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Calhoun: The NPS Institutional Archive DSpace Repository Theses and Dissertations Thesis and Dissertation Collection 1965-06 A high-power one-millisecond pulse-forming network Walker, William George http://hdl.handle.net/10945/12290 Downloaded from NPS Archive: Calhoun N PS ARCHIVE 1965.06 WALKER, W. A HIGH-POWER ONE-MILLirECOND PULSE -FORMING NETWORK WILLIAM GEORGE WALKER /^©©©LPLrSLl©©' GENUINE PRESSBOARD BINDER no. BF 2507 EMB ACCO OGDENSBURG. LONDON. MEXICO. CHICAGO. N.Y. TORONTO. D. F. A HIGH-POWER ONE-MILLISECOND PULSE -FORMING NETWORK by WILLIAM GEORGE WALKER S. B. , United States Coast Guard Academy (1959) SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June, 1965 Library U- S. Naval Postgraduate School Monterey. California Z^R^ Y KN0X {. IBRARY A HIGH-POWER ONE -MILLISECOND PULSE-FORMING NETWORK by William George Walker Submitted to the Department of Electrical Engineering on May 21, 1965 in partial fulfillment of the requirements for the degree of Master of Science. ABSTRACT Design and construction of a breadboard model of a pulse-forming network to be used in a line-type generator for a space vehicle radar system is described. The is unique in that it produces a one-millisecond, PFN high-power pulse and uses linear, ferrite-core inductors. It is designed to be space-flight worthy, reliable, efficient, and most important, the smallest and lightest weight unit that is compatible with the other pulsegenerator components. A study of a pulse generator is made to determine the parameters that describe the optimum PFN. A pulse transformer and a charging reactor are discussed in detail and a description is given of the operation of the pulse generator using silicon-controlled rectifiers as switching elements. Thesis Supervisor: J. Francis Reintjes Title: Professor of Electrical Engineering -2- ACKNOWLEDGEMENT wish to thank James R. Sandison and Joseph A. Bosco for suggestion of this topic as a thesis subject and for the encouragement and assistance I freely given and gratefully received. -3- TABLE OF CONTENTS TITLE PAGE page 1 ABSTRACT 2 ACKNOWLEDGEMENT 3 TABLE OF CONTENTS LIST OF FIGURES CHAPTER I CHAPTER II A. B. III A. 5 INTRODUCTION 7 THE PULSE FORMING NETWORK DESIGN PARAMETERS SELECTION OF MATERIALS C. D. E. CHAPTER A. B. 18 18 2. Inductors 18 a. Description of Requirements 18 b. Choosing the Proper Core and Wire Size 24 Typical Inductor Design Procedures 28 TESTING THE PULSE FORMING NETWORK MEASUREMENT OF INDUCTOR CORE SATURATION VOLTAGE LEVEL CONSTRUCTION OF THE PFN TESTING CIRCUIT CORRECTION OF THE PFN OUTPUT PULSE WAVEFORM MEASUREMENT OF PFN EFFICIENCY ENVIRONMENTAL TESTING SUMMARY IV APPENDIX A 13 Capacitors . B. 13 1. c. CHAPTER 4 30 35 35 42 46 47 A PARAMETRIC STUDY OF THE OPTIMUM PULSE GENERATOR THE PULSE TRANSFORMER THE CHARGING REACTOR APPENDIX B 30 SILICON-CONTROL-RECTIFIER SWITCHING DEVICES AND TIMING CIRCUIT BIBLIOGRAPHY 52 52 59 65 69 -4- LIST OF FIGURES 1. Radar Transmitted Pulse Train 2. Original Ten-Section PFN 3. Block Diagram Pulse Generator 4a. Odd Periodic Rectangular Waveform 15 4b. Approximation 15 5. Five Section, Type-C, Guillemin Network 16 6. Inductor Construction 20 7. B-H Curve 8a. C-type Cut Core 25 8b. Uncut Toroidal Core 25 9. Circuit for Displaying Inductor Core Saturation Voltage Level 31 10. Core Hysteresis Loop 31 11a. Five lib. Breadboard Model 12. Dummy Load 13. Output Pulse Waveform from the First 14. Output Pulse Waveform from the Second 15a. Output Pulse Waveform from the Final 15b. Leading Edge 16. Graph 17. Relation Between Power Supply Voltage, Output Pulse Voltage PFN of of the page and Charging Reactors for Z-type Hyper sil 21 Inductors of the 9 II Rectangular Pulse to a 9 32 PFN for Testing of the Final and the Charging Reactor PFN 32 36 PFN Version PFN Version PFN Version Output Pulse Waveform Voltage-Squared Versus Time for an Output Pulse PFN 39 39 41 41 43 Voltage, and 44 18. Simplified Pulse Transformer Model 54 19. Equivalent Charging Network 54 -5- LIST 20. OF FIGURES Power Supply Level and of the (Continued) the d-c Resonant Charging PFN page 61 21. PFN 22. Pulse Generator Timing Circuit 66 23. Timing Pulses 68 Oscillations after an Output Pulse -6- 61 CHAPTER I INTRODUCTION Microwave radar has resulted capable of producing in the need for pulse generators The convention a rapid series of pulses. is to use essentially rectangular pulses of high power and short duration. The length of the pulses are from a few nanoseconds to several microseconds, 1* more depending on or However, there have been the specific application. some iong duration pulse generators developed primarily astronomy and space communication radar systems. microwave research application is the Haystack Lincoln Laboratory. A for use in radio An example facility of of this M.I.T. pulse generator that will produce a series of long duration (one millisecond) pulses for use in a specific space vehicle radar system presents some unique problems. Rigid restrictions on size and weight require new construction techniques to minimize these quantities. The Electronic Systems Laboratory (ESL) model of a space vehicle M.I.T. has the vehicle would be shot at of the with bursts of rf energy at X-band. a near-miss trajectory. to-noise calculations were made at As it flies surface of Venus will be illuminated Comparison of the reflected to transmitted energy will give a measure of surface reflectivity. of 20, 000 breadboard Should the experiment be formally scheduled, Venus on successive small portions approach a radar system for making measurements of the reflectivity of the surface of Venus. by, at ESL based kilometers plus elognation 3 Signal- on the closest point of of the returned echo due to curvature of the surface of Venus and relative velocity between the planet and spacecraft. These calculations resulted TT— in peak-power and pulse -duration Superscripts refer to numbered items in the Bibliography. -7- — transmission requirements respectively. one kilowatt and one millisecond, of 4 This radar system uses a klystron which requires an input pulse of 8-kv at 0.60 ampere for one millisecond to produce a one kw output pulse, or a pulse generator output of P The pulse train is shown = 3e Eq I = q that this radar in Fig. (8, 000) (0. 60) = 4. 8 system will transmit Four one-millisecond pulses 1. portion of the surface. A twenty-millisecond is (1) normal operation will be directed at each delay between pulses is required to prevent overlap of the echoes which second period between bursts in kw per pulse may be elongated. A fifteen- required to insure reception of the entire burst echo and change the antenna position prior to transmission of the next By reference burst. to Fig. 1, the average pulse generator output power is seen to be P average " = When considering (total power output) (total period) (4x 10 of it is )(4, 800) 15.0 1.28 watts (2) a line-type pulse generator for use in this application, the pulse -forming network (PFN) is the since _3 the bulkiest and heaviest. most critical item Analytical procedures for the design pulse-forming networks are well established, but the physical realization of these networks for high-power application usually results in units considerable size and weight. constructed by ESL for the Figure 2 shows the original breadboard model of this PFN of that radar system. was It is 22 inches long, has a volume of about 800 cubic inches and weighs 15 pounds -9- •/&— SMC « * «" 10.m% I Ml -Sf- -tf- FIG. I RADAR TRANSMITTED PULSE TRAIN '-fM FIG. 2 - -f- T~T~ " ^ ORIGINAL TEN SECTION PFN AND CHARGING REACTOR -10- The reduction obtained. and weight was highly desired but not too of size Commerical manufacturers of easily- pulse-forming networks declined to undertake the problem. The object model of an of this thesis is to design, build optimum PFN for a one millisecond, 4.8 generator using as criteria for optimization: 2) reliability, kw peak power pulse minimum 1) "space flight worthiness, efficiency, 4) 3) and test a breadboard " size and weight, and compatibility 5) with the other components of the pulse generator. A PFN can "optimum" only be regarded as use results in the if its smallest and lightest weight pulse generator of this type that can be built. In order to determine the parameters that describe the optimum PFN, a study was conducted of a hypothetical pulse generator, the details of which may be found in Appendix A. The circuit in which the PFN is used shown is in Fig. configuration meets the desire to reverse saturate, or "reset, pulse transformer between pulses. that the pulse This 3. " the This resetting feature reduces the chance transformer will saturate during the long pulse. pulse generators of this and other types is Operation of described in detail in Reference The pulse generator described here differs from conventional types 5. in the use of high voltage silicon-controlled rectifiers (SCR) as switching devices. Operation begins with the supply is assumed to upon receipt of a initially uncharged. have a constant d-c output system are small, the 2E PFN PFN of E The power volts. If will charge d-c resonantly to approximately timing signal at the gate electrode of SCR-1. current passes to ground through the pulse transformer causing The resetting Ri is losses in the accomplished by during the charging period. a voltage appearing The value of R, it Charging to reset. across the resistance is set to supply just the -11- s Uj Uj IA -J k O CD O 00 « -12- necessary voltage required to reset the that charging current is flowing. pulse transformer in the interval This charging interval is a constant value given by where: VL c Tc = T = Charging interval L. = Inductance of charging reactor Cn = Total capacitance of r U | 3 is the total PFN inductance. L A more in of 10 . electrode impedance PFN of E SCR-2. If PFN the much larger than JL , charging reactor of the upon receipt impedance of a is discussed. timing signal at the gate of the load and the characteristic are matched, the voltage appearing across the primary transformer and duration T. is L. This establishes a practical lower limit on will discharge of the of the pulse PFN detailed explanation of the charging process is given Appendix A when design The (3) x ' based upon the assumption that Equation L. Cn is an approximately rectangular pulse of amplitude The pulse transformer secondary then sees N E T = output pulse duration N = pulse transformer turns ratio E = DC power where: supply output level At the end of the pulse there will be a small amount of residual magnetizing current flowing in the primary winding of the pulse transformer. cause a large negative voltage spike, called "fly-back voltage, across the transformer primary. the klystron R, from The function of the diode D " This will to is to from possible damage from the fly-back voltage and the circuit during discharge of the rate is set by a timing circuit to meet PFN. appear to protect remove The pulse repetition the requirements of the radar system. CHAPTER II THE PULSE -FORMING NETWORK A. DESIGN PARAMETERS Selection of parameters to be used in designing the based on the results is that pulse of Appendix A, PFN was the significant feature of which transformer size and weight in this application are independent of other parameters for the three values of operating power supply voltage assumed. that would simplify the This result allowed selection of supply voltage PFN construction. PFN must The be constructed to operate at twice the supply voltage; therefore, the obvious choice, in this case, is 300 volts. ' from available the pulse generator. Table This power supply A summary that will actually be of the Es lowest value of is the that will be used in the important parameters complete is given in 1. Table Summary of 1 Pulse Generator Design Parameters E s = power supply voltage = 300 volts N = pulse transformer turns ratio = 26.7 = PFN characteristic impedance r C = total Ln E = total PFN PFN = pulse transformer secondary voltage I = pulse transformer secondary current = 0.6 T = output pulse duration = 1.0 millisecond a = pulse rise time factor L. = charging reactor inductance =130 millihenrys Z • turns n capacitance inductance = -13- = 18.7 ohms 26.7 microfarads = 9.35 millihenrys J = 5 = 8, 000 volts amp percent -14- The PFN design procedure generator are small and the is as follows: PFN If losses in the pulse considered to be matched is to the load, the pulse transformer turns ratio is approximately N jf = (4) s The characteristic impedance a matched load condition is _ The PFN was chosen pulse-forming network required for of the - rrr" n <e /i x o' ; o) type-C, Guillemin network with to be a five- section, parameters: The choice of a periodic of PFN waveform T cn = Ln = (6) n TZ n (7) 2 configuration was based upon the Fourier analysis of the type shown This in Fig. 4a. an odd is periodic function and can be used to calculate an approximation to the desired output pulse. A rectangular pulse of current can be approximated fairly well by a pulse that has parabolic leading and falling edges and a flat top, shown as shown in Fi in Fig. g. 4b. The odd periodic waveform of this shape 4a can be represented by a Fourier series in the form: co i(t) =1 ^ b v Sin ( ^ ; V = 5 3 l > ' ' • * ' (8) -15- Time FIOT. 4a. ODD PERIODIC RECTANGULAR Y/AVEFORM A }L aT H aT <£- FIG. 4b. APPROXIMATION TO A RECTANGULAR PULSE Time -16- H ismsu] x> o »0 <sj -J K UKXJOJ O -J -4 3 ismor <*% -J r>4 H O <LMM7 <m <M -J H 10 iMoor H O -17- Only the odd harmonics will be present, the coefficients of which are given by m sinvrra, _4_ v v vir = I p A five section, v ' v-rra NI o ' (10) v ' type-C, Guillemin network is shown in Fig. 5. The element values are given by sin .ry Ck ^TTZ n v where: k = 1, 2, 3, 4, 5 = v-rra 1 '-T tt Z T Lk 1 -j sin — vua Z -j ^-f^1 v-rra The has shown < 12 > .corresponding to the appropriate network section. in Table Z. that the contribution to rapidly. ? > The calculated element values and the current network are given ^ ? > PFN was i(t) Examination from the higher i, (t) in each section of the of the values of i, (t) shows harmonic components decreases limited to five sections primarily because experience that addition of more sections would not improve the resulting pulse waveform significantly to warrant the additional weight and space. -18- Table 2 Theoretical Coefficients and Parameters Type-C, Guillemin Network for a Five Section, C 1 . W) L k (mh) 21.6 1 B. k i 4.69 k (t) 20.3 sin (^) 2 2.36 4.77 6.65 sin (1^-) 3 0.824 4.80 3.87 sin (5zJ_) 0.399 4.82 2.67 sin (ZljL) 0.226 4.85 1.9 sin (2Zj-> SELECTION OF MATERIALS Capacitors The capacitors used in construction of the breadboard model are standard commerically available, high quality, 600v paper type. a Size and weight are normally a consideration, but since the exact values of capacitance needed had weight to be obtained by of the combinations of standard values, size and experimental units are not too important. single, light-weight units will be manufactured to It is expected that meet space application specifications and used in place of the experimental units. 2. Inductors Description of requirements a. was based upon . The selection a high saturation flux density. material of this type is a grain-oriented tape-wound cores under the trade names Table 2 3 of a core material The most readily available /o silicon steel that comes in of "Silectron, " shows that the highest frequency harmonic in 7 i(t) and "Hypersil. that will be " 8 -19- significant is the to a frequency component 1.9 sin (jut), where 9lT u) At this frequency the of 4, 500 cps. = -m- . This corresponds H and Z type, 4-mil cores will have reasonably small eddy current losses 7 and will be suitable for this application. The Z-type material is preferred over the H-type because slightly higher saturation flux density 8 operation with fewer turns of wire than which if may it has a allow satisfactory the H-type were used. Otherwise either material is completely equivalent and the final choice is based upon availability. The characteristics the B-H curve in Fig. 7. of Z-type Hypersil are given approximately by This curve shows that the permeability of the core remains essentially constant throughout most of the range of flux density and changes radically only at the extremes where saturation occurs. Pulse shape depends upon maintaining a constant value of inductance throughout Therefore, the pulse period. it is essential that operating points near saturation flux densities be avoided. The range of flux density (AB) taken as 1.45 webers per square meter which is just where saturation begins as shown the flux density is in Fig. 7. If was short of the point assumed to be constant over the core cross section, then the change in flux density is given by the general relationship T AB = NA J e(t) dt where: A N = core cross-section area = number e(t) = applied voltage t = time duration of applied voltage of turns in coil < 13) -20- 1 Ul ^1 1 1 in en o Ui 0: O o % o r «•«. ^c o ,/ ^» Qc o £- § i K J <5 ^ 1 _. . J Tt _. -21- J .....; . _ 1 __ I 1 .±t .it It in ' ...... .1 IT 4- ----- jr — : 1 ' 1 i — 1 1 H- """'".......... ij~ L_ ... ... Mi M -U- -i i r; ' i 1 i 1 1 ± ± zr 1 i _ j t —J i— I . ._ IT 1 it i t it 1 Se Sp - & i 1 r 4^ s i ! 1 j£ ^K - -M ! it i '""'"' O " ^e '"- aa ^ j£ ^5I — 1 "j 1 4- I ..... ... p ^ .,,...,... . . 4 -H 5 -T t F1 PS H ^ it "^ Z ^5 w ^ I <fi ' 1 a \ 4 4- 4c& \ ^ \-J- CX <~"> 00 m ^ V T \ CJ 1 a 1 -* \ P^-'i 1 1 M A. 1 1 1 1 hq 11 1 1 1 1 1 1 1 1 ^ <T-i— i-tHj P 19 ^ \v I u \ 1 1 fi^ • I . "Si-u E* 1 cd «£ 4V cc *"! 4t 35 4 " " o- it IE Eh J 1 ~ " 411 f 4- . 1 ir —IS i .. — .,,. i ilQ" _l51 . 1 i . ffi A-' i it MS%o >J |hI ' -- 1 ' : J 1 1 ' ._._... - ^ Mi! 1 . 1 I 1 .i ; 1 1 11 -4+j- l i "" I — M , —L ^ — „„__ — 1 1 i 1 i P5 ,t^ i 1 i bs 1 1 1 *• 1 1 V 1 hi w V \ _\ y A v O » ci- tp *- i»r - 01 GO • » »*< ^ Jf ' o~~ -1' i___ ta^a^ts^vnts/JGCGii -^^i^thct^p"^ 1 z: ~r ' i -22- Assuming constant inductance, T L[i(T) e(t) dt = S Substituting Eqs. 8 and 14 into 13 and solving for NA where ' = b J "SB" P v - i(0)] NA (14) for the k-th inductor, ^F sin < in this case: K = ex. v = C, J 1 t L,3, L , , , . . , . k + n for In s 0, 1,2, ... The cores must not saturate during the time the applied voltage or for one-half the pulse interval. t T/2 and Eq. = 15 reduces to L, At this point, adequately specified. It I b J^l (16 , on the right of Eq. 16 are known and all the quantities will essentially is positive, Therefore, for this particular case, NA= is 15 > NA has been shown that minimizing core volume minimize losses in the inductor. There are additional relationships that can be written, but there is a danger of over-specifying the core resulting in conflicting requirements and confusion. of core and wire size selection is simplified method is used instead if The procedure a modified cut-and-try of attempting to constrain all the variables. procedure described here does minimize the core volume and The is straight- forward and practical. Coil resistance is usually determined by the allowable temperature rise. In this application, the peak power from Eq. 1 that must be passed -23- by the PFN is 4. 8 kw. If power dissipated in the PFN is limited to less than five percent of the peak power, then P dissipated Most of this most of the total = (°-0 5 )( 4 . 80 °) = power would be dissipated A energy. 24 ° watts/pulse in inductor L, reasonable figure is to since (17) it is supplying allow Li to consume ninety percent of the total loss. PL T (0.90)(240) = 216 watts per pulse = (18) l Average power can be calculated from T P avg The pulse current -r = in JL. 2 (t) i dt (19) x taken from Table (t) i R \ U = 2 is 20.3 sin (^t) (20) x Let t = T and substitute Eq. 20 into Eq. 19 R. P (20.3)' -X. = = ^1 is a good figure will be shown, it 2 (^) dt (21) and using Eq. 18 gives the result Solving Eq. 21 for Rt This sin J to (2) (216) = 1<05ohms (22) (20.3)^ use for all of the PFN inductor coils since, as will result in reasonable coil sizes. -24- A completed by must yield coil the proper value of inductance given 1 Aug N Lk 1|— = (»> Figure 8a shows the standard type-C core that will be used with air gaps The number adjusted to satisfy Eq. 23. of turns of wire on each core large, requiring the air gap to be relatively large. most of the magnetic energy will be stored is can be assumed that It in the air gap. In this case fringing cannot be neglected and the terms are defined as: = \i p, the permeability of air i = length of air gap A = effective cross section of the air gap The effective cross section but is difficult to calculate, it can be estimated by the empirical approximation i i A where D and E are give an answer = 8) (D + the dimensions (E + -J-) shown in Fig. (24) 8a. Use of Eq. 24 will for inductance correct only to within a factor of 2 or 3 . By adjusting the length of air gap and measuring inductance with an impedance bridge, each inductor can be set to any required value. b. The correct wire Choosing the proper core and wire size. size can be found from reference 1,000 to wire tables R^ w = w R = = coil resistance in i = average length in feet r r T entering the table with NT^ (25) wire resistance in "ohms rper 1, 000 feet" ohms as given by Eq. of a turn of wire 22 — 8 -25- STRIP WIDTH WINDOW LENGTH CUT HERE G BUILD UP r -I FIG. a. F kwiNDOW WIDTH C-TYPE CUT CORE STRIP INSIDE DIAMETER WIDTH BUILD UP •+• OUTSIDE DIAMETER F/G.SL UNCUT TOROIDAL CORE 26- From the entire window area is geometry shown of the core, in Fig. 8a, and assuming the will be used, the average length of a turn of wire given approximately as i F = 2E + 2D + (26) Nyclad magnet wire was used primarily because sizes and easy to work with. mately as shown in Fig. wire (size given by Eq. 6. 25) same The required core window area was found with Formvar which The insulation thickness is is slightly much less than the rated value and between layers. to insulate lighter core with smaller N for turns of it rated at 860 volts greater than one The operating voltage any core will be subjected to is 600 v. is many the aid of a table of turns per mil and there are several layers of wire on each core. volts-per-turn in Nyclad insulation has approximately 11. insulating characteristics as per mil at 25 C. was available The coils were hand wound on a lathe approxi. square inch found in Reference the it maximum Therefore, the was not necessary This provided a more compact coil and a window area was required than if an unnecessary insulating layer had been used. The smallest core given by the product that can be FG used in Fig. 8a, is one that has the window area, completely filled with wire. For each inductor, calculations were carried out for several core sizes and the results and coil. compared in order to determine the best combination of core The choice usually came down to two cores, one had a larger cross section and was also usually heavier than the other. In each case, calculations showed the smaller core required a larger coil in order not to saturate at a given voltage level. Resistance of the two coils was the -27- same, about one ohm, and therefore the choice seemed easy to make-select the smaller core to minimize core losses. to be the best choice. When these two inductors were assembled and tested, as discussed in Chapter III, cross section invariably saturated the inductor with the smaller core at a lower voltage level than was Whereas, the inductor with a larger core cross indicated by the calculations. section saturated at about the calculated level. is that the This did not prove A simple explanation for this larger number of turns of wire required by the core with the smaller cross section resulted in weak linkage of flux with the core from For the turns in the outermost layers. a criteria for choosing this reason, between two theoretically equivalent cores for a given inductor is to select the core with the larger cross section. The cores and wire sizes that were selected and the charging reactor are summarized in Table 3. PFN inductor The figures in are the result of calculations similar to the sample calculations this table shown in for the Part C of this chapter. Table 3 List of Inductor Construction Material Characteristics L. L, L Inductor 1 8 7 Core number Dimension (in.) ' D E F G Weight (lbs.) Cross sec. (sq. in) Window area (sq. in.) i c (feet) Wire size (AWG)" LI r w (ohms/1000 ft .) * 2 3 • ^4 L 5 ^L6 Z-216 H-41 Z-1 Z-4 Z-2 Z-5 0.750 0.375 0.500 1.500 0.354 0.281 0.750 0.229 0.625 0.250 0.500 1.312 0.500 0.250 0.500 1.125 0.375 0.375 0. 187 0. 187 0. 170 0. 156 0. 122 0. 114 0.250 0.625 0.038 0.063 0.656 0.562 0.375 1.000 0.056 0.063 0.375 0. 187 0. 167 0. 0.750 0.375 0.625 1.250 0.334 0.253 0.780 0.240 19 8.051; 125 0. 156 0. 135 22 16. 14 24 25.67 24 25.67 24 25.67 16. 14 952 1,596 1.596 1,596 952 22 ' Winding density (turns/sq. in.) 473 -28- Typical inductor design procedures c. methods used sample in constructing the inductors initial calculations for . The procedures and are shown by a set o£ one inductor. Then it is shown how these figures had to be changed after the inductor had been tested. The sample calculations are shown Chapter of the inductor is the subject of the initial ones made to in this part, whereas.the testing determine if III. The following calculations are the particular core and wire size are adequate for the element under consideration, in this case L,. value of the element The shown in is given in Chapter first step is to select a Table Z-216 core, from Eq. 3. The III. core and tabulate its characteristics as With the core cross section area from Table the required number final of turns of 3 for the wire for L, can be calculated 16 N (4.69xl0- = 3 )(l6 0)(1.27) (1.81x 10 = 362 turns (2?) )(1.45) where: 69 millihenrys Li, = 4. I = 16.0 amperes P 1.27 b, = AB = 1 A = 4 (0.281)(6.45 x 10" . 45 webers/square meter ) = 4 1.81 x 10" square meters The wire size can now be determined from Eq. 25 and a wire r w ~ (1.05)(1,000) (362) (0.229) " table , . /, Q00 £teett 2 * 7 ohrns / 000 1Z 1 ' (2.8) — -29- This corresponds directly to number 21 wire, but number 20 wire was selected because of its lower resistivity. The Z-216 core has a would be adequate for The required = 362 0.583 square inch j-jt- - window area of air gap 2 T L.. = (362) 1 ' is it this inductor. can be estimated with the aid = (1.750)(1.375)(6. and the inductance (29) 0.750 square inch, therefore an air gap of one inch on each side of the core A to the coil winding is Window area If 20 wire has a winding The window area required density of 621 turns per square inch. accommodate Number 4 45 x 10" ) = of Eqs. 23 and 24. assumed, Eq. 23 becomes is 4 15.5 x 10" sq. meters (30) approximately 4 7 (15.5 x 10~ )—(4ir x 10~ )— -j (2) (2.54 x 10) • = ... n ..... 5.03 millihenry s , w(31) ,„ (_ _} Equation 31 shows that a total air gap of two inches will give approximately the required inductance for L>, . Exactly the required value of inductance can be obtained by shimming the air gap and measuring inductance with an impedance bridge. This is the extent of the PFN inductor. initial calculations that Based upon these calculations were made the five PFN constructed and assembled for tests as shown in Fig. 11a. the completed breadboard model which is the final for each inductors were Figure lib shows version of the PFN. Preliminary versions differed from this photo only in that capacitance decade boxes, which were easier manipulate during tests, replaced the capacitors shown. PFN to The exact nature and extent are described in Chapter III. of the tests performed on the CHAPTER III TESTING THE PULSE FORMING NETWORK A. MEASUREMENT OF INDUCTOR CORE SATURATION VOLTAGE LEVEL It was desirable satisfactorily under determine to if the individual inductors would perform normal operating conditions without having and test the complete PFN. to assemble Equation (13) states that the flux density in a ferrite core inductor is proportional to the time integral of the voltage This assumes that the resistance of the applied across the coil terminals. coil is zero, or at least very small compared to the coil When reactance. the coil resistance cannot be ignored, the circuit of Fig. 9 can be used to subtract the voltage drop caused by the coil resistance and display a picture of the hysteresis loop, which in this case would be more accurately described as a plot of coil flux versus coil current. The operation at point the currents Y l Which By summing of this circuit is as follows: c ' »R + % < 32 > is vR. dv V R v - v v c-*--itf--^-V + where: v = vT + v i = coil voltage in volts = inductor current in amperes r = inductor coil resistance in R= 10 C one microfarad = R. — <R ohms ohm, 50 watt potentiometer ' ? = one megohm -30- - v V- (33) -31- L R, I * .T-i* -\ C * Y - V R2 ':> R X R FIG. 9 l >V R, Rpt CIRCUIT FOR DISPLAYING INDUCTOR CORE SATURATION VOLTAGE LEVEL 20 volts/cm 20 volts/cm FIG. 10 CORE HYSTERESIS LOOP -32- FIG. FIG. lib 11a FIVE PFN INDUCTORS BREADBOARD MODEL OF THE PFN AND THE CHARGING REACTOR -33- The resistance of the parallel than the reactance of and if we measure in the coil, and in C R } and R £ combination of The reactance at 60 cps. the coil resistance and set R much will be larger than R to this value, or i_ i . On v small the current this basis 2 R = -ir v c - c - n R^-R-;(33) larger can be made: v Then equation much of the coil is also 1 the following approximations will be (34) can be written v = cry J c vdt - dq J idt < 35 ) But RR c r therefore V The hysteresis loop c onnecting the = C ciq I < v - ir of the inductor core > dt 06) can be viewed directly by horizontal and vertical amplifiers of an oscilloscope to points x and y, respectively. This circuit is used by first calculating the flux density level that the inductor must absorb under operating conditions and relating this level to an rms voltage reading across the here for L, coil. Sample calculations are given . The voltage drop across an inductor e(t) = I^- coil is ' (37) -34- Coil current in L under operating conditions = i(t) o sin^- (38) LI o i T cos^TT e(t)= The flux density level I is (39) u is T B = LI f e(t) dt = (40) Or This corresponds to one-half the total change in flux density that a inductor will experience during a discharge pulse. It is PFN required that the inductance remain constant during this interval or that the flux density remain in the linear region of the hysteresis curve T 2 J at 60 cps this e(t)dt = (2)(4. 69 corresponds -, 3 x 10" )(20. to a — = (0. 190)(0.707) of Fig. minimum volt-seconds (41) voltage across the inductor of 00833 This must be the 3) = 0. 190 = w . ,,,. l4 0>/ro volts RMS . ( 4 * * voltage reading at the point where the curve 10 begins to change slope in order to insure a constant value of inductance during a pulse. Figure 10 shows the hysteresis loop obtained for L, by The voltage level corresponding saturate: is 19.0 volts perform satisfactorily RMS. in the to the point where this method. the core begins to This result indicates that this inductor should PFN under normal operating conditions. -35- CONSTRUCTION OF THE PFN TESTING CIRCUIT B. The to do this For PFN was tested by observing was necessary it testing the to assemble dummy network a its output pulse waveform. shown the pulse generator shown load, as in Fig. 12, was is made variable to provide an exact matched load for the PFN. pulse waveform referred to is the voltage The function discharges. while charging the PFN appearing across of the diode is to in Fig. 3. used in R R place of the pulse transformer, klystron, and elements D, and order In The output R T when PFN remove R_ from the circuit improve charging efficiency. to The power supply used was a large nonregulated d-c unit that was available in the laboratory. It was arranged with voltage to be varied from arrangement to protect 500 volts and a current limiting circuit breaker to from overloads during it The charging reactor for tests. the test circuit could have been any reactor had low coil resistance, provided a satisfactory charging interval and that The one did not saturate. that was used throughout reactor described in detail in Appendix and a variac to allow the output A all the tests is the and referred to in 1, 3, 7. The timing circuit and switching SCR's are discussed in Appendix B. ator. PFN However, and is detail in This part of the test circuit requires a lengthy discussion to properly emphasize C. Tables its this deferred importance in the design of discussion is this type of pulse gener- not pertinent to the actual testing of the to a later part. CORRECTION OF THE PFN OUTPUT PULSE WAVEFORM Requirements summarized that the output pulse as follows: than 50 microseconds, 1) 2) rise time waveform must meet can from the to oe 90 percent level less overshoot and ripple less than 10 percent, -36- Oroo a Fig. 12 Dummy Load for Testing PFN -37- 3) approximately one millisecond in duration, energy. Item number 4 until the final The waveform was obtained and first three The first but is significant, items are covered in PFN version of the it 4) contain was not actually measured the PFN efficiency that was tested had approximately The actual measured element values differed it was glas stock and air gap. slightly of from the Chapter II. the theoretical inductor air gaps precisely using plexi- diff icult to adjust the mylar shims which was The element values for was calculated. this section. element values calculated from the theoretical discussion because 4.8 joules of the method used to the first PFN version are listed in Table The resulting output pulse waveform is shown in Fig. 13. obtain the required 4. This pulse meets rise time and duration requirements, but the ripple is about 25 percent and gets worse toward the end of the pulse. Table 4 Element Values for the First Version of the Measured PFN Measure :d C (M<f) k ^(mh) 1 4.70 21. 5 2 4.80 3. 1 3 4.97 0. 775 4 4.80 0. 370 5 5.05 0. 180 Reference 1 indicated that an increase of sixteen percent over the theo- retical values of inductance resulted in substantially In order to k determine the amount following approximations of improved waveform. increase required in this case, the were made: -38- TO T/ - = z "V Z T = 18 (43) TT (44) n ohms (approximately) = one millisecond Solving these equations yields This is L, = 5.75 mh C1 n,f = 17.5 (45) an increase of twenty-three percent over the theoretical value of The second version of the PFN was made by increasing the inductance values all by approximately twenty-three percent. are listed in Table L., These element values 5. Table Element Values for the 5 Second Version of the PFN Measured C (M.f) k Measured Calculated L (mh) L^mh) k 15.0 1 5.75 5.75 2 5.85 5.85 1.512 3 5.88 6.05 0.495 4 5.90 6.00 0.241 5 5.95 6.20 0. The resulting output pulse waveform an undesirable overshoot is shown of about twenty-five in Fig. 14. percent and 130 This pulse has is also too narrow. In order to reduce the overshoot, the amplitudes of the higher harmonics -39- 100 0.20 Fig. 13 msec cm. PFN Version 30 Fig. 14 msec cm. cm. Time Output Pulse Waveform from the First 0.20 volts Time Output Pulse Waveform from the Second PFN Version volts cm. -40- were decreased by successively increasing The ments final of version of the PFN was arrived at by trial-and-error adjust- element values until a satisfactory pulse waveform was obtained. This waveform in Table 6. shown is in Fig. 15a and the element values are summarized This waveform meets the first three requirerre nts verywell. Figure 15b shows the rise time than fifty microseconds. to the ninty Table Element percent voltage level Figure 15a shows the pulse duration one millisecond, and the overshoot and rippj.e is is approximately 6 L^mh) PFN C k (^f) 1 5.80 2 6.25 1.60 Z3 7.40 0.464 4 8.30 0.194 5 9.35 0.103 The adjustment 19.7 of inductance values for the final was carried out with E = 100 volts. When number version of the the supply voltage give a 300 volt output pulse, the pulse shape core saturation was beginning. less are less than ten percent. "Values for the Final "Version of the k to the values of inductance. PFN was increased became distorted indicating This was remedied by recalculating the required on each inductor, as shown here for L,, and of turns making the additions. XT N = —5.80 3 x 10" x 2 1.81 x 10 r w = 445 xO^ 16. x 1.27 = ..- . 445 turns ,.,. (46) x 1.45 = 9.8 ohms/1,000 ft. (47) -41- ^— Nj -L X + i ! J J. X J. * i i i i.i i TW \i • T"; ; x I + X \/' L 1 1 Ml J volts 100 1 cm. : 0.20 Fig. 15a msec Time cm. PFN Output Pulse Waveform from the Final Version j. X X X. X I j / / 1 / I / / 1 Li J. I III! Ml! MM I 1 II Ml' 100 X 1 X 50 Fig. 15b i- sec cm. Time Leading Edge of the Final Output Pulse Waveform volts cm. -42- This corresponds to number wire which has a winding density 19 of 473 turns per square meter. 445 Window required This is = -r^pr the effective window area to of the large air gap which increased approximately one square inch. MEASUREMENT OF PFN EFFICIENCY The efficiency of the PFN effects of the charging reactor for the the (48) larger than the window of the Z-216 core, but the additional wire was accommodated by taking advantage D. 0.94 square inch - PFN. PFN of the Figure charges PFN is to is difficult to must also be included shows 17 describe independently. that for a d-c in the efficiency figure power supply 450 volts in about five milliseconds. about 0.2 ohm and The level of 240 volts, The d-c resistance the charging reactor resistance is 3.84 ohms, Substituting this value of resistance into Eq. 78 gives v(T The attenuation of the ) = 1.925 PFN x E = 462 volts (49) voltage could be reduced but only by making a larger reactor coil winding to reduce coil resistance resulting in a heavier element. When the The resulting pulse voltage level PFN of about was tested with 20 msec between pulses. from the in Fig. 17 as 200 volts. full power if the PFN were lossless. at a continuous repitition rate of The average power input power supply was measured as to its This loss shows up as a lower one ohm. level output pulse than would be expected PFN shown discharges, each inductor dissipates some power due own winding resistance The is to the pulse generator -43l I I I I !rr I t~\ i 1 ,d U.\ 1 i > ti\ / pi 1 j I i 1 ! /^V / 1 i \ i II 1 ' , 1 i ' i 1 1 i i ' 1 ! XI \ / \ i \ f 1 ! i—v 1 > : \ -tt i\ / 1 \ ^/ ^*^ / 1 iSj \Jr\ / ' V I 1 ' \,/ : / i\ i/ II i^i \ / \ \ ; / ' j I / \ i ' ! i i I 1 / f -'*-' I 1 ! \ H-\fI />^n 1 f* 1 1 ll MM | I fpTH' r'oi'DTi 4 lfAiTir !? 'cAiTinrrx uKArn O.I VULiAliiL-fcQUARll.L> VS rlMk U LI -r\ FOR 'AM OUTPUT i~;i-Lc! HPULSE in/^"^^s. y. \ x I II I 1 i l| Jr T^ OUA >> i i 1 ill ' 1 i i i i i i ii iii,i | 1 : ! | , i i ' i 1 1 1 : i i i 1 i 1 1 I 1 I M 1 1 1 ' 1 i 1 II '1 1 1 1 1 11 1 i It I ! | 1 1 1 1 1 1 I'll 1 1 1 III 1 ' ! • ' 1 1 i 1 —--,.. 7r\ fU ' ! -J .......... ' 'III' i I ' 1 1 i i 1 ' i 1 1 ! i i '1 1 ' 'II 1 1 i i i 1 1 II ' 1 1 ' 1 II M 1 bU j^jO L ! H Q o ^ ' 1 1 ' X 1 i 4-" C 1 1 41 i it I 'i ^hT" A A/l o = Ir^Q 7 y.^ 'ao^'a AKLA I r-/^ >bU 1 c<~*r'r\r^T\ (VOLIS) -SECOND | 1 | i M4- 4- ~-P 44 o H W -|ill /\Tr\j' rvc* \ ; ' 1 | i 1 j | 4- '-' 4- | 1 ' 1 4_ -£ IT Mi ! GM IS H 40 *SM */u >J i i ' 1 , ! . ' .. I L Q> ' 4- rU ^M 4- - -f'rJ *M - SX H 1j 3/-\ <J 4- -L 444 4- 4 t ' l 44 111 Ml II i i *i<-> 1 I!' 1 VJ i* --44 1 1 4TL 444-41 ' i I ii 1 l i i 1 j j I l 1 I or\ £XJ- 1 1 - 1 Ii i I 1 i i l i , i 1 i__ \ ' I i tfS' IV .... u...-. \1 ... 1 i I Ll t i l V ' i i 1 1 1 —T ME Ml "T^ii a a it r 1 1 , 1 rr~ i Jt i i i '<"* " IA rttrrS .4 'i f M i i i t I 1 /** !/™\ 1 1 1 1 v. X Ml f* i 1 ' \. 1 1 .8 -- ; 1 \ 1 i4 r\ c\CQN DS M 1 • ' \ ' ! ' 1 ' I 4^sT4-44 IX I.O 1 I 1 I -44- > o to «l 4-" —4 o > o o — Oh 3 ft o ni <D 60 d 4-> i—l o > Z ft ft © 60 o. i—i O > i—i ft ft CO h o ft (1) a) a o 60 • i-i ft : -45= P~ in I E E I s s 0.75 x 380 = 285 watts = power supply output current = = power supply output voltage The average power per pulse is in (50) v ' amperes in volts given as P— .IJ^d* R pulse t J (51) T wher e t = 10 -3 seconds PFN e(t) = output pulse voltage in volts R T =1.75 ohms The integration for Eq. was carried out graphically as shown in Fig. 51 The resulting pulse power is P pulse . The average power output n P out = — =£Hr 17. 5 is kw ( v 52 ) ' defined as 4.53 x 10 ot; Z0 t~ pulse repetition rate s^rri The resulting efficiency 3 00 , watts = 226 /c _. (53) v is "-y^-MI in It is = 4 - 53 power r—pulse c 16. " °- 794 (54) not sufficient to discuss efficiency just in terms of power transfer. In this case, it may be more meaningful to describe the requirements of the pulse generator in terms of energy transfer and output pulse shape. The pulse generator must deliver, to the klystron, 4.8 joules of energy in one millisecond. The pulse shown output requirement. required 4. 8 joules. in Fig. 15 does not quite The energy output is meet the energy only 4. 53 joules instead of the -46- The voltage level cannot be increased because would adversely Therefore, the only thing that can be done effect the klystron. the this energy in the pulse is to it will reduce the a poorer match with the load (Re: values can only be made PFN Eq. One adverse effect characteristic impedance causing A 5). increase This could be accomplished increase its duration. by increasing the capacitance values some small amount. of doing this is that to final determination of element with the pulse generator actually driving the klystron under operating conditions. In any case, the adjustments would be minor and we can assume that the power requirement can be met without too much difficulty. E. ENVIRONMENTAL TESTING In order to insure a degree of space flight worthiness, the PFN inductors and the charging reactor were tested in a hot-cold chamber. inductors alone were tested because cal items since they the were all it was handmade. felt that they The capacitors breadboard model would not be usedin a final were the most that version of The criti- were used this PFN in and there was no point in testing them. The inductors were enclosed generator was operated with full in the hot-cold perceived. the test pulse operating voltage levels at -25 C for two hours and at +50 C for two additional hours. was monitored chamber and The output pulse waveform for this entire period and no change in shape or level was CHAPTER IV SUMMARY AND CONCLUSIONS SUMMARY A. This problem originated when the Electronic Systems Laboratory at M.I.T. constructed a breadboard model system for making measurements radar of a space vehicle This breadboard model had a line-type pulse generator which used a that to was 22 inches long and weighed about minimize fifteen pounds. It it was felt that if it PFN was desired the size and weight of the entire pulse generator. the largest and heaviest item and Venus. of the reflectivity of the surface of The PFN was could be optimized, then the entire pulse generator would also be optimized. Subsequent in- vestigations verified this assumption. The problem was first step in the investigation of the to make a study of the proposed line-type modulator to determine the parameters that described the A optimum PFN and hence guiding factor in the determination of the the optimum pulse generator. PFN was that the associated components, such as the pulse transformer and the charging reactor, had to be physically realizable.. It the combination of these was assumed that the study components that resulted in lightest weight complete pulse generator. This is the details of which are in Appendix A, but there would reveal the smallest and what the study revealed, was the unexpected additional result that the physical size and weight of the pulse transformer was independent of other parameters for the three values of power supply voltage that were assumed. The power supply that would be used in the capable of operation at any fixed level between this reason, the 3 complete system 00 and 500 volts. is For values of power supply voltage taken for the study were -47- -48- 300, 400, and 500 volts. For each of these three operating values, the pulse transformer had a calculated weight figure of about 2.5 pounds. This is less than the complete transformer would actually weigh because the weight of insulation and packaging was not considered. figure indicated that any of the supply voltage levels This weight was satisfactory and that final determination rested on the value that optimized the was PFN, which the original assumption. Two chosen. factors indicated that the lowest power supply level should be First, the higher voltage levels would require heavier insulation in the inductor coil construction, and second, the higher voltage levels would require more turns in each factor was coil to prevent saturation. the relative ease in obtaining 600 volt A final SCR's as compared to 1,000 volt SCR's for use as the switching devices. There were two factors this PFN It was made the design and construction of These are the high power and long pulse a difficult problem. duration. that felt that the size and weight of the considerably by using ferrite core inductors. PFN The inductors had linear, however, to obtain a satisfactory output pulse meant had that the core material throughout its to could be reduced to be waveform. made This be one that had a linear permeability range of flux density. This led to the examination of the "square loop" materials and Z-type "Hypersil" was selected because it has a higher saturation flux density than the other materials considered. One small problem with this in certain standard sizes. material was that it was readily available only The manufacturer's delivery time on these "stock" sizes was two-to-three weeks, and the non-standard items had to be specifically made and took up to nine weeks for delivery. For this reason -49- one of the more readily available H-type Hypersil cores was used in the construction and testing of the The completed PFN inductors are shown in Fig. 11a with a reference scale to indicate their size. inductors was used compares is listed in PFN. Table The important characteristics The 7. of these statistics for the charging reactor that in the tests is also included in the table to indicate to the one used with the original Table Summary of PFN PFN how it which weighed 5.8 pounds. 7 Inductor Characteristics Total Number Wire Size(AWG) Resistance (ohms) Weight Inductor Core Li Z-216 19 442 1. 11 0.917 L2 H-41 22 280 1.04 0.312 L3 Z-1 24 230 1. L4 Z-4 24 290 1.24 0.129 H Z-2 24 253 1.22 0. of Turns 10 N Inductors Lc Z-5 3.84 Total Weight of All Inductors The small size and weight of the PFN capacitors used in the final version of this the total PFN weight to 5.6 pounds. inductors Consideration was given 187 099 0.790 2.434 is significant. PFN weighed lbs The four pounds bringing This weight can be reduced considerably by having capacitors specially manufactured ments. 0. 1.644 lbs 500 22 (lbs) to meet space application to the fact that the require' highest operating voltage -50- required the smallest amount of capacitance. considerable weight to the PFN the capacitors will be lighter This voltage. may if Since these items contribute a superficial examination the PFN is would indicate that designed to operate at the highest not true, however, because although less capacitance is be required, the units are larger and heavier than for a similar lower voltage rating and no net savings can be realized. The original PFN, shown in Fig. twenty-two inches long. about one-third as 2, weighs fifteen pounds and is This new PFN, shown in Fig. 11a, weighs only much and could be packaged in about six inches by four inches by four inches depending upon the capacitors and the arrange- ment used. The efficiency figure for the PFN, given reasonable considering that a certain amount PFN in order to make it compact. by reducing the resistance Although larger. above it still would have may be may to this of the Some in Chapter of loss III as 79.4 /o, is was designed into the saving in power could be realized charging reactor by making the coil would certainly improve the efficiency figure given not be a desirable thing to do. Any increase in coil size be accompanied by a larger core and the additional weight more undesirable. This efficiency figure also does not include any loss that would be incurred by resetting a pulse transformer by the method described in Appendix A. In conclusion, the a satisfactory efficient, It answer PFN to the that was constructed and tested provides problem of size and weight. and operates satisfactorily over a wide range produces a pulse waveform that meets all the It is of reliable, temperatures. requirements but energy -51- content. This deficiency is small, however, and can be easily corrected by making the pulse duration a little longer by increasing the capacitance a small amount. The circuit that was used to test the PFN is a complete pulse generator with the exceptions of a pulse transformer and proper power supply. also the optimum pulse generator of this type for this application. refinements in the timing circuitry to It is With meet environmental requirements would be ready for further application in the complete radar system. it APPENDIX A A PARAMETRIC STUDY OF THE OPTIMUM PULSE GENERATOR The object The of this thesis is initial step in the an optimum PFN PFN construction of this voltage at which the system will be operated. as described in Chapter is to II. determine the supply- The power supply voltage be used in the pulse generator can be any level from 300 to 500 volts. that would This appendix studies the effect of power supply voltage on the components of the pulse generator. All calculations are based upon three values of E as shown in Table 8. A. THE PULSE TRANSFORMER The elementary theory transformers of pulse is sufficient for the purpose of describing the smallest possible transformer that will work in this pulse generator. must consider and ease The actual construction design details of of construction. minimum transformer distortion of the pulse shape, efficiency, These items will not be evaluated here since they are not too important in the determination A of this simplified model of a transformer of size is and operating voltage. given in Fig. 18. The relation- ships between primary and secondary quantities are E I = I p p = I p E Es (55) NI s (56) E -^ N (57) = p s E E /I _£.= _£*. X N^ p (58) The transformer being considered here will drive a klystron with an input pulse of 4. 8 kw at 8, 000 volts. -52- -53- so' E E = = 8, 000 volts =1 I = 0. 60 (59)' K amps. (60) E ~- 13,300 ohms = (61) s This pulse transformer must meet the following specifications: not saturate during a pulse, must not store 2) magnetic energy during a pulse, 4) must be compact and If 3) a large must have low amount 1) must of residual resistive losses, and light weight. the voltage input to the primary is in the form of a rectangular pulse, T e(t)dt = : ET (62) Because the transformer will be reset between pulses, core, as shown in Fig. 8b, can be used. but it does not during a pulse make if This may transformer unfeasible. the a gapless toroidal complicate construction, The cc::e will not saturate the turns-cross section product satisfies NA = ||. The number of turns in the (63) primary winding must be the residual magnetizing current to a minimum reasonable figure that gives good results is that sufficient to keep at the end of a pulse. magnetizing current should be less than five, percent of load current. I m =0.05x1p The primary inductance is (64) given by T I m Lp = I tJ e(t) dt A (65) -54- > Cn—^sr /» R ,-rm rv^_ L <r /V~A° R Ls : S^ v /;/v SIMPLIFIED PULSE o TRANSFORMER MODEL AAA C* ^ V ¥ * FIG. 19 EQUIVALENT —.J .J CHARGING NETWORK -55- E T L =-=E- In addition, the (66) primary inductance is related to the core material by N 2 Aia L —— pi m = A = core cross section = M. m= 1 (67) v ' T ^ core permeability magnetic path length to r ° Z-type Hypersil has an incremental permeability of approximately o 8, 000 over the operating range of flux density. able answers but This figure gives reason- probably lower than the actual permeability. is of permeability taken as the average slope of the operating limits is about 44, 000. 7 because the frequency components This value is of the pulse lower of these two values of permeability is The value d-c.B-H curve between higher than can be expected are at least 500 CPS. used for The all calculations to allow for the higher frequency components. Calculations were made for several toroidal cores before a choice reached. However, only the calculations for the Z-361 core are shown since this is the one finally selected. 1 Volume Core Z-361 A(in (in3) 7.85 Assume source Primary 2 1.00 ) m Window Weight (in) (in 2 ) (lbs) 7.85 3.14 1.95 voltage of 300 volts. turns: N = P 300 x *° _3 4 (6.45 x 10" )(2.9) = 160 turns (68) was -56- Secondary turns: Turns ratio Ns lj°°2 = = (26.7)(160) = The winding resistance is = 26. 7 (69) 4,275 turns determined by limiting it to five percent of the load impedance. R primary = (°- 05 >< 18 - 7 Secondary The average length is = < > = °- 97 oh ™s 05 >< 13 300 > = 665 oh ' ' turn of a winding ™s calculated from the core geometry approximately i c = F + 2E + 2D = 0. 583 feet (70) Primary winding resistance r This corresponds w to = (l oQKQ^si) = 10 5 - ohms /^ 00 ° ft ' ( ?1 ) number 20 wire. Secondary winding resistance r w= This corresponds to |i&= 2ttohWM00ft. (72) number 34 wire. The winding stacking factor was determined by examining a pulse trans- former of in the laboratory. This transformer has a primary widning consisting 400 turns of number 24 wire and a secondary winding consisting turns of and 8, which number 32 wire. 4,200 The primary and secondary voltages are 300 volts 000 volts, respectively. is of The core window area is 2. 06 square inches completely filled with wire and insulation. By taking the total wire area and dividing by the window area a stacking factor was determined for use in further calculations. -57- X (Number primary turns)(Area = + 20 wire) of no. (Number secondary turns)(Area /window area 32 wire) of no. (73) X Stacking factor = 0.163 turns = In addition, a hole large enough to pass a winding shuttle Most the center of the window. inch diameter hole. shuttles can be must be left in accommodated by a one- Therefore, an area of 0.785 square inches must be subtracted from the core window area. The window area required to accommodate the windings can now be obtained from Eq. 73. w Window area required . . . . 000802)— + (160)(0. — = - . . = 1.6 square inches = 3.14 Available window area If 275)(0. — 000031)L 163 (4. A -s , 0.785 =2.36 square inches - the weight of insulating materials and other attachments such as terminals is ignored, measure a of the total transformer weight can be calculated for comparision purposes. Weight of winding (Number = Primary winding (4, Total coil weight = 0.588 = 1.950 = 2.538 Primary inductance = p gfe0> (74) . (75) is 2 L ) 275)(0. 00012)(0 583) = 0.300 lbs. Secondary winding= Transformer weight turns)(Weight of wire)(i (160)(0. 00309)(0. 583) = 0. 288 lbs. = Core weight of (6.45xl0- 4 )(8 . OOOH^xlO- 7 £0 ) = Q g32 he -58- The minimum primary inductance required . L = p is 3 300 x 10" .__ = n 0.375 henry' n— 0. , These calculations show that the Z-361 core (77) is adequate in respects. all Similar calculations for supply voltages of 400 volts and 500 volts show that the same core can be used. The results shown in Table pulse transformer size is are interesting because they show that 8 independent of the supply voltage. This means PFN that the size of the optimum pulse generator depends solely on charging reactor. All other elements are fixed in size by the power the and handling requirements. Table 8 Summary of Pulse Generator Parameters and Pulse Transformer Characteristics Supply voltage E Char, impedance Z Total PFN cap. C Total PFN ind. Ln Load current I Load voltage E Primary current I Pri. mag. current n n o I o m N No. pri. turns N 400.0 500.0 Ohms 18.7 33. 3 52.0 V* 26.7 15.0 9.6 ,16.7 26.0 0.6 mh 9.35 Amps 0.6 0.6 Volts 8000.0 8000.0 Amps 116.0 12.0 8000. 9.6 Amps 0.80 0.48 0.60 Turns 26.7 20.0 16.0 Turns 160.0 214.0 267.0 20.0 21.0 22.0 4275.0 4275.0 34.0 34.0 P Number Pri. wire size Sec. wire size 300.0 P Trans, turns ratio No. sec. turns Volts s Ns Turns Number ' 4275. 34.0 -59- Table Max. 8 (Continued) pri. resistance R Ohms 1.0 Max. sec. resistance R Ohms 665.0 2.60 1.67 665.0 665. Min. pri. induct. Henry 0.3 0.667 1. Calc. pri. induct. Henry- 0.832 1.49 2.32 Pri. coil weight lbs. 0.288 0.305 0.340 Sec. coil weight lbs. 0.300 0.300 0.300 Core weight lbs. 1.950 1.950 1.950 Total weight lbs. 2.538 2.555 2.590 B. THE CHARGING REACTOR The principle of resonant charging 5 is used to charge the PFN This method works best approximately twice the supply voltage. to when the resistive losses in the charging network are small and the value of charging inductance large with respect to the total inductance of the is PFN. If these conditions are met, the equivalent charging circuit is shown in Fig. 19. assumed zero Solution of this network, with v n (t) = Es[ L 1 - e -at E . ... l (t) s —r— = e (cos -at cot sin + — w sin initial conditions, is cot)]J (78) . (79) cot c where: R (80) 2T7 R = total L ° = Cn network resistance = inductance of charging reactor ( trrr c n = total ~ 1/2 R 1 " 4L. PFN capacitance (81) 04 -60- If losses are small, the solutions reduce to the approximations v (t) = E (1-cos (82) cot) E i The PFN voltage n (t) =-r~ coi-< will reach a sin (83) cot c maximum 2E when s of t = tT\I L> * c C~ n At . this time network current will be zero. The normal method of applying this principle is to trigger the discharge at the resonant frequency completely and then allowed to Tr It is with the original Figure PFN 2 = by using much it Lc made ma is about ten times L Secondly, an L. is too large, the to be satisfactory. are similar to must be used SCR 13. of a charging L. n . SCR In this Any value ' A value generally requires about 30 to microseconds, q to turn it on; will not fire because the timing A value of L = 130 for this reactor using a those for L, given previously. in place of e(t) in Eq. was required First, the charging period will SCR The calculations that in the calculations. pulses are only about ten microseconds long. found The use of gate current, sustained for several the reactance of discharged would require a very large as small as desired. larger will cause two complications. long. is (84) this principle. this will not justify ignoring become excessively PFN n-\flTC n shows the charging reactor case the c practical lower limit on smaller than which case the charge again with the repetition rate allows the charging inductance to be if in not disirable to do this here because charging reactor. 150 co, PFN The value of v(t) mh was Z-5 core from Eq. 86 -61- & -H-t- ++++ +*++ M-H- ++H +« 100 VOitS Cm. -/ 2.0 Fig. 20 msec Time cm. Power Supply Level and DC Resonant Charging of PFN T 4!• •.•.I ' i.i i ' - i i j,'-' 100 2.0 Fig. 21 PFN msec cm. Time Oscillations After an Output Pulse volts cm. -62- The charging period T c is 3 6 (130 x 10" x 19.7 x 10" })* = 5.05 = PFN Figure 20 shows the clearly in Fig. 21. the PFN mismatch is shown mismatch is required end of a pulse. SCR PFN voltage In this figure, the the end of a pulse and the ripples the result of the in Fig. 20 are matched PFN stops conducting, the is oscillation. to the load. small reflection The This is turned This off at the not zero at the end of a pulse losses are very small and it is slight of the load pulse. SCR insure that the discharge PFN voltage shown more not allowed to recharge at is show up as a damped 15 as a in Fig. The PFN not being perfectly to (85) voltage and-power supply voltage during the charging The small ripples on period. ms when the therefore These oscillations in no way adversely oscillates with little damping. effect the pulse generator operation since they do not appear across the load. The possibility the of eliminating the charging reactor primary winding of the pulse The voltage across a reactor v L., L (t) = transformer in its completely by using place has been considered. as in Fig. 19, is E cos w t (86) The reactor must not saturate during the charging interval. This corre- - sponds to satisfying the equation T AB NA If L. is = f v(t)dt = E Y'Lc" s n sin (ttL CJ (87) taken as the calculated transformer primary winding inductance from Table 8, this reduces to AB NA whereas the pulse transformer = (E s )(208 x 10' 9 was designed AB NA = E x S ) (88) to satisfy 10" 3 (89) -63- The difference between Eq. 88 and Eq. 89 indicates former would not be reset in the charging process it would most to this: use a cut-core with an air gap, which would result in a much larger transformer, 3) and that There are three solutions likely saturate during the next pulse. 1) that the pulse trans- 2) reset the gapless core from an external source, or use a separate charging reactor. able since it The third solution will lead to the lightest pulse generator. former must be reset during the charging period. is the most accept- But, the pulse trans- This requires that a large voltage appear across the transformer primary winding in order to reverse saturate the core. In order to protect the klystron the series combination of D, and from large negative fly-back voltages, R, is The diode protects the klystron used. while the resistor provides the necessary voltage to reset the pulse trans- former. The equivalent charging circuit becomes similar The assumptions are than R, and that R, 1c k primary winding reactance that the is much larger than & Rn . is to that of Fig. much The voltage across to 19. larger R. k is approximately E v(t) = ft * Rk s j-2. sin (90) cot c Substituting to - (91) C ifL c n \ yields v (t)dt = 2Rk E s -^ =2R Therefore, the value of R, required the charging period is to k E Cn s (92) reset the pulse transformer during -64- r> R, = N2 3 x 10" Yn the resistances R and n 2 x E , to to a 600 volts. xl0" 3 7T 1Q nnn 000 ~ 18» ,. /Q (93) . ohms . system will be reduced due Instead of the PFN charging to to damping by approximately k the final value, found s corresponds PFN of the R 2 39.4 x 10 n The charging efficiency = (26.7) from Eq. i 78,» will be about 1. 6 x E required supply voltage of 375 volts in order . to . This s charge the APPENDIX B SILICON-CONTROLEED-RECTIFIER SWITCHING DEVICES AND TIMING CIRCUIT When this thesis first proposed, one questions that had effectively be used as At the time, commerically available SCR's had a switching devices. peak-forward-voltage rating at least one of the was whether or not SCR's could to be investigated maximum was of 850 volts. 9 There was, however, manufactufef who indicated that an SCR with Ratings volts and 110 amperes was available. 13 There was no indication of i, of the availability and cost of this higher rated unit nor of its performance. was when a contributing factor Once the power supply voltage had been determined as 300 and an unmarked SCR that was tested and found of an SCR proper times. by opening the circuit or first method maximum is used 2) for SCR-1 have the proper voltage for to switch the means; 1) to SCR off and on non-conducting interrupt the flow of current to turn off SCR-1. When the PFN voltage reaches during charging, the charging current, through SCR-1, SCR-2. The 9. apply a negative voltage from anode to cathode. and the SCR stops conducting used to The switching from conducting states can be accomplished by two a A 2N-691 was used are given in detail in reference primary problems faced here were simply how The volts, the was used as SCR-2. The characteristics at the This power supply voltage was selected. the SCR's were selected from the laboratory stock. rating 200 until triggered again. The mismatch between is zero The second method the load and PFN characteristic impedance causes a small negative step at the end of the pulse which is sufficient to cause SCR-2 to stop conducting. -65- is .66- o o <* I or O K <r 8 UJ -I a cvj -67- In order to trigger the SCR's on at the proper times, the circuit of Fig. 22 was constructed. Basically, this circuit produces two sets of timing pulses as shown in Fig. 23. In each set, the pulses are twenty milliseconds apart and the two sets of pulses can be shifted with respect to one another. One set of pulses is set is used to trigger between the sets the PFN used to trigger SCR-2 of pulses and discharging The timing circuit is SCR-1 for charging the to discharge the PFN and the other PFN. The amount of the offset merely determines the delay between charging it. capable of operating continuously at a pulse repetition rate between five and twenty-five milliseconds or, by closing the toggle switch, as a burst generator that will produce a four pulse burst at intervals from one-half second to about five seconds. rate Fig. was decreased from 1, to more The burst-repetition the required fifteen second interval, as easily view the tests by oscilloscope. shown in -68- 2E s E Time PFN VOLTAGE E. Time PFN OUTPUT PULSES 6 volts k— 20. i( 20 -5* -; IT.S ns Tims TIMING CIRCUIT CHARGING PULSES 6 volts 2017.3 H-« 20 ms > 20 ras i— Time TIMING CIRCUIT DISCHARGING PULSES FIG. .23 TIMING PULSES BIBLIOGRAPHY 1. Glasoe, G.N. and Lebacqz, J.V.; "Pulse Generators", Radiation Laboratory Series; McGraw-Hill, 1948.. 2. Weiss, H.G., "Haystack Microwave Facility", IEEE Spectrum, February, 1965. 3. Roberge, J.K., "Design of Spacecraft Radar Systems for Investigation of the Planet Venus", Electronic Systems Laboratory, M.I.T., 1962. 4. Dertouzos, M.L. and Bosco, J. A. "Design of a Radar System for Measuring the Electromagnetic Reflection Characteristics of the Earth's Surface from a Satellite", Electronic Systems Laboratory, M.I.T., 9461-M5, September, 1963. 5. Reintjes, J.F. and Coate, G.T., "Principles of Radar", McGraw-Hill, 1950. 6. Jordan, R.L., "Semi-Conductor Magnetic Pulse Generators", S.M. Thesis, M.I.T., 1962. 7. Arnold Engineering Company Bulletin SC 8. Westinghouse Company Descriptive Bulletin 44 9. General Electric Company, "Silicon-Controlled Rectifier Manual", , - 107A, March, 1963. - 550, December, I960 1961, 10. M.I.T. Department of Electrical Engineering Notes for Experimental Electronics Laboratory, 1963. 11. Terman, F.E., "Radio Engineers Handbook", McGraw-Hill, 12. International Telephone and Telegraph Corporation, "Reference Data for Engineers", American Book - Stratford Press, 1956. 13. Texas Instrument Newsletter, Volume -69- 2, Issue 3, 1943. October, 1964.