Jude Levasseur Claude Brassard. Universite du Quebec. Abstract- Research in high technology has produced a large variety of novel electronic devices.
Session 24B4
Conceptual Representations of Electrical Circuits Michel Lavoie Jude Levasseur
Addeljali Metioui Claude Brassard
Universite du Quebec
Abstract- Research in high technology has produced a large variety of novel electronic devices. Full exploitation of their capabilities requires that the engineer has fully assimilated and accomodated, as defined by Posner et all, the concepts of current and voltage, and of measurement and characterization. Results of an investigation involving 170 students, 17 to 20 years of age, conducted in technical schools during 1990, revealed a large proportion of alternative eoneeptions. In particular, this study confirmed the students’ inability to manipulate models. In order to alleviate the difficulty, a computer aided interactive strategy is proposed, which will guide students in constructing the models they need to understand electronic devices. This strategy directly addresses the problem of modelling methodology. Simulation software is used to support the characterization process, on carefully selected dcvices. Studentslearn to identify the operators describing the relationships between voltage and current waveforms, V(t)and I(t).Components and circuits are treated uniformly, in a systemic approach.
STUDENTS’REPRESENTATIONS OF SIMPLE ELECTRICALCIRCUITS
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In a recent research2 supported by the Minissre de 1’Enseignement supbrieur et de la Science (Provinceof Qubbec), a qualitative approach was used in an effort to characterizethe conceptual representations of teenage students (17to 20 years of age) attending technical schools in the field of electrical engineering. Some of their alternative conceptions of current and voltage, of Ohm’s law and of Kirchhoff’s laws are summarized in the table. These representations may appear to be naYve from a scientificpoint of view; they nevertheless constitute the epistemological basis of their reasoning when analyzing simple electrical circuits. Surveys in other countries have shown that university level students in science and engineering exhibit similar conceptxal representations, and thereby show no better understandin of electrical circuits. Consistent with these findings, Rohrei chal. lenged the traditional approach of teaching circuits theory. F e expressed a deep concern in the following terms :
INTRODUCTION
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A number of electronic circuit simulators are presently available. Computer programs such as SPICE3, MICRO-CAP 1114 and others provide powerful experimentationenvironments for the designer. Given the capabilities of modem microcomputers, the engineer can optimize a circuit design in a relatively short time. These programs have gained widespread acceptance, and their usefulness remains unquestioned.
“No, today S electronic realig is not resistors, inductors and capacitors. It is black boxesfull of black boxesfull of black boxes. ... Much of theproblem lies with the abilities and attitudes of today$ students. But much of the problem lies too, with what we are trying to teach in the introductory circuit course. I am not advocating that we pander to students and wcter down the introductory circuit course. We’ve already done that. What I do advocatefor openers is that we reevaluate the present course with respect to our main goals as circuit and systems engineers :to explain the interrelationships among circuit concepts, and to provide students with an undzrstanding of thefield as a cohesive set of basicprinciples from which many useful result%can be deducted.”
As a result of the present trend in microcomputer and software prices, electrical circuit simulators are presently appearing in undergraduate courses and in technical schools. Such simulators, however, are primarily intended as rofessional tools. More recent programs, such as ASETE ,E L B 6 and others, are designed for begimiers and take into account the conceptual representations of students. In this research, the computer is used as a tool permitting a direct interaction of students with models.
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A brief survey of findings2 concerning alternative conceptions of students is presented first. These students were enrolled in technical schools, and had from l to 5 semesters of courses in electrical and electronic circuits. Scenarios are then proposed to guide students in discovering the basic electrical properties of carefully selected components, and in modelling these components accordingly.
SYSTEMIC APPROACH TO THE THEORY OF ELECTRICAL CIRCUITS Progress in microelectronics, and the constantly shifting level of integration, lead to an ever increasing variety of devices. As a consequence of this evolution, the traditional dis-
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Scientific Representation
voltage,
A current source establishesthe current in its branch. Only one current exists in a given conductor.
Different currents can coexist in the same conductor. Components act independently on these currents. A black box cannot supply power.
A black box may contain any circuit element, including power sources. Currents may flow to or from the ground. Currents always flow towards the ground. I Any two-terminal black box can be replaced with an equivalent A black box can be used to represent any type of circuit element, which may not always be assimilated to a resistance. resistance : its value is calculated using Ohm’s law. At an intersection, the current divides itself in inverse proportion Ohm’s law involves the potential differencebetween the two nodes correspondingto terminals of the resistance. to the value of the first resistance met downstream. Kirchhoff’scurrent law applies only to intersectionsin the circuit. Kirchhoff’s current law applies to any closed surface which does not intersect a component boundary. Kirchhoff’svoltage law applies only to components connected in Kirchhoff’s voltage law applies to any sequence of nodes.
1 Ohm’s law
Kirchhoff‘s
tinction between circuits and (so-called elementary) components is no longer relevant. Furthermore, the proliferation of devices, their increasing complexity and their reduced lifespan with respect to the design of new products, are challenging traditional teaching to the point where many consider the introduction of a more systemic approach7p8.
A thourough discussion of the notion of system is beyond the scope of this presentation. The reader may refer to the works of Rescherg, of Blauberg et allo, of Buckleyll and of Chestnut12. With these authors, we consider the systemic approach as a scientific modelling of the systems under study, leading to a constructivist approach to electrical circuit theory. The following characteristics,which contrast with the traditional approach, are considered as indicative of a systemic approach : No essential distinction is made between components and circuits. Black boxes are used consistently,for a single resistor to the most complex circuit, and the characterization process is considered as fundamental. Models are distinguished explicitly from physical devices. The model is the primary reference; the component or circuit is considered as an imperfect implementation of the model, instead of the model being an approximate descrip tion of the physical component.
of signals and power in the conducting network. The second category adresses the characterizationof devices (modelling them, or establishing their current/voltage relationships). These two aspects are fundamentally different in nature, and they play complementary roles in the analysis and in the synthesis of circuits. In this view of electrical circuit theory, circuit analysis and circuit synthesis become mathematical games in the manipulation of the above mentioned concepts. Engineering and physics play a role through practical considerations, and when considering deviations from models. The present trend, in the electronics industry, is to encapsulate most second-order effects within commercially available components; as a result, modern circuit analysis and circuit synthesis tend to involve more mathematics and less physics. Experimentation Since 1985, entering students in Digital Systems Technology at Coll6ge Lionel-Groulx have been taught in a systemic approach, consistent with the above guidelines. From 1985 to 1991, five professors and close to three hundred students have been involved in this experimentation. In addition, several mathematics teachers have collaborated in the effort.
The conducting network, which carries signals and power, is valued more than the components. Currents are defined in conductors (and extend to branches), while voltages are attributes of pairs of points (extendingto pairs of nodes). Currents and voltages are only indirectly associated with component terminals.
Of these students, 59 participated in the above mentioned qualitative research2. The results of the written test designed to evaluate the understanding of basic concepts indicate a marked improvement in student’s representations : 50% correct answers as compared with an 11% average for 169 students following a traditional curriculum. Detailed results of this investigation will be publised.
The general waveforms V(t)and at)are treated extensively : the constant (DC) and the sinusoid (AC) are treated strictly as particular cases.
THE DIDACTICALSTRATEGY
Circuit analysis and circuit synthesis are valued equally in the learning process. The physics of components is clearly distinguished from circuit theory : it is dealt with as the need arises. Concepts related to electrical circuit theory can be divided into two distinct categories : the first category concerns circuit topology and Kirchhoff ’s laws, and deals with the transmission
A didactical strategy centered on modelling is proposed herein, as a further improvement on the experimentation mentioned above. In the first phase, students are to tackle the first aspect : circuit topology (identifying nodes and branches) and Kirchhoff’s laws. In addition, they are expected to understand the measurement of voltage and current, using ideal voltmeters
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and ammeters. These subjects are presented in the classroom, and experimented in the laboratory as well. They may be supported by other specializedsoftware, such as ASETE5. The electrical circuits contain various types of components, including resistors, transistors, capacitors, etc. At this point in time, students are told the names and given the physical appearance of components. Ohm's law remains unknown. Postponing the detailed study of components serves a major purpose :very early in the learning process, students realize that they can draw conclusionsfrom actual measurements in a circuit, even though the characteristics of some or all components remain unknown to them. This is clearly required of present day interventions in electronics, in any work environment. Informal experimentation indicates that approximately fifty hours of theory and practice suffice to a achieve a reasonable working knowledge of topology, of Kirchoff's laws and of I-V measurements. The second phase begins thereafter. Students explore curretit/voltage relationships of representative devices. These components are carefully selected for their impact on the students' representations, and they are introduced in a sequence of increasing difficulty. Extensive experimentation will definitely be required in order to validate this choice of models and their order of appearance. The following deals with these issues, and discusses the use of software in support of the proposed strategy. THE COMPUTER-AIDED MODELLING ENVIRONMENT The classic laboratory environment permits an experimentation with circuits and with components. However, in the systemic approach, models are considered more important than the circuits used to implement them :therefore, the need arises for an environment supporting the direct manipulation of the models themselves. Microcomputers,when programmed to support a direct interaction of students with models, constitute promising environments.
unknown to the student, who is to explore them. Their behavior is, however, known to the simulator.
A built-in circuit editor permits the installation of circuit elements, supports their visual and functional interconnections, and offers means of defining voltages and currents. List of supported activities The scenario described below follows a natural progression of activities, from the very simple to the relatively complex. 1- In a first activity with the simulator, students learn to build circuits, to install voltmeters and ammeters, and to program simple waveforms.
2- Then, combinationsof sources and of measuring instruments are explored, including those which lead to conflicts (such as a voltage source with an ammeter in parallel). This second activity serves the purpose of building familiarity with the system, and of reviewing Kirchhoff 's laws, as well as the proper installation of voltmeters and ammeters. Voltages and currents are displayable as a function of time, and in relation to one another (the X-Y mode of an oscilloscope). Switches controlled from the keyboard in real time liven up the simulation.
3- In the activities of the third type, students are guided in exploring and in characterizing the various models represented by conventional symbols. These include : - on-off switch (interactive,keyboard controlled), - resistance (model of the resistor), - Thevenin equivalent circuit, - semiconductor diode model, - capacitance (model of the capacitor), - inductance (model of the inductor), - diacmodel, - two-terminal oscillatormodel, - incandescent lamp model, - three-terminal amplifier model. Desk File Edit
Student are provided with idealized voltmeters and ammeters, which respectively record voltage and current waveforms. They are also given voltage and current sources, capable of generating programmable waveforms. Overflow indicators warn of saturation conditions, as shown in Figure 1 (short-circuited voltage source, open-ended current source...).
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3w Graphs
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Vonobles Options
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Sources are checked against the instruments. These instruments and sources are then considered "known", and become available as tools to characterize all other devices, in accordance with standard testing practices.
In addition, the environment of the simulator supplies a number of devices, some represented by their conventional symbols (capacitors, etc), others shown as black boxes. All of these devices (except instruments and sources) are considered
Fig. 1.The user copies symbolsfrom the toolbox and edits a schematic. The symbols represent black boxes and models of
the usual components.
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4- In the fourth activity, students are asked to test unknown black boxes, in an attempt to recognize previously studied models.
Selected components The investigation2 mentioned above revealed that students, after 1to 5 semesters of traditional instruction in electronics, suffer from a pathological tendency to replace any circuit element by a so-called “equivalentresistance”.For example, they replace a closed switch with a small resistance, and an open switch with a large resistance. They will go as far as replacing a current source with a resistance, applying Ohm’s law in order to compute its value!
5- Students then characterize circuits constructed from several components. They realize, for example, that two resistances in parallel exhibit the same functionality as a single resistance (of the appropriate value). 6- In the last and most difficult activity, students are invited to synthesize given functionalities,using system components to design the corresponding circuits.
Most of these students also believed that for any component, instantaneous voltages determine instantaneous currents, and vice-versa. One consequence of this belief, is their unwillingness to accept the behavior of the capacitance and of the inductance for any waveform other than the sinusoid.
Supported waveforms Students undertake the six activities described above, using only staircase waveform generators at first, where each source is programmed to undergo transitions (repetitive or not), and to remain constant between transitions.
Finally, these students experience major difficulties in understanding components with more than two terminals. They incorrectly refer, for example, to “thecurrent through the transistor” or “the voltage of the transistor”.
In a second learning cycle, the above-describedsix activities are repeated with trapezoidal waveforms, as in the example of Figure 2, thereby supporting finite risetimes and piecewise linear approximations.
These clearly identified misconceptions may presumably be attributed to hasty generalizations. In the above list of component types to be explored, every effort has been made to introduce very early, models and devices which confront the identified misconceptions. This is intended to thwart the development of hasty generalizations, to the expense of an increase in complexity.
Finally, the same six activities are tackled with still more complex sources, capable of incorporating sinusoids. The simulation
The semiconductor diode has been included as a simple nonlinear element.
The simulator assumes that no electrical energy is stored in components at the initial time t = 0. From these initial conditions, it proceeds to solve differentialequations, taking into account non-linearities. Transient behavior is always present, as in real life situations, and if the sources are repetitive, a steady state evolves.
The diac serves as an example of a circuit element which exhibits more than one stable current for a given voltage, leading to a memory effect of the discrete type. The two-terminal oscillator is introduced as representative of unstable circuit elements. The incandescent lamp is a perfect example of a very complex circuit element, which exhibits a relaxation effect : its short term response is linear, but as the temperature of the filament increases,the current drops. And of course, the three-terminallinear amplifier model is included to provide a simple example of components with more than two terminals. The activities mentioned above will be supported by the * _ simulator. They may also be carried out in the laboratory. The components in the list exhibit a visual signature on the X-Y display of the simulator, which is easily reproduced in the laboratory,using an oscilloscope in the X-Y mode. Simple operational amplifier circuits can be utilized to transform current waveforms into voltage waveforms, for display on the Y axis of the oscilloscope. Tools supporting model identification
Fig. 2. Voltage and current waveforms from the circuit of Fig. 1 are displayed as functions of time and in relation to one another. Numerical values of time, voltage and current at the cursor are displayed numericallyin a window. In the lower right hand graph, a voltage is shown in relation to the derivative of a current,for the waveforms displayed on the left-hand side.
Graphic display of any voltage or current is provided as a function of time. In addition, a time-based cursor supports the reading of numerical values, as shown in Figure 2. The X-Y display makes it possible to visualize the relation between any
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and the inherent difficulties associated with the process of understanding the theory of electrical circuits.
two wavefonns &I, V-V or V-I curves). It is also possible to display and to read the power entering a region of the circuit, as a function of time.
These strategies represent examples and do not cover all of the students’conceptual difficulties. We intend to verify the efficacy of the proposed strategies by conducting controlled experiments with representative groups of students.
The resistance, the diode, the diac model and the Thevenin equivalent model are easily recognized on the V-Z display : the resistance and the Thevenin equivalent remain on straight lines, regardless of the waveform supplied by the test source, and the diac shows as disconnected branches.
ACKNOWLEDGEMENT
The capacitaice and the inductance, on the contrary, exhibit a seemingly erratic behavior. Much can be learned from the qualitative and quantitative observationsof this behavior : for example, the difficulty i~i rapidly changing the current through an inductance (the current source driving an inductance shows a transient saturation, when it attempts to step).
This research conducted within the Programme de Kecherche-dkveloppementpour les Formateurs was funded by le Ministkre de la Science et de I’Enseignement sup6rieur du Qu6bec. BIBLIOGRAPHY
However, more appropriate tools are needed to express the exact relationship between voltage and current in an inductance or in a capacitance. What is required in this case is a display of the derivative or of the integral of current and voltage waveforms.
1- Posner, G., Strike, K., Hewson, P., and Gertzog, W., (1982), “Accomodation of a Scient@ Conception :Toward a l2eory of Con-
ceptual Change”,Science Education, 66,212-228.
2- Mktioui, A., Lavoie, M., Levasseur,J.,and Brassard, C., (1991), “L’assimilationdes concepts de base de la thiorie des circuits chez les 612vesdu coll6gialprofessionnel”,Technical report, Ministere de I’Enseignement supkrieuret de Sa Science, Direction Genkrale de I’Enseignement Collegial, Qc. G1R 5K9, Canada.
Then, an X-Y display of the voltage across an inductance, as a function of the derivative of the current through this same inductance, will plot on a straight line, and permit the extraction of the value L of the inductance. In the example of Figure 2. which applies to the circuit of Figure 1, the relation between dIl Vu and -plots as three discrete points, one at the origin and dt the other two moving on a straight line with slope equal to the inductance L, as the risetime of the trapezoidal wavefonn is modified. The same plot, with a sinusoidal waveform, will show this straight line directly.
3- Nagel, L.W., (1975), “SPICE2:A ComputerProgram to SimulafeSemiconductor Circuits”,Memorandum No. M520, University of California, Berkeley, CA. 4- Roden, M.S., (1991), “TheStudent Edition of MICRO-CAPHI”, Addison-Wesley.Benjami~CummingsPublishing Co., Inc., ISBN 0-201-50605-X.
5- Brassard C., “Unenvironnementpourl’apprentissagede 1’6lec-
The system will support any linear combination of currents, voltages, and of their derivatives and their integrals. Therefore, in the circuit of Figure 2, where
trotechnique: ASETE Y”, (1991) Institut d’ordinique du Qu6bec, Ste-Thkrese,Qc J7E 5B3, Canada. ((
6- Bma, P., (1988), "Confronting Mkconceptions in the Domain of Simple Electrical Circuits”,Instructional Science, 17,29-55. 7- Rohrer, D.A., (1990), “TakingCircuits Seriously”,IEEE Proceedings on Circuits and Devices,July 1990,27-31.
students will obtain a straight line when displaying the quantity in brackets in relation to vb. The simulator will assist L
1
R
RC
8- Hartel, H., (1982), “TheElectric CIrcuitas a System :A new Approach”, European Journal of Science Education, 4,45-55.
them in establishing the values of - and -.
9- Rescher,N., (1977), “MethodologicalPragmatkm. A ,$stem TheoreticApproach to the Zheory of Knowledge”,Basil Blackwell, N.Y. University Press, New York, NY.
FUTURE DEVELOPMENTS
As the development of the simulator progresses, experimental investigations of its efficacy will be carried out regularly. Should the simulator prove to be a valuable learning tool, the addition of models for transistors, operational amplifiers, 555-type timers and other electronic devices will be considered.
10- Blauberg, I, Sadovsky,V., Yudin, E., (1977), “SystemTheory”, Philosophicaland MethodologicalProblems, Progress Publishers, Moscow, USSR.
11- Buckley, W. (ed.) (1969), “ModemSystemsResearchfor the BehavioralScientkt”, Aldine Pubs., Chicago, E. 12- Chestnut,H, (1967), “Systems Engineering Methods”,John Wiley, New York, N Y n
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CONCLUSION
Xn this article, we have proposed some didactical strategies which take into acount the cognitive processes of the students. 1991 Frontiers in Education Conference
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MICHEL LAVOIE
ABDELJALIL MiTlOUl
M. Lnvoie is a professor of Computer science in the Dkpartement de Genie hectrique of kcole de rIi.cIiiiologie Supkrieure since 1983, where he teaches, and performs research on graphic user interfaces (GUI) and in students' representations of concepts on electrical circuits. M. Lavoie received the B.Sc.A. degree in engineering physics and the M.Ing. degree in electrical engineering from kcole Polytechnique i n Montrkal, in 1971 and in 1978, respectively. From 1971 to 1983, M. Lavoie worked as a systems design engineer (hardware and software), in real time applications of computers. Mr. Lavoie is a member of l'0rdre des ingitnieurs du Qukbec.
A. MCtioui received the B.Sc. degree in physics from the Mohanied Fifth University, Morocco, in 1977, and the D.E.A. degree in physics from Bordeaux-1 University, France, in 1980. He also received the Ph.D. degree in didactics and the M.S. degree in Physics from Laval University, Canada, in 1987 and 1988 respectively. From 1977 to 1979, Dr. Mktioui taught physics at lyck Zaynab, Tangier, Morocco. From 1983 to 1984, he was a teaching fellow at Laval University. He then worked as a research fellow, at the Universiti: du Qukbec i Hull, in 1988 and 1989. Since 1989, he is an associate professor at the Ditpartenient de Genie Electrique, Ecole de TeclmologieSuHrieure, Montreal, Canada. Dr. MCtioui has several publications to his credit. His research interests involve optical pattern recognition, and teachers' and student's representations.
JUDE LEVASSEUR
CLAUDE BRASSARD
J. Levasscur was boni in Qukbcc. i n 19.59. I le received tlic B.Tech. (Electricity) degree from kcole de l'cclniologie SupPrieure, Montrkal, in 19S2. He is a professor at the DPpai'tcrncnt tl'~lcctro~cclii~ic~ue, College Andr&Laurendcau, L a Salk, Qukbcc, siiice 1982. I IC was involved in educational research on power electronics for three pour years, with PRDF (Programme de reclierclie-dCvelop~~et~le~lt les fonnateurs). He developped instrumentation for tcaching power electronics and co-authored a book on this sulijcct. In 1990-91, he worked for the Direction gknitrale de I'eiiseignement collegial in redefining the curriculum of the provincial program in electrodynamics. He is presently involved in educational research on the basic concepts of electrical circuits. Mr. Levasseur is a member of I'0rd1e des ing6nieurs du Qukbec.
C . Brassard was boni i n I\.lontr-i.ali n 1943. IIc received the B.Sc. degree from I'Uiiiversiti. de MoritrCal in 1963.and the 1'11.1). degree in nuclear physics from Yale University, CT. in 1970. His past research activities include nuclear physics and iris(nirnentation, at Yale and in the Centre d'ittudes nuclkaires de Saclay. France, and nuclear medicine instrumentation, in the Universitk de Sherbrooke, Canada. He was an associate director of the Laboratoire de physique nttcleaire de I'Universiti. de hlontrcal from 1973 to 1984, where he conducted research on particle accelerator physics and on ion-beam analysis of materials. Ne is currently a professor at Coll6ge Lionel-Groulx, SteThi.rese, QuCbec, teaching software and hardware. He is involved in redefining the provincial curriculum in Digital systems tecllnolOgY. Dr. Brassard is a member of Sigma-Xi.
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