directly connected transformers and output in which m is greater than n and FIG. l2 showing capacitive isolating connections between transformers and output in which n is greater than m;

FIG. 13 is a view similar to FIG. 12 and showing by way of exemplification the manner in which a 3:2 voltage transformation ratio can be obtained through the use of two single-input-turn transforme-rs, each of which is formed in a manner comparable to that shown in FIG. 2; and

FIG. `14 is a schematic representation of .a single multiple-input-turn transformer which is the equivalent of the two transformers shown in FIG. 13.

In this specification ZL will represent the load impedance to which the high-impedance output end of the transformer is to be matched, and n will represent the number of consecutive turns in the transformer measured from one end thereof to the other in a given rotative direction. When considering a single transformer in which the input is applied only across the first operative turn, n will there- -fore also represent the voltage transformation ratio of the autotransformer. (It will be understood that the terms input and output are used arbitrarily. The transformers function in both directions, so that the input in one application may be the output in another application.) The explanation will first be carried out, in conjunction with FIGS. 1-9, for the situation where the input and output voltages are to be related by whole integers (1m, where n is a whole integer), after which, with reference to FIGS. 11-14, the use of the present invention for a transformation in which the magnitudes of the voltages are not related by whole integers (mm, where neither n nor m is evenly divisible into the other) will be explained.

In accordance with the present invention the impedances between adjacentoperative turns, measured across the end of one turn and the end of the immediately preceding operative turn, are progressively related to one another and a predetermined impedance-usually the irnpedance to which the transformer is to be matched. When the input is applied across only one turn of the autotransformer the inter-turn imped-ances will vary in accordance with the formula ZX=ZL/n(nT), where n is the tot-al number of operative turns measured in one rotative direction, ZX is the impedance between the end of a given turn and the end of the operative turn immediately preceding that turn, and nT is the number of that given turn measured from the load (high impedance) end of that transformer. (As mentioned above, either end of the transformer may be considered as the load end, depending upon whether the transformer is considered as a step-up or step-down transformer, but for purposes of consistency in explanation, the output end will be here considered the high voltage end, which is connected to ZL.) When this relationship is achieved, the transformer, when viewed from either end, not only matches the impedance designed to be connected to that end (in accordance with the number of turns or voltage transformation ratio of the transformer), but also has the electrical appearance of an appropriately designed transmission line with a Very high coupling coefficient in which the distributed capacitance is effectively at zero value.

One way in which this desired impedance relationship between turns can be achieved is schematically shown in FIGS. 4 and 5. There a coil form A is -disclosed on which three conductive serially connected turns are wound,

those turns being designated 1, 2 and 3 respectively. (In that figure, and elsewhere in the drawings, those reference numerals -relating to the consecutive number of operative turns (counting from the input or low impedance end of the transformer) will be enclosed within a circle for purposes of ready identification.) The input e is connected across turn 1, and the output circuit (ZL) is connected across all of the turns (1, 2 and 3). Therefore, in accordance with well known transformer theory, a voltage transformation of 3:1 is produced. Turn 1 is spaced from turn 2 by a distance approximately one-half that between turns 2 and 3, and those distances are so chosen in accordance with the dimensions and other electrical factors of the transformer that, as indicated in FIG. 5, the impedance between turns 3 and 2, measured between points 10 and 12 in FIG. 5, equals ZL/3, while the impedance between lines 1 and 2, measured between the points 12 and 14, equals ZL/ 6. Relating the embodiment of FIGS. 4 and 5 to the formula set forth .above for ZX, n has the value of three, that being the number of consecutive operative turns in the transformer, while nT, for the impedance between turn 3 and turn 2, has the value of one, since turn 3 is the first turn measured from the load end of the transformer. For the impedance between turn 2 and turn 1, nT has the value of t-wo, since turn 2 is the second turn measured from the load end of the transformer.

Instead of providing for a physically different spacing between the turns of a single continuous winding in order to produce the desired inter-turn impedance relationships, which requires a somewhat complicated winding technique, the same results ycan be achieved, as rindicated in FIGS. 1-3, by winding about the coil form A a pair of parallel conductors generally designated B and C, the input e being connected across the conductors B and C at one end of the transformer and the output being taken from the end of the last turn of the conductor C. The specific embodiment of FIG. 2 dis-closes a transformer in |which each of the parallel conductors B and C forms two turns about the coil forrn A. The end of the first turn of conductor B is connected, by lead 16, to the beginning of the first turn of conductor C, and the end of the second turn of conductor B is connected by lead 18 to the beginning of the second t'urn of conductor C. This produces, in effect, an autotrans'former having three consecutive operative turns and a voltage transformation ratio of 3:1, as may be demonstrated by following the path from the beginning of the first turn of conductor iB around the coil form A (turn 1), then down through lead 16 along the first turn of conductor C (turn 2) and then along the second turn of conductor C (turn 3). The same total number of operative turns will be counted if one traces the first two turns of conductor B (turns 1 and 2), and then via lead 18 follows along the second turn of yconductor C (turn 3). In the embodiment of FIG. 3 the parallel conductors B and C form three turns about the coil form A, and similar analysis will reveal that as a result an effective four-operatiVe-turn autotransformer having a 4:1 voltage transformation ratio is produced, the embodiment of FIG. 3 being otherwise similar to that of FIG. 2, and with the lead 20 connecting the end of the third turn of conductor B to the beginning of the third turn of conductor C.

FIG. 1 is a schematic representation of the type of arrangement embodied in FIGS. 2 and 3, generalized for any number of turns, the total number of operative turns being designated n. The leads connecting the ends of a turn of conductor B to the beginning of the corresponding turn of the conductor C are designated 16-24. Shown on FIG. 1, by means of headed arrows, are indications of the instantaneous currents flowing in the various parts of the network when a current i is owing through the load impedance ZL. With a voltage transformation ratio of n, the input current must be n(). The current and voltage relationships between the various turns of the conductors B and C produce the desired impedance relationships, as indicated. n V d In the embodiment of FIGS. 6 and 7 there is wound about the coil form A a single turn of four parallel conductors A, B, C and D, with conductors A and C being connected to one another in parallel at both ends, as indicated by leads 26 and 28. The beginning of the single turn of conductor D is connected to the lead 28 at 30. The input is applied between conductor B on the one hand and interconnected conductors A and C on the the other hand. The operative turn 1 may be considered the turn of conductor B, that turn at its end fbeing connected by lead 32 to the beginning of the turns of conductors A and C, those turns collectively thus constituting operative turn 2 of the transformer, operative turn 3 being defined by conductor D. The spacing between conductor D and conductor C is such as to cause the impedance therebetween to equal ZL/3, as shown in FIG. 7. The spacing between conductor B and the parallel connected conductors A and C is the same as that between conductors C and D, thus producing an effective impedance between turns 1 and 2 which equals ZL/ 6, which is the desired relationship.

Another way in which the desired progressive relationship between the turns of the autotransformer can be produced is illustrated in FIG. 8, where the conductor 34 is in the form of a strip of uniformly progressively increasing width which is helically wound edgewise about the coil form A, the input e being connected across the first turn thereof at the large width end thereof, where the inter-turn impedance is the smallest, the output impedance ZL being connected to the end of the conductor 34 at its narrow width end, where the inter-turn impedance is the largest. The spacing between the indvidual turns of the conductor 34 and the changes in width of that conductor from one end to the other will be selected to produce the desired inter-turn impedance relationship.

In the embodiment of FIGS. 9 and 10 a conductive strip 36 having a varying width, such as is schematically shown in FIG. 10, may be wound about the coil from A, with suitable insulation 38 interposed between its superposed turns, as shown in FIG. 9, the input and output leads being connected thereto as shown, the varying width of the strip 36 producing the desired inter-turn impedance relationship. Alternatively or combinatively, the thickness of the insulating layer 38 could be varied so as to alter the spacing between different turns of the winding, thereby to further contribute to the attainment of the desired inter-turn impedance relationship.

Thus far the explanation has proceeded on the basis of an autotransformer having n turns, with the input connected across the first turn so as to produce an 11:1 voltage transformation ratio. In many instances the magnitudes of the impedances to be matched call for a voltage transformation ratio of mm, where neither n nor m is divisible by the other (e.g., 3:2, 9:5). One way in which this result can be achieved while still attaining the objectives and advantages of the present invention is, as illustrated inFIGS. 1l and 12, to utilize a pair of single-inputturn autotransformers E and F, each made in accordance with the teachings of the present invention, the transformer E. having an 11:1 step-down voltage transformation relationship, and the transformer F having a 1:m step-up voltage transformation relationship, the input voltage e being connected across all n turns of the transformer E, the output being taken from the first turn thereof and applied as input, via lead 4t), to the first turn of the transformer F, the overall output being taken across all m turns of the transformer F. The inter-turn impedances in transformer E will correspond to the relationship set forth above, but with the impedance ZI of the input circuit substituted for ZL, and likewise the inter-turn impedance relationship in transformer F will correspond to the relationship described above, with the impedance of the output circuit constituting ZL. The voltage applied to the output circuit, as indicated on the drawings, will be em/ n.

6 Thereare two differences between FIGS. 11 and 12. In FIG. 11 rn` is greater than n--the output voltage is stepped up from the input voltage-whereas in FIG. 12 n is greater than m-the output voltage is stepped down from the input voltage. Secondly, in FIG. l1 there is a direct conduct-ive connection between the transformers E and F and between the transformer F and the output impedance ZL, whereas in FIG. 12 capacitors 42 and 44 are employed respectively between the transformers E and F and the transformer F and the load impedance ZL for isolation purposes. It will be understood that either of those differences could be present without the other.

Analysis reveals that the lowermost turns of transformers E and F, which are connected by the lead 40, have the same voltages applied thereacross, although the impedances of tho-se turns differ. The same considerations apply as between each of the turns on the transformer having the larger number of windings which correspond to the turns on the transformer having the smaller number of windings. Thus having reference to FIG. 13, where a 3:2 step-down transformer network is disclosed connected lbetween input impedance ZL and output impedance ZL, the transformer E is the same as that disclosed in FIG. 2, but with the voltage input 3e applied between the end of turn 3 (a part of conductor C) and the beginning of turn 1 (a part of conductor B). The output is taken between the beginnings of conductors B and C (turn 1). The transformer F is formed of a single turn of parallel conductors B and C', with the end of the B turn connected to 4the beginning of the C' turn by lead 50'. The output voltage of transformer E, taken from across turn 1 thereof, has a value of e, and that voltage e is applied, via leads 52 and 54, across turn 1 of transformer F, the output vol-tage 2e being derived from the end of turn 2 of transformer F. Thus, turnl of transformer E and turn 1 of transformer F are connected to one another in parallel, and may be substituted for by a single turn having an impedance ZG equivalent to the parallel-connected impedances of 4turn 1 of transformer E (ZE) and turn 1 of transformer F (ZF). As shown in FIG. 14 a single transformer G may be employed, with two turns of the pair of conductors X and Y electrically connected as by leads 16 and 18, in the manner shown in FIG. 2, with the load impedance ZL electrically connected to the end of turn 2 by lead 56. The impedance of turnl (ZG) is in any appropriate manner, as by spacing of the windings, made to equal ZEZF/ZE-l-ZF. With this arrangement a single transformer unit G is formed having a 3:2 voltage transformation ratio which Will effectively match the impedances ZI and ZL.

In the above explanation it will be undenstood that the voltage .transformation ratio of the transformer will be so chosen as to correspond as closely as possi-ble to the ratio of the impedances ZI land ZL of the input and load circuits respectively between which the transformer is to be connected. Hence in a given circuit, where the irnpedances ZI an'd ZL are known, an autotransformer will be selected having .the number of consecutive operative turns required to give it a Voltage transformation ratio appropriate to the ZI/ZL ratio, and the turns will be so formed that their impedances will correspond to the relationshiphere specified. When that is done lthe input and load circuits will be effectively matched even though their impedances may be widely different, and the coupling transformer will function substantially as a transmission line in which the distributed c-apacitance is effectively zero, and with a very high coupling coefficient.

While but a limited number of specific embodiments of the present invention have been here disclosed, it will be apparent that many variations may be made therein, all within the scope of the invention as defined in the following claims.

I claim:

1. An autotransformer comprising a plurality of conductor turns, an input connection across one section thereof, and an output connection across all the turns thereof, in which the impedance between adjacent operative turns varies in accordance with the formula ZX=ZL/ n1(nT), Where nT is the number of a given operative turn counting from .the high impedance end of the transformer, ZX is the impedance between that given turn and the operative turn next adjacent thereto in a direction away from said high impedance end of the transformer, n` is the total number of consecutive operative turns in the transformer measured from one end to the other in one rotative direction, and ZL is a predetermined impedance.

2. An autotransformer comprising a plurality of conductor turns, an input connection across one section thereof, and an output connection across all the turns thereof, in which the impedance between adjacent operative turns, starting with the turns at the high impedance end thereof and moving sequentially toward the low impedance end thereof, follow the series ZL/n, ZL/Zn, ZL/3n, etc., where n is the total number of consecutive operative turns in the transformer measured from one end to the other in one rotative direction, and ZL is a predetermined impedance.

3. An 111:112 turn autotransformer, n1 being larger than n2, comprising a plurality of conductor turns, an input connection across n1 operative turns thereof, and an output connection across n2 operative turns thereof, in which the impedance between operatively adjacent turns varies, where n2 nT n1, in accordance with the formula where nT is the number of the given turn measured from the n1 end of the transformer, ZX is the impedance between said given turn and the operative turn next operatively adjacent thereto in the direction of the n2 end of the transformer, and, where n2 nT 1, consists of the equivalent of the parallel combination of ZX1 computed on the basis of an nlzl turn transformer and ZX.A2 computed on the basis of an n2:l turn transformer.

4. An 1111112 transformer network comprising an nlzl turn autotransformer comprising n1 operative turns with an input across all turns thereof and an output across one turn thereof and a 11112 turn lautotransformer and comprising yn2 turns with an input across one turn thereof and an output across 112 operative turns thereof in each of which autotransformers the impedance between operatively adjacent turns varies in accordance with the formula ZX=ZL/n(nT), where 11T is the number of a given operative turn -counting from the high impedance end of the transformer, ZX is the impedance between that given turn and the operative turn next adjacent thereto in a direction away from said high impedance end of the transformer, n is the total number of `consecutive operative turns in the transformer-n1 for the first named transformer and n2 for the second named transformer-and ZL is a different predetermined impedance for each of said transformers, the output of said nlzl transformer being connected to the input of said 1:112 transformer across corresponding turns of said autotransformers.

5. The autotransformer of claim 1, in which said conductor turns comprise a pair of substantially parallel conductors, one of said `conductors being connected at one end to ground, means for supplying an input across said one end of said one Vconductor and the corresponding end of the other conductor, means for taking an output from the other end of said other conductor, and means for electrically connecting said one of said conductors, at the end of a turn thereof, to the beginning of the corresponding turn of said other conductors.

6. The autotransformer of claim 1, in which said conductors comprise a plurality of pairs of adjacently extendling turns, and electrical yconnections between said turns effective to cause said turns to define the equivalent of a plurality of electrically connected parallel wiretransmission lines.

7. The autotransformer of claim 1, in which said conductors comprise a plurality of pairs of adjacently extending turns, Iand electrical yconnections between said turns, including a -connection from the end of one turn to the beginning of a second turn axially preceding said one turn, effective to cause said turns to define the equivalent of a plurality of electrically connected parallel wire transmission lines.

3. The autotransformer of claim 1, in which said conductors comprise a plurality of adjacently extending turns, the axial spacing between said turns being non-uniform, thereby to contribute to the production of said defined impedance relationship.

9. The autotransformer of claim 1, in which said conductors comprise a plurality of adjacently extending turns, and electrical connections between said turns, including a connection from one end of one turn to the beginning of a second turn axially preceding said one turn, effective to cause said turns to define the equivalent of a plurality of electrically connected parallel wire transmission lines, the axial spacing between said turns being non-uniform, thereto to contribute to the production of said defined impedance relationship.

10. The autotransformer of claim 1, in which said conductors comprise a plurality of adjacently extending turns, some of said turns being connected in parallel with one another, thereby to contribute to the production of said defined impedance relationship.

11. The autotransformer of claim 1, in which said conductors comprise a plurality of adjacently extending turns, and electrical connections between said turns, including a connection from the end of one turn to the beginning of a second turn axially preceding said one turn, effective to cause said turns to define the equivalent of a plurality of electrically connected parallel wire transmission lines, some of said turns being Iconnected in parallel with one another, thereby to contribute to the production of said defined impedance relationship.

12. The autotransformer of claim 1, in which the conductor forming .said turns is of varying width, thereby to contribute to the production of said defined impedance relationship.

13. The autotransformer of claim 12, in which said conductor is `wound with its width perpendicular to the axis of said transformer.

14. The autotransformer of claim 12, in which said conductor is wound with its width parallel to the axis of said transformer.

15. The autotransformer of claim 1, in which said conductor turns are of smoothly progressively varying width, thereby to contribute to the production of said defined impedance relationship,

1-6. The .autotransformer of claim 15, in which said conductor is wound with its width perpendicular to the axis of said transformer.

17. The autotransformer of claim 15, in which said conductor is wound with its width parallel to the axis of said transformer.

1S. The autotransformer of claim 1, in which electrically successive `conductor turns are variably spaced from one another, thereby to contribute to the production of said defined impedance relationship.

19. The autotransformer of claim 1, in which electrically successive conductor turns are variably spaced from one another axially of said series of turns, thereby to contribute to the production of said defined impedance relationship.

References Cited by the Examiner UNITED STATES PATENTS 1,608,047 ll/l926 Taylor et al. 333-27 1,762,775 6/1930 Ganz 333-32 1,876,971 9/1932 Kroger 333-27 2,545,544 3/1951 Doherty 333-32 (Other references on following page) UNITED STATES PATENTS Williams 343-861 Schmidt 3334-32 General Elec. Ltd. 336-148 De Long 333-32 Hogan S33-32 Kandoian 343-861 10 2,864,060 12/1958 Batchelor 333-32 2,913,681 11/1959 Lyman S33-70 2,971,173 2/1961 Kahihara S33-32 5 HERMAN KARL SAALBACH, Primary Examiner.

E, LIEBERMAN, C. BARAFF, Assistant Examiners.

Claims (1)

1. AN AUTOTRANSFORMER COMPRISING A PLURALITY OF CONDUCTOR TURNS, AN INPUT CONNECTION ACROSS ONE SECTION THEREOF, AND AN OUTPUT CONNECTION ACROSS ALL THE TURNS THEREOF, IN WHICH THE IMPEDANCE BETWEEN ADJACENT OPERATIVE TURN VARIES IN ACCORDANCE WITH THE FORMULA ZX=ZL/N(NT), WHERE NT IS THE NUMBER OF A GIVEN OPERATIVE TURN COUNTING FROM THE HIGH IMPEDANCE END OF THE TRANSFORMER, ZX IS THE IMPEDANCE BETWEEN THAT GIVEN TURN AND THE OPERATIVE TURN NEXT ADJACENT THERETO IN A DIRECTION AWAY FROM SAID HIGH IMPEDANCE END OF THE TRANSFORMER, N IS THE TOTAL NUMBER OF CONSECUTIVE OPERATIVE TURNS IN THE TRANSFORMER MEASURED FROM ONE END TO THE OTHER IN ONE ROTATIVE DIRECTION, AND ZL IS A PREDETERMINED IMPEDANCE.

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