AN ELECTRONIC ?OR TRANSIENT STUDIES

A THESIS Presented to the Faculty of the Division of Graduate Studies Georgia Institute of Technology

In Partial Fulfillment of the Requirements for the Degree Master of Science in Slectrical Engineering

by Marshall Joseph McCann September 1949 107545

ii

AN ELECTRONIC SWITCH FOR TRANSIENT STUDIES

Approved:

zf r ~~v

Bate Approved by Chairman A up. d±, f^4f ACKNOWLEDGMENTS

I wish to express my sincerest thanks to Prof. M. A. Honnell for his patient guidance and assistance, which were an immense aid in the prosecution of this work. I am also indebted to the Photographic and Repro­ duction Laboratory at the State Engineering Experiment Station of the Georgia Institute of Technology for their splendid cooperation with the photographic work herein. iv

TABLE 0? CONTENTS

PAGE Acknowledgments iii List of figures vi I- Introduction 1 II- A Survey of the Literature 3 Mechanical Systems.. • 3 Electronic Systems 4 III- Design Considerations for an Electronic Switch 8 General , , 8 Possible Approaches 8 IV- The Switch 12 V- The Generator 16 Design Requirement s 16 Symmetrical Multivibrator 16 Improvement of Waveform 22 VI- The Synchronizing Section 37 General 37 Phase Shifting 27 Amplification and V/ave shaping 29 Synchronization of the Multivibrator 39 Summary of the Synchronizing Action 31 VII- Operation 34 VIII- Siamples of Operation 37 Lumped Constant Circuits 37 V

P-4GE VIII- Examples of Operation (continued) Transmission Line Transients 41 IX- Summary • 46 appendix I, Analysis of Plate-Inductance Compensation of the Multivibrator 47 appendix II, Scaling of Circuits for A-C Transients 50 appendix III, Parts List 55 Bibliography .... 58 vi

LIST OF FIGURES

FIGURE PAGE 1 A Gas Tube Switch 9 2 Another Switch 9 3 The Switching Circuit 13 4 Multivibrator, Initial Design 17 5 6SN7 Plate Characteristics 19 6 Multivibrator Grid Voltage, Initial Design 23 Multivibrator Output, Initial Design 23 8 Multivibrator Grid Voltage, Final Design 23 9 Multivibrator Output, Final Design 23 10 Multivibrator, Final Design 25 11 The Synchronizing Circuit 28 12 Synchronizing Section Input Voltage • 30 13 Grid Voltage, Tube VI 30 14 Plate Load Voltage, Tube VI 30 15 Output Voltage, Tube V2 30 16 Multivibrator Grid Voltage with Synchronization. 32 17 Synchronized Multivibrator Output 32 18 Maximum Transient in R-L Circuit 38 19 Minimum Transient in R-L Circuit 38 20 Transient in R-C Circuit 38 21 Transient in a Detuned Resonant Circuit 40 vii

FIGURE PAGE 22 Transient in Resonant Coupled Circuit, Over Critical Coupling • 40 23 Transient in Resonant Coupled Circuit, Coupling Greatly Reduced 40 24 Transmission Line: Receiving Snc Current with Load Switched On 42 25 Transmission Line: Sending End Current with Load Switched On 42 26 Transmission Line: Sending 2nd Voltage with Load Switched On 42 27 Transmission Line: Sending End Current with Load Switched Off 44 28 Transmission Line: Receiving ±±nd Voltage with Load Switched Off • 44 29 Transmission Line: Receiving End Current with Inductive Load Switched On 44 30 Schematic Diagram • 57 AN ELECTRONIC SWITCH FOR TRANSIENT STUDIES

I

INTRODUCTION

It is the purpose of this research to develop an electronic switch capable of producing transients in a-c systems. Such a device has two uses: first, as a teaching aid, and secondly, as a means of finding the transient re­ sponse of networks which are so complicated that they are not readily solvable by analytical methods. As a teaching aid, it permits the student to see the waveforms which occur in switching a-c systems, and thus he does not have to rely entirely on his faith in mathe­ matics. To fulfil this purpose the switch need not meet any rigorous requirements, since only qualitative results are necessary. The transient response of networks to alternating voltages becomes laborious to calculate except for the simplest of systems. Whenever long and involved calcula­ tions are made, the risk of error becomes great, and the time required may not be worth the results obtained. Hence a device which would permit us to cause a transient and measure it directly would be useful. Here the results 3 desired are quanitative in nature, and the switch must meet more rigorous requirements. Strictly speaking, an electrical transient is a phenomenon which occurs only once in time, or, to put it another way, it is non-periodic. If, however, we wait un­ til the effects of a transient have subsided, we may cause the transient again. If the initial conditions of the second transient are the same, it will be an exact dupli­ cate of the first. Thus the transient ma;> be made peri­ odic and its voltage and current may he displayed on a cathode-ray oscilloscope. The problem to be considered, then, is the develop­ ment of an electronic switch to produce a-c transients. An ideal switch to show switching transients on an oscillo­ scope would be one which would present an infinite imped­ ance when open, and an impedance of zero when closed. Fur­ ther, the device should open and close periodically at a fixed point in the a-c cycle, the period of opening and closing being under the control of the operator• 3

II

A SURVEY OF THE LITERATURE

Mechanical Systems. A commutator driven by a syn- i chronous motor has been used by Turner . The commutator a voltage from the same source that supplies the motor. Since the commutator will revolve in step with the supply voltage, the commutator will switch at the same point in the cycle. The point in the cycle may be varied by moving the commutator brushes. The chief advantage of a mechanical commutator is that it is easily constructed and can be nude to work well at low frequencies. Its disadvant­ ages are that it is generally limited to CO cycle voltages, and the frequent erratic operation of brushes and commutators. .mother mechanical method has been used by Reich and Marvin . This system uses a relay which is actuated by a thyratron oscillator circuit, which is synchronized in turn to the frequency being switched. The phase at which switch­ ing occurs is varied by varying the grid bias on the thyra­ tron. The disadvantages of this circuit are that it is

burner, H. H., "Transient Visualizer,,r Transactions of the American Institute of Jilectrioal Engineers, 43:80^-813, June, 1924. i-ieich, H. J., and G. S. Marvin, "A Combination Sweep Circuit and Periodic Contactor for Studing Circuit and Line Transients with the Cathode Ray Oscillograph,rl Review of Scientific Instruments, 5:7-9, January, 1934. 4 very limited in the range of frequencies it can handle, and that the relay will be a constant source of trouble due to bouncing and other erratic action, Mechanical systems generally are easy to construct and operate. On the other hand they will always be limit­ ed in their speed of operation by mechanical inertia, and are therefore limited to extremely low frequencies, Electronic Systems. A large number of electronic switches have been described in the literature. Their oper­ ation is generally accomplished by Ttgatin&" the signal through a gas tube or a vacuum-tube . Some have been designed to demonstrate transients; most, however, are for use with double-trace oscillography. A switch described by Sewig3 uses a pair of thyra­ trons for switching. The thyratrons are controlled by one of the signals being switched. The operation is such that alternate half-cycles appear on the oscilloscope screen. Thus this switch is rather inflexible in application. Davidson reports a similar circuit, except that the thyratrons are controlled by the sweep signal of the oscill-

°Sewig, Rudolf, "Simultanaufzeichnung mehrerer Vor- gange mit dem Kathodenstrahloszillographen," Zeits. f. tech Physik. 14:152-153, March, 1933.

^Davidson, I. B.f "Double-wave Device for Use with a Cathode Ray Oscillograph," Journal of Scientific. Instruments, 11:359-361, November, 1934. 5 oscope. This feature permits the switching frequency to be varied over a wider range. A circuit discussed by George, He iff, Mayer and Roys5 uses pulses from a thyratron to vary the grid bias on two vacuum-tube . The amplifiers are thus gated on and off, and therefore act as a switch, Garceau6 discusses a circuit in which two pentode tubes are turned on and off by a signal] on the screen °rrids of the pentodes. This signal is of much higher frequency than the signal being switched.. A circuit due to hughes7 employs a thyratron square- wave generator to modulate the suppressor grid of two type 57 vacuum tubes. This circuit is thus very similar to that of George, Heim, Mayer and Roys. Shumard8 describes circuits in whict the signal being switched is passed through a gas tube. These circuits are

5George, R. H, , H. 0". Helm, H. F. Kuyer, and C. S. Roys, "A Cathode Ray Oscillograph for Observing 2 Waves," Electrical Engineering, 54:1095-1100, October,~~1935. 6Garceau, L., "Dunlex Cathode Ray Oscillograph," Rev. Sci. Inst.t 12:171-172, June, 1935.

•n 'Hughes, H. K., "Thyratron Selector for Double Trace Cathode Ray Oscillograph," Rev. Sci. Inst.. 7:89-92, February, 1936. 8Shumard, C. C, "Some Electronic Switching Circuits," Elect. Eng., 57:209, Fay, 1938. 5

primarily employed as counter circuits. Kurokawa and Tanaka9 describe a transient visualizer which uses the output of a phase-shift circuit to operate an impluse generator. The impulse generator either operates a thyratron switch or a relay. The application of this de­ vice is apparently at power frequencies* A switch described by Hughes and Koch1*-1 uses pentode amplifier stages. The pentodes are switched by a square- wave input to the cathode circuit. The square wave is ob­ tained either by clipping or by overloaded pentode amplifiers operated on a sine-wave input. Cosby and Lampson1^ describe a circuit in which a pair of 6L7 mixer tubes are used as switches. The tubes are switched by the output of a multivibrator on one of the control grids. A circuit employing triodes as switches has been

%urokawa, K",, and S. Tanaka, "A Direct Visualizer for Transient Phenomena," Electrotechnical Journal (Japan), 4:51-55, March, 1940. Hughes, H. K., and K. F. Koch, "Combination twitch for Double Trace Oscillograph, Audio Amplifier and Mixer," Rev. Sol. Inst.. 12:183-187', April, 1941. -^Cosby, J. R., and C„ W. Lamp son, "Electronic Switch and Square Wave Generator," Rev. Sci. Inst., 12:187-190, April," 1941. 12 discussed by Reich • The square wave for switching is ob­ tained from a flip-flop circuit which is triggered by the sweep signal of an oscilloscope. 'iLhus the switching fre­ quency is under the control of the oscilloscope which may be synchronized in turn to some sub-multiple of the fre­ quency being observed. Reich 13 , also discussed, in another article, several switching methods for transients. These all employ gas discharge tubes as a switch, with arrangements made so that the gas tubes will also act as relaxation oscillators. He reports, however, that difficulties were encountered when the tubes were operated at low currents,, ]?urther the de­ vices described will only demonstrate responses to step functions of voltage, although they might be modified to in­ clude other types of driving functions.

12Reich, H. J., "Electronic Switch for the Simult­ aneous Observation of Two Waves with the Cathode Ray Oscill ograph," Rev. Sci. Inst., 12:191-192, April, 1941. 13Reich, H. J"., "Electronic Transient Visualizers," Trans. A.I.E.E., 55:1314-1318, December, 1936. 8

III

DESIGN CONSIDERATIONS FOR AN ELECTRONIC SWITCH

General. The switch with which this paper is con­ cerned was designed with the following considerations in mind: A. The switch should he electronic in nature. This will free it from the limitations inherent in mechanical devices. B. The switch must act with the greatest speed poss­ ible. That is, the time required for opening and closing must have negligible effect upon the ex­ ternal circuit being studied. C. The length of on and off periods must be under control, as must be the phase of the voltage at which switching occurs. D. The ratio of "open" to "closed" impedance must be as high as possible. E. The device should be designed to switch voltages of 1000 cycles, and should operate over as wide a band of frequencies as possible in this neigh­ borhood .

Possible Approaches. A possible method of switching is shown in Fig. 1 on page 9. Two gas-filled tubes with keep-alive anodes are used. The a-c voltage used should not _i Load-* r \ • t t tL i.

'3^nc (ttfput^ -t.rt iu 5 w U A rt t" wv 4 vc GtHzrlfi I Of-C

F, *3 Cos lube Switch

v--\ Llkjcj ~~ \ 9 c r "• y L r (venerator

1 q. cl - Another Switch j 10

be high enough to cause the tubes to breakdown. Hence con­ duction will only occur when the keep-alive anodes are fired. These could be fired by a square-wave generator synchronized at a sub-multiple of the line frequency. The synchronizing voltage could be phase shifted so that the switch would operate at any desired point in the cycle. Another possibility is illustrated in Fig. 2. Here again the a-c voltage would not be high enough to cause the tube to conduct. Also the square-wave current must be much larger than the a-o current to keep the tube fired. A blocking condenser C v:ould be necessary to keep the d-c cur­ rent out of the rest of the circuit. The principal difficulties of these two circuits lie in the very nature of gas-filled tubes. First, the exact voltage at which a gas tube fires is a function of age, am­ bient temperature, and immediate previous history. There­ fore this voltage is apt to fluctuate erraticly. Second, gas tubes require heavy currents to maintain conduction, and it would be difficult to build a square-wave generator to furnish these currents. Third, the impedance of gas tubes is a non-linear function of the current through them, and is also a function of its temperature and history. This would affect the response of the circuit being studied. It might be possible to modify these circuits to use vacuum tubes. The high dynamic plate resistance of vacuum 11

tubes tends to discourage any design of this sort. A gated amplifier such as is described in the lit­ erature might be used. Such a circuit would be very easy to control. The disadvantages are that its output imped­ ance would be relatively high and that it does not act as a switch but rather as a generator turning on and off. This excludes a large class of transients which are due to switching at some point remote from the source. The reliability of high-vacuum tubes as switches en­ couraged the development of a transient visualizer employing them. Such a switch is described in detail in the following section. 12

IV

THE SWITCH

The switch employed in the final design is shown in Fig. 3 on page 15. Use is made here of the low output impedance of the cathode-follower circuit. A push-pull arrangement is used so that no transients caused by the d-c plate current will appear in the secondary of the trans­ former Tl. The tubes are switched on and off by a square- wave voltage between the center-tap of the transformer and the grids of the tubes 75 and V6. When the tubes are con­ ducting, the impedance presented to the primary terminals

of the transformer is approximately 2/gm where gm is the 14 transconductance of the tubes. When the square wave drives the grids of the tubes below cutoff, this imped­ ance is infinite. Thus when the tubes are conducting, the impedance at the switch terminals (the secondary terminals of the trans­ former) is approximately ™ •"•#- where n is the turns ratio of the transformer. When the

-"•^arguimbau, L. B., Vacuum-Tube Circuits» John Wiley and Sons, New York, 1948, pp 348-355. 13

£ O" I HE SWITCHING CIRCUIT 14 tubes are not conducting, the impedance is the open-circuit impedance of the transformer. A perfect transformer has an infinite open-circuit inroedance. Perfection and infinity are rarely achieved, but the transformer must have a hi^h open-circuit impedance and a low short-circuit impedance. To obtain such a transformer, the open- and short-cir cuit impedances of a large number of transformers were mea­ sured. The transformer chosen is an output transformer Navy type T-173.&, manufacturer unknown. This transformer has an open- to short-circuit impedance ratio of 327:1. an­ other transformer tested has tin impedance ratio on the order of 200:1. iill of the rest have ratios of less than 100:1, so that it may be safely said that 327:1 is about as high a ratio as is generally obtainable. The tubes V5, V6, employed in the switch should have a high transconductance and a large signal handling capa­ bilities. If the transconductance of a single tube is not high enough, tubes may be paralleled to achieve the desired value of transconductance. Tube tyne 6L6 was chosen on this basis. It is a beam-power pentode with a transconduct­ ance of about 6000 microrrhos. Tube type 6V6 , a beam-power pentode with a somewhat lower transconductance, was also tested in the circuit, but. yielded inferior results. With a single pair of eLe's, an off-to-on impedance ratio of 15

800:1 was obtained. C9 and CIO are screen bypass condensers of 0.05 mfd. each. R16 is a screen-voltage dropping resistor of 40,000 ohms. P-17 and R18 serve the same purpose for tube V6, R17 is a fixed resistor of 30,000 ohms and hl8 is a variable resistor of 20,000 ohms. The variable resistor enables the screen voltage of one tube to be varied, so that the d-c plate current of the two tubes may be balanced, thus eliminating any d-c flux in the trans­ former. 16

THE SQUARE-WAVE GENERATOR

Design Requirements, A square-wave signal is needed to actuate the switch. The generator of this square wave must meet the following requirements: A. Its output must have a fast rise and fall time.

B# Since the design center for the a-c voltage be­ ing switched is 1000 cycles, the square-wave frequency should have a design center of 50 cycles. The frequency must be easily adjustable over a range in this neighborhood. C. The generator must easily synchronize with a sub- multiple of the frequency being switched. D. The amplitude of the output must be sufficient to drive the grids of the switching tubes V5 and V6 well below cutoff during the negative half of the cycle.

E. The waveform of the positive half of the cycle must be substantially flat so that the a-c being switched will not be undesirably modulated by irregularities on the top of the square wave. Symmetrical Multivibrator. The square-wave generator was initially designed as a symmetrical multivibrator as shown in Fig. 4 on page 17, This circuit employs a positive To -31* stc A

"IG. A "MULTIVIBFMTOR, IhllTML Dt5|G N 18 grid return, which improves the frequency stability and synchronization, and also affords an easy method of fre­ quency control. This circuit was first discussed by a. u. 15 B. Bartelink. A tubs type 6SN7 was chosen, since it conveniently encloses two triodes in a single envelope. Plate resistors RIO and Rll of 10,000 ohms each are used, since this value yields the maximum output for this tube. & separate power supply with the positive side grounded is necessary to give the proper polarity to the output. The circuit is designed to operate with a supply voltage E,. of 300 volts. The 6SN7 plate characteristics with a 10,000-ohm load line are shown in Fig. 5 on page 19. From this curve the plate volt­ age Ep of the tube, when conducting, is found to be 130 volts. (This is the intersection of the load line with the E„ = 0 curve.) The peak-to-peak voltage output of the square wave produced across the plate resistor will be

Eo = Ebb " ^p = 300 " 130 = 17° volts

This will also be the voltage to which the grid of the sec­ ond tube is driven negative when the first tube starts con-

15Bartelink, E. H. B., "A Wide Band Square Wave Gen­ erator ,M Trans. A.I.E.E., 60:371-376, June, 1941. HG 5- 65IV7 PLATE CHARACTERISTICS

L Qcd l/r/e f?L= /0,OOo^

/o& Pfate v- 20

r ducting. The second tube will remain non-conductin : , until the voltage of the condenser at the grid discharges across the resistor and the grid voltage reaches the cutoff voltage ilco. In the case of tube v"3, the condenser and resistor in question are C8 and R13* The other resistances are small enough to be neglected. The voltage across a capacitan discharging through a resistance obeys the law t_ RG (2) E = %Q where E = voltage across Si = Initial voltage across capacitor t = time R = resistance C = capacitance In the case at hand, the grid voltage will rise toward the voltage at which the R19 is set. Let this voltage be called Efl. Letting Sc be the grid potential, (2) becomes t IiC (3) Sd - Sc z (Sd / 20)Q or

(4) t = RC log^. / fo 31

To find the time T1 for a half period, set

(5) EG = 3C0

(6) T' - HO log gg ^ fo

From (6), the design parameter (EC) can be obtained. Solving this eouation for RC sdves

(7) RC : £• log jfo r fe ^d - ^co but

(8) Tf = -i- v ; -£—S - Sf where f is the frequency. Substituting this into (7) eives

(9) RC z 1 _ 2f log && f &n . Ea - ico From the characteristic curves on page 19, for Sy^ 300,

Eco z -18 volts. Maximum frequency will be obtained when sd " ^bb- ^f ™e chose our maximum frequency to be 100 cycles, then, upon substitution of these values,

RC = 0.0129 ohm-farads.

If a nominal value of C is chosen to be 0.05 mfd., then R will be 258,000 ohms. A resistor of 1270,000 ohms was actually used since it was the highest quality resistor readily available in this neighborhood. 23

Returning to (9), and solving for the frequency gives

(10) f = 1 _ 2HC log -jj;fl r ^Q ^d - sco The minimum frequency will occur when E^ is zero. Using (10), the minimum frequency is 16.5 cycles per second. This will certainly give a wide enough frequency range to allow the frequency of the voltage being switched to vary over a considerable band. Equations (9) and (10) derived here are similar to those given by Barteli.nk. ° They differ in that these are adapted to use with data from the characteristic curves, while Bartelink assumes straight-line characteristics and uses the amplification factor and plate resistance of the tube. A multivibrator was built using the calculated values. The initial design had a circuit as shown in Fig. 4. The waveform of the grid and output voltages are shown in Fig. 6 and 7 on page 23. This waveform has an exponentially curved positive half-cycle output. The negative half is also curved, but this is not important as the grids of the switching tubas will be below cutoff during this part of the cycle. The positiva half, however, will modulate the wave passing through the switch. Improvement of Waveform. This departure from an ideal square wave is due to two causes. First, as a tube be-

16Bartelink, op. cit. 23

Fig. 6- Multivibrator Grid Volt Pig. 7- Multivibrator Output, age, Initial Design. Initial Design.

Pig. 8- Multivibrator Grid Volt­ Pig. 9- Multivibrator Output, age, Final Design. Final Design. 24 gins conducting, its grid will be driven highly positive by the other tube which is cutting off. This peak may be seen clearly in Fig, 6. The peak causes a dip in the -plate voltage of the tube as it starts to conduct. The result is a dip in the first part of tV:e negative half cvcle of the output. This effect cannot be entirely eliminated, but it can be greatly reduced by placing resistances in series with the grids. The grid current which flows through these re­ sistors will develop a voltage which will tend to level off the peak. Fig. 8 on page 23 is an example of the grid voltage with these resistors of 47,000 ohms in the grid circuit. This value was determined experimentally. Notice how the positive peak has been greatly reduced. The curve in the positive half cycle is caused by current flowing through the plate resistor to charge the condenser to the supply voltage. Viewed from another point, the voltage on the capacitor which is connected to the plate cannot change instantaneously, and therefore the plate voltage must rise slowly from its conducting value to its non-conducting value. This brings to mind the fact that the current through an inductor cannot change dis- continuously. An inductance added to the plate circuit could furnish the current necessary to charge the capaci­ tance, and thus yield a square waveform. This was tried experimentally, using various values f&l /?/0 C7 cs 3 u -Ih 'Swttc/r tH2 / RM &*5 / -*- V3 (- /^-^AATNA ^-4 ) j/^ R/3

3-

U'G. 10- MuLTl VIBRATOR, ! I N/V DE SIGN

^ 26 of plate resistors and inductances. The optimum circuit tested was found to be that shown in Fig. 10 on page 25 F using a plate resistance Rll of 5000 ohms and an inductance Ll of 3 millihenries. This circuit gives the output shown in Fig. 9 on page 23. An analytical study of this circuit may be found in Appendix I. From this study, it v^as found that the R, L, and C should be a critically damped circuit. The circuit used is over-damped, to prevent any undesired modes of os­ cillation from occurring. 27

VI

THE SYNCHRONIZING SECTION

General. In order that switching will occur at the same point in the cycle, the square-wave generator must be synchronized to the frequency of the voltage being switched. The synchronizing section fulfills this need* The requirements of the synchronizing section are:

A# It must produce a voltage of such magnitude and waveshape that the multivibrator will be easily synchronized. B. It must include means of varying the phase of the synchronizing voltage so that switching may occur at any desired point in the cycle. C. It must isolate the square-wave generator from the circuit being switched, so that no "backwash" from the multivibrator will appear in the circuit. The circuit of the synchronizing section is shown in Jig. 11, page 28. It consists of a phase shifter and two stages of triode clipping.

Phase Shifting. The voltage of the generator sup­ plying the circuit being switched is introduced to the syn­ chronizing section through the switch SW1« This switch ser­ ves to reverse the polarity of the voltage. The waveform of the voltage at this point Is a sine wave and is shown in Fig. 12 on page 30. C3

c. V'/ \ C ?iz i /' r! i/.c A X//1 — , R& V ' K \ H3 n'6- .- < c I /?/ £%4 Y /?5" /?& To Mtt/ttv/bralor

C6 £KL^r.k// Ckt, Z?^

F b. (HE SYNCHRONIZING CIRCUIT 29

This voltage is then applied across resistors Rl, R2, R3, and capacitor Cl. These components form a familiar type of phase-shifting circuit. The output of this com­ bination is applied between the grid of VI and ground. By varying Rl, the phase of the output may be varied through 170° at 1000 cycles. In conjunction with the switch, 340° of phase variation may be obtained, Amplification and Waveshaping. The grid of tube VI is driven positive by the output of the phase shifter. This causes grid current to flow and results in a grid voltage shape as shown in Fig. 13, page 30. A bias developed through the phase shifter causes clipping of the tops of the sine wave. This voltage is then amplified and applied to the grid of the next tube, V2, The waveform at the plate of VI is shown in Fig, 14, page 30. The wave is distorted due to saturation of the first stage. The voltage at the grid of the second stage is of such magnitude that the grid is driven below cutoff. This clips the lower half of the cycle, in addition to further clipping of the upper half due to heavy grid current through resistor R6, The resultant output is virtually a square wave as is shown in Fig. 15 on pa^e 30. Synchronization of the Multivibrator. The almost square wave produced by the synchronizing section is con­ sidered the most satisfactory form of wave for synchronizing 30

Fig. 12- Synchronizing Section Fig. 13- Grid Voltage, Tube Input Voltage. VI.

Fig. 14- Plate Load Voltage, Pig. 15- Output Voltage, Tube Tube VI. V2. 31 the multivibrator.17 The problem of choosing the point to inject this voltage into the multivibrator must now be con­ sidered. It could be injected at many points in the multi­ vibrator circuit — between either grid and cathode, across a plate resistor, or across a cathode resi3tor. Tf it were injected across the plate resistor RIO, none of the synchro­ nizing voltage would appear in the output, a-'his would be a desirable condition. Synchronization can, however, be ac­ complished at lower amplitudes in the grid than in the plate circuit. Hence grid synchronization was chosen. By syn­ chronizing at the grid of the tube from which we take the output, the positive half of the wave will be free from the synchronizing voltage. The synchronizing \jltage appearing in the negative half of the cycle can be tolerated in this application. Fig. 16, page 33, shows the grid voltage of the multi­ vibrator with the synchronizing voltage injected. Fig. 17 shows the synchronized output of the multivibrator. Summary of the Synchronizing Act ion. The synchro­ nizing action can be recapitulated briefly with references to the illustrations as follows: A, A sine wave (Pig« 12) is introduced and phase shifted.

•"•'Andrew, Victor J"., "The Adjustment af the Multi­ vibrator for Frequency Division," Proceedings of the Instit ute of Radio Engineers. 19:1911-1917, November, 1931. 32

Pig. 16- Multivibrator Grid Voltage with Synchronization.

Fig. 17- Synchronized Multi­ vibrator Output. Its positive peak is clipped by grid current, (Fig. 13). It is amplified, (Fig. 14). It is further amplified and clipped at the top and bottom, (Fig. 15). It is injected into the multivibrator grid, (Fig. 16). The multivibrator gives a synchronized output, (Fig. 17). 34

VII

OPERATION

The operation of the equipment is straight forward. The switch terminals are connected in the system at the point where switching is desired. Connections are also made between the generator of the system and the synchronizing terminals of the switch- An oscilloscope is connected to the points where measurement is desired,, It is a good prac­ tice to synchronize the oscilloscope sweep frequency exter­ nally from the system generator. The power supplies are turned on and the frequency of the square-wave generator is adjusted so that it will synchronize at some sub-multiple of the system generator frequency. If the system generator is cut off and short circuited, a voltage may appear on the oscilloscope. This indicates that the two switching tubes are not balanced and that R18 should be adjusted to balance the tubes. The square-wave generator may drop out of synchro­ nization when the phase-shift control is varied. This in­ dicates that the multivibrator is synchronized at an un­ stable sub-multiple of the system generator frequency. The most expedient cure of this ill is to cnange the multivibra­ tor frequency to the next higher or lower sub-multiple, which will usually be much more stable« Some power frequency disturbances may appear in the 35 oscilloscope pattern. This is usually due to the fact that there are four connections to the power line (two power sup­ plies, the system generator, and the oscilloscope). This can usually be remedied by turning over one or two of the plugs in the socket. The phase at which the switch is acting can be varied by the phase-shift control HI and the phase-reversing switch SW1. The value of the t:hase is best determined by direct observation on the oscillograph. The phase-shift dial might be calibrated, but such a calibration would hold, -ood for only one value of the generator frequency and square- wave frequency. Transients occuring in highly reactive circuit elements may so distort the waveform that phase de­ termination is difficult,. In these cases, a resistance whose impedance is of tie same order of magnitude as the re­ active elements may be momentarily substituted for the re­ active elements. The initial phase may t)en be easily de­ termined, and the reactive elements replaced in the circuit, The impedance of the circuit being studied must be much less than the open-circuit impedance of the switch. Otherwise the current flowing during "open1* nertods will be of the same order of magnitude as that flowing during "clos­ ed" periods. The value of the open-circuit impedance at 1000 cycles is (107,000 / j3S,700) ohms. It is also desirable for the impedance of the cir­ cuit being studied to be high compared to the closed-circuit 36 impedance. If this is not the case, the iirpedance of the switch may have more effect upon the transient than the cir­ cuit elements. In certain cases it may be possible to in­ clude this impedance as part of the circuit to be studied. ^t 1000 cycles the closed impedance is (555 / jl66) ohms, another method of avoiding these difficulties is to scale the circuit. This procedure is discussed in Appendix II. In order that the desired transient be clearly shown, the output of both sides of the multivibrator are available for use as Z-axis modulation signals on oscilloscopes equip­ ped with this feature. The polarity of the output chosen is dependent upon the part of the switching action to he view­ ed, In oscilloscopes not so equipped, a blanking circuit may be easily added. 37

VIII

EXAMPLES 01 0KEB4TI0N

In this section, oscillographic records of trans­ ients produced by the switch are given. In all of the ex­ amples, a Hewlitt-Packard 200-B audio oscillator was used as a generator. This oscillator has an internal impedance of 125 ohms, which is almost wholly resistive. A DuMont type 175-a oscilloscope was used for observation. These ezamples indicate the capabilities and uses of the switch in tran­ sient studies. Lumped Constant Circuits. The current in a resist­ ance-inductance series circuit is shown in Fig. 18, page 38. The total inductance of the circuit is 0.847 henries, in­ cluding the closed inductance of the switch of 26.5 milli­ henries. The total resistance of the circuit is 2080 ohms, consisting of 125 ohns resistance of the generator, 1400 ohms resistance of the circuit and 555 ohms resistance of the switch. This is an example of a circuit in which the switch impedance can be made part of the circuit under study. The frequency is 2500 cycles per second. The dot­ ted line is the calculated value of the transient component of the response expected of this circuit, showing the order of accuracy which may be obtained with this switch. The switch is acting at the point in the cycle {about -10°) 38

Fig. 18- Maximum Transient Fig. 19- Minimum Transient in R-L Circuit. in R-L Circuit.

Fig. 20- Transient in R-C Circuit. 39

which will produce the maximum transient. Fig. 19, page 38, is the response of the same cir­ cuit with the phase angle adjusted for zero transient re­ sponse. This illustrates one of the primary advantages of transient visualizers; namely, that the phase of the switch­ ing may be rapidly varied to find the maximum and minimum conditions. Similarly the values of the circuit elements and frequency may be changed, and the results of these changes may be quickly seen. The transient response of a capacitative circuit is shown in Fig. 20. This photograph is a record of the volt­ age across a capacitance of 50 mfc . in parallel Ti"ith a re­ sistance of 500 ohms. The frequency is 1000 cycles, and the phase angle at which the switch is acting is about 90°. In Fig. 21 on page 40, the current through a parallel RLC circuit is shown. The circuit consisted of one inductive branch of 0.5 henries and 900 ohms resistance in parallel with a capacitance of 0.2 md „ The experimentally determin­ ed resonant frequency of this combination ?s 540 cycles. An excitation frequency of 640 cycles was used to obtain this transient. The large negative peak is due to the inrush of current to charge the capacitor when the switching oc­ curs at -90° phase angle. The current flowing to a resonant coupled circuit is shown in Fig. 22, page 40. Coupled inductances of approxi­ mately 0.159 henries each were connected to capacitances of 40

Pig. 21- Transient in a De- Pig. 22- Transient in Resonant tuned Resonant Circuit. Coupled Circuit, Over Critical Coupling,

Pig. 23- Transient in Resonant Coupled Circuit, Coupling Great­ ly Reduced. 41

0.16 mfd. The inductances were adjusted to make the coupl­ ing closer than critical coupling. The circuit was excited at an experimentally determined resonant frequency of 910 cycles. Fig, 23 on page 40 shows the current flowing to the same circuit with the coupling greatly reduced. This is an­ other illustration of how the effect of variation of circuit parameters upon the transient may be quickly determined. Transmission Line Transients. The following six examples, Fig. 24-29, were made on an artificial transmis­ sion line. The use of artificial transmission lines for transient studies of actual long lines has been discussed 18 by Weber and DiToro. This type of transient is especially difficult to calculate since the solution involves partial differential equations as compared to the ordinary differ­ ential equations of lumped constant circuits. The excitation frequency was 950 cycles per second in all cases. The artificial line represented a trans­ mission line of No. 0 AWU open wire line, approximately 200 miles in length. The characteristic impedance of the line is approximately 670 ohms. Fig. 24, page 42, shows the receiving-end current when a load is suddenly switched on. The switch itself

' Weber, Ernst, and M. J". DiToro, "Transients in the Finite Artificial Line," Trans. A.I.B.E.. 54:661-663, June, 1935. 42

Pig. 24- Transmission Line: Re- Pig. 25- Transmission Line: Send- ceiving End Current with Load ing End Current with Load Svitch- Switched On. ed On.

Pig. 26- Transmission Line: Send­ ing End Voltage with Load Switch­ ed On. 43 served as a load with an impedance of 570 ohms at an angle of -16°. The length of the line and the frequency are such that approximately two full cycles take place before reflec­ tions from the sending end return to the receiving end. This causes the two initial cycles to be smaller than the succeed­ ing cycles. The sending-end current for the same circuit is shown in Fig. 25, page 42. For approximately one full cycle after the load has been switched on the current is small since it is the charging current of the line. Approximately two more full cycles transpire before the reflection from the genera­ tor makes a "round trip" to the receiving end and back. This causes the next two cycles to be slightly smaller than the final steady state cycles. Fig. 26, page 42, shows the receiving-end voltage when the load is being switched at the same point in the cycle as in Fig. 25. Since the switch is not acting at the point of zero current, a slight exponential transient may also be noted. These examples point out another feature of this switch; that is, the effect of a switching transient upon the voltage or current anywhere in the circuit may be rapid­ ly found. The sending-end recovery current after the load has been switched off is shown in Fig. 27 on page 44. About one full cycle passes before the generator "becomes aware" of the fact 44

Pig. 27- Transmission Line: Send­ Pig. 28- Transmission Line: Re­ ing End Current with Load Switch­ ceiving End Voltage with Load ed Off. Switched Off.

Fig. 29- Transmission Line: Re­ ceiving End Current with Induc­ tive Load Switched On. 45 that the load has been removed. Multiple reflections than take place between the sending and the receiving end of the line* The steady-state condition is reached in the last two cycles shown. This is the open-circuit value of the line current. The recovery voltage at the receiving end of the line is shown in Fig. 28, page 44. Here again the reflections take place before the voltage assumes its steadv-state value. Fig. 29, page 44, is the receiving-end current with a highly inductive load of 0.82 henries and 1400 ohms resist­ ance in addition to the load of the switch. In addition to the reflection phenomena, the exponential transient of the load is also shown. 46

IX

SUMMARY

The cathode-follower type of electronic switch devel­ oped and demonstrated here provides a new tool for the study of transients. It does not have the limitations of the mecnanical type of switch previously used for this purpose. It is limited, however, in that it may only be used with a sinusoidal generator. This limitation should not prove to be too severe since this is the most common type of genera­ tor encountered.

Further improvement in performance may be obtained by using tubes having a higher transconductance and by using more nearly ideal transformers. It might also be desirable to derive the sweep voltage for the oscilloscope from the output of the square-wave generator. This would assure a steady pattern on the oscilloscope screen. 47

APPENDIX I

a&AXYSIS OF PLaTE-INDUCTrtlJCE COMPENSATION OF THE MULTIVIBRATOR

The complete analysis of the circuit shown in Fig. 10 would involve so many variables that it would not only be laborious to make the study but also be difficult to draw conclusions from the mass of equations which would result. Therefore this study will be confined to the cir­ cuit composed of Rll, Ll, and Ce, which will hereafter be referred to as R, L, and C, respectively. The stud:/ will be further limited by considering only the time immediately after tube V4 ceases conduction. Assumptions, where made, will be justified by experimental evidence. Immediately after V4 ceases conduction, the grid of tube V3 will be at, or very near, cathode potential. This can be seen in Fig. 8. Thus it may be assumed that the cir­ cuit is composed of L, R, and C in series with the power supply. The result desired is to obtain a condition for which no current flows through this path vhen T4 is not conducting. The differential equation of this circuit is

(11) Ebb= Lfi / Hi / -fcjut

When t is zero, there will be a current E0/R flowing through L, since the current through an inductance cannot change 48

instantaneously, and a voltage of (Ep - Eco) on the conden­ ser C. These are the boundary conditions for (11), Using the Laplace transform method to solve (11) gives

(12) Els) - I(s)(sL / H / -1_) where

E EcQ (13) E(s) « ^Sh / ^£Q - P "

" sLSp / R(Shh- En / Sco) sK

Substituting (13) in (12) and solving for I(s) 4/ (En / Boo)) (14) I(s) = j-^ m0 / R (s2L / sR / -1-

Applying the inverse transform to both sides gives

fa S (15) R(En / Eco) / -R -TfR-T^-4X/I C -R -VR -4L,/C i - E£° Eo + 2 & 2L R VR2- 4L/C .1 2 3 R(En / EQn) , -R /VR -4L/C -R /TR -4L/C E, " ^ 2 —> 2L 1/R2- 4L/C

For (15) to be identically zero, the first term in the brack­ ets must equal the second term, By inspection, this will be possible if

(16) R2 r 4L/C

In the actual circuit it is not possible to use this value, since the circuit will become oscillatory when V4 conducts, A smaller amount of inductance will, however, improve the waveform as has been previously shown. Another solution exists if

L = 0

-Ec0= E0

This is a trivial solution, however, since 3uch a multi­ vibrator would have an infinite frequency. It is possible that values of cutoff and output voltages approaching this would give better waveforms. This was not investigated ex­ perimentally since the resulting output would be too small for use with the electronic switch* 50

iiTPSKDIX II

SCALING OF CIRCUITS FOR A-C TRANSIENTS

It will frequently be desirable to scale circuits for several reasons. First, to obtain a good off-on action from the switch, the circuit whose transient is being stud­ ied must have an impedance intermediate in value between the "on" impedance and the "off" impedance of the switch, as has been previously pointed out. Second, the response of a sys­ tem to the switching of a frequency which is beyond the range of the switch may be desired. Third, it may sometimes be desirable to build a model of a system which contains elements which cannot be easily realized in a laboratory. Thus a method of altering the circuit or its excitation fre­ quency will be of use. The logical place to start to develop a method of scaling is the differential equation of the system. In gen­ eral for a one loop system, the equation will be

(17) e(t) = S^idt / Ri(t) / L~£^

where e(t) Is the excitation or voltage function, i{t) is the response or current function and S, R, and L are the elastance (reciprocal of capacitance), resistance, and in­ ductance of the circuit. This integro-differential equation might be solved by a number of methods, but will be handled here by the Laplace transform method. 51

Defining the Laplace transform of e(t) plus the in­ itial conditions as £(s) and the L-transform of itt) as I(s), and taking the transform of both sides of (17) yields

(18) E(s) = I(s) (&/S / ft / Ls)

or (19) I(s) S --S/s/1 Ks

Taking the inverse L-transform of both sides gives

(2o) i-1 *"> = i-1 s/. yg^ u, =i(t)

The excitation function will, in the cases under consider­ ation, be of the form lAsin(27rft / )J • Suppose that the frequency is changed by a factor of 1/a, that is,

(21) e(t/a) z Asin (Z7T^ t / £ ) a '

This is equivalent to changing (t) by the factor of 1/a. Then if all functions of t can be similarly changed to func­ tions of (t/a), the waveform of the transient will be pre­ served, altering only the time scale and possibly the magnitude. That is to say, we wish to fine another cir­ cuit whose response to e(t/a) is Bi(t/a), yjhere B is a constant. 52

To achieve this end, consider a theorem of Gardner and Barnes-1-9: "'i'neorem: If the function f(t) is L-transformable and has the L-transform F(s) and (a) is a positive con­ stant, or a second positive variable which is inde­ pendent of t and s, then, L[f(a)j= aF(as'-'? applying this theorem,

(22) L e(t/a) = aE(as)

Suppose the parameters of the circuit are also cnanged so that

(23) 3' - S/a R» = R Lf r aX

Using these new parameters, and the new excitation trans­ form of (22), the response transform I'(s) of the new cir­ cuit will be

<24> I,(3) =av Wi'.

iyGardner, M. F., and J". L. Barnes, "Transients in Linear Systems, Vol. 1, p. 226, John Wiley and Sons, New York, 1942. 53

Making the substitutions indicated in (23), leaves

a£ (a s (25) T i / Qi - aaiasj 1 (S) " S/as / R / L(as)

Taking the inverse transform of both sides and applying the inverse of the previously stated theorem yields

(36) L-l IM.) = L"1 M^J^/ Ll..) = ilt/a)

Thus this change of frequency and parameters, gives a re­ sponse identical to the response of the original circuit except for the new time scale• As an example, suppose it is desired to double the frequency. In this case (a) is J-, If the resistance of the circuit remains fixed, and the capacitance and induct­ ance are each halved, then the transient of the new circuit will be the same as the transient of the original circuit except that it will take place in one half the time. This procedure applies equally well to multiple loop systems, since multiple loop systems merely involve the simultaneous solution of a set of equations of the same nature as those used here. It should be noted that (21) and (25) are not the only changes in frequency and parameters which will pre­ serve the waveshape. For instance, if (21) is retained, 54 and the parameters are changed in accordance with the equations

(37) S» = S R1 : aR L' = a2L then the waveform of the transient will be preserved. Here the response will be

(28) IT1 IMS) = ii{t/a)

There is an infinite number of other parameter changes which preserve the waveform. The only requirement is that the power of (a) associated with S, R, and L be ascending in that order. APPENDIX in

PARTS LIST

Resistors Symbol Value Function

Rl 20,000 ohms, variable Phase shift control R2 100,000 Phase shift circuit

R3 100,000 Phase shift circuit R4 2,000 Cathode bias, VI

R5 220,000 Plate load, VI R6 250,000 Grid leak, V2 R7 2,000 Cathode bias, V2

R8 100,000 Plate load, V2 R9 50,000 Coupling impedance RIO 10,000 Plate load, V3 Rll 5,000 Plats load, V4 R12 47,000 Grid current limiter R13 270,000 Frequency determining R14 270,000 Frequency determining

R15 47,000 Grid current limiter R16 40,000 Screen dropping, V5 R17 30,000 Screen dropping, V6 R18 20,000 variable Screen balancing R19 250,000, potentiometer Frequency control Capacitors Symbol Value Function CI 0.1 microfarads Phase shift circuit C3 25 Cathod3 re3istor bypass C3 0.1 Interstage coupling C4 25 Cathode resistor bypass C5 0.26 Sync coupling C6 0.1 Sync coupling C7 0.05 Frequency determining C8 0.05 Frequency determining 09 0.05 Screen bypass 010 0.05 Screen bypass Tubes VI i 6SN7 Sync amplifier V2 i 6SN7 Sync amplifier V3 i 63N7 Multivibrator V4 | 6SM7 Multivibrator V5 6L6 Switch V6 6L6 Switch Miscellaneous LI 3 millihenries Output peaking inductance SW1 DPDT switch Phase reversing switch Tl Transformer, Navy type T-173E Cathode load O Ictnkmci Veffag&s i

Sync /rtput { 6.3 v. AC { )c? v. DC £ > XX?v DC £ JO y/LtfXL +7&J7 'ST

V\g,30~ ScHEMAT/C D\AGRA w 58

BIBLIOGRAPHY

Andrew, Victor J., "The Adjustment of the Multivibrator for Frequency Division," Proceedings of the Institute of Radio Engineers. 19:1911-1917, November, 1931. Arguimbau, L. B., Vacuum-Tube Circuits, John Wiley and Sons, New York, 1948, 668pp. Bartelink, E.H.B., "A Wide Band Square Wave Generator," Transactions of the American Institute of Electrical Engineers. 60:371-576. June. 1941. Cosby, J. R., and C. W. Lampson, "Electronic Switch and Square Wave Generator," Review of Scientific Instru­ ments. 12:191-192, April, 1941. Davidson, I. B., "Doubls-wave Device for Use with a Cathode Ray Oscillograph," Journal of Scientific Instruments, 11:359-361, November, 1934. Garceau, Lovett, "Duplex Cathode Ray Oscillograph," Rev. Sci. Inst., 12:171-172, June, 1935. Gardner, M. F., and J. L. Barnes, Transients in Linear Systems, vol. 1, John Wiley and Sons, New York, 1942, 389pp. George, R. H., H. J. Helm, H. F. Mayer, and C. S. Roys, *A Cathode Ray Oscillograph for Observing 2 Waves," Electrical Engineering, 54:1095-1100, October, 1935. Hughes, H. K., "Thyratron Selector for Double Trace Cathode Ray Oscillograph," Rev. Sci. Inst.. 7:89-92, February, 1936. , and R. F. Koch, "Combination Vacuum Tube Switch for Double Trace Oscillograph, Audio Amplifier and Mixer," Rev. Sci. Inst. , 12~:183-187, April, 1941. Kurokawa, K., and S. Tanaka, "A Direct Visualizer for Trans­ ient Phenomena," Electrotechnical Journal (Japan), 4:51-55, March, 1940. Reich, H, J., "Electronic Switch for the Simultaneous Ob­ servation of Two Waves with the Cathode Ray Oscillo­ graph," Rev. Sci. Inst.. 12:191-192, April, 1941. , "Electronic Transient Visualizers," Trans. A.i.E.E., 55:1314-1318, December, 1936. 107545

59 , and &. S. Marvin, rtA Combination Sweein Circuit and Periodic Contactor for Studying Circuit and Line Transients with the Cathode Ray1 Oscillograph," Rev. Sol. Inst,. 5:7-9, January, 1934. Sewig, Rudolf, "Simultanaufzeichnung mehrerer Vorgange mit dem Kathodenstrahloszillogra-ohen," Zeits. f. tech. Physik. 14:153-153, March, 1933. ' Shumard, C. C, "Soma Electronic Switching Circuits," Elec. Eng.. 57:209, May, 1938.

Turner, H. M., "Transient Visualizer," Trans. K.I.E.E., 43:805-813, June, 1924. Weber, Ernst, and M. J. DiToro, "Transients in the Finite artificial Line," Trans. n.I.E.S., 54:661-663, June 1935.