Dec. 17, 1946. R. LEE PULSE TRANSFORMER Filed Oct. 21, 1943 WITNESSES: éyyjj? —- 72w. ‘ 2,412,893 3 Sheets-Sheet l INVENTOR L——-——————— Eel/ban lee‘ $24,444; {#45 A'a‘TORNEY Dec. 17, 1946. R. LEE 2,412,893 PULSE TRANSFORMER Filed Oct. 21, 1945 @796? > 65% Ca‘ 3 Sheets-Sheet 2 5195.9. Fig/z -- -- 4H“ ILL-LIL iii 1 --X dx INVENTOR E€Ub€f2 L as. BY ATTORNEY Patented Dec. 17, 1946 , 2,412,893 UNITED STATES PATENT OFFICE 2,412,893 7 PULSE TRANSFORMER Reuben Lee, Catonsvill e, Md., as'signor to West inghouse Electric 00rporation, East Pittsburgh, Pa., a corporation of Pennsylvania Application October 21, 1943, Serial No. 507,120 4 Claims. 1 (Cl. 178-44) 2 My invention relates to pulse transformers,_ Figs. 13, 14 and 15 are views illustrating curves such as are used between a pulse generator and a load device to transform the voltage produced showing the relationship between certain electri cal quantities corresponding to the equivalent circuits shown in Figs. ll, 5, and 6, respectively. output voltage than that of the pulse generator. Referring to Fig. l of the drawings; a pulse The pulses produced by'such generators are us CR generator l is illustrated comprising a source of ually of short duration, that is, l. to 15 micro electrical energy 2 connected to a circuit includ seconds, and may be rectangular in shape, or ing the resistor 3 and. inductances 4 and capaci nearly so. It is desirable that the pulse wave tors 5, 8, and "i for delivering electric pulses shape applied to the load be as nearly as pos through the terminals 8 and 9 of the pulse gen sible that of the generator supplying it. When ‘by the pulse generator to a higher or a lower erator and a pulse transformer l l to a load l2. a rectangular wave pulse is generated and a transformer is employed between the pulse gen erator and the load device supplied therefrom‘, there are certain distortions that may be in» troduced into the wave by the transformer such as a slanting of the vertical edges of the pulse wave‘ or oscillations distorting the top of the pulse wave. Either form of distortion may ren der the pulse unsuitable for practical use. 20 It is an object of the invention to provide a pulse transformer in which the above-mentioned distortions of the wave form are minimized or The pulse transformer H comprises a primary winding I 3 and a secondary winding I4 induc tively related to each other. The tube l5 serves as a switch for controlling the circuit between the pulse generator I and the transformer H and is shown as a grid controlled electronic tube‘ of well known character and is used in a well known manner to control the emission’ of electrical pulses from the pulse generator. The pulse gen erator I and the tube ID for controlling it are conventional and are not a part of my inven tion but are illustrated for the purpose of show the use of the pulse transformer II in the Other objects and advantages of the invention N) (A ing circuit in which it is employed. will be apparent from‘ the following description substantially eliminated. of a preferred embodiment of the invention, ref erence being had to the accompanying drawings, Referring to Fig. 2 of the drawings, the full line wave a is a rectangular wave pulse typical of that generated and supplied by the pulse gen I Figure 1 is a diagrammatic view illustrating a 30 erator I to the transformer ll delivering the electric energy to the load. The dotted line wave pulse generator and‘ transformer supplying a b represents the wave form that it is desired to load; ‘ impress across the load and which is similar in Fig. 23 is a View illustrating forms of wave pulses; form to the primary pulse a except differing in Fig. 3 is a diagrammatic illustration of a cir the voltage value thereof. The curves 0 show cuit equivalent to the circuitv of Fig. 2 relating two forms of distortions that may be introduced circuit constants either to the primary‘ or‘ to the in which: into the transformer output wave by the trans former if its electrical characteristics are not Figs. 4, 5, and 6 are equivalent circuits illus properly designed. The curve 25 shows a slant trating the circuit characteristics in parts which result in forming the front of the pulse, the top 40 ing of the vertical edges of the pulse, and curve 2? shows oscillations distorting the top of the of the pulse, and the trailing edge of the pulse, pulse. If the transformer windings have too respectively ; much electrostatic capacity, the sides of the Fig. '7 illustrates the shape of a pulse wave de pulse will be sloped as in curve 26, and if the in livered to a load from a pulse generator through ductance of the windings is preponderant, 0s-‘ a pulse transformer; V cillations may be developed as shown in curve Fig. 8 is a view partly in- section and partly 2'! of Fig. 2. secondary circuit; shown diagrammatically illustrating the capaci ties between the several parts of the transformer structure; ' Figs. 9 and 10 are side and end views, re spectively, of a transformer core and coil as sembly; 7 Either form of ‘wave distortion may render the pulse unsuitable for practical use. It has been commonly thought that a transformer 50 capable of operation at frequencies several times that of Figs. 11 and 12‘ are diagrammatic views illus-' 1 trating voltage gradient along parts of the appa; pulse duration ratus'; and 55 would transform a pulse satisfactorily. This is 2,412,893 3 not, however, always true. It may be that such a transformer would have distortions of the char 1 4 1:1 ratio transformers should be designed so that acter shown in curves 0 of Fig. 2. In accordance with my invention, I have de veloped a transformer having characteristics necessary to minimize these irregularities and to prevent Wave distortion in the pulse transformer. With the. open circuit inductance sufficiently high that itmay be neglected, the transformer equivalent circuit which refers to either the pri _i 572 mary or secondary side of the transformer can 222-411; 7, be represented in Fig. 3. This ?gure includes all elements of the circuit to the right of the ter If R2>>R1 and 01:02, this reduces to minals 8 and 9 in Fig. 1. If the transformer steps 15 _i 2_LZ up the voltage, the primary capacitance C1 can Rliu "a; usually be neglected. If the transformer steps down the voltage, the secondary capacitance C2 lc=0.2 to 5.0 in this also. can usually be neglected. The transformer iron The criteria here given are for a rectangular loss is combined with R2 and in some cases may or flat topped pulse impressed upon the trans constitute the whole load. former from some source. . In the circuit of Fig. 3 and in the following dis in Fig. '7, and a generalized circuit for the am pli?er is shown in Fig. 1. So far as the trans former action is concerned, the equivalent cir cuit for such an ampli?er is given in Fig. 3. A voltage is impressed across the terminals 8 and 9 of the load circuit through the switch S to the cussion, the following symbols are used: L1'=primary inductance with secondary open circuit in henries L2=pri1naryv inductance With secondary short > circuited, in henries C1=primary capacitance in 'farads , .1 ' . 2 2‘=secondary capacitance><<§€> in farads Np=primary turns Ns=secondary turns _ 1R1=resistance in source 111 ohms ' . . > ' Np 2. R2=res1stance in loadX —N—s 1n ohms In all transformers, L1 should be large enough so that a comparatively small fraction of the total pulse current is required to maintain a pulse voltage ' constant, or nearly so, throughout the pulse du ration. ' . Step-up transformers should be designed so that Such a pulse is shown circuit having the electrical characteristics shown. This is the circuit which applies to the front edge Q5 of the pulse which is shown in Fig. 30 7 as rising abruptly from zero value to some steady value E. The dotted line in Fig. 7 shows the impressed or original pulse and the solid line the impulse wave delivered to the load. This change is such that the transformer open-circuit 35 inductance can be considered as presenting prac tically in?nite impedance to such a change, and. is omitted in the circuitof Fig. 3. On the other hand, the transformer leakage inductance is of appreciable in?uence and is shown as inductance 40 L in Fig. 3. The resistor R1 of Fig. 3 represents the source impedance; the transformer winding resistances are generally negligible compared to the source impedance. The transformer winding capacitances are shown as C1 and C2 for the pri mary and secondary windings, respectively. The transformer load resistance, or the load resistance into which the ampli?er works, is shown as R2. All these values are referred to one side or the other of the transformer; that is to say, the load resistance R2, the leakage inductance L, and sec ondary capacitance C2 are multiplied or divided by a factor which is the square of the trans former turns-ratio Np/Ns in order to treat these quantities as if they actually existed on the pri mary side. and R2>>R1, this reduces to: R1: E ; Step-down transformers sho'uldbe designed so that ' ' ’ ‘ 79‘ < . ratio and therefore voltage-ratio affect these ea former, C1 may be neglected and for a step-down transformer, C2 may be neglected. The discus sion here will be con?ned to the step-up case, although the step-down and the 1 to 1 ratio cases 70 are not markedly different. R1+R2 iii-2a The‘ step-up transformer is illustrated by Fig. and 70:02 to 5.0. a _1_ capacitances will become preponderant. Turns pacitances in such a Way that for a step-up trans ' 2 i If it were more convenient to treat the transformer completely on the secondary side, then the quantities R1, C1 and L would be multiplied by a reciprocal factor. Since there 60 are two capacity terms C1 andCz, it follows that for any considerable deviation of the transformer turns-ratio from unity, one or the other of these # If L2 » R201 this reduces to: R2 zizk‘i/éii 4. When the front of the wave, Fig. 2(a), is suddenly impressed on the transformer, it will ‘be-simulated by the closing .of switch S. At this initial instance, the voltage e across R2 is zero, 2,412,893 5 and the current entering from the battery 2t’ is whose output power is zero. In the case of the latter curve, the value c need not be multiplied by any ratio of resistances; its ?nal value is the also zero. This furnishes us with two initial con ditions to be used in the derivation of a formula which expresses the rate of rise of voltage 9 from its initial value of zero to its ?nal steady value same as that of the battery. All the curves are exponential, having a common point at 0, 1. Again the abscissae are not time, but are the product of time and ratio of E times the ratio R2 divided by R1 plus R2. It is apparent from this that the smaller R1 is made, the more e?icient will the ampli?er be. The curves in Fig. 13 show the rate of rise of the transformed wave pulse for an ampli?er 10 where R1 is negligibly small. However, if the value E for the top of the pulse is multiplied by the ratio . R2 _ R1+R2 the curves are reasonably accurate. The scale of abscissae for these curves is not time but percentage of the time constant T of the transformer. The equation for this time constant is given on the curve, and is in turn a function of the leakage inductance and the capacitance C2. The rate of voltage rise is governed to a marked extent by another factor k which is the ratio of the decrement to the angular velocity for an oscillatory circuit, but retains the same form even when the circuit is not oscillatory. The relation of this factor k and the various constants of the transformer is given directly on the curve. Other things re maining equal, the greater the transformer leak age inductance and distributed capacity, the slower is the rate of rise, although the effect of the two resistances R1 and R2 is also of consider able importance as they affect the factor It. It will be noted that if a slight amount of oscilla tion can be tolerated, the wave rises up much faster than if no oscillations are present, and if the circuit is far removed from the oscillatory conditions, the rise is indeed very slow. On the other hand, if the circuit is damped very little, the oscillation may reach a maximum initial value of two times the steady state voltage E and often such marked peaks would be objection able. The values for is given on the curve appear to be those which fall within the most practicable R1 f the time in this case being the duration of the pulse between points I8 and #9 in Figs. 2(a) and 7. Obviously, the greater the inductance L, the less deviation from a ?at top pulse there is in traversing this amount of time. At time instant is in Fig. '7, we will assume that the switch S in Fig. 5 to he suddenly opened. The circuit now reverts to that of Fig. 6, in which L is in the open circuit inductance, but C2, the secondary capacitance, is again present to an ap preciable extent. It will be assumed that the current through L has not increased to an ap preciable amount, and therefore the flat top wave was practically unimpaired at instant ill; but if this is true, it is the same as saying that there is no initial current in the inductance L, so when switch S is open condenser (32 supplies all the load current momentarily to R2. This is the basis upon which the curves in Fig. 15 are drawn. The abscissae of these curves are plotted again in percentage of the transformer time constant but the time constant is now determined by the open circuit inductance L with capacity C2 rather than by leakage inductance and capacity C2 as was the case on the curves in Fig. 13. The constant 70 on these curves is again the product of decrement and VL2C'2, but the decrement has a different meaning as indicated on the curve. Lest it be assumed that the time constant is so great in this case that it precludes satisfactory performance, attention is drawn to the fact that higher open circuit inductance L1 results in higher values of 7c, and the curves with higher values of is drop much more rapidly than do the smaller, values, but only with reference to the time constant T. range. This does not mean that such a wave will drop Once the pulse top is reached, the value E is dependent upon the transformer open-circuit in ductance for its maintenance at this Value. If the pulse stayed on inde?nitely at the Value E, it would require an in?nite inductance to main more rapidly in time, but only with reference to the‘ time constant which is determined by open-circuit inductance and capacitance. It does mean, however, that the slope of the trailing edge can be kept within tolerable limits, provided the capacitance of the transformer can be kept small enough. The accurate predetermination of this capacitance is therefore of ?rst importance. tain it so, and of course this is not practical. There is, therefore, always a drooping tendency to the top of such a pulse. The equivalent circuit during this time is shown in Fig. 5. Here the inductance L is the open circuit inductance of the transformer, and R1 and R2 remain the same as before. Since the rate of voltage change is relatively small during this period, the capaci tances C1 and C2 disappear from the picture. Also, since the leakage inductance is usually small compared to the open-circuit inductance, it is neglected here. When the switch S is ?rst closed, the voltage e across R2 is assumed to be at the steady value E, which is strictly true only when Therefore, the curves for the top of the wave, Fig. 14, need to be corrected _ R1 is negligibly small. the same as those for the front of the wave, in that 6 should be multiplied by the ratio R2 divided by R1+R2. Several curves are given, representing several types of pulse ampli?ers ranging from a pentode where R2 is T10 of R1, where the source resistance is very high, to an ampli?er whose load resistance is in?nite or By means of the three sets of curves we can now construct the pulse shape delivered to load R2. Suppose a transformer with the following measured constants be required to deliver a ?at top pulse of 15 microseconds duration, ~ L2 leakage inductance (secondary short circuited) 1.89>< lib4 H Lrprimary open-circuit inductance ____ __ 0.1 H Primary/secondary turns ratio Np/Ns_____ 1:3 R1 source resistance _____________ __ohmsi_ R2 load resistance (primary equivalent) 800 ohms__ 5900 C2 capacitance ________________ __mmfd__ From the expressions given in 388 13, we ?nd m=2.38><106 T=1.'7 microsecond k=0.65 The front of the Wave will follow a curve be ' tween those marked lc=0.4 and 16:0.8 in- Fig. 13. 2,412,893 O 7 pacity between the primary winding and core, or The value E will be reached in 0.5T or 0.85 micro second, and a peak of about 10% occurs in 1 mi crosecond. ' The top of the wave will slope down to a value determined by the product between the secondary winding and core or be tween the primary and secondary windings, but usually exceed these values if the transformers Cl are step-up transformers, and are less than these values if the transformers are step-down trans t_R_1 =0.12 formers. In any transformer, regardless of L turns-ratio, these values must be taken in terms of voltage gradient. ‘ and by a curve between those for R2=w and For example, in the transformer whose cross R2=2R1 in Fig. 14. The value is evidently 0.91E. 10 The trailing edge is given by the curves in Fig. 15. Here 1,5 so that the load voltage reaches zero in 0.115T or 4.5 microseconds. There is a slight negative loop of ‘7% at 0.3T or 11.7 microseconds beyond the pulse edge IT. section is shown in Fig. 8, a core 2| is provided having a winding leg 22 about which the primary turns 23 and secondary turns 24 are each wound each in a single layer concentrically. It will be assumed that they are wound in the same rota tional direction, and in the same traverse direc tion (right to left). It willyfurther be assumed that the right ends of both windings are con nected to ground (or core) through large capaci tances, as shown dotted, so that the right ends The pulse delivered to load R2 as shown in Fig. are at substantially the same alternating-current 7 is a combination of these three curves. potential. Capacitance C1 is composed of many The primary leakage inductance used is the small incremental capacitances Cp and C2 of inductance measured on the primary terminals many small incremental capacitances Cs each of of the transformer when the secondary terminals which has a di?erent voltage across it. Likewise, are connected together, and this is a measurable 25 there exist many small incremental capacitances inductance. Ca between primary and secondary which have The equivalent capacitance is not directly different potentials across them. If the trans measurable but can be evaluated from measur former is step-up, able capacitance. A capacitance, across which a uniformly tapered voltage exists, may be given an effective value in terms of a ?xed voltage E. Referring to the sketch shown in Fig. 12 in which __ 2 C1: }622Cp and C2: %[ZC's+ the voltage gradients between the primary and secondary windings are shown by the sloping lines Hll and H32, the minimum voltage difference If the transformer is step down between the two windings is shown at one end as e1, and the maximum voltage difference being shown at the other end as 62 with the gradients and C2=1/3[2Cs] 20a] cars) a] “ __ 2 If the ratio is 1:1, C1=1/3[2Cp+1/2ZCa,] and C2=1/3[ECs] between the opposite ends of the windings pro For transformers with opposite angular rota gressing linearly between these two values. If 40 tions of primary and secondary windings, or with the primary voltage is represented by E, it can opposite traverse directions (but not both), the be shown that the equivalent capacitance re factors ferred to the primary side of the transformer is Np — Ns 2 N s — Np 2 < NP > and where CM is the measured capacity between the two windings. in the foregoing equations become N10+ Ns)2 N11 . The capacitance between the primary winding and the core and between the secondary winding and the core should be included after evaluation of these quantities in terms of their respective voltage gradients. If it were desired to refer this capacitance to the secondary winding, the secondary voltage 5; should be used in place of the primary voltage E in the above formula. Also there are normally differences in the num ber of coil turns in the primary and secondary. NP there is no other change. For transformers with both angular rotations and traverse directions opposite there is no change at all in these equa tions. If there is a shield between primary and secondary, omit terms containing Ca in these equations, and make 20.9 and 20p include the ' capacity of secondary and primary to shield, re spectively. Note that 20s is the measurable ca pacity of the short-circuited secondary to ground (or core), and 20p the measurable capac Call these Am and Anz. Then the formula can be (it) written ' ity of the short-circuited primary to ground (or core). , For moreinterleaving of primary and second ary windings, more elaborate evaluation of ca where Np is the number of turns in the primary winding. “ If the voltage between the left ends of the two windings is zero, the above formula is reduced to Ce or Ce The capacitances C1 and C2 must, as pointed out above, be evaluated in terms of voltage gradients in the windings. That is, the values C1 and C2 are not the ordinary measurable ca~ pacitance is necessary. This will be illustrated below by the description of an actual trans former. , , As shown in Fig. 9, the primary is wound in two layers 3! and 32, interleaved between three sec ondary layers 33, 34 and 35. This interleaving is done to reduce leakage inductance. The trans former is, used to couple an electronic tube to a pair of cathode-ray'tube plates. The plates are an open circuit; hence R2 would be in?nite, but the transformer has su?cient iron and dielectric 2,412,893 9 loss to give R2 a ?nite value. The measurable constants are: Np=112 turns (56 per layer) Ns=360 turns (120 per layer) R1=800 ohms R2=5000 ohms The capacity from secondary to core is 100 mmfd. The capacitance (average) between pri mary and secondary layers is 46 mmfd. All Ang 3 -N=240—112=128 windings are wound in the same direction of ro tation, but the directions of traverse are: Secondary Primary a 1st section Left to rt. for M 2nd section 3rd section 1st section 2nd section Rt. to left Left to rt. Left to rt. Rt. to left . Pg-Sg, 15 Ce= Designate these winding sections, in the order above, as S1, S2, S3, P1, P2. The voltage gradi 20 ents along these windings are as shown in Fig. 11, except that turns are used instead of volts. for This is permissible since 2r =52 es Ns In the space Turn gradient is— Srcorc O to 1:? S1-P1 0 t0 ivg~l?a Sz-Pz 131-82 '§‘%g $13272 2%LN1) to Pz-S3 2TN8—Np to N8“? S3-corc 2% to Ns An2=Ns=360 30 01:0. C2 is the sum of all the layers Ce’s plus Ce of S1-core. It has already been referred to the primary side in the above calculations, and hence the multiplier (e NP 2 is unnecessary. Hence, C2=75+38+5+84+35+l78=415 mmfd. \R Adding another 25 mmfd., for tube, load and in cidental capacity, 02:440 mmfd. If it had been referred to the whole secondary winding, this The transformer is so constructed that there is 10.3 mmfd. from S3 to core. The secondary-to core capacitance is mostly S1 to core. The pri mary effective value of this capacitance is value would have been 1122 20s X &s)2 The measured value of capacity from second ary to primary and core is 240 mmfd. Contrast this value with 42 mmfd., and the importance of Putting the numerical values N5 and Np in this expression from the above table we have the above calculations becomes apparent. It will be apparent from the above description that modi?cations in the arrangement of the parts illustrated may be made within the spirit of my invention, and I do not wish to be limited otherwise than by the scope of the appended _(l00—- 10.3) X (120)2 =38 mmfd. 3X 1122 for the eifective value when referred to the pri mary. Thus, because of the high voltage across it, the small Sz-core capacity becomes appreciable. Since the secondary winding intervenes be tween any primary winding section and the core, For the inter-winding spaces We can use the equation claims. 0 C6 =3A7-‘ap2 (A7112 + A7122 + A’l'llAng) 60 Thus, we get for Sl-Pi, An1=0 I claim as my invention: 1. In a system for transforming substantially rectangular voltage wave pulses with substantial ly no wave distortion, a transformer having pri— mary and secondary windings connected respec 65 tively to a source of electric energy and to a load circuit in which the relation between R1 (the re sistance of the primary circuit in ohms), L2 (the primary leakage inductance in henries) and Ce (the equivalent capacity of the transformer in terms of primary voltage in farads) are related for ' by the following equation: 131-82, A7L1= T15 Ce where k is a value between 0.2 and 1.5. 2,. In a system for transforming substantially 2,412,893 12 winding turns and Ns is the number of secondary winding turns) are related by the following equa rectangular voltage wave pulses with substantial ly no wave distortion, a transformer having pri mary and secondary windings connected respec tion: 7 tively to a source of electric energy and to a load circuit in which the relation between R2 (the re sistance of the secondary circuit in ohms), Ls (the secondary leakage inductance in henries), and Ce (the capacity of the transformer in terms of secondary voltage in farads) are related by the following equation: where k is a value between 0.2 and 1.5. 4. In a system for transforming substantially rectangular voltage wave pulses with substantial 10 ly no wave distortion, a transformer having in ductively related windings connected respectively to a source of electric energy and to a load circuit and having a fewer number of secondary winding turns than primary winding turns so that the secondary winding will deliver a lesser voltage than that impressed on the primary winding and in which the relation between R2 (the resistance where k is a value between 0.2 and 1.5. 3. In a system for transforming substantially rectangular voltage wave pulses with substantial ly no wave distortion, a transformer having in of the ductively related primary and secondary wind ings connected respectively to a source of electric number of secondary winding turns than primary winding turns so that the secondary winding will deliver a greater voltage than that impressed on the primary winding and in which the relation between R1 (the resistance of the primary cir 25 cuit in ohms), L2 (the primary inductance with the secondary short-circuited, in henries), and Ge (the equivalent secondary capacity of the N3 2 in farads where Np is the number of primary Np 2 in ohms), L2 (the primary inductance with the secondary short circuited, in henries), and C1 (the primary capacity in farads) are related by the following equation: where 10 is a value between 0.2 and 1.5. 30 secon dary voitageX Np . load circuitX energy and to a load circuit and having a greater transformer in terms of ‘ . REUBEN LEE.

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