LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 510.84 I^6T no. 188-199 cop.SU Digitized by the Internet Archive in 2013 http://archive.org/details/someinvestigatio191gree , Report No. 191 SOME INVESTIGATIONS IN THE' AREA OF HIGH VOLTAGE, HIGH CURRENT D-C AMPLIFIERS by October 1 1965 Marlin Everett Greer DEPARTMENT OF COMPUTER SCIENCE • UNIVERSITY OF ILLINOIS • URBANA, ILLINOIS Report No. 191 SOME INVESTIGATIONS IN THE AREA OF HIGH VOLTAGE, HIGH CURRENT D-C AMPLIFIERS* by Marlin Everett Greer October 1, 1965 Department of Computer Science University of Illinois Urbana, Illinois * This work was submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering, August, 1965 ACKNOWLEDGMENTS The author would like to express his gratitude to Professor K. C. Smith for his inspiration and guidance in this project. The author also wishes to express thanks to his wife, Karen, for the typing of this report, and for her patience and encouragement. -111- TABLE OF CONTENTS Page INTRODUCTION 1 1. AVAILABLE TRANSISTORS , . . • . 2 2. THE PREAMPLIFIER 5 3„ A HIGH VOLTAGE AMPLIFIER 13 4. INCREASING DRIVE CAPABILITIES 15 5. HIGH CURRENT DRIVES 18 5ol Complimentary Emitter Circuit • 18 5.2 Emitter-Follower Circuit • • • • 22 6. HIGH VOLTAGE-HIGH CURRENT DRIVE 32 CONCLUSION 3^ BIBLIOGRAPHY 36 -iv- INTRODUCTION A d-c amplifier, to be truly versatile, umst satisfy a diversity of normally ©onf lie ting requirements It must be, for example, tol- erant of both large and small loadings, and to be capable of large output swings, at least for small loads e Available devices incorporating solid-state circuitry normally have a very limited range, being either high voltage, low current, or high current, low voltage amplifiers o In fact 8 it appears that the present state of the art, as far as marketable fairly-high-speed amplifiers is concerned, provides up to + 20 volt swings and load current limits of 0o5 amp with some specialized amplifiers extending one of these parameters at the expense of the other • The intent of this paper is to investigate the feasibility of extending the ranges of both output parameters considerably; and, at least, in some special way make available both high voltage and high current output capability in the same amplifier * Problems involved in this area will be investigatedo A search will be made for promising circuit designso It is anticipated at the beginning that the time will not nec- essarily permit a complete solution to the problem stated in the following pages; but, rather the intent is to devise possible areas of attack and to explore the feasibility of designs suggested from these possibly different points of viewo Excluded are the class of slow d-c amplifiers which are available as reconnections of modern versatile regulated power supplies o 1. AVAILABLE TRANSISTORS High current transistors have been available for some time, though the technology for high voltage transistors has been slower in developing; however, devices are now available rated up to 600 volts (maximum collector to emitter voltage )o An example of a moderately priced NPN device is the Industro Corporations TRS3605S5, with the following specifications: Absolute Maximum Ratings Collector to emmiter voltage 420 volts Collector to base voltage 420 volts Emitter to base voltage 5 volts Collector Current 400 ma Total dissipation @ 25 C Ambient 2 watts Typical Values Hp E at 10 ma 30 Hpg at 200 ma 25 Both PNP and NPN high current transistors are available • How- ever, high voltage transistors are at present limited to NPN polarity. A further difficulty is that both high voltage and high current transistors have rather poor gain The possible combined use of high voltage transistors to extend the maximum output voltage ratings and high current transistors to extend the maximum output current ratings will be investigated. It is intended by this means to produce an amplifier which, though limited in total power drive capability, is versatile by being able to provide both relatively high voltage output into high resistance loads, and relatively high current output into low resistance loads. One possible output characteristic of such an ampli- fier is shown idealized in Figure 1. Incidentally, to be very useful, the desired amplifier configura- tion should not compromise bandwidth, linearity, or any of the other criteria of standard amplifier merit o The design problem seems to lend itself to separation into two parts? A preamplifier using more common low power, low voltage transistors, and a high power, high voltage stage 1 V/A WL 7V?Vm7f/?7?( t % 22 77777777777777? WB WSBB& i + A FIGURE I. IDEALIZED OUTPUT CHARACTERISTICS OF AN AMP PLIFIER STAGE WITH GROUNDED LOAD. 1* FIGURE 2. A DIFFERENTIAL AMPLIFIER STAGE. 2. THE PREAMPLIFIER For one possible intended use of the completed unit, as an operational amplifier, the preamplifier will need high d-c gain of per- haps several thousando Because of its d-c gain and d-c coupling, this stage will tend to be unstable » It will, for example, tend to drift due to changes in leakage current in the transistors caused by temper- ature changes o Accordingly, a decision was made to use a differential amplifier as the standard building block because of its inherent stability against such drift o Figure 2 is an example of such an amplifier The two transis- tors ideally would be identical to each other or closely matched in a variety of parameters and their thermal coef f icients The two transistors should also be physically and electrically close to each other, located. in a thermal and electrical enclosure such that the environment of each is identic alo The latter precautions are to ensure that the transistors will be subjected to the same temperature so that they will have identical leakage current, base to emitter voltage, and current gain changes Identical leakage current changes will affect the circuit in the same manner as does a common mode (CM) signal A CM signal is one in which signals of the same phase and magnitude are applied to the bases of both transistors o A differential mode (DM) signal is represented by a signal to the base of one transistor and a signal of the opposite phase but same magnitude to the other baseo It is important to notice that a differential amplifier has a CM and a DM gain which are different • The CM gain needs to be made as low as possible in order to enhance the stability of the circuit against drift o There is also another important reason to do this. For pre- amplifier use 9 only one signal is normally available* Therefore, no corresponding out of phase signal will be applied to the corresponding base of the other transistoro This one-sided signal is in effect a com- bination of a CM and a DM signal • A differential mode signal of two volts, for example, would consist of a positive one volt signal on the left base and a negative one volt signal on the right base Note that a positive one volt signal on the left with no cor- responding signal on the right is in effect a DM signal of one-half volt raised by a CM signal of one-half volt* This occurs because the signal divides across the two emitter resistors or their equivalent. If the CM gain is large, therefore, this common mode signal would cause an equal but undesirable change in the two collector voltageso If, for example, the output is considered to be taken from one side of the amplifier only, the resulting CM output is indistinguishable from an amplified DM signalo To demonstrate a means of overcoming this problem, the circuit will be investigated in more detailo 8R 2 i co 8i c ■«■ IioJL b i,!d CQJL £bO n h U4 ©0D + 0- •d v; i v '° VOD O ( > 8(R2+r E )i 2C0 X J FIGURE 3. DIFFERENTIAL MODE EQUIVALENT HALF CIRCUIT FOR AN UNBALANCED DIFFERENTIAL AMPLFIER. 8 Consider the circuit in Figure 3 as an equivalent half -circuit for the differential amplifier in the differential raode The square represents the usual controlled generator of a transistor models The circle generators represent uncontrolled generators • The symbol <£ is a measure of the degree of unbalance in the circuit The following parameters are defined? v i0 ^^ J-ID 2 The letter W D" subscript indicates states due to differential mode effects and the letter M C" (to appear later) to common mode effects. The symbols Vg„. and V RE 2 are ^° L@ Dase to ©natter voltage drops of trans- istor, T-j and T2 respectively and Iqq^ and Iqq^s are their leakage currents, The 8 generators represent current and voltage changes in the circuit due to the CM part of the signal voltage ■ where : V, c = V BU + VBE2 -Lie - 2 v_ is the common mode signal and v™ is the differential mode signalo The differential mode voltage at the output (v QD ) is then: -R,CX I0 + 5/3,0 Therefore, to make the circuit a true DM amplifier we need to nullify the effects of the common mode currents (suffixed with the letter "C M )o The immediately obvious way to do this is (by lcoking at the expressions for the CM currents) to make Ro arbitrarily large; however 9 to do this directly is to reduce the current capabilities of the amplifier At a fixed current level, R~ must act as a current source; there- fore, if R« were to be exchanged for an ideal current source, the amplifier would see infinite impedance at this pointo A solution to the problem is to replace R~ by the circuit in Figure 4o 10 ZENER = © FIGURE 4. CONSTANT CURRENT GENERATOR. FIGURE 5. CIRCUIT FOR BALANCING THE DIFFERENCE OF BASE TO EMITTER DROPS. 11 In this current generator the zener diode controls the voltage drop across R^ and with appropriate values of zener voltage and resistance for Rj, 9 any desired current can be obtainedo Appropriate choice of zener temperature coefficient will compensate over a meaningful range for varia- tion of emitter -base voltage drop and other parameters of T-, The differential amplifier now sees r of the transistor which c is the order of several megohms e The equation for Vq« has now been effectively reduced to: I 1n can be made reasonably small by carefully choosing the two transistors to be well matched This matching process also helps lower Vjrj—the dif- ference in base to emitter drops of the two transistors. These differences can be further reduced by using a balance resistor as in Figure 5° The differential mode gain can now be approximated as: A~ -=*& R i+ r E where r^ includes the appropriate part of the balance resistor o However, as was discussed earlier, the gain will be reduced by a factor of two when used as an unbalanced-input preamplifier o This is due to the fact that the corresponding out of phase signal will not 12 be applied to the opposite base. The ideas redeveloped in this section will be used in the next chapter to build and test an actual preamplifier with a high voltage output stage. 2 For a more complete discussion of d-c amplifiers, see R. D. Middlebrook, Differential Amplifiers (John Wiley and Sons, Inc., New York), 1963* 13 3* A HIGH VOLTAGE AMPLIFIER Tho circuit in Figure 6 is capable of driving small loads with large voltage swings. By virtue of high impedances its response will be somewhat slow*, The differential stage on the left is the preamplifier. The resistor to ground on the collector of T., is to balance the effect of the voltage divider on the collector of T % The purpose of the voltage divider to the negative 350 volt supply is to translate the available signal toward ground permitting the base of T to be negative with respect to the collector in order to permit negative swings The gain of the circuit is about: which checked closely experimentally. The output stage, including the adapting voltage divider 3 has a small gain of about three, allowing the preamplifier to be used with slightly smaller swings,, The circuit will handle output swings of up to + 200 volts for small loads of the order of one megohm. o + o Z> a. h- 3 O o (0 fO c/> or l'j- > 10 CVJONO 8 ro i ae UJ Ll J Q_ 2 a: a. 15 4o INCREASING DRIVE CAPABILITIES Circuits of the type exemplified by the output stage of the previous high voltage amplifier must be abandoned, because of their inher- ent ineffectiveness in the use of the current and power ratings of the output transistor o This combined -transistor resistor design forces several times the maximum available current for one polarity of output swing to exist as additional useless load on the transistor for the other output polarity. In an attempt to allow the circuit to handle low resistance load, the concept introduced earlier (Figure 1) of supplying the necessary current for low resistance within a restricted output voltage range, is incorpor- ated in the circuit to followo The circuit in Figure 7 is noted to look proraisingo It would be conceived of as a high power output stage driven by a preamplifier For Rt large, current drain will be small, leaving the collector voltages large in magnitudeo The diodes will, therefore, keep the low voltage supplies out of the picture o For positive swings only the top transistor will conduct, and conversely, the lower for negative swings Large loads will reduce the magnitude of the collector voltages allowing the circuit to reduce to that of Figure 8 The transistors are now not inhibited by collector resistors, allowing the amplifier to drive small resistance values easily over a limited voltage ranges Typically, but de- pendent upon applications, the available current would be limited by fuses, resistors, or the inherent characteristics of the power supplies o Although this configuration reduces greatly the problem of high dissipation which occurs if both large voltages and currents are allowed, it does, of course, have the practical limitation that there are no high voltage, high current devices presently in existence . Thus, in an amplifier designed with present 16 INO- •<* FIGURE 7. HIGH POWER OUTPUT STAGE WITH ALTERNATE HIGM CURRENT OR HIGH VOLTAGE CAPABILITIES APPROXIMATING THE OUTPUT CHARACTERISTICS OF FIGURE I. + 10 Rl -A- l -10 FIGURE 8. HIGH CURRENT OUTPUT EQUIVALENT CIRCUIT. 17 technology a high current limit would have to be traded for lower voltage capabilities and/or conversely high voltage for low currento A further difficulty is that no really high voltage PNP devices are presently available o Possible methods of overcoming the problems of this simple approach will be studied in the next section Q 18 5. HIGH CURRENT DRIVES The problems of driving large loads are now explored, ignoring for the moment the difficulties of incorporating large voltage swings • 5°1 Comp limentary Emitter Cir cuit It was noticed earlier that the circuit in Figure 7 has high current drive properties which operating in the mode shown in Figure 8„ A stage of this type provides current drive with no voltage amplification. The load voltage nearly follows the input (with the ex- ception of a lag of 0<>5 volts or so depending on V" BE of the device )• This stage has the advantage that it draws no standby current and only one transistor is working at a time. For example, with a positive signal, the top transistor drives the load with the bottom transistor acting as a reverse biased diode. It also will handle very large loads before being overcome by collector dissipation since it may have limiting resistors in either the emitter or collector paths Despite its very promising first appearance the stage has a very serious problem—it will not amplify small signals. The base-emitter voltage drop creates a nearly "dead" region of twice Vgg in magnitude.. This problem gives the stage the output characteristic as shown in Figure 9. The circuit also has the disadvantage of needing complimentary transistors, which are, however, available in high-current, low-voltage devices. To overcome the first problem a small standby current may be set up through the two transistors as is shown in Figure 10* 19 30.5v FIGURE 9. OUTPUT CHARACTERISTIC OF A SIMPLE COMPLIMENTARY EMITTER FOLLOWER OUTPUT STAGE. INO- IOK 0.5v 510 510 -0.5v iOK FIGURE 10. BIASING CIRCUIT TO OVERCOME DEAD REGION PROBLEM. 20 This will allow the drive of small signals as desired, but the solution creates another difficulty— the possibility of a short circuit, or at least an uncontrolled current, through the two transistors from the positive to negative supply » Experimentally, if the bias resistors are increased to 820 ohms— that is, biasing the base somewhat above the Vgg drop required, to ensure that the dead region is completely eliminated—a complete short is not found but a large uncontrolled standing current does result o It is further verified that once this condition is set up, the application of a signal does not shut off one of the transistors o For instance, for a positive signal, although the base voltage is raised tending to shut off the lower transistor, there is a short circuit path through the two emitters and the emitter will therefore follow the base up leaving the short circuit path still available » The detailed behavior is, of course, load dependento An attempt at controlling this short might be made by observing that when the top transistor is conducting, the bottom one should be shutting of and vice versa as is shown in Figure 11, For example, when T 2 is conducting sufficiently that 1^ drops enough voltage to allow the control transistor Th to conduct, base current is drawn away from T., through the collector of the control transistor T^o This system when tried in the simple form shown in the figure turned out to oscillate, for no input signal, between three states: T 1 on, T 2 on, and both T. and T 2 off „ 21 FIGURE II. HIGH CURRENT DRIVE STAGE WITH SHORT CIRCUIT CONTROL. O TO CONTROL TRANSISTOR FIGURE 12. BIASING METHOD TO PROVIDE STANDING CURRENT OUT OF REACH OF THE CONTROL TRANSISTOR. 22 The system can be made more stable by providing T-i and T_ with *■ 2 a minimum current out of reaeh of the control transistors This idea is illustrated in Figure 12 R would be large to keep the standby current smallo Stability can also be enhanced by reducing loop gain with series emitter resistors in the control transistors o Though it may be perfected 9 the system appears not to have surmounted the "dead" region problem The control transistor technique attempted above, in fact 9 only disguises the inevitable problem of this class of circuit—that of change of base-emitter voltage offset with imposed loado Difficulties experienced in improving the circuit from this point of view led to the development of another configuration which will be described nexto 5o2 Emitter-Follower Circuit In the search for a configuration that does not have the in- herent problem of base-emitter voltage cutoff with load, consider Figure 13c The circuit shown operates as a class A type output stage with release of pulldown current during pullupo This property overcomes the problem of changing from negative signals 9 where T£ is expected to conduct, to positive signals where it is to cut off. This also prevents the pos- sibility of a short through T- and T^o Uncontrollable current through T and T is not a problem in 1 2 this type of configuration since T. sees the collector impedance of T , which acts as a current source 23 ♦ 10 4 + 10 -100 >R 2 too INO- SM5334 SIMILAR TO 2NII32. SMI530 SIMILAR TO 2N22I9. DIODES ARE FAST SILICON VARIETY. FIGURE 13. EMITTER FOLLOWER HIGH CURRENT OUTPUT STAGE. Zk Since T, needs only a small amount of standby current and T ? cuts off for negative drive, the stage has very efficient current drive capability o The resistor, R, , is present as a drive for T30 But, it is made small so that T, will not saturate out as load increases • Ideally, To should bias T„ off for positive signals , drive the base of T ? for negative signals; and establish a controlled standing current through T* and T for the no signal caseo Positive signals will bias To off 9 turning T 2 off and allowing T. to drive only the load with no loading by T„o For negative signals To will be biased on providing base current for T 2 o Since R^ tends to saturate T« at large loads, it is desirable to bypass it, if possible 9 after its role in turnoff of T~ is complete and before it has this effect on the circuit o For zero input, the voltage drop across IL is about one volto It takes very little increase in this drop to completely turn To off o If this drop 9 after reaching one and one-half volts or so could be held at this point with the resistor bypassed, the circuit would still operate in the desired mannero This effect is achieved by the series diodes shunting Rjo Since each diode has a junction voltage drop of about o 8 volts at a few milliamps, the drop across R^ must be I06 volts before the current will flow freely through the diode patho One further major effect must be considered The negative feedback loop through the three transistors is a possible source of 1- Uations. 25 ihe circuit was actually found to oscillate when the first model was tested* However, a new model, laid out as efficiently as possible, keeping leads short and with power supplies bypassed, was apparently free from oscillation. A first order attempt was made to investigate the possibility of loop oscillation as follows: The loop was first studied to see at what frequency the phase shift attributed by individual transistors reached a total of 3&0 , The loop gain was checked to see if it is greater than unity at this frequency o For this test T* and T 2 were SM1530 , s and To was an SM533^ transistor These were picked because of their similar frequency characteristic So This choice tends to increase the possibility of oscil- lation o The current gain of both T~ and T (each in grounded-base con- figuration for the purpose of this discussion) roll off at their alpha cutoff frequency while To gain degenerates at its beta cutoff frequency because of its grounded emitter use. Since the beta cutoff frequency is only one over beta as large as the alpha cutoff, the tendency for oscillations might be increased by a choice of T ? with a higher beta cutoff This is unrealistic, however, since in any real circuit, power considerations would force T^ and T2 to be of the same type. The beta cutoff was found to be about 500 KC (see Figure 16) for both transistors o Midband gain for the SM1530 was found to be 26 140 9 while that of the SM533^ was 110 3 Since the alpha cutoff for the SJH53C will be ?0 megacycles and that of the SM533 i J' will be 55 megacycles The phase shift of a transistor is very nearly 90* at one decade above its three db point « Since the alpha cutoff of Tj^ and To are well above the plus one decade point for T« (by 5 megacycles), the phase shift in Tp can certainly be considered to be 90° (in addition to the current reversal in the base and the collector of T 2 )<> This means that the necessary phase shift for oscillations will come at approximately the three db point of T* and T~ where a total of 90° phase shift will have to be contributed by the pair This fre- quency is found in Figure 1^ to be 60 megacycles o Input impsdance at this frequency was not measured , but it can be seen from Figure 15 that it will be very lowo To calculate the gain around the circuit 9 it is "broken" at some point t, If 9 for instance^, this is done at M A*% a small oscillation trying to develop will split between R, and the impedance looking into the emitter of T~ which is z E =4( z m + iooo/ioo) -'For a discussion of methods of measurements of high frequency para- ra soe J. F« Cleary, G >JLJ£raz^s^r_Mamial (General Electric Co , Syracuse, New York),, 19&C" 27 0° -L0P-2O -40* -eo -^ PHASE SHIFT FIGURE 14. PHASE SHIFT IN THE COMMON BASE TRANSISTOR CON NECTION OF T 3 +T, IN FIGURE 13. 28 Oi 2 — K « 3 j i r< ') Q O ENCY OKC CC CC O CC UJ 2 UJ z o 2 o o Q UJ CC i UJ 2 8 Q Z < o ro £ 2 cfl UJ I o X H o 3 S a: o 2 ^&^~ o SM5334 ■8 m (7) o 2o o o ID O O UD O o 8 o o O O UJ o ui o z < Q UJ 0. r- a z Q UJ CC < UJ 2 ui CC o O E SWHO Nl 30NW3dWI 29 where Z^ n is the input impedance of the transistor in the common emitter configuration as was shown in Figure 15 ° If this current splitting situation and transistor gain at 60 megacycles are considered around the entire loop, the loop gain is found to be somewhat greater than unity , creating the tendency to oscillate, This tendency was observed experimentally when the input was driven with a fast rise input (pulse or a square wave)o One method that can be used to avoid those oscillations is to use a transistor for T~ which is very high speed with respect to T. and T ? o This staggers the corner frequencies, making the loop gain lower at the 180 degree phase shift frequency <> Another method is to observe that the phase shift in the loop is due to the transistors appearing as R-C equivalent circuits, causing a lag in the current around the loop An artificial lead time can be introduced by inserting a capacitor of 10 to 100 pf across the collector and emitter of T~o This also has the desirable characteristic of reducing the rise time of the circuit output by a factor of two or three o The loading that an output stage places upon its driver is very important. This circuit was found to have the very desirable low loading characteristics shown in Figure 17 o Figure 18 shows that the output voltage lags the input voltage by a very small amount even for large loads The circuit of Figure 13 does then have the properties being sought for a high current drive output stage 30 56ii IOO& >500J2 -5 -3 -10 1 DRIVE VOLTAGE FIGURE 17. LOADING OF A SIMULATED IK PREAMPLIFIER STAGE AS A FUNCTION OF LOAD RESISTANCE AND DRIVE VOLTAGE. (POWER SUPPLIES OF #10 USED.) 56 a 100X2 5ooa FIGURE 18 -5-3-10 1 3 5 DRIVE VOLTAGE — •» OUTPUT LAG VOLTAGE AS A FUNCTION OF LOAD RESISTANCE AND ORIVE VOLTAGE. 31 If the properties of the circuit in Figure 7 could now be com- bined with those of Figure 13> an amplifier having the properties of Figure 1 would result* An attempt at this goal is described in the next sectiono At the present the amplifier output stage discussed in this section is the most appropriate yet found, as an answer to the general problem originally posed© 32 60 HIGH VOLTAGE-HIGH CURRENT DRIVE In the attempt to combine the two capabilities of high current and high voltage drive, the circuit in Figure 19 was considered,, This circuit does have some of the properties that were being sought? that is 9 the capability of either high voltage swings or alter- nately high current drive at lower voltages^ depending on the size of the loado The transistor T. has relatively high current capabilities while T has high voltage potential o The diode isolates the positive 100 supply from the low-voltage transistor T^° T,. provides voltage amplification and drives the base of T ?0 A large load will tend to isolate the positive 100 volt supply and 10K resistor „ allowing T. the major roleo T does not have any voltage 1 1 amplification., but is adaptive to large loads For small loads ? T with its collector resistance will provide additional voltage amplification and permit large voltage swings • This amplifier,, however 9 does not allow both positive and negative swings and from that standpoint alone probably would not be a very useful device o There is further the possibility of uncontrolled currents through the T l9 T£ path., introducing the problems encountered earliero 33 + 100 +100 A 10 K >Ri FIGURE 19. UNBALANCED OUTPUT STAGE USING BOTH HIGH VOLTAGE AND HIGH CURRENT DEVICES, APPROXIMATING ONE HALF THE OUTPUT CHARACTERISTICS OF FIGURE I. 3* CONCLUSION The original goal has been the generation of an amplifier with output characteristics as shown in Figure 1; that is 9 of providing capa- bilities of high current, high voltage drive, though not simultaneously <> For the driver stage, a differential amplifier was chosen because of its low drift properties. A driver stage of the same type was considered, but was not used because of its inherent current driving inefficiency produced by the split of total supply current between the load and the active element This particular problem of circuit effectiveness was surmounted by use of complimentary emitter follower circuits and the coupling circuits between T^ and T of Figure 13 • Although there was an apparent solution in the circuit of Figure 7 and a partial solution in the circuit of Figure 19 9 the push- pushj or pull-pull nature of these configurations introduced the problem of deadband, or alternately, uncontrolled currents between supplies o The original problem seems now to be modified and to have re- moved itself then from the design of configurations with the desired properties of Figure 1 to the design of a configuration controlling dead band and uncontrolled current flow As was discovered, attempts to control dead band seem to increase the possibility of uncontrolled currents, and preventing the short cir- cuit possibility seems conversely to insert dead band. A final solution appears to lie in an attempt to stay in between o two states. When this was tried in the circuit of Figure 11, the 35 problem of instability was introduced Possibly this might be controlled in the circuit of Figure 11 by an investigation of the effects of the base biasing resistors on the rest of the circuit in the various conducting states and by a reduction of the positive feedback introduced by the control transistors In the search the possibly unique circuit of Figure 13 was discovered o The circuit had the extremely useful property of being able to drive small loads efficiently within a limited voltage range This circuit could possibly be incorporated in a circuit in an attempt to achieve the output characteristics of Figure 1» 36 BIBLIOGRAPHY lo Angelo, E. J., Jr. Electronic Circu its <, McGraw-Hill: New York, 1958* 2c Cleary, Jo F. G. E. Transistor Manual » General Electric Co: Syracuse, New York, 19&4. 3o Korn, Granino, and Korn, Theresa Electronic Analog Computers . McGraw-Hill: New York, 1958. 4. Hilbiber, David . M A New DC Transistor Differential Amplifier. H IRE Transactions on Circuit Theory , Vol* PGCT-8, No. b (December, 1961 ) 9 pp by+MO . 5o Middlebrook, R. Do Diff eren tial , Am plifier S o John Wiley & Sons: New York, 1963° 6c Slaughter^ D. W. "The Emitter -Coupled Differential Amplifier." IRE Transactions on Circuit Theory. Vol. CT-3, No» 1 (March, 1956), PPo 51-5^ 7o Stanton 9 Jo W» "A Transistorized Amplifier o" IRE Transactions on Circuit Theory. Volo CT-3, No 1 (March, 1956J, pp7~65-67 . UNIVERSE OF ILLWO^ Intarnat report I