A TRANSISTORIZED REGULATED POWER SUPPLY ,f A THESIS Presented to the Faculty of the Graduate Division Georgia Institute of Technology In Partial Fulfillment of the Requirement s for the Degree Master of Science in Electrical Engineering By Lincoln PhelpsRice August 1954 A TRANSISTORIZED REGULATED POWER SUPPLY Approved: • / • - y - • — •- ' " • • - ~ " " Date Approved by Chairman: ^0<^ .2.1, /iSJ* In presenting the dissertation as a partial fulfillment of the requirements for an advanced degree from the Georgia Institute of Technology, I agree that the Library of the Institution shall make it available for inspection and circulation in accordance with its regulations governing materials of this type. I agree that permission to copy from, or to publish from, this dissertation may be granted by the professor-under whose direction it was written, or, in his absence, bw the Dean of the Graduate Division when such copying or publication is solely for scholarly purposes and does not involve potential financial gain. It is understood that any copying from, or publication of, this dissertation >• which involves potential financial gain will not be allow^dcilf *». ACKNOWLEDGMENT I wish to express my appreciation to Doctor B. J. Dasher for his suggestion of the subject for this project and for his invaluable assistance in its prosecution. TABLE OF CONTENTS Page ACKNOWLEDGMENT ABSTRACT ii „ vii CHAPTER I. II. III. IV. V. VI. INTRODUCTION ....... BASIC PRINCIPLES OF TRANSISTOR OPERATION . . THE TRANSISTOR AS A CIRCUIT ELEMENT .... 1 3 14 DISCUSSION OF THE REGULATED POV7ER SUPPLY . . 29 CONCLUSIONS 61 RECOMMENDATIONS 63 APPENDIX I, DERIVATION OF GROUNDED-EMITTER TRANSISTOR EQUIVALENT CIRCUIT APPENDIX II, DERIVATION OF EQUATION (51) . . 65 68 APPENDIX III, PARAMETERS AND COMPONENT VALUES 71 APPENDIX IV, BRIDGE CIRCUITS APPENDIX V, OSCILLOGRAPH CIRCUITS BIBLIOGRAPHY .... 79 .... 81 $2 LIST OF TABLES Table 1. 2* 3. 4. Page Values of Stabilizer Parameters Determined by Various Methods 55 Values of Various Parameters, Components, and Constants . . , 76 Results of Numerical Computations Compared with Corresponding Experimental Data 77 Point-by-Point Measurements of Stabilizer Currents and Error-Signal Voltage 73 LIST OF ILLUSTRATIONS gure Page Diagram of pnp Transistor Showing Bias Batteries . . . . . . . . . 12 2. A Two-Terminal Pair . . . . . . . . . . . . . . 15 3. Static Characteristics of a pnp Junction Transistor 17 1. 4. 5. Grounded-Base Equivalent Circuit for a Transistor • 19 Grounded-Emitter Equivalent Circuit for a Transistor . . . . . . • • • • 20 Schematic of Transistorized Regulated Power Supoly . . . . . . . . . . • . . . • . . • • • 30 Simplified Schematic of Voltage Stabilizer . . 31 ?*• Generalized Schematic of a Voltage Stabilizer . 35 9. Equivalent Circuit of Regulated Voltage Supply 37 10. Equivalent Circuit of Stage One of Voltage Regulator . „ . . . . . . . . . . . . 39 Equivalent Circuit of Stage Two of Voltage Regulator • , . • . . . . . . , . . . . . . . . . 39 Equivalent Circuit of Stage Three of Voltage Regulator for Derivat i on 01 n . . . . . . . . . 41 Equivalent Circuit for Stage Four of Voltage Regulator for Derivation o f R . . . . . . . . 41 6. 7. 11. 12. 13. 14. 15. 16. 17. . Equivalent Circuit of Stage Three of Voltage Regulator for Derivation of 3 44 Equivalent Circuit of Stage Four of Voltage Regulator for Derivation of S 44 Oscillogram of Current-Voltage Characteristics of Silicon Diode D]_ . . . . . . . . . . . . . 51 Oscillogram of the Zener Region of the CurrentVoltage Characteristics of Silicon Diode Dn . . 51 Pag Modified Error-Detector Circuit with Venier Control for Varying the Output Voltage . . . . 53 Regulation of Voltage Stabilizer . . . . . . . . 56 Regulation of Voltage Stabilizer on Expanded Voltage qcale . . ..... 56 Steps in the Derivation of the GroundedEmitter Equivalent Circuit . . . . „ . • • • • 66 Regulation of Rectifier-Filter Unit 73 Rectifier Regulation on Expanded Voltage Scale 74 Error-Signal Voltage Versus Output Current • . 75 Error-Signal Voltage Versus Output Current, Expanded Voltage Scale . . . . . . . . . . . . 75 Bridge Circuit for Measuring R . . SO Bridge Circuit for Measuring S . . . . . . . . SO Circuit for Obtaining Current-Voltage Characteristics of Silicon Diode . . . . . . . 61 Circuit for Obtaining Regulation Curves ... SI ABSTRACT Smaller size, absence of heater elements? resistance to shock, reduced power requirements and reduced heat generation are among the advantages which a. transistor circuit enjoys over an electron-tube circuit. The low power require- ment of a transistor circuit has made possible the economical use of a battery as a power source. In those applications not suited to the use of batteries, it is desirable to have a regulated d-c power source which posseses the same attributes with respect to size, heat generation and absence of heater elements as the circuit it supplies. The develop- ment of such a power supply was chosen as the problem for this Droject. The supply which was developed consists of a conventional full-wave rectifier using 1N93 diodes and a transistorized stabilizer. The stabilizer is composed of three sections, a regulator, a three-stage d-c amplifier, and an error detector. The error detector varies the error-signal voltage across the input terminals of the d-c amplifier in proportion to the variation in the output voltage of the stabilizer. The d-c amplifier converts this error signal to a current, amplifies it and reverses its phase. This current acts as a variable bias for the regulator which Vlll consists of a bank of transistors in parallel connected in series with the output terminal. The voltage across the regulator varies in such a manner as to cancel any changes occurring in the output voltage. The stabilizer will deliver thirty volts over a current range of zero to forty milliamperes. It has an output resistance of 3.5 ohms and a stability factor of thirty-five. The operation of this regulator differs from that of an electron-tube regulator in two basic ways. First, the error detector must maintain the correct errorsignal voltage independently of the base current which it supplies to the first transistor in the d-c amplifier. Second, the regulator is controlled by a current instead of a voltage. The drift inherent in semi-conductors affects the operation of the stabilizer in two ways. The drift in the silicon diode used as the reference element will cause a direct and equal drift in the output voltage. The drift in the transistors will cause a negligible variation in the output voltage but will change the current limits over which the regulator will function. Included in this work are a discussion of basic transistor principles, the discussion of a. method, of determining stabilizer performance in terms of its stability factor and output resistance, and the derivation of these parameters in terms cf the small-signal transistor constants. CHAPTER I INTRODUCTION From their inception transistors have been a potential solution for many problems in the field of electronics. Their advantages over vacuum tubes include their small size, high efficiency, absence of heater, long life, resistance to shock, and reduced heat generation. These are of great importance to the designer of the miniature and subminiature electronic equipment required in aircraft, portable, and other mobile applications. These favorable characteristics have caused a stampede to transistorize virtually every known electronic circuit whose power level was not too large. The vast majority of this work is still in the development stage where it is hampered by the present transistor limitations. Foremost among these are the sensitivity of their parameters to temperature change and the present lack of uniformity among supposedly similar transistors. The latter has made their introduction into military applications particularly difficult because of the necessity for readily interchangeable components. The power source for most transistor circuitry to date has been the dry cell. This has been possible because of the low voltage and low current requirements. The Bell Telephone Laboratories are developing a telephone carrier system in which o (L- transistorized components are supplied by batteries which will require replacement once every five years. Applications: exist, however, in which it is impractical to supply transistorized circuits from batteries. Aircraft electronics is a field in which transistors offer a tremendous advantage ir the saving of weight and space. This would be largely offset by the bulk and weight of batteries if they were used as sources of power. A subminiature rectifier-stabilizer which converts the aircraft alternating current to a regulated d-c voltage is preferable. This unit should generate as little heat as possible, since heat dissipation is one of the major problems of subminiaturization. It should be as light and small as possible and have regulation characteristics comparable with conventional regulators. A miniature supply using a magnetic amplifier as a stabilizer has been introduced. It is believed that a transistorized circuit to regulate the voltage after rectification will yield the best regulation characteristics and equal or exceed the magnetic amplifier in the saving of space and weight and lack of heat generation. The development of such a power supply was undertaken as the project for this thesis to determine the principles involved. The succeeding chapters give a discussion of basic transistor principles followed by a detailed discussion and analysis of the regulated supply8 CHAPTER II BASIC PRINCIPLES OF TRANSISTOR OPERATION Semiconductors.—In order to gain fuller understanding of the applied operation of transistors, the principles of operation of semiconductors should be investigated particularly the characteristics that distinguish them from insulating and conducting materials. In 1897 J. J, Thomson obtained evidence to substantiate the existence of electrons by determining that the ratio of charge to mass of a cathode ray is a constant. About this time scientists had also been observing the various radiation phenomena and were attempting to ascertain the structure of an atom. Thomson and Rutherford each proposed a model con- sisting of a configuration of positive and negative charges. Rutherford*s model conformed more closely to existing theory. The Rutherford atom consisted of a planetary arrangement, similar to the soler system, in which the positive charge and most of the mass of the atom were concentrated in a nucleus at the center with negative charges traveling in orbits around it. However, according to current theory, these negative charges, subjected to a continual centripital acceleration, would radiate energy causing them to lose their electrostatic potential and spiral into the nucleus. This, of course, is not the observed case and constitutes a defect in the Rutherford atom. 4 In order to explain the spectral series of singleelectron atoms, Niels Bohr introduced two important postulates(l). The first was that an electron can exist only in certain stable orbits which satisfy the following quantum condition nh mvr r 2 where n is the quantum number (an integer), m is the electron' mass, v is the electron's speed, r is the radius of the orbit corresponding to the quantum number, and h is Planck's constant. Each value of n leads to a different stable orbit. The electron will not radiate energy while it remains in one of these orbits. The second postulate was that, when the energy of an atom changes from a value W]_ to a lower value V*'2, the difference in energy is emitted as a quantum of radiation given by the Einstein frequency condition hf = Wi - % 2 where f is the frequency of the emitted radiation. The con- clusion to be drawn from the Bohr postulates is that the electron of a free atom changes levels in discrete jumps. Methods using quantum mechanics support the Bohr postulates and are also applicable to multi-electron atoms. 5 This discussion has been confined to free atoms. When atoms are compressed together into a solid, interaction occurs between the various electrons. Pauli's exclusion principle says that tv/o interacting electrons cannot have the same set of quantum numbers. Therefore the energy level of each of the interacting electrons must be slightly different from the rest and the group of levels farm into bands. In semiconductors a band of low energy levels occurs which is filled. This is called the valence or filled band. Above it in energy is an energy region known as the forbidden band or energy gap to which an electron will not jump. Still high- er exists another band of energy levels to which electrons can be made to jump. This is called the conduction band. So far this discussion has assumed that an electron is a particle or corpuscle. In 1923 Louis de Broglie(2) conclud- ed that electrons could be diffracted in a manner similar to the optical diffraction of light waves. The deduction made from de Brogliefs work was that electrons must have the characteristics of waves if they are subject to such diffraction. This was later demonstrated using a "grating" made of nickel crystals. Therefore two concepts of the electron, corpuscular and wave-like, have been proposed. It will be convenient to super- impose the two and consider the electron as being a "wave packet" consisting of a concentration of waves at a single point. 6 The electrons in the conduction band possess the most energy and consequently are the most susceptible to being removed from the atom. Electric current flows as a result of the migration of these free electrons. Conducting mate- rials have no energy gap and the conducting band may overlap the valence band. The electron migration occurs readily in these elements with thermal agitation frequently being a sufficient driving force. Other elements have an energy gap of the order of magnitude of one electron volt across which an electron must cross before it reaches the conduction band. These elements are called semiconductors. A third group of elements have considerably larger energy gaps and are called insulators. Germanium is a semiconductor. of 0.7 electron volts (ev)(3). It has an energy gap It has four valence electrons and forms into face-centered cubic crystals of the diamond type. Each atom shares each of its four valence electrons with an adjacent atom in a covalent structure. of each atom is called a lattice site. The location In this situation most of the electrons are bound and very few are available to become carriers of electric current. In the previous paragraph it was presumed that the germanium is completely free of impurities. This is impossible in practice but the presence of impurities is frequently desirable in semiconductors. Suppose that a smal 1 portion of melted arsenic is added to the melted germanium and the mixture 7 allowed to cryatalize. Arsenic atoms would be found occupy- ing certain lattice sites in the predominantly germanium structure. These arsenic atoms would be bound covalently to the germanium atoms in the lattice. However arsenic is a pentavalent element and only four of its valence electrons would be engaged in attaching it to the adjacent germanium atoms. This leaves an additional electron which can easily be induced into the conduction band and become a carrier. It has been found that only 0.05 ev is required for this electron as opposed to 0.72 ev to force one of the covalent electrons into the conducting band, A pentavalent element added to the germanium is called a donor because it adds electrons to the semiconductor. In a similar manner a trivalent element such as boron will occupy a lattice site and combine covalently with three adjacent germanium atoms but will lack a valence electron for the desired fourth bond. having a positive charge., This creates a "hole" This hole will attract an electron from a nearby bond and leave a hole at this new location. Another electron will be attracted to this hole filling it but creating another., In this fashion electrons jumping successively to nearby holes cause the holes to migrate in the opposite direction. A trivalent imparity is called an acceptor because it creates the holes which accept electrons from adjacent atoms. 8 Germanium, containing principally donors is called an n-type semiconductor,, while that containing principally acceptors is called p-type. These impurities are deliber- ately inserted into the germanium until an optimum proportion is obtained. The holes and electrons in the semiconductors are known as "carriers11 of electricity. In an n-type semi- conductor there exists an abundance of potentially migratory electrons due to the presence of the donor impurity. Traces of other impurities, which cannot be completely removed, will create some holes in the semiconductor. These holes are much fewer in number than the carrier electrons and are called minority carriers. carriers. The carrier electrons are majority Similarly, in a p-type semiconductor the electrons are minority carriers and the holes are majority carriers. Since holes and electrons are both always present in a semiconductor the electrons are continually filling the holes they encounter in a process known as recombination. The life of a carrier electron from the moment it leaves the conduction band of its parent atom until it recombines with a hole is about five to twenty microseconds depending upon the electron velocity and the relative prevalence of electrons and holes. P-N junction.—A p-n junction consists of an n-type semiconductor united to a p-type semiconductor(4). The surface between the two is the junction. The bond between the two cannot be created mechanically because the crystalline 9 structure must be continuous across the junction* One common method of forming a junction is to diffuse acceptor impurities through a portion of a piece of n-type germanium. That portion through which the diffusion occurred is thus converted to ptype germanium and a junction is established. It would seem that an excess of holes on one side of a junction and an excess of electrons on the other would cause diffusion in the entire germanium block until the holes and electrons were uniformly distributed throughout. How- ever, at room temperature, the holes in the p region are prevented from crossing the junction by the donor atoms on the opposite side. These atoms have a positive charge which will repel the holes. In the same manner electrons attempting to cross in the opposite direction will be repulsed by the negatively-charged acceptors in the p layer. This repelling charge can be thought of as a potential hill which cannot be traversed by a majority carrier unless it receives additional energy from an outside source. Minority carriers on either side can easily cross the junction because they are aided by the potential hill in making their transition. The current created in the semiconductors by the transition of minority carriers is small because they are few in number. Another analogy for the potential carrier at the junction is a small battery with its positive terminal connected to the n-type and its negative terminal connected to the p-type segment. Consider a battery to be connected across the p-n .junction with its positive terminal attached to the n-type segment. The potential thus placed across the junction will aid the potential hill already established by the ionized atoms at the junction. This will further prevent crossing by majority carriers but will cause slight increase in flow of minority carriers. This is called the reverse-current or high resistance condition. If the reverse potential is in- creased sufficiently a voltage breakdown, known as the Zener effect, will occur. Reversing the battery polarity will give the junction a low resistance or forward-current bias. This results because the battery potential opDoses the potential hill at the junction and effectively flattens it out. Majority carriers can now cross the junction barrier freely creating an electric current. This current will not be without limit, however, because, as it begins to flow it creates a potential drop in the germanium segments themselves due to the resistivity of the germanium. This drop will tend to counteract the battery potential and introduce a current-limiting action. A higher battery potential must then be used to obtain a current increase. If the battery potential is made too high the junction will be damaged due to the heat generated by an excessive current. A few tenths of a volt external potential are sufficient to generate a forward current. 11 Junction transistors.--A junction transistor consists of a pair of p-n junctions placed "back-to-back". It can be one of two types depending upon which type of germanium is common to both junctions: pnp or npn* As its name implies, a pnp transistor consists of a segment of n-type germanium flanked on either side by a piece of p-type germanium while an npn transistor consists of a segment of p-type germanium between two n-type pieces. The operation of the two is almost identical except for the fact that the bias voltages and the carrier types are reversed. Therefore, in the interest of simplicity and clarity, we shall confine ourselves to a study of pnp transistors with the understanding that the principles involved in the npn type are analogous. Fig. 1 is a diagram of a pnp junction transistor showing in dashed lines the batteries equivalent to the potential hills at the junctions. The block of p-type germanium to the left is called the emitter, the center segment of the n-type is the base, and the p-type on the right is the collector. In the configuration shown the base is grounded and the emitter and the collector are biased with respect to the base by the voltages E e and E c respectively. Note that the emitter junction is biased in the forward direction while the collector junction Is biased in the reverse direction. With an adequate bias, the emitter will become a source of holes, the carriers in a pnp transistor, which will cross over into the base. The number of holes 12 -l\--. r-»i—I i EMITTER i _L BASE COLLECTOR * Pig, 1 Diagram of a pnp transistor showing bias batteries, 13 which will receive sufficient energy to jump into the conduction hand and cross the emitter junction into the base is determined by the emitter bias. After the holes have entered the base they become minority carriers and will recombine with electrons present unless they are first swept across the collector junction. The base is made very thin, about one mil,, in order to increase the probability of a hole reaching the collector before it recombines. Since the collector junction is biased in the reverse direction its potential hill is enhanced and an electric field is set up aiding the diffusive migration of minority carriers from the base to the collector. After entering the collector, the holes which were minority carriers in the base are once again majority carriers and support the flow of current to the collector terminal, Under these conditions the collector resistance is very low. However, as the collector voltage is increased the holes available from the emitter will increase only slightly and the collector resistance increases suddenly. Since some of the holes are lost in the base due to recombination, the collector current will be less than the emitter current. This means that o(; the current gain of a junction transistor, will be less than unity. CHAPTER I I I THE TRANSISTOR AS A CIRCUIT ELEMENT Open-circuit p a r a m e t e r s . - - T h e p r e v i o u s c h a p t e r d i s c u s s e d some of t h e p h y s i c a l c h a r a c t e r i s t i c s of t r a n s i s t o r s . ness l i e s in t h e i r trical networks. performance as c i r c u i t Insight Their components i n usefulelec- i n t o t h i s b e h a v i o r can b e o b t a i n e d by u s i n g a t w o - t e r m i n a l - p a i r a n a l y s i s . This i s t h e familiar p r o b l e m of d e t e r m i n i n g the p e r f o r m a n c e o f t h e c o n t e n t s o f a " b l a c k b o x " by making m e a s u r e m e n t s on i t s f o u r e x t e r n a l ter- minals. The l o o p - b a s i s d i f f e r e n t i a l pair, equations for a two-terminal shown i n F i g . 2 , a r e v-, == — i , + _A i 9 1 aix di2 av2 av2 vP = — ai-L I-, + — (1) /L io (2) ai2 in which v-,, v 2 , in, and ip represent incremental changes in V, , Vp, I,, and I ? respectively. If the frequency is limited to a range in which the reactive components of the internal transistor impedances are negligible, and the analysis is restricted to the linear region of the transistor, the partial 15 _J_I I 1 '2 i i • • »- FiK. 2 A two-terminal pair. • 16 derivatives in equations (1) and (2) will show little variation and can be regarded as constant resistances. av 1 3 V1 11 91. BT2 h 31, 81 2 r 12 y dv? 21 = s i„ 1 (3) r 22 - The static characteristics of a junction transistor are shown in Fig. 3. Inasmuch as V e , Vc, I e , and 1^ are equal to V-,, Vp, I]_, and 1^ respectively, the open circuit parameters of this transistor at a given operating point can be found from the slopes of these characteristics. The curves are so steep that an accurate determination of their slopes by graphical means becomes difficult. Better results can be obtained by biasing the transistor to the desired operating point, applying a small a-c signal at the driving point, and measuring the a-c response of the transistor. SheaTs(5) detailed description of this technique was followed in determining the various transistor parameters listed in Table 2. Transistors can be connected into a circuit in three different ways,, These are designated by the terminal which is connected to the return paths of both the other terminals. These configurations are listed below opposite their vacuumtube equivalents. -20 1 -20 l e constant -16 -16 2 iz -12 _ -- — 3 >° | 1 4 >°-B - "1 5 1 I 1 -4 lc, 3 le, 4 ma 250 \ 3* 2 -5 ma 250 200 I* S"'2 -8 1 l c constant 5 /-3 200 2" 1 /-. / - 2 *B0 — E > 150 E 100 100 50 50 l e constant 5 lc, 0 l c constant 2 3 le, ma Pig. 5 Static characteristics of a pnp junction transistor. ma /_4 IS Transistor Vacuum Tube Grounded-base Grounded-grid Grounded-emitter Grounded-cathode Grounded-collector Grounded-anode (cathode-follower The f i r s t two a r e the mast commonly used connections and w i l l be studied in g r e a t e r d e t a i l . Grounded-base connection.—Fig. 4 shows a configuration of equivalent r e s i s t a n c e s which approximates the of a grounded-base t r a n s i s t o r . characteristics The inclusion of the equiv- alent voltage generator i n the c o l l e c t o r c i r c u i t i s necessary because the t r a n s i s t o r i s an active element. This scheme i s analogous to the use of an equivalent voltage in vacuum tube circuit analysis. The voltage added in the c o l l e c t o r c i r c u i t by t h i s generator i s a function of the emitter current and a r e s i s t a n c e , r , called the "mutual r e s i s t a n c e . " It can be shewn r ll * r 21 s r b + r b + :r that e r m r 12 = r b (4) r r 22 - b + r c then the solution for the t r a n s i s t o r parameters i s r e ~ r H " r 12 *b *12 r r (5) r r r m " 2 1 " 12 c 22 " r l2 19 ^VW AAAr o 'm'e v Fig. 4 Grounded-baae equivalent circuit for a transistor. 20 With the load, Z^, attached as in Fig. 4 (6) zx + Two equations for v in terms of i e v v e e = (r ~ (r and i e e + r,)i b e - r )i e r n e are c + r,i be - (r c (7) + ZT ) i L c (3) Subtraction of (£} from (7) ^ives 0 = r (i b e + i ) + (r + ZT ) i c c L c (9) + r i me from which the collector current i s found to be -i (r.,+ r ) e b ra r b + r Substitution for i c e = L e \ r r0. e 21 22 + (10) Z L in (7) gives r v + -i + r e - r,(r1+ r ) b b b m b c L ID and so 7 „ ^1 ~ (r, + r ) I r + Z_ ) + r ( r b e c L b e — r, + r + Z_ b c L - r ) m ,— (12) I f the open-circuit parameters are inserted into (12) the result is 21 z r l - (r 11 r 21 + Z ) + r ( r - r ) L_ 12 1 1 21 12 f + 22 Z L r Z + r r - r 2* 11 L 11 22 12 21 Z-, » r rnZ Z, + 22 Z + L (13) (14) L |r (15) F " + 22 Z L i n which I 2* I = r r I I 1122 This r e s u l t i s —r r 12 21 i d e n t i c a l to t h a t obtained for p o s e d of p a s s i v e , linear., b i - l a t e r a l e x c e p t i o n t h a t r , « i s not equal t o The t r a n s f e r impedance i s Z = ?l components w i t h the r^,. defined as (16) — x a n e t w o r k com- e Now v = i ZT c L c: and from ( 1 0 ) t h e c o l l e c t o r v o l t a g e v c - Z (17) becomes - i «e ( r Kb + rm m) L r b + r + ZT c L (13) 22 Whence -ZT (r + r ) m Z9, = L b ^ r + r + Z b c L (19) The substitution of open circuit parameters directly into (19) gives -7 r Z21 = _2L±Lr 22 + (20) h which i s again in agreement with the p a s s i v e , l i n e a r , bi- lateral case. Since a junction t r a n s i s t o r i s p r i m a r i l y a low i n p u t impedance device i t s s h o r t - c i r c u i t current amplification f a c t o r , «, i s an important index to i t s c h a r a c t e r i s t i c s . o< can be derived in terms of the equivalent t r a n s i s t o r r e s i s t ances in the following manner: I f the c o l l e c t o r i s shorted as i s i n d i c a t e d by the dashed line i n Fig. !+ i t i s seen t h a t - 1 ie v c The e x p r e s s i o n for curriait g a i n with a load i s , from e q u a t i o n (10), A± . r, + r P2 r, + r + ZT b c L (21) 23 = ex = A. b + rm r V° ,= a r, b +r (22 c r, « r b m r « r b c (23 where a is defined a s a -• r m In terms of open-circuit o< = (24 IT c parameters 21 (25) r22 Carrier diffusion in the base w i l l limit the value of c* below unity in a junction t r a n s i s t o r . Amplification i s achieved because the c o l l e c t o r current i s delivered a t a higher impedance l e v e l than the input. Following i s the derivation of the voltage gain of a t r a n s i s t o r . Consider again the configuration i n F i g . 3 with the load Zj i n s e r t e d between the c o l l e c t o r and base t e r m i n a l s . The voltage gain i s then defined by A, The substitution of equations '21 (26) (12) and (19) into (26) gives 24 Av = (r b + -ZL(rb + r m ) r, + r + Z, 5 2 h , r } (r + Z + r (r r e c L> b e - m> r b + r (27) c +Z L -ZT(r. + r ) AV = L m b ( r + r ) (r + Z_ ) + r, (r - r ) b e c L b e m (2S) In terms of open-circuit parameters the voltage gain becomes A v - .- - Z LL r h n T 27\ 1 + (29) M To find the open-circuit voltage gain the limit of (29) is taken as Z^ approaches infinity. AVQC = lim ZL^oorn -r 0 1 AVOC - _ " r 21 - — ^ — (|r|/Z L ) + -r, + r 2 r (30) ^ =_^ r ll b + r » e ox) Grounded emitter.--Figure 5 shows the equivalent circuit for the ^rounded-emitter configuration. Proof of i t s electrical equivalence to Fig. 4 is given in Appendix I . the open-circuit parameters become In this case 25 r 11 = r + r e 12 b e y 21 r 22 r = r + r e c - r m =r e + r ( 1 - a) c The e x p r e s s i o n s f o r i n p u t and t r a n s f e r d e r i v e d by t h e substituticn (20) r e s p e c t i v e l y by i n t e r n a l circuit S, (32) i n t o e q u a t i o n s changes in the e "black ZL + r c [ r e (15) and affected box." + r ) Z + r r + r (r + r b L e c b e c _ r + Hh <r m _, ( r e + r b ) Z. of i m p e d a n c e s can be s i n c e n e i t h e r of t h e l a t t e r i s (r 1 (32) - r e m • rb(l - r ) m (33) a)] = ZL + rc(l z 7 L := 2\ T- The c u r r e n t a m p l i f i c a t i o n c '21 L^rm " r r t + vAl r e> == - i ZT c L -A (34) - a) + Zi can be d e r i v e d from OhmT s l a w v -a) (34) using 26 A/W- ^WVrJI-a) o r t 4 m'b J - FI*, 5 Grounded-emitter equivalent circuit for a transietor. 27 -i Z r n A^_ = _ 2 . = -ii = Z -r iu b The s h o r t - c i r c u i t - r m e r + r - r + Le c ra L L current; a m p l i f i c a t i o n t h e n 35) becomes r - r A = m e A r + r - r isc e c m > (36) A, c n = b .ISC r b == _ c ra « r e m r « ( r - r ) e c m where by definition The v o l t a g e a m p l i f i c a t i o n (33) and m a l-a can be d e r i v e d from (3V equations (34) v c = Z n 21 Z.(r - r ) L rn e Av = ( r + r . )ZT -*- r r + r (r + r e b L e c b e To f i n d t h e o p e n - c i r c u i t approach i n f i n i t y L voc (38) - r ) m v o l t a g e g a i n Z. i s a l l o w e d in equation m > to (3$). e z. m r + r r + r, e b e b (39) 0<r> -co The t r a n s f e r conductance of the grounded-emitter configuration i s defined as 0.r 21 - ^ v A Z l (40) l l r n J 21 (r + r, ) ZT e b L - r m e + r r + r, (r ec b e (41) + r - r ) c m By definition m ,J 21 (42) zL - o Then r - r m e G m r r + r, (r + r - r ) e c b e c m G. m (43) m r r e c + r b (r (44) c r„,) m; r << r e c << r e m r ra r e +r b^- a) r No attempt has been made to derive or even mention a l l various types of parameters or methods that have been proposed for t r a n s i s t o r analysis* The subject of power gain has not been covered because no significant the resulting expressions. insight i s gained from The limited area t h a t has been covered was chosen because i t lays a general base for the following description of the voltage regulator with a minimum of extraneous material. CHAPTER IV DISCUSSION OF THE REGULATED POl/ER SUPPLY The power s u p p l y c o n s i s t s o f a r e c t i f i e r age s t a b i l i z e r . The r e c t i f i e r is a conventional r e c t i f i e r w i t h an R-C f i l t e r . diodes. I t u t i l i z e s a p a i r of 1N93 silicon elements. The c o m p l e t e s c h e m a t i c of t h e Fig. 7 is a simplification s u p p l y i s shown i n F i g . of F i g . 6 i n which a l l e l e m e n t s a r e lumped t o g e t h e r and t h e r e c t i f i e r - f i l t e r r e p r e s e n t e d by a T h e v e n i n g e n e r a t o r , E r a n g e of l o a d v o l t a g e of t h i r t y v o l t s o v e r a zero to f o r t y m i l l i a m p e r e s . can b e a l t e r e d by m e t h o d s t o be shown The v o l t a g e s t a b i l i z e r subdivisions: Error detector.-—The Zener diode, section Any v a r i a t i o n a d-c major amplifier, sectiai c o n s i s t s of a R, , inserted I d e a l l y the a finite reverse i n t h e o u t p u t v o l t a g e must t h e r e f o r e across the r e s i s t o r . current later. D.. , i n s e r i e s w i t h a r e s i s t o r , for fur- a s shown. error-detecting diode i s constant unit specifications i s composed of t h r e e a c r o s s t h e output of t h e s t a b i l i z e r . a c r o s s the These an e r r o r - d e t e c t i n g s e c t i o n , and a v o l t a g e - r e g u l a t i n g parallel and R . The r e g u l a t e d power s u p p l y h a s b e e n d e s i g n e d t o n i s h a nominal volt- full-wave The s t a b i l i z e r u t i l i z e s t r a n s i s t o r s and diodes as i t s non-linear 6. and a potential current. appear S i n c e t h e a v e r a g e v o l t a g e a c r o s s R-^ is 50 / S| 117 v 6 0 cps g A/W -vw • =Fc I -re- TR, C^—0.07 u f d . , 50 v. capacitor R4—250 ohm resistor C 2 , Cz—40ufd., 100 v. e l e c t r o - R^—10,000 ohm resistor l y t i c capacitor ^ a * ^ b * R7a» R7b> ^ c * R7d» R7e» Dl—50 v. Zener s i l i c o n diode Rjf, Rg, RQ—47 ohm r e s i s t o r D2> D*~5 v. Zener s i l i c o n diode S^—S.p.s.t. switch D4—10 v. Zener s i l i c o n diode ?l* T^a, Tz b —G.P.C. 2517 transistor T D^, D5—1N95 diode 2» ? W %h, T4C> T ^ , T ^ , Titf— R^—12 ohm resistor Raytheon CK722 transistor Rg—4^0 ohm resistor TRi—Power transformer, 50-0-50 v. Ri—5»050 ohm resistor at 100 ma. (All resistors are rated at one third watt.) Pig. 6 Schematic of transistorized regulated power supply. Pig. 7 Simplified schematic of voltage stabilizer. \x 32 is about 0.3 volts, a deviation in output voltage of thirty millivolts (a 0.1 per cent change in E~) will result in a ten per cent change in the drop across this resistor. How- ever, due to the finite resistance of diode D^, only about thirty per cent of the total error voltage appears across R . This voltage increment, e f , is the input signal to the d-c amplifier. D-e amplifier.--The d-c amplifier contains three stages in the following configuration: npn grounded-emitter, pnp ^rounded-base, nun grounded-emitter using transistors T^, T , and T respectively. D , D , and D are Zener diodes ~ 3 ' 2 3 4 used to keep the operating points of T 9 and 'I\ relatively constant. If current I -. is zero, T~ will conduct and be limited by the emitter biasing action of resistor R~. In this condition the amplifier produces its maximum output current. An incremental positive increase in the voltage e1 appearing across the input terminals of the direct current amplifier will be amplified by transistor T-, into an increase in I C T . This current flowing through Ro will increase the bias on T_ decreasing its output current. cut-off by D and R T is biased to and will conduct only when driven by current Ic2 A decrease in I c2 0. 0 causes a decrease in current I . Thus the d-c amplifier generates a current increment c3 which is proportional to an input voltage,. This can be expressed mathematically as a transconductance G1 m 33 Gf m « — »» (45) from which if = G» e ' «= (} e n rn (46) m 0 where ef i s the amplifier input voltage increment, i f i s the amplifier output current , eQ i s the output voltage of the s t a b i l i z e r , and, by d e f i n i t i o n G = G' ( e ' / e ) = G' k. rn m o (47) m l This is the expression for the combined trans conductance of the d-c amplifier and the error detector. Regulator.--The regulator section consists of six Raytheon Type CK722 transistors operating in parallel. They are connected directly between the rectifier and the output terminals in a grounded-emitter configuration and are driven at their bases by the output current from the d-c amplifier. An increase in load voltage has been shown to be converted by the detector and amplifier stages into a negative or decreasing increment in the current Ic3» This decrease in the; current supplied to the base of the regulator transistor T, [the group of six being considered as a unit) causes its operating point to shift closer to cut-off with a resultant decrease in collector current. By virtue of Ohmfs law, this reduction in current supplied to the load lowers 34 the load voltage. The magnitude of the reduction in load voltage in the limit will approach the value of the initial positive change in load voltage. Regulator parameters.—It has been shown(6) that the operation of an electronic voltage stabilizer can be defined by a stability factor, S, and an internal resistance R. o (42) (49) ;r R + RL The lower-case characters here represent the partial differentials of the variables denoted by the respective uppercase characters in Fig. £. the rectifier. E is the Thevenin voltage of r The Thevenin resistance, R , of the rectifier is included in the stabilizer circuit. E is a test voltage inserted in series with the load R_• From equations (4$) and (49) and the Ohmfs law equation for the outnut branch. E. I0R E the following expression for the output voltage has been derived in the appendix (50) 55 Fi£. 8 Generalized schematic of a voltage fltabilizer. 36 E + K-, E„ - _ I _ - T „R O (51) 1 + R/RL Circuit a n a l y s i s . - - T h e parameters R and S for t h i s voltage r e g u l a t o r are valid only when a l l the t r a n s i s t o r s in the c i r c u i t are operating in t h e i r l i n e a r region in which case the e n t i r e c i r c u i t is functioning l i n e a r l y . This permits the use of the small-signal techniques discussed in Chapter I I and the use of an equivalent circuit. The r e s i s t a n c e s external to the t r a n s i s t o r s in Fig. 9 are designated by upper-case c h a r a c t e r s . The i n t e r n a l t r a n s i s t o r r e s i s t a n c e s are designated by lower-case chara c t e r s and t h e i r l e t t e r s u b s c r i p t s . Each numerical sub- s c r i n t a s s o c i a t e s t h a t component with the r e s p e c t i v e l y numbered t r a n s i s t o r in Fig. 7. The lower-case e ' s and i ' s represent changes in voltages and c u r r e n t s . The non-time - varying components have been removed by application of the theorem of superposition. In solving for i n t e r n a l resistanc e;, R, the chosen method of attack i s to l e t e equal zero, to c a l c u l a t e the amplification in each stage and thus obtain i 0 in terms of e T , and to eliminate a l l v a r i a b l e s except i and e. The output impedance of each of the f i r s t three stages i s large in comparison with the input impedance of the following stage so that the value of the c o l l e c t o r current is v i r t u a l l y independent of the load impedance ( 7 ) . This permits < HWW-AA/VT! X bl r ,(i-o,) Q-- d r <rb2 2 92 'cl .. R ' r i — ^ A A ^ _ — < *• ^-r r ml'bl 'b3 'C2 VSAr^^- e2 c2 r AAA, r^L* m2'e2 'b3 -AAAr^Qr rc 3, d ' - 0 ,3') t — W V — f r> < m3b3 r '•3 el 'r* 'b4 b4 r ^0'°A) rm4J b4 K . Q • 4 o*S"L rl_. STAGE I .1 STAGE 2 STAGE 3 J. STAGE 4 Pig. 9 Equivalent circuit of regulated voltage supply. ^ 33 the use of s h o r t - c i r c u i t out, put current c a l c u l a t i o n s for these two stages with negligible loss in accuracy. The f i r s t stage, shown in Fig. 10, can now be con- sidered s e p a r a t e l y . By a p p l i c a t i o n of equation transconductance of t h i s (44) the stage i s determined immediately. a. IT (52) T ml e» ~ The second stage, " r el + r blU~alT shown in Fig. 1 1 , may be solved by use of the c u r r e n t - d i v i s i o n rule snd equations (12) and (22). -H^i , 2 cl e2 R 2 + 2 (53) 1(2) 2 2 cl ss «.o< 1 1 c2 ^ e2 K "1(2) *2R2 1 Cr 2 A . 0 - _ -12 1 cl 2 (54) lu 2 + (55) n(2) (r le b2 + r m2 ) R 2 R~(r, +r ,.)+r ^r +r, (r +r - r J b2 c2 ' e2 b2 eo 9 ~ 9 rr.9 ? 1h9 r*9 o 9 c2 r»9 ^9 m2 a A R 2 2 i2 * 7 R + r + -r, 0 ( 1 - a.) 2 e2 b Similarly the current amplification for stage t h r e e r is found bv the a p p l i c a t i o n of equations (33) and (36) to the c i r c u i t shown in Fig. 12# (56) 39 r r ci(,-°|) -AAAr ibi -VsAr 'cl V n O 6' PiK. 10 Equivalent circuit of stage one of voltage regulator, r r '(•2 AA/V -VW'cl •„.: 'e2 ;R2 Z I(2) c2 C2 — m2'»2 o ! r b2 Pin. 11 Equivalent oircuit of stage two of voltage regulator. 40 c2 3 R„ + Z. •3 1(3) e:J (57) c2 i s c 3 3 c3 i s c 3 e3 i3 + 3 c3 -A. R isc3 3 c2 R '13 A R 3 + Z Z (5B) K3) (59) K3) -(rm3 " re3)R3 r r 0 +(R. + r , J ( r _ + r _ - r . ) c3 e3 3 b3 e3 c3 m3 > (60) —a~ R_ i3 The t o t a l r . + (R- + r , J ( l ej 3 b3 t r a n s c o n d u c t a n c e of the now b e e x p r e s s e d - a„) 3 d-c a m p l i f i e r , G1 , can as G* = G -.A, „A.~. ra ml 12 (61) 13 Stage four is analyzed by the simultaneous solution of the three independent equations fo r the input voltage designated as ei in Fig. 13. r 3 For ease of manipulation let = R + r , + r 4 b4 e4 (62) r. = r . (1 - a. ) + R. + R 4 c4 4 L r The voltage equations are 41 r c3 (l-o 3 ) r m3'b3 Fig. 12 Equivalent circuit of stage three of voltage regulator for derivation of R. ir c4 <l-o 4 ) r ro4 , b4 -AAA/ "KD"1" AAAr'C3 r Q e4 'b4 ' V Fig. 15 Equivalent circuit of stage four of voltago regulator for derivation of R. '04 42 \ = "ic3(R4 * V (63) ^4*4 e = ~i R 4 - i ( r + r ) + i ( r + R ) 4 c3 r b4 b4 e4 c4 e4 r (64) e=*i(r + r ) -i (r - R ) -e 4 b4 b4 m4 c4 4 r (65) The solution for i, , from equations (64) and (65) subb4 s t i t u t e d i n t o (63) and ( 6 4 ) , with t h e e l i m i n a t i o n of e 4 y i e l d s the following e x p r e s s i o n i n terms of the v a r i a b l e s i , i , and e: c3 c4 i + fh (r c3 I 4 r m4 hh [r4r3 + r e4 ) - R r r ;3 e4 (R 4 + r b4 (66 + W ] + er 3 ° ° I t is seen from F i ^ s . 3 and 7 r e s p e c t i v e l y t h a t i RT - e o L (67 1 -, c3 = i1 T With the a i d of t h e s e e x p r e s s i o n s and e q u a t i o n (46) t h e s o l u t i o n f o r i -3 becomes c3 i = G ( i R - e) c3 m o L (62 Without l o s s of accuracy the assumption can. be made t h a t x (69) c 4 * ~1o Then eouation (65) can be e x p r e s s e d in t e r m s of i and e o 43 ^ 1GmRL [R4(rm4 " W - [r4r3 + r e4 (R 4 + r b4 " Rrr3] + (70) W ] } + e [~(1 - GmR4 (rm4 - re 4)]J - 0 m [_ + a_)ro J From equation (49) the expression for R is (71) - R, R = i0/e t h e c o m b i n a t i o n of ( 7 0 ) and ( 7 1 ) q;ives R + R W L * ^ (r m4 ~ re4} "Vs 3 + V 3 I1 + W r 3 (72) + r (R + r + r ) e4 4 b4 m4 ~ x R. ( r , - r , ) m4 m4 e4 which r e d u c e s t o T? « [R r + r , ( 1 - a ) J r + r , (R, + r . , + r ) c4 4 ^ 3 e4 4 b4 m4 (73) ( 1 + G R ) r „ -G R, ( r ~ - r , ) m r 3 ' m 4 "ni4 e4 The procedure for calculating the stability factor S is similar to that for R. In this case e is equal to zero and e_ r becomes the indeoendent variable and then all variables are eliminated excent e and e . The evaluation of the first o r two stages i s i d e n t i c a l to t h a t f o r the evaluation of R. The t h i r d sta^e contains the v a r i a b l e e r in i t s collector c i r c u i t . Therefore i t s output current i s a r r c5 (l-o 3 ) m3'b3 AM—^y Fig. 14 Equivalent circuit for stage three of voltage regulator for derivation of S, W'V Fig. 15 Equivalent circuit for stage fcoir of voltage regulator for derivation of S, r,n4 b4 ' 45 function of both i and e . c2 r The method c h o s e n t o solve t h i s network i s t o w r i t e t h r e e i n d e p e r d e n t e q u a t i o n s the voltage e' and t h e n t o e l i m i n a t e i t and iu_ . jj e» = -i 3 e' 3 e? , 3 for D> R - i R c2 3 b3 3 (74) - i,0(r + r ) + i r b3 b3 e3 c3 e3 (7$) :r (76) \, lr o b3 These e a u a t i o n s + bj r .) m3 - i r (1 - a ) + e c3 c3 3 r yield the following solution for ir-i' (77) i - * A' „ e + A i c3 3 r i 3 c2 where A._ is defined bv eouation (60) and i3 R 3 + R A' T, r ,o +• (- v o e3 c3 r c3 I .i e3 + r b3 *re3 -a) r r o + r o^ 1 ~ a ^)1 b3 3 L e3 R 0 + r. . + r .. 3 b3 G3 + v < R + M) 3^ rb3 I1 - c3 3J > (78) a 3 The fourth stage is solved in a similar manner usin^ Fie:. 15 - -i Q (R + R ) - i,.R + i .R + e 4 c3 3 r b4 4 c4 r r (79) , = -i 0 R +i. , (r, . +r )+i , (r +R )+e 4 c3 r b4 b4 e4 C4 04 r r (SO) *.,, [,r, ^, , r ,. . ,. - i . fr . (1 - a. ) + R,(£1) 1 eT 4. , - i, b4 o4 , + m4 c4 [ c4 4 4J These equations will -^iv e the following expression in terms of the three variables i ->, i . , and e : c3 c4 r 46 - r „,.' e4 ~Kr{] "" r 3 r 1 m, c3- [K4 I m4 + . [ rr .,.rr., *„,. c4 [ 4 3 ++ r r (62 . (R. ++r w. r , . + •r x Jj . »,.<*,. mm4 e4 4 b4 + e r r 3 " ° i , i s a ^ a i n a p D r o x i m a t e l v e q u a l t o ~ i from w h i c h c4 ' o c4 " — (63) " "o L Bv the substitution of equation (46) into (76) it is seen that = if c3 = G e + A' e m o 3 r (64 The expression for 3 is finally obtained by the substitution of (?3). and (?4) into (62) 1 0 ra e0/cr + G i'R, ( r . - r . ) - R r.~ [ 4 m4 e4 r 3_ A'3 [R4(rm4 - r e / f ) - L Ir4r3 + r e4 (R 4 + r b4 + (65) R ^ W + r3 S i •C- (R . r .-P. r J + ( l / R T ) (V . ( 1 - a . ) r 0 + r , r L [ c4 4 3 e4 m4 m 4 m4 r 3 A? R r 3 4 m4+r3 Note t h a t 5 i s n o t i n d e p e n d e n t of t h e l o a d 3 becomes i n f i n i t e when t h e o u t p u t t e r m i n a l s a r e resistance. short- c i r c u i t e d and r e d u c e s t o a c o n s t a n t when t h e y a r e o p e n . former i s t h e o r e t i c a l because t h e d-c a m p l i f i e r 66) would The saturate 47 first and the assumed conditions of linearity, upon which these derivations are based, would not exist. Even though S is not independent of the load resistance the expression for E equation R in eauation (51) is(6). In this appears only in the denominator of the first Jb term of the right hand member. S 1 + R/R RLS = S' (37 R + RL Sf can be evaluated if equation (&5) is multiplied by R^ and divided bv eouation (72). The result is 51 - (1 + G R )r, - G R. (r . - r . ) n r 3 m 4 m4 e4 71 - A'TRTr" + A' R (r , ~ r " T 3 r j 3 4 m4 e4 (^ ) which is independent of R-r. The expression for the relation between the output voltage, output current, and the Thevenin rectifier voltage in terras of the circuit components can be obtained by the substitution of equations (73) and {$&) into (51). E ° (E.+KJ rU-A' R )r, + A' R. (r . -r . )" 1 -1 L 3 r 3 3 4 m4 e4 J (1+G R )r_ m r 3 -I *R +r . (1-a. )1 r +r (P. +r, +r . ) o _ r c4 4 J 3 e4 4 b4 m4 -G R. (r -r . m 4 rn4 e4 (39) 1+8 The requirements for EQ to have a minimum of variation are that the coefficients of (E^ + K-^) and I Q , l/ST and R respectively, be as small as possible. This means that a. and G must both be large. 4 m The parameter a. does not appear directly in l / S 1 . A large r . is the major factor in making it small. show a decided increase as a, becomes smaller. 4 R will Therefore r , m4 must approach as close to the value of r , as possible. is decreased by making A' as small as possible. l/S 1 From equa- tion (7$) i t can be seen that this can be best achieved by the use of a transistor in sta^e three which has a large collector resistance. The two grounded-emitter stages in the d-c amplifier are the controlling factors in the value of G . These two m transistors should also have as large current araplificati on factors as possible. The amplification through stage two is less than unity. I t s purpose i s to increase the range of control of stage three by supplying i t with an input current of the correct d-c polarity. If stage three were supplied directly from stage one resistor R^ would have to be connected to the regulated output to provide a d-c return path for the collector current of stage one. I t has been found difficult to drive a transistor to cut-off by this means whereas positive control is achieved by the utilization of the additional stage. R«, R^, and R. each reduces the 2? y 4 gain of its stage and should be as large as practicable. 49 A practical upper limit is placed on the gain of the d-c amplifier by the tendency of the entire loop to oscillate at a frequency near three kilocycles. This tendency is caused by the phase shift in the transistors and is minimized by the insertion of a (3.7 microfarad capacitor C-j connected from the output of stage three to the input, of stage two. The resistor values chosen give the greatest gain through the amplifier and still provide a satisfactory margin of stability against spurious oscillations over the desired forty-milliampere current range. Silicon diodes.---The schematic of the voltage regulator (Fig. 7) shows that the circuit is designed to utilize four diodes exclusive of the rectifier. These are all silicon diodes with prescribed Zener voltages. D-. has already been discussed. The reference diode D« provides a fixed bias for the base of To. D^ and D, together prevent the collector voltage of To from exceeding the maximum allowable limit of thirty volts,, Two diodes were used in series in order to permit the biasing resistor R~ to be connected across an optimum negative bias voltage. Only a few Zener diodes were available for experimentation and their Zener voltages did not all correspond to the circuit requirements. Therefore, after it had been as- certained that the individual stage would function properly, dry cell batteries were substituted for all diodes except D-j_. 50 The current-voltage characteristics of the reference diode are shown in Fig. 16. Fig. 17 shows the Zener region of the diode characteristics on an expanded voltage scale. The loop in this trace is caused by either the change in temperature of the diode during a sweep or the diode capacitance or both. These oscillograms were photographed with a sixt3/-eycle sweep frequency. A few millivolts of noise are evident at the Zener knee. This noise does not affect the normal operation of the detector because the diode current always exceeds three milliarnperes. The Zener vcltage(B) is that voltage required to create an electric field of sufficient intensity through a p-n junction to cause tunneling between the valence and conduction bands of the atomic structure. The factors that affect the Zener voltage are the barrier width and the resistivities of the p- and n-type silicon layers. This field is 2,50,000 volts per centimeter and the resistivity of the silicon varies, being in the order of magnitude less than one ohm-cm. Pearson and Sawyer(9) have shown that the Zener voltage is a linear function of the junction temperature. In the example cited this variation was 0.023 volts per degree centigrade. A drift of about 0.1 volts was observed immediately after the load on the regulator was increased from zero to full. This caused a six-milliampere drop in the current through the reference diode which, if its 10 • • t -2 . > o a ^ o © -M « og -2g -4S« — ! - -6 -10 .50 -20 -10 Volte Fig. 16 Oecillogram of ourrent-voltage characteristics of silicon diode D^. -10 .^O.O -29.5 -29.0 Volts -28.5 Pig. 17 Oscillogram of the Zener region of the currentvoltage characteristics of silicon diode D]_# Accuracy of absolute voltage ie about g0«5 volte vn 52 characteristics are comparable to the example given, reduce the diode dissipation sufficiently to give a 3.5° drop in diode temperature. Altering; the specifications.--The nominal output voltage is established by the Zener voltage of the reference diode, D-^. This voltage can be charged in steps by the use of several diodes or combination of diodes having different Zener voltages. These could be inserted one at a time into the error detector by a wafer switch. Since this would change the biases on the transistors in the d-c amplifier, provision for switching in different biasing resistors and diodes would be necessary. The rectifier voltage would also have to be varied in order to maintain the desired current range without either driving: the regulator transistors to saturation or exceeding their maximum voltage rating. A continuous voltage. variation between these steps can be achieved with a sacrifice in the regulation characteristics by using the modified error detector shown in Fig. 1.3. The factor k-, in equation (47) now becomes a variable dependent on the resistance between points a and b which will vary with the setting of the potentiometer. The maximum output current can be increased by adding additional transistors in parallel with the regulating transistors. The d-c amplifier is considered, adequate to control an eighty-milliampere regulator because none of 55 -»< R lo To transistor 'la T, Fig. 18 Modified error-detector circuit with vernier control for varying the output voltage. 54 the transistors in the d-c amplifier exceed half its maximum collector current rating at forty milliamperes. Results.--The numerical values of 3 and R are given in Table 1. The value of R obtained by measuring the slope of the oscillogram trace in Fig. 19 compares favorably with that obtained directly using a bridge. The oscillogram was made with a sixty-cycle test voltage while the frequency of the a-c source for the bridge measurement was one thousand cycles. This frequency difference is a possible cause for the discrepancy between the two results, The difference between the value of R calculated from the measured transistor parameters and component values and that obtained experimentally is felt to be principally due to the difficulties involved in making accurate measurements of the transistor parameters. Although regarded as constant these parameters vary with temperature, frequency, and operating point. Since none of these can be fixed in a voltage stabilizer it is to be expected that its internal resistance and stability factor should vary. A broad null in the bridge used to determine the stability factor made an accurate determination difficult to obtain. S varied between fourteen and forty-one with the lower values predominating when large resistances were used in the bridge arms. This is equivalent to increasing the rectifier resistance which will, according to equation (£5), reduce the stability factor. The average of the 55 Table 1. Values of Stabilizer Parameters Determined by Various Methods. Parameter Calculated from component values R £.9 S 270 Calculated from static measurements on d-c amplifier 5.0 Determined by bridge measurements 3.65 35 Determined from slope of oscillo/;ram trace 3.5 5<S 40 1 (0 320* o > 10 10 20 Ki H i amperes 50 Pig. 19 Regulation of voltage s t a b i l i z e r . 50.15 50.10 •p iH 50.05 50.00, 20 Mil Hamper ©a Fig. 20 Regulation of stabilizer on expanded voltage scale. Accuracy of absolute voltage is about f0#5 volts. 4C 5? values obtained using low resistance in the bridge arras was chosen as the most representative. The calculated value of stability differs considerably from the measured value. It is considered that the methods used in this calculation should give a result having an accuracy comparable to that obtained for P. The problem of drift of the output voltage was mentioned in the discussion of the silicon diodes. Equipment limitations precluded quantative measurement of the temperature characteristics of the stabilizer. Qualitatively it was noted that a variation of the temperature of the reference diode would change directly the average value of the output voltage with no discernable change in the slope of the regulation curve. TV-is indicates that the effect of temper- ature change on the slope of the current-voltage characteristic of the reference diode operatin : in its Zener region is negligible. Therefore kn in equation (47) is essentially independent of temperature. No significant change in the error-signal voltage results from the diode drift. The drift in the error detector makes a point-by-point measurement of the regulation curve meaningless unless sone provision is made to keep the temperature of the reference diode constant. In order to observe the characteristics of the stabilizer and exclude the variables introduced by the reference diode, the error signal , E f , was measured. This is an 56 i m p o r t a n t parameter because i t s v a r i a t i o n would be i d e n t i c a l t o t h e v a r i a t i o n i n the output v o l t a g e i f t h e reference diode were an i d e a l u n i t t h a t was t e m p e r a t u r e - s t a b l e and had zero r e s i s t a n c e in t h e Zener r e g i o n . No d r i f t was observed in E* a l t h o u g h i t i s f e l t t h a t a small d r i f t i s p o s s i b l e due t o t h e i n h e r e n t t e m p e r a t u r e - s e n s i t i v e n e s s of transistors. T h i s d r i f t would p r o b a b l y not exceed a few h u n d r e d t h s of a volt. The v a r i a t i o n i n E caused t h e r e b y would be l / k n o times as great. - l A drift in E* would ha ve to be caused by a change in the characteristics of T-, because any drift caused by transistor T_ or T_ would be counteracted by T 2 3 •* I b e f o r e i t could reach a s i g n i f i c a n t magnitude. The o p e r a t i n g p o i n t s of the t r a n s i s t o r s i n the d-c a m p l i f i e r have been a d j u s t e d so t h a t T2 and To a r e a p p r o a c h i n g c u t - o f f when the output c u r r e n t i s zero and T^ i s approaching c u t - o f f when the output c u r r e n t is f o r t y m i l l i a r n p e r e s . A change in o p e r a t i n g point caused by t e m p e r a t u r e variations could cause a t r a n s i s t o r to be cut off w i t h i n the r a t e d o u t put c u r r e n t r a n g e , i n which case the v o l t a g e r e g u l a t o r would not f u n c t i o n . A change i n the i n p u t v o l t a g e w i l l l i k e w i s e change the range of r e g u l a t i o n . If t h e input v o l t a g e should i n c r e a s e , the range of r e g u l a t i o n would s t i l l be f o r t y m i l l i a r n p e r e s but would extend between h i g h e r l i m i t s , e. g. l i v e t o f o r t y - f i v e arnperes. or t e n to f i f t y milli- I f the i n p u t v o l t a g e should drop, t h e upper l i m i t of the c u r r e n t r a n g e would be r e d u c e d . A p r o t e c t i v e device 59 employing relays or warning signals or both should be used to prevent overloading and to alert the operator when the limits of regulation have been exceeded,. This has not been done here because it is considered to be a special problem dependent upon the specific application for which the supply is intended. A prime advantage which a transistorized supply enjoys over one employing electron tubes is the absence of the requirement of a warm-up period. The unit vail function the instant the power switch is closed. With an ideal ref- erence diode the output voltage would be drift-free immediate ly. The diode presently used will allow the output voltage to drift a few seconds until its temperature becomes stable. With maximum output current, the ripple on the regulated output voltage is about thirty millivolts peak-topeak. This is a 0.1 per cent ripple. Superimposed on the ripple is a five to ten-millivolt noise which is believed to be caused by the transistors. It was noted earlier that capacitor CN was used to eliminate a three kilocycle oscillation. It accomplished this purpose by reducing the gain through the amplifier at higher frequencies. The regulator therefore is limited in its operation to lower frequencies. This is not considered a handicap because a capacitor can be placed across the output terminals to insure that the supply presents a low output impedance to the load at higher frequencies(1). This capacitor would serve two additional purposes. It would reduce the 60 output noise level to less than one millivolt and it would provide positive stability against oscillation within the stabilizer, C-. would no longer be required. This capacitor was not used because it was felt that it would not be an integral part of an electronic voltage regulator and it was desired to establish a design for a regulator that would be inherently stable. CHAPTER V CONCLUSION'S As lias been the usual case in transistor circuit development work, the stabilizer in a transistorized rower supply uses current rather than voltage variables. This nlaces a severe limitation on the error detecting section in that the error signal, a voltage, is required to be independent of the transistor currents flowing through the detector* Amplification is lost in stages three and four due to the increase in equivalent emitter resistance caused by the insertion of the isolation resistors. The reference diode drift affects the output voltage. Any transistor drift affects only the current range of the stabilizer. Although the internal resistance of this power supply is not as low as that of a good commercial regulated supply of conventional design, it has a high stability factor and its resistance can be decreased by increasing the transconductance of the d-c amplifier. Perhaps the simplest method of improvement would be to select transistors having larger current amplification factors than were available. 62 The purpose of this study, however, was directed toward discovering the methods and principles involved in the transistorizing of a regulated supply rather than merely toward producing a finished model, CHAPTER VI RECOMMENDATIONS A. means of obtaining a continuously variable output voltage from zero to the desired maximum is necessary to increase the versatility of this power supply. A compen- sator to counteract the change in Zener voltage in the reference diode due to temperature changes would eliminate the drift in the output voltage. These are two avenues in v;hich further study could be conducted. A P P E N D I X APPENDIX I DERIVATION 0? GROUNDED-EMITTER TRANSISTOR EQUIVALENT CIRCUIT Given the grounded-base transistor equivalent circuit of T^ig. 21(a) , first consider the circuit rearranged with the emitter grounded as shown in (b). The loop equations for the grounded-base circuit are r , == i ( r , + r ) + i r, 1 e b e c b > (90) v = i (r + r 2 e b m <v These + i (r, + r c b c are valid for both (a) and (b). With the application of Kirchoff's voltage and current laws, (c) is seen to be eauivalent to (b) with the following 1 V1 = -v = V 2 - 2 (i "b If -^ e definitions » -v1 v 1 V 1 - v' 1 - + i ) c i = -(i e + i ) b e (91) is substituted into (90) the r e s u l t -v 1 V - v (ib + ic^b {i b + r e} + i (91) is crb + i ) (r + r ) + i (r + r ) c b m c b e (92) (93 A/Wr AAAr -vy^ c -rm(ib*ic) b 1 < • \ (c) - ^ v. AAA/ f 'WV o r i m't ?.. (b) Fig. 21 Steps in the derivation of the grounded-emitter equivalent circuit* * 67 Rearrangement of (92) w i l l give t h e f i r s t loop e q u a t i o n the g r o u n d e d - e m i t t e r c o n f i g u r a t i o n in ( c ) . for The s u b t r a c t i o n of (92) from (93) and rearrangement w i l l give t h e second. vT V 1 = i ( r b e S = i J r - rm) + r ) + i r b c e I + 1 r e + r c (1 - a (94) APPENDIX II DERIVATION OF EQUATION (51) Given the following equations in which the lower-case characters represent the partial differentials of the variables identified by the upper-case characters in Fig. S o (43) 1 (49) e r R +R L F, . I RT - E O (50) O L It is desired to find an expression for the stabilizer outnut voltage, E Q , in terms of the rectifier Thevenin voltage E r , and the output current, I0(ll). The solution of the differential equation (4$) for Eo is E SG - + F(E) (95) in which F(E) is the oonstant of integration, a function of the voltage E. to E 2;ives Differentiation of (95) and (50) with respect 69 f(E)1 o e (96) S e 1 o _ oR _ j e~~ e~~ L (9? Substitution of (49) into (97) ^ive, o e R ~R (93 R + RL R •»• R , From (96) and (93) (99 f(E) « R + R, and so t h e s o l u t i o n for F(E) is -SRE F(E) - — + KR + RL { 100 Eouation (95) now becomes Eo = Er + K, 1 RE (101 R + RL To eliminate E from (101) equation ($0) is utilized. E + K. r 1 R(I RT - E ) o L o R + RVL (102 70- R E0 (1 E + K, I L R r 1 _ o L S R + R, • ) « R + Ri From which the d e s i r e d e x p r e s s i o n E EQ . _ r is (103) obtained + K, 1 _ 1 + (R/R L ) „ I-R (51) APPENDIX I I I PARAMETER APID COMPONENT VALUES T r a n s i s t o r p a r a m e t e r s . — T h e p a r a m e t e r s of v a r i o u s were measured by following by S h e a ( 5 ) . i n d e t a i l t h e methods described Those t r a n s i s t o r s which a r e c o n n e c t e d t o i n p a r a l l e l w e r e measured, a s a g r o u p w i t h t h e r e s i s t o r s i n c l u d e d i n the measurement. isolating resistors i n the circuit in- analysis. R - , and R, , w e r e d e t e r m i n e d e x p e r i m e n t a l l y i n t h e sistor the n e c e s s i t y for B i a s r e s i s t o r s . — T h e v a l u e s of t h e b i a s r e s i s t o r s , The f i r s t operate isolating This r e d u c e d number of m e a s u r e m e n t s and e l i m i n a t e d t h e c l u d i n g the transistors R-j_, Rp> laboratory. r e q u i r e m e n t f o r t h e s e v a l u e s w a s t h a t each tran- s h o u l d o p e r a t e i n i t s own l i n e a r r e g i o n t h r o u g h o u t e n t i r e forty-mi11iampere current range. t h e s l o p e of the r e g u l a t i o n curve, s h o u l d be a s s m a l l a s The second was t h a t shown i n F i g . 19 a n d 2 0 , possible. Load r e s i s t a n c e . - - 1 0 0 0 ohms was a r b i t r a r i l y r e s i s t a n c e , R^, for the p u r p o s e s of c a l c u l a t i o n . chosen for the The c h o i c e load is immaterial as far as the c a l c u l a t i o n s a r e concerned because d o e s not a p p e a r i n t h e f i n a l r e s u l t . d u r i a g t h e b r i d g e m e a s u r e m e n t s for the T h i s v a l u e was u s e d stability was c h o s e n b e c a u s e i t was f e l t t h a t a p e s s i m i s t i c factor. result It it 72 would be obtained with t h e supply delivering t h i r t y m i l l i amperes to the load without danger of exceeding the maximum current r a t i n g . R e c t i f i e r resistance-—The i n t e r n a l r e s i s t a n c e of the r e c t i f i e r f i l t e r unit was obtained from the mean slope of the r e c t i f i e r regulation curve in the expanded scale in Fig. 23 over the operating range shown. Ratio of output t o e r r o r - s i g n a l v a r i a t i o n . --This r a t i o , k-, , was obtained from the r a t i o of the slope of the e r r o r - s i g n a l c h a r a c t e r i s t i c s (Fig. 25) to the slope of the r e g u l a t i o n curve (Fig. 21). All of the above data i s given in Table 2. Computation s.—The r e s u l t s of computation of the i n t e r n a l r e s i s t a n c e , R, and s t a b i l i t y f a c t o r , 3, and the intermediate constants required for t h e i r computation are l i s t e d in Table 3. The number of the equation used to obtain each r e s u l t i s given. Each use of an approximation i s so designated and i s included in the equations. When a r e s u l t has also been obtained from d i r e c t measurements i t is l i s t e d for comparison. The information in the column headed "Point- by-point measurement" i s based on the data in Table 4. 73 70 60 V 50 40 CQ -P o 50 20 10 20 4C 60 Milliamperes Fig. 22 Regulation of rectifier-filter unit. 80 100 74 Boraal operating ltnH.» -^ -XV \ , %. <> 20 40 60 Milliampere8 80 ?i|5. 25 Rectifier regulation on expanded voltage scale, 100 75 u.^v ^»^—»^__.____ • 0.25 0.20 So.15 > 0.10 0.05 , 10 20 Milliamperes 40 50 Fig. 24 Error-sigial voltage versus output current. 10 20 Milliamperes 50 40 Fig. 25 Error-si^ial voltage versus output current, expanded voltage s c a l e . 76 Table 2. Values of Various P a r a m e t e r s , Components, and Constants. Transistor parameters. Transistor number 1 2 3 4 re (ohms) b ( ohms) c {ohms) m (ohms) 3 92 150 94 62 b2 4.9 4.9 0.42 0.42 1.5 1.5 50,000 50,000 d 6,000 6^,000 23,000 23,000 23,500 23,500 45,000 45,000 64,600 64,600 lg,400 IS,400 21,150 21,150 Comnonent s (ohms) R-p-12 Ri—450 Ro--3050 Rj£—.230 Constants. P.I--1000 ohms R P _ _ 3 5 0 ohms kx—0.256 r 0,9 0.95 0.S 0.9 77 Table 3. Results of Numerical Computations Compared with Corresponding Experimental Data. Item 1 Parameter or constant °ml Equa- Computed tion value number Pointby-point measureraent (52)* 0.093 0.075 2 A i2 (56)# 0.79 0.90 3 A,13 (60)*- -3.21 -3.04 t n (61) -210 -395 5 Gm (47) -67.5 -113 6 A' f 7^ U 7 R (73) (73) $.9 tf.9 (d5) 270 S* t m \ • 1 -•• Bridge From oscmeasure- illographic ment data 0.0001£3 5.0 5.0 3.65 3.5 35 * Equation -riving an approximate s o l u t i o n was u s e d . 78 Table 4. Point-by-Point Measurements of Stabilizer Currents and Error-Signal Voltage. Item 1 2 3 4 5 6 7 g 9 E T (v.) I ,(na.) cl 0.2rJ 0.28 0.27 0.27 0.26 0.26 0.25 0.2S 0.24 5.0 4.4 4.1 3.? 3.4 3.1 2.7 2.3 2.0 -I 0(raa.) c2 I -(ma.) c3 0.5 0.9 1.3 1.5 1.3 2.1 2.5 2.5 3.2 0.9 1.7 2.6 3.7 4.7 5.7 6.8 8.0 9.1 -I .(ma.) I (ma.) c4 o 25 30 35 41 46 51 56 61 66 0 5 10 15 20 25 30 35 40 APPENDIX IV BRIDGE CIRCUITS The b r i d g e c i r c u i t s ( 1 2 ) used f o r t h e d i r e c t ment of R and 3 a r e shovgn i n F i g s . former i n a balanced measure 26 a n d 2 7 . With t h e condition R,R T R = L L (104 R2 With the l a t t e r in a balanced condition v3 t = _i R 2 (105 80 OSCILLATOR I o yujL> 1 stfpF^. Afsfa m tt ^^^ DETECTOR Pig. 26 Bridge c i r c u i t for measuring R. -^RRr^ r• o OSCILLATOR Pig. 27 Bridge olroult for measuring S. * APPENDIX V OSCILLOGRAPH CIRCUITS CATHODE RAY OSCILLOSCOPE OSCILLATOR Pig. 28 circuit for obtaining current-Voltage characteristics of silicon diode. CATHODE RAY OSCILLOSCOPE OSCILLATOR Pig. 29 Olrouit for obtaining regulation curves. Switch S^ is with S2 open, to obtain the rectifier regulation (Pig. b. with S2 closed, to obtain the stabilizer regulation in position o to obtain the error-signal voltage ourve in position a, 25) j in position (Pig. 20)j and (Pig. 2^)« t3 I B L I 0 G R A P H Y Literature Cited 1. Van Name, F. W. , Jr., Modern Physic: s, New York: Prentice-Hall, Inc., 1952, P. 9:<?-l3CT. 2. Hausmann, Erich and Edgar P. Slack, Physics, 3rd ed. . New York: D. Van Nostrand Company, Inc., 194?, PP. 759-761. 3. Coblenz, Abraham and Harry L. Owens, "Transistor Action in Germanium and Silicon," Electronics, 26 (June, 1953), 166-171. 4. Coblenz, Abraham and Harry L. Owens, "Point-Contact Transistor Operation," Electronics, 26 (July, 1953), 15S-160. 5. Shea, Richard F., editor, Principles of Transistor Circuits, Hew York: John Wiley and Sons, Inc. , 1953, 'PP. 4?5-495. 6. Hunt, F„ V. and R. 17. Hickman, "On Electronic Voltage Stabilizers," The Review of Scientific Instruments, 10 (1939), 6-9. " 7. Shea, Richard F., editor, Principles of Transistor Circuits, New York: John V/ilev and Sons, Inc., 1953, pp. 65, 66. £. Pearson, Gerald L. and Baldwin Sawyer, "Silicon P-N Junction Alloy Diodes," Proceedings of the I. R. E., 40 (1952), 1349. 9. Pearson, Gerald L. and Baldwin Sawyer, "Silicon P-N Junction Allov Diodes," Proceedings of the I. R. E., 40 (1952) 1350. 10. Terman, Fredrick Errnions, Radio Engineers1 Handbook, 1st ed., New York: McGraw-Hill Book Company, Inc. , 1943, r). 615. 11. Hunt, F. V. and R. W. Hickman, "On Electronic Voltage Stabilizers," The Review of Scientific Instruments, 10 (1939), 7. " — 12. Hunt, F. V. and R. W. Hickman, "On Electronic Voltage Stabilizers," The Review of Scientific Instruments, io (1939), 20, ~~?r. 34 Other References Bardeen, John .and Waiter H. Brattain, "Principles Involved in Transistor Action," Physical Review, 7$ (1949), 1203-1225. Conwell, Esther LI. , "Properties of Silicon and Germanium," Proceedings of the I. R.'E., 40 (1952), 1327-1337. Keonjian, Edward, "Temperature-Compensated DC Transistor Amplifier," Proceedings of the I. R. E. , 42 (1954), 661-671. Rvder, Robert M. and R. J. Kirch er, "Some Circuit Aspects of the Transistor," Bell System Technical Journal, 28 (1949), — 367-400. " —~ Schockley, William, "The Theory of p-n Junctions in Semiconductors and p-n Junction Transistors," Bell System Technical Journal, 2S (1949), 435-4^9. Shockley, William, "Transistor Electronics: Imperfections, Unipolar and Analog Transistors," Proceedings of the I. R» £., 40 (1952), 12.^9-1313. Shocklev. William, "Transistor Physics," American Scientist, 42 (1954) 41-72. Shockley, William, M. Sparks, and G. K. Teal, "p-n Junction Transistors," Physical Review, S3 (1951), 15l-lo2. Stuetzer, Otmar MI., "Transistors in Airborne Eauipnent," Proceedings of the I. R. E., 40 (1952), 1529-1530. Wallace, Robert Lee and William J. Pietenpol, "Some Circuit Properties and Applications of n-p-n Transistors," Bell System Technical^Journal, 30 (1951), 530-563.