Reference / Paper
Electronic Counting Circuits
- electronic counting
- dekatron
- cold cathode
- counting circuits
- valves
Reference / Paper
ELECTRONIC COUNTING CIRCUITS J.B. DANCE, M.Sc., B.Sc. LONDON ILIFFE BOOKS LTD NEW YORK AMERICAN ELSEVIER PUBLISHING COMPANY INC. © J. B. Dance, 1967 First published in 1967 by lliffe Books Ltd., Dorset House Stamford Street, London S.E.1 Published in the U.S.A. by American Elsevier Publishing Company Inc., 52 Vanderbilt Avenue, New York, N.Y. 10017 Library of Congress Catalog Card Number 67-13048 Franklin Press, Budapest Chapter pened Appendix CONTENTS Preface Acknowledgements Introduction Electro-magnetic counters Single cathode gas filled counting tubes and their circuits Multi-electrode gas filled counting tubes and their circuits EIT decade counting circuits Beam switching tubes Valve scaling circuits Solid state scaling circuits Ratemeter circuits Readout Nuclear-counting and instrumentation Further applications of counting circuits Valve equivalents and near equivalents Index 7 9 11 32 40 67 154 181 216 232 276 295 310 341 375, 379 PREFACE In spite of the importance of counting circuitry in modern electronic equipment, it is understood that no book has appeared in the English language specifically on this subject since W. B. Lewis’s ‘Electrical Counting’ was published by Cambridge Univer- sity Press in 1942, At that time very few counting techniques were known. A paper- backed book entitled ‘Elektronische Zahlschaltungen’ by K. Apel was published in German by Franckh’sche Verlagshandlung, Stuttgart, in 1961. Although numerous papers have been published on counting circuitry, a search of the literature consumes a great deal of time even if the required publications do happen to be available when they are needed. In addition, some papers are not easily read by those who do not already have a reasonable knowledge of the subject. This book has been written to meet the needs of students, designers, servicemen and users of electronic counting equipment who require the theory of operation and practical information on all of the normal types of counting circuit in one volume. It is assumed that readers have a reasonable knowledge of basic physics and of the operating principles of thermionic valves and transistors. Where other devices (such as trigger tubes and tunnel diodes) are employed in counting circuits, the basic prin- ciples of operation of the devices are discussed. Many of the circuits reproduced in this book are those recommended by the manu- facturers of the tubes or semiconductors employed. This should ensure that they are some of the best and most reliable circuits available, since the component manufacturers normally know far more of the advantages and limitations of their own products than anyone else and can make due allowance for these limitations in the circuits they design. A practical approach has been adopted throughout the book and component values are given in most circuits. A fairly large number of references have been included to assist those requiring further information on any particular topic. The circuits have been classified according to the type of component employed for the counting operation rather than the particular type of circuit (ring, binary, binary coded decade, etc.) used, since it is felt that this approach is a more practical one. Each chapter has been written so that it is essentially complete in itself and may be understood by anyone who is reasonably familiar with the material of the first chapter; this has neces- sitated a small amount of repetition, but should assist readers who require information on one specific type of circuit. Some of the older types of circuit which are now seldom used have been included to make the book as comprehensive as possible. As in most other fields of electronics, there is a general trend for solid state devices to replace the larger circuits employing vacuum or gas filled tubes and this has inevitably resulted in some types of decade tube becoming obsolete. The basic principles of counting are discussed in Chapter 1. The various types of counting circuit are described in detail in Chapters 2 to 9 inclusive. Readout devices not covered in the earlier chapters are discussed in Chapter 10. A short survey of nuclear radiation detectors (often referred to as ‘counters’) is given in Chapter 11 together with some details of the circuits with which they are normally used. An attempt has been made in Chapter 12 to outline some of the more important uses of counting circuits in industry and in instrumentation (other than in computers) and to provide general information on some particular types of application. Alcester, 1967 J.B.D. ACKNOWLEDGEMENTS The author wishes to acknowledge the assistance given to him by the following companies and persons who have provided information or photographs and have permitted the reproduction of their circuits in this book. Beckman Instruments Ltd. Bell Telephone Laboratories, U.S.A. Bendix Electronics Ltd. Britec Ltd. Brush Clevite Co. Ltd. Burndept Electronics Ltd. Burroughs Corporation, U.S.A. B. & F. Carter & Co. Ltd., Centrex Publishing Co., Holland. Cerberus AG, Switzerland. Dr. G. B. B. Chaplin (Plessey Ltd.) Compagnie Général De Télégraphie Sans Fil (C.S.F.), France. Coulter Electronics Ltd. Counting Instruments Ltd. Digital Measurements Ltd. Ecko Electronics Ltd. Electronic Associates Ltd. The Editor, Electronic Engineering. The Editor, Electronics (U.S.A.). Elesta AG, Switzerland. Elliott Brothers Ltd. Ericsson ‘Telephones Ltd. Evans Electroselenium Ltd. §.G.S. Fairchild Ltd. Ferranti Ltd. Dr. E. Franklin (A.E.R.E., Harwell). General Electric Co., U.S.A. Gloster Equipment Ltd. The Editor, Helvetica Physika Acta, Switzerland. Hewlett-Packard Ltd. Hivac Ltd. The Institute of Electrical and Electronic Engineers, U\S.A. The Institution of Electrical Engineers. I.B.M. United Kingdom Ltd. K.G.M. Electronics Ltd. Labgear Ltd. Marconi Instruments Ltd. Motorola Semiconductor Products Inc., U.S.A. Mullard Ltd. Mullard Equipment Ltd. Pacific Semiconductors Inc., U.S.A. Philco International Ltd. Philips Gloeilampenfabrieken, Holland. Racal Instruments Ltd. The Editor, The Radio and Electronic Engineer. Raytheon Co., U.S.A. Semiconductors Ltd. Société des Compteurs de Genéve (Sodeco), Switzer- land. The Solartron Electronic Group. Solid State Products Inc., U.S.A. Sprague Electric Co., U.S.A. Standard Telephones & Cables Ltd. Stonebridge Electrical Co. Ltd. Sylvania Electric Products Inc., U.S.A. Telefunken G.m.b.H., Germany. Texas Instruments Ltd. Mr. T. D. Towers (Newmarket Transistors Ltd.) Transistron Electronic Ltd. Tung-Sol Inc., U.S.A. Twentieth Century Electronics Ltd. The United Kingdom Atomic Energy Authority, Harwell. Veeder-Root Ltd. Walmore Electronics Ltd. Introduction Enormous advances have been made in all types of electronic instrumentation during the last twenty years, but this progress is most apparent in the design of modern electronic counting equipment. Much of the earlier work on counting circuitry was stimulated by the very great post war develop- ments in nuclear physics and in the applications of radio-isotopes in research, industry and medi- cine. For these purposes high speed counting equipment is essential. Counting equipment is, however, very useful for many purposes other than that of counting nuclear particles. It is an essential part of most automation processes in modern factories, enables high speed computers to be constructed and when used in laboratory equip- ment allows many kinds of measurements to be made quickly. The answer is often presented in the form of actual digits to many significant figures. Electronic methods of counting are gradually replacing many of the mechanical systems used in industry, since they are very much faster, more versatile and generally more reliable. 1.1 BASIC COUNTING METHODS . There are two basic types of measurable quantity. The first type consists of a whole number of discrete individual events, for example the number of articles coming off a production line. If each event is converted into an electrical impulse (e.g. by means of a photocell), the number of pulses and hence the exact number of articles can be counted electronically. If the equipment is working correctly, there should be no error whatsoever. The second type of measurable quantity may vary continuously and need not have an integral value; examples of such quantities are time, the rate of flow ofa liquid through a pipe and the electrical potential between two points. Such a quantity can normally be con- verted into electrical impulses, the number of im- pulses or the frequency of the impulses being a measure of the quantity concerned. The impulses can be counted electronically, but the accuracy of the overall measurement is obviously limited by the fact that a fraction of a pulse cannot be gener- ated. Thus counting equipment can, in principle, be used to make almost any kind of measurement and may be designed to provide outputs which can be used to control even the most complicated machinery. One of the first methods by which electrical pulses were counted involved the use of an electro- magnetic register. This type of register consists of a relay mechanism and a drum on which the digits 0 to 9 are painted. Only one of these digits is visible through the viewing aperature at any time. When a suitable pulse of current is passed through the magnetising coil, an armature is attracted and the drum is moved so that the succeeding digit is indicated. When the drum returns from 9 to 0 at the tenth pulse, a mechanical linkage may be used to cause a second similar drum to move so that the latter indicates the digit 1. The two drums together indicate the number 10. This arrangement may be used to count up to 99 pulses, but more drums may be used if necessary so that larger numbers may be indicated. The type of display from an electro- magnetic register is similar to that from the mileage indicator of a car. The registers are described in detail in Chapter 2. 11 ELECTRONIC COUNTING CIRCUITS The maximum speed at which an ordinary electro- magnetic register can operate is about 10 to 25 pulses per second. This is much too slow for many applications. Valve counting circuits were therefore designed which would divide or scale down the number of incoming pulses by a suitable factor. The output pulse frequency from the valve circuit could be counted by an electro-magnetic register. If the scaling factor is ten, the valve circuit provides one output pulse for each ten input pulses applied to it. Such valve circuits became known as scalers because they scale down the input pulse rate. The valve scaling circuit and the succeeding electro- magnetic register were often placed in the same unit, the whole of which became known as a scaler. Nowadays any piece of counting equipment which counts each individual pulse is known as a scaler. A circuit which provides one output pulse for each ten input pulses applied to it is known as a decade counting circuit, or merely as a decade. Valve decades were the first type to be designed, but are relatively large and require a considerable amount of power. Various special tubes with many electrodes have been designed which enable count- ing circuits to be constructed in a much smaller volume, only one of these special tubes being required in each decade circuit; such tubes are known as decade counting tubes or decade tubes. The three main types of decade tube are the gas filled cold cathode tubes (Chapter 4), the E1T cathode ray tube (Chapter 5) and beam switching tubes (Chapter 6). Most types of decade tube first came into production about 1950. Modern scalers for very high speed operation often employ semi- conductor counting circuits. 1.1.1 Ratemeters Scalers count each individual pulse separately. Another type of circuit amplifies, shapes and smooths out the incoming pulses and uses the resulting current to deflect a meter. The meter indicates the rate of arrival of the input pulses with a reasonable degree of accuracy. Instru- ments using this principle are known as rate- meters. They have the advantage that they are 12 rather simpler to use than scalers, since they give direct readings and no time measurements need be made. 4.1.2 Pulses The units which are counted by electronic circuits are electrical pulses. An electrical pulse consists of a transient change in the potential difference be- tween two points in a circuit ora transient change in the current flowing at a certain point in a circuit. The duration of the pulse may vary from a very small fraction of a microsecond to many seconds, after which the voltage or current returns to its former quiescent value. If the potential at a point in a circuit becomes more positive for the duration of the pulse, the latter is said to be a positive going pulse at the point concerned. At another point in the circuit, the pulse caused by the same initial event may be negative going. An ordinary valve amplifier in a common cathode circuit or a tran- sistor amplifier in a common emitter circuit will in- vert a pulse; that is, a negative going pulse applied to the input of the amplifier will be converted into a positive going pulse at the output and, of course, vice-versa. The simplest type of pulse is formed when the voltage (or current) at a certain point in the circuit is switched from its quiescent value to another value and remains constant at this new value until the end of the pulse, when it is switched back to its quiescent value. If the switching process could be carried out instantaneously, the pulse would be a theoretically ‘ideal’ pulse in which the graph of the voltage (or current) during the pulse plotted against time would be rectangular in form. Such pulses are known as rectangular or square pulses. The difference between the two voltages is the amplitude of the pulse; the only other variable in the case of a rectangular pulse is the duration. Any actual pulse can only approximate to a rectangular pulse, since the electrical potential or the current flowing at any point takes time to rise or fall to a new value owing to the presence of stray capacitance and inductance in the circuit. The time taken for the voltage to reach its maximum value (or, in the case of a negative going pulse, the time taken for the voltage to reach its minimum value) is known as the rise time of the pulse or as the duration of its leading edge. The fall time is the duration of the trailing edge. The slope of the leading or trailing edge is often important and may be expressed in volts per microsecond or some similar units. The slope of a pulse edge multiplied by the rise or fall time is equal to the pulse ampli- tude if the edge is linear. Some pulses are more or less triangular in shape and remain at their peak value for only a very short time; in this case the sum of the rise and fall times is equal to the total duration of the pulse. Other pulses may have curved leading or trailing edges and may have a flat or un- dulating top. Pulse shapes may be determined by means of an oscilloscope which has an adequate frequency response. An electronic circuit will not count every type of pulse. A pulse with a duration of a microsecond would be too short for the direct operation of an electro-magnetic register or some types of decade tube. On the other hand if a counting rate above 1 Mc/s is to be attained, the input pulses must have a duration of less than a microsecond or neigh- bouring pulses will partly coincide. Normally a minimum input pulse amplitude and a minimum duration for which this voltage change should be present are specified as the input requirements for any counting circuit. If the amplitude or the dura- tion of the input pulses are too small, the circuit may not count every pulse. Counting circuits may also become unreliable if the input pulses are many times too large, but the amplitude of large pulses is normally adjusted by the input stages of the equipment before the pulses reach the actual count- ing circuits themselves. In addition there may be upper and/or lower limits on the slope of one or both of the pulse edges. Circuits are available which will alter the ampli- tude and the duration of pulses to a value which is suitable for the operation of a given counting circuit; some of these pulse shaping circuits are discussed later in this chapter. In fact the shape of a pulse is altered somewhat by any amplifier, but this alteration can be kept fairly small by choosing an amplifier which gives constant amplification over a suitably wide range of frequencies. INTRODUCTION 1.1.3 Resolving Time If two pulses which are closely spaced together in time are fed into a scaler, only one count will be recorded. If the time interval between the pulses is gradually increased, a point will be reached at which the two pulses will just be counted sepa- rately. This time is known as the resolving time or the resolution time of the scaler. An instrument with a small resolving time can count at high speeds. If a counting circuit has a resolving time of, say, 100 wsec, it can count at frequencies up to 10 kc/s without any counts being missed provided that the incoming pulses are evenly spaced in time. The pulses will be evenly spaced if they are derived from such things as an electrical oscillator or from 4 rotating shaft by means of a suitable pick-up device. In some cases, however, the incoming pulses have a random distribution in time. For example, the particles from radio-active materials are emitted at random times. If two particles which are spaced very closely together in time enter a Geiger tube, only one output pulse will be obtained from the tube. Thus a Geiger tube has its own resolving time (which is normally of the order of 100 psec). There is always a certain probability that two particles will enter a Geiger tube within the resolv- ing time of the equipment and the number of nuclear particles counted in a given time will, there- fore, always tend to be slightly less than the number which would have been counted if the apparatus had had an infinitesimal resolving time. The per- centage of particles not counted (because they enter the Geiger tube at a time which is too close to the time of entry of another particle for each to be resolved individually) will increase as the counting rate increases. The percentage error also increases as the resolving time of the equipment as a whole increases. The resolving time of a Geiger tube is not nor- mally known accurately, since it varies from tube to tube, with the age of the tube and with the applied voltage. It is normal practice to intro- duce a resolving time into the counting apparatus which is somewhat longer than the resolving time of the Geiger tube itself, but which is accurately known. The resolving time of the whole apparatus 13 ELECTRONIC COUNTING CIRCUITS then becomes equal to this resolving time. Al- though a larger error is thus introduced, it is pos- sible to correct for this error in the case of random pulses by the method discussed below, since the resolving time is now known. 1.1.4 Correction for Losses due to Finite Resolving Time Let n = the number of counts recorded per second t = the resolving time of the apparatus in seconds The counting equipment is effectively inoperative for a time of ¢ seconds following each count which is recorded. Therefore, the total inoperative time per second will be n¢ seconds and the time during which the apparatus is sensitive is (1—at) seconds for each second of the counting time. The count rate per second, N, which would have been obtained if the apparatus had had an infinitesimal resolving time is therefore: n N= 1 1—nt () This equation is strictly correct only if the parti- cles which enter the Geiger tube during the inopera- tive periods do not extend the dead time or if the dead time is determined entirely by the resolving time of the preamplifier probe unit or the scaler. Each particle which enters a Geiger tube during the dead time renders the tube inoperative for a further period equal to the tube dead time. In such a case the corrected counting rate, N, may be obtained from the expression: n = NeXt (2) where ¢ is the resolving time of the Geiger tube and e is the base of natural logarithms. This equation should only be used where the dead time is deter- mined entirely by the dead time of the Geiger tube. In any case, equation (1) which. is much simpler than equation (2) is accurate enough for most pur- poses unless the counting rate becomes greater than about 1/10¢. If equation (2) is expanded, it can be shown to be equivalent to equation (1) if Nt is small compared with unity. As the actual number of particles entering a Gei- ger tube per second increases, it can be shown 14 from equation (2) that the count rate will reach a maximum and then decline. A Geiger counter placed in a field of intense radiation can, therefore, indicate a small count rate, since the particles are entering the tube so quickly after one another that the tube is inoperative for a large part of the counting time. The percentage error introduced at various count- ing rates for various resolving times is shown in Table 1.1. Table 1.1 Counts / . Resolving | Percentage sec Counts|min time error 104 6 x 105 1 usec 1 10 600 1 msec 1 100 6,000 1 msec 10 1 60 100 msec 10 Whilst it is possible to state the approximate maximum rate at which a certain scaling unit will count pulses which are evenly distributed in time, it is obvious from the table that it is not possible to quote a maximum counting rate when the incom- ing pulses are randomly distributed in time. One can only state the maximum counting rate which will ensure that the percentage of missed counts 1s kept below a certain value. Any value quoted for the maximum operating frequency of a counting circuit, therefore, refers to the case when the input pulses are evenly distributed in time and when they satisfy the input requirements of the circuit. Tf an electro-magnetic register of long resolving time is preceeded by a very fast scaling unit which provides one output pulse for each ten input pulses, it might be thought that the maximum operating speed would be ten times that of the electro-mag- netic counter alone. This is, in fact, true for pulses which are evenly distributed in time, but in the case of randomly distributed pulses, the maximum count- ing speed is increased by a factor of more than ten for the same percentage of missed counts. This is because the randomness of the distribution of the pulses in time is reduced by the first fast scaling unit. The percentage of lost counts for such systems has been computed, The resolving time of a counting circuit can be determined experimentally by feeding pulses of known frequency into the circuit from a pulse gener- ator, but care should be taken to ensure that the pulses conform to the specifications for the input to the counting circuit and that the correct power supply voltages are applied to the circuit. Methods are available for the measurement of the resolving time of Geiger counting equipment by means of radioactive sources), 1.1.5 The Statistics of Counting Random Pulses If a source of randomly spaced pulses is counted for a number of equal intervals of time, the results obtained will not be exactly the same in each case, but will fluctuate around a mean value in a statis- tically predictable manner which is determined by the Poisson distribution. If the time for which each set of counts is taken is increased, the actual differ- ences between the results will tend to increase, but the percentage differences will decrease. In radio- isotope measurements it is normally desired to find the mean count rate which would be obtained if the counting were carried out over a long time. It is not, however, always convenient to continue the counting for a long time and in any case this would not give the desired result in the case of a short lived isotope. Statistical methods can be used to deter- mine the number of counts which must be obtained to ensure that the probability of a statistical error being greater than a certain percentage of the count is small enough for the result to be acceptable. A quantity known as the standard deviation is normally used as a measure of the statistical error likely to be present in any particular case. This is the square root of the average value of the square of the individual deviations from the mean. Al- though the mean count is not known in practice, the square root of the actual number of counts can normally be taken as being equal to the standard deviation without an appreciable error being intro- duced provided that the number of counts is not very small. It can be shown that (in the case of random pulses) there is a 31.7% chance that any actual count will differ from the mean count by more than the INTRODUCTION standard deviation. If 100 counts are taken, there is, therefore, a 68.3% chance that the statistical error in this one measurement will be less than 10 counts (that is, V 100). Thus the standard deviation is 10% of the count. In order to reduce the standard deviation to 1% of the count, it would be necessary to take 10,000 counts and there would still be a 31.7% chance (about 1 in three) that the error would exceed 1% of the total number of counts ta- ken. The time necessary to take the requisite number of counts does not enter directly into the statistics. Although the standard deviation is the most com- mon unit in which statistical deviations from the mean value are expressed, there are two other units which are sometimes used. The probable error is that which has a 50% chance of being exceeded. It is equal to 0.6745 times the standard deviation. The reliable error has a 90% chance of not being exceed- ed and equals 1.64 times the standard deviation. Itis also useful to note that there is a 95.5% prob- ability that the statistical error does not exceed twice the standard deviation and a 99.7% proba- bility that it does not exceed three times the stan- dard deviation. The quantities discussed above are useful for checking that the pulses which are being counted are, in fact, randomly distributed in time and that the counting apparatus is not affecting this random distribution. For example, if one finds that a count differs from the mean by more than about 2.5 times the standard deviation, it is almost certain that the equipment is not functioning correctly. The H.T. supply may, for example, be drifting and causing a non-random variation in the counting rate. Simi- larly a long paralysis time will result in closely spaced pulses being counted as one pulse and the deviations of the results from the mean value will then be less than those which would be expected from statistical considerations. When a background count is taken and is deduct- ed from the number of counts obtained with a radio-active sample in position, the standard devia- tion of the resulting net count is equal to the square root of the sum of the squares of the standard de- viations of the counts made on the background alone and on the sample plus background. The accuracy with which it is necessary to determine the 15 ELECTRONIC COUNTING CIRCUITS background count rate depends on the ratio of the counting rate plus background to that of the back- ground alone. If the sample plus background count rate is little different from that of the background alone, approximately the same length of time should be spent on the determination of the background count rate as is spent on the determination of the background plus sample rate. If, however, the sample plus background rate is about one hundred times that of the background alone, the time spent on the determination of the background rate can be about one tenth of that Spent on counting the sample plus background. This results in minimum standard deviation of the net count rate for a given total counting time. 1.1.6. Principles of Counting The operation of any type of counting circuit other than a ratemeter depends basically on some form of Switching from one stable state corresponding to a certain number of counts to another stable state which corresponds to one count more than the previous state. The Switching is triggered by the arrival of the input pulses, Our normal counting system is based on a scale of ten because people first learned to count on their fingers (which are sometimes called ‘digits’), When we refer to the number 2,350 we are really using an abbreviated form for the expression: (2 x 103)+ (3 x 10°) +(5 x 104) +(0 X 10°). This system is known as decade counting, or decimal counting, ten differ- ent digits being required. Electronic circuits which count in this Manner must have ten stable states in each decade, Each input pulse causes the units decade to advance one Position until the tenth pulse returns this decade to the zero state and an output pulse is provided for triggering. the second decade which indicates the number of tens. Similarly, the hundredth pulse causes the first two decades to be returned to zero and the third decade to be switched to indicate the digit one. Although decade tube and various other types of circuit have been designed to count in scales of ten, it is not easy to design a simple valve or transistor circuit which has ten stable states, A scale of counting in which fewer digits are employed 16 is more convenient when valve or transistor cir- cuits are to perform the counting operation. The simplest counting system of all is the binary scale or scale of two. On the scale of two the num- ber quoted previously (2,350) would be represented as 100100101110 which is really an abbreviated form for the expression: (1 X2™)+(0 219) 4 (02%) + (128) 4 (0X2?) + (0x28) 4 (1 x25) + (0x 24)-+-(1 x23)+1 x2)-+(1 x 2')-+(0 x 29), The only digits which appear in any binary num- ber are 0 and 1, because the next number, two, would be represented as a ‘1’ in the next column, that is as 10. In decade counting there is no Single digit to represent any number above nine and similarly in the binary scale there is no single digit to repre- Sent any number above one, When the binary System is used the simplicity in the number of differ- ent digits employed must be paid for in the actual number of digits which are required to represent a given number. The decade method of writing the number 2,350 requires only four digits, but the binary system requires no less than twelve digits. Scales other than the binary and decade systems are sometimes used in electronic counting. The scale of twelve is useful for converting pence to shillings and, in combination with a scale of five, for con- verting seconds into minutes or minutes to hours. A scale of three (ternary) has also been used. 1.1.7 Basic Binary Circuits Hard valves and transistors are normally used in groups of two in counting circuits, each pair form- ing a bistable binary counting circuit. At any one time only one of the two valves (or transistors) is conducting, the other being cut off. Normally, cir- cuit diagrams are drawn so that the binaries are in the zero state when the right-hand valve or transis- tor is conducting. The first input pulse will switch the circuit so that the left-hand valve or transistor conducts and the right-hand one is cut off; this state of the circuit is interpreted as a count of one. A second input pulse will switch the circuit back to its Zero state. A single binary circuit can count only up to one, but larger numbers may be counted if the first binary provides one output pulse (each time it is og INTRODUCTION 4th 3rd and ist. . BINARY BINARY BINARY BINARY oes COUNTER COUNTER COUNTER COUNTER \ ! 4 H ! ! H ! Y ¥ READINGS ¥ Y TOTAL COUNT 4th 3rd 2nd ist AS A BINARY | AS A NORMAL COUNTER COUNTER COUNTER COUNTER NUMBER NUMBER 0 0 0 0 0 0 0 0 0 0 0 0 1 000-1 1 0 0 i 0 0010 2 0 0 I \ oot 3 0 i 0 0 01 0 0 4 0 | 0 1 otot 5 0 \ 1 0 otto 6 0 I i o1itt 7 i 0 0 0 10 00 8 i 0 0 \ 1 oot 9 { 0 } 0 1 01 0 10 0 { 1 Lott il { i 0 0 i 10 0 12 | 1 0 1 104 13 { \ i 0 1 1 40 14 \ I i 1 ttt 15 0 0 0 0 0 0 0 Of oa (oR 16) Fig. 1.1. Four cascaded binary counters forming a scale of 16 reset to zero) for each two input pulses which are fed into it. The output pulses may be fed into a second binary stage which will provide one output pulse for each four pulses fed into the first binary circuit. Such a circuit employing two successive bi- nary stages can count up to three. The four cascaded binary counting circuits shown in Fig. 1.1 can count up to fifteen. If all of the bi- naries are initially set to zero, the first input pulse fed to the system will cause the first binary stage to register a count, but the other three stages will re- main in the zero state. A second pulse applied at the input will reset the first stage to zero and a pulse will be fed from the first to the second binary; the latter, therefore, indicates a count. As this indica- tion is being given by the second binary, it is inter- preted as the binary number 10, that is two. A third input pulse causes the first binary stage to indicate a count and leaves the second stage also indicating a count. Thus the total count is the number 11 which is three. A fourth pulse will reset the first binary to zero, the output pulse from this stage will reset the second stage to zero and a pulse from the second binary causes the third stage to indicate a count. Thus the total count is the binary number 100 which is four. Further pulses cause the units to indicate the counts shown in the table of Fig. 1.1. Jt can be seen that no two lines are the same and, therefore, the binary system indicates these num- bers unambiguously. Successive binary stages may be added until it is possible to count up to any desired number. If six binary stages are cascaded, the circuit will count up to 63, whilst twelve binary circuits connected in the same way can count up to 4,095. In general, if there are m binary circuits in cascade, the maximum count which can be indicated is (2”—1). Each binary circuit acts as a ‘divide by two’ stage. The four cascaded binary circuits of Fig. 1.1 actas a ‘divide by sixteen’ circuit. When the total count is 1111 on the binary scale (that is, fifteen), a further input pulse will reset each of the four binary stages to zero. This is analogous to the resetting of a de- cade scaler to zero when the count was previously 9,999. 1.1.8 Decade Counting Using Binary Circuits Most people are much more familiar with a scale of ten than with a scale of two. It is, therefore, usually desirable to employ decade circuits where possible in order to avoid human errors and to achieve a somewhat greater simplicity in reading the state of the count. In the case of valve and transistor counting circuits, it is possible to obtain a decade circuit by converting the scale of sixteen circuit 17 ELECTRONIC COUNTING CIRCUITS provided by the four cascaded binary stages of Fig. 1.1 into a scale of ten. This conversion can be accom- plished by the use of a suitable feedback or gating system in which six of the counts shown in Fig. 1.1 are automatically omitted. In principle it does not matter which particular six counts are omitted provided that an output pulse is obtained from the system for each ten input pulses and provided that each of the ten states is represent- ed in a known and unequivocal way. The ten fourth binary to be switched and a pulse will be fed from this stage to the first stage. This extra pulse will cause the total count to advance to nine on the binary scale. Another seven pulses will be required to cause the binaries to reach sixteen and to reset themselves to zero. The circuit will, therefore, be counting on the scale of fifteen. In practice it may be necessary to delay the fed back pulse slightly so that it does not arrive at the first binary stage at the same time as the end of the input pulse. In some B OUTPUT PULSES 4th 3rd ond jot apu TO NEXT DECADE <t————-{ BINARY =< BINARY BINARY BINARY PULSES COUNTER COUNTER COUNTER COUNTER COUNTER 1 A j A A Fig. 1.2 A decade counter using binary counting circuits digits of a decade can be represented by any ten of the binary numbers shown in Fig. 1.1, the infor- mation about the state of the count in the circuit being indicated in a binary code. The ten states may be chosen from the sixteen binary numbers in 4,Py) = = = 29,059,430,400 ways. In most cases, however, the ten states are chosen so that as the decade digit increases, the binary number carrying the information also increases. If this is the case and if the binary zero is always to be used to indicate the zero of the decade, the number of ways in which the ten binary numbers can be chosen is equal to the number of ways in which six binary numbers can be omitted from lines one to fifteen inclusive of Fig. 1.1, no importance being attached to the order in which the six are selected. This num- b ; . 15! er of ways is thus equal ,.C, = = 5,005 ways. 619! In order to show how feedback can modify the scale in which four cascaded binary circuits count, let us consider the effect of taking pulses from the fourth binary and feeding them to the first binary. The circuit will count up to seven in the normal binary manner, but the eighth pulse will cause the 18 cases, however, normal delay in the circuit is ade- quate. If the pulse from the fourth binary had been fed back to the third stage, it would have added four to the total count. Thus the eighth pulse would cause the total count to increase to twelve on the binary scale and another four pulses would be required before the counter would reset itself to zero. It would, therefore, be counting on a scale of twelve. One of the numerous methods in which four binary stages can be operated as a decade counter stage can be illustrated by the block diagram of Fig. 1.2. The system counts up to nine in the normal binary way, the additional connections marked A and B being ineffective. When the tenth pulse is fed into the system, the first binary counter is switched to read zero and the output pulse from it switches the second binary to indicate a count (actually two counts, since it is the second binary). A pulse from this stage is fed along the connection marked B to the fourth stage. This pulse switches the fourth bi- nary to zero and a pulse from it passes along the wire A so that the second binary is switched to zero. The switching of this second counter would nor- mally provide a pulse to switch the third binary, but the switching of the third binary can be prevented by a pulse fed along 4 from the fourth binary to the third binary. All of the binary stages have thus been reset to zero after ten input pulses have been applied. The system is so arranged that the fourth binary is not affected by the pulse received direct from the second stage along B unless it is actually indicating a count at the time (that is, eight counts, since it is the fourth binary). Thus when the second, fourth, sixth and eighth pulses are fed into the system, the pulse from the second binary to the fourth binary has no effect, since the latter is indicating zero. The necessity for preventing the simultaneous arrival of an input pulse and the fed back pulse at any stage may somewhat limit the maximum fre- quency of operation of decade circuits which employ feedback. This limitation can be eliminated by the use of diode gating circuits instead of feedback to convert the scale of sixteen to a scale of ten. A gate is either open or closed according to the potential applied to it from one of the binary stages. Each decade consists of four cascaded binary stages but, when a certain number of input pulses have been applied to the circuit, the switching of