Teaching Award from Columbia University in 2003, and the IEEE Undergraduate Teaching Award in 2005. References [1] Y. Tsividis, “Teaching circuits and electronics to first-year students,” in Proc. 1998 IEEE Int. Symp. Circuits and Systems, Monterey, May/June 1998, vol. 1, pp. 424–427. [2] R. A. Rohrer, “Taking circuits seriously,” IEEE Circuits Devices Mag., vol. 6, no. 4, pp. 27–31, July 1990.
[3] Students create hands-on electrical engineering course. The Institute [Online]. Available: http://www.theinstitute.ieee.org [4] Student branches boost membership with hands-on projects. The Institute [Online]. Available: http://www.theinstitute.ieee.org [5] Y. Tsividis, A First Lab in Circuits and Electronics. New York: Wiley, 2002. [6] Available: http://he-cda.wiley.com/WileyCDA/HigherEdTitle/productCd-0471386952.html [7] Available: http://www.engr.uconn.edu/ece/crsdata/210sy01.pdf [8] A. Emami-Neyestanak, private communication.
Charles Trullemans, Laurent De Vroey, Stanislas Sobieski, and Francis Labrique
From KCL to Class D Amplifier Abstract From a circuit point of view, the starting point of the students coming out of the secondary school is roughly limited to describing the flow of electrical charges through a simple loop. Nevertheless, one and a half years later, they can design, simulate, build and test the core of a Class D amplifier while meeting demanding learning objectives. This paper relates the story of a project conducted in the context of an undergraduate electrical engineering program. Circuits and system concepts are introduced from the beginning of the first year in a physics course, and are applied to a project during the second term. A circuit theory course and the Class D amplifier project are run in parallel during the second term of the second year. Effective learning is facilitated by a mixture of lectures covering the necessary concepts and self-directed laboratory experiments allowing active acquisition of problem solving skills. At the end of the project, enthusiastic students can listen to the sound of their MP3 player through the amplifier that results from their teamwork. A survey indicates that the outcomes of the project are in line with the expected results of a problem- and project-based learning environment.
1. Introduction ignificant changes have taken place since the end of the 1990s in the undergraduate (Bachelor’s) program in engineering at the Louvain School of Engineering (EPL). During the academic year 2007−2008, we tested an ambitious project: to build a Class D amplifier. This paper focuses on that project.
S
The Development of the Bachelor’s Program at EPL Before 2000 The traditional program started with a hard core of basic mathematics, physics, chemistry, and computer Digital Object Identifier 10.1109/MCAS.2008.931747
science. On this supposedly sound basis, students were eventually exposed to real electronic circuits. Projects have been included in the first two years of the program since the early 1970s. This has been a nice feature of the program, much appreciated by the students. However, these projects were merely illustrations. They were only weakly connected to the lectures. 1997−2004: The Candis 2000 Project In 1997, a small group of EPL professors decided, on their own initiative, to explore new approaches to teaching and learning, mostly because of their dissatisfaction with the results achieved through traditional means. The project addressed the first two years of the course (called the ‘candidature’) and was aimed at launching a new curriculum in September 2000. After a lot of reading about active learning, many hours of heated discussion, and several visits to institutions practicing active learning, the team focused its attention on the problembased learning (PBL) approaches used at Delaware, Maastricht, and Sherbrooke Universities and the projectbased curriculum at Aalborg University. Their preference was for active, small group, partially tutored project and problem-based learning. This model fits very nicely into a socio-constructivism learning theory. Problems and projects are situated as far as possible in realistic professional contexts, and students are systematically encouraged to build upon existing knowledge to acquire new knowledge, while interacting with other learners. In this learning-oriented approach, the objective is not the ‘result’ (e.g. the prototype, the model, etc.), but the competencies acquired during the project [1]. An ‘Impact Group’ was put in charge of coordinating the evaluation of this
Charles Trullemans, Stanislas Sobieski, and Francis Labrique are with the Louvain School of Engineering, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium. E-mail:
[email protected]. Laurent De Vroey is with Laborelec, B-1630 Linkebeek, Belgium.
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1531-636X/09/$25.00©2009 IEEE
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edge acquisition. Clear positive effects of a curriculum shift to problem-based learning were found. [3]
Ch
ar
ge
From 2004: The Present Bachelor Program The present Bachelor’s program is partly the result of the Bologna Process that aims at creating a European Higher Education Area and introduces a unified threecycle-system (Bachelor’s/Master’s/Doctorate) across Europe, with easily comparable degrees. Previously, the two-year program of the first cycle was common to every engineering course at the University of Louvain. In the Bologna system, the first cycle has to last at least three years. The EPL has regarded this as an opportunity to start specializing within engineering during the second year of the Bachelor’s degree. This means that specific projects oriented towards electrical engineering can be introduced earlier in the program. The Class D amplifier is one of them. The present Bachelor’s program is also the result of the accumulated pedagogical experience inherited from Candis 2000, and, from a pragmatic point of view, it is the result of a compromise dictated by the availability and skills of staff members.
Flow
Circuits and Systems in the Bachelor’s Curriculum
Figure 1. The starting point: Negative charges flowing through a loop.
V(t)
VS
R1 V(t)
+ −
C R2
Req
+ −
C Veq
Figure 2. End of Year One: Equivalent network and first order dynamic circuit.
radical curriculum change. The results of their work are consistent with Dochy et al.’s [2] conclusion that— in quasi-experimental studies—the impact of PBL on knowledge application is stronger than its impact on knowl64
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Starting point: charge flow through a single loop From a circuit point of view, the starting point of the students coming out of secondary school is depicted in a simplistic way in Figure 1. Negative electrical charges may flow through a simple single loop circuit. First year: first order dynamic circuits Fundamental concepts of electromagnetism and electrical networks are taught during the first term of the first year. At the end of this course a student should be able to use an equivalent network to simplify the schematic of a first order dynamic circuit (Figure 2) and to solve its equations in the time domain. During the second term of the first year, a more formal treatment of electromagnetism leads to Maxwell’s equations. A project to build an electrical device is included. Section II (below) contains some teaching examples and reflections about the first year program. Second year: the SD modulator project From the second year onwards, students aiming at a major or minor degree in electrical engineering follow a specialized program. During the second term, a course on circuit theory and a related project are run in parallel. The ultimate objective is to pass from a low-level description of a Kirchhoff network in the time domain, to a high level functional description of the modulator FIRST QUARTER 2009
in the Laplace or Fourier domain (Figure 3). There is a long way to go between the kind of simple circuit illustrated in Figure 2 and that of the SD modulator depicted in Figure 3. Section III is a report of this journey. Third year: signals and electronic circuits After they have completed the design and testing of a Class D amplifier, it is expected that the students will feel the need for more training in signals and systems. In this way, the project leads on to courses in applied mathematics (signals and systems) and electronic circuits in the third year. Section IV is an attempt to balance the dreams of the teaching staff against the learning outcomes actually achieved by students at the end of the project. 2. First Year A partial view of the EPL Bachelor’s program restricted to the topics related to electrical circuits and system is given in Table 1.
Reconstruction Filter H(s)
yout
xin
ysum
yint
∫ Summing Block
Integrator 1/s
Hysteresis Trigger
Figure 3. End of Year Two: An analog oD modulator at the functional level.
let alone an engineer, these expressions convey concrete meaning. Thus the first column of Table 2 tells us that material characteristics and device geometry act separately on the value of the element; the table implies that it is impossible to move energy instantaneously because this would require an infinite power; and so on. Solving problems requires that kind of understanding as a guide to the manipulation of formal expressions. Some educational models assume that learning is a logical, sequential process where each step is accomplished once and for all. But this is not necessarily true. Getting acquainted with new concepts and gaining skills, is usually a progressive, back-and-forth process. The design of the curriculum, and the course contents, must account for such progressive processes. In this specific
Basic Physics Unlike most physics textbooks, we decided to direct the electricity lectures towards the modeling of basic circuit elements. The fundamental concepts of charge, current, voltage, fields, energy, and power are introduced first. The classical Coulomb, Gauss, Biot-Savart, Faraday and other laws are used only as far as they are needed to explain the internal physics of a resistor, a capacitor and an inductor and to derive their mathematical models. The final result is apparently the set of formulae shown in Table 2. However, the actual result is not limited to the information in this table. The learning objectives are not limited to collections of unrelated facts and formulae, even though the formulae alone are efficient tools for solving circuit problems. An essential objective is to train the students to build dense-link netTable 1. works between related concepts. Therefore, CAS related courses in the bachelor’s program. whenever possible, special care is taken to Year One 1st term Basic physics: Electricity (8 h)† make these links apparent. For instance, the 2nd term Electromagnetism power related to the movement of an elecProject: Electricity (10 h), material tric charge in an electric field is connected science to both its mechanical counterpart, and, to 1st term — Year Two 2nd term Circuit theory (60 h) the power absorbed or supplied by any twoProject: Class D amplifier (60 h) terminal circuit element. Applied mathematics Year Three To be admitted to the School of EngineerElectronic circuits (Major degree electrical ing, all students have to pass a math entrance Device physics eng. only) test. An unwanted side effect of the training Telecommunications in pure mathematics that they undertake Electromechanical converters Control theory when preparing for this test is that they tend Project to look at mathematical expressions as formal and abstract entities. Yet for a physicist, FIRST QUARTER 2009
†
Total student working time on this subject
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world is however preserved. Such a thought process is completely new for most students. Yet this is nothing but modeling, a basic method that Physical Parameters Absorbed or of Element Element Constraints Energy Storage Supplied Power allows complex systems to be handled, a method whose scope is much V=RI G = s gG dV C = e gC broader than circuit theory. CV2 I =C WC = dt In the same way, a first-order dy2 P=VI 2 dI L = m gL LI namic circuit is just a special case of a V=L WL = dt 2 first-order system. The first-order differential equations are addressed siR, G = 1/R, C, L: resistance, conductance, capacitance and inductance; s, e, m: conductivity, permittivity, multaneously in the math course. The permeability; gG, gC gL: geometric coefficients; V, I: element voltage and current (passive convention); WC, WL: stored energy; P: power. circuit example enables the students to discover that differential equations case, the first physics course is merely a first look, which may be a useful tool for solving technological problems, leads on to a more in-depth electromagnetics course in and also that an equation can be a magnificent tool for the second term of the first year. There are several ex- describing a physical problem, even when it is not posamples of this principle in this paper. sible to solve the equation in a formal way. An explicit link is made here with the slope field plot that appears Basic Circuit Theory in the math course [4]. In a slope field plot (Figure 4), The basic physics course in the first term includes the the slopes are pictured at selected points (V, t) by short basic concepts of circuit theory, notably Kirchhoff’s arrows that have the same slope as V(t) and so should Current Law (KCL), the Thevenin and Norton equiv- be tangential to the curve V(t). It is easy to sketch the alents, etc. At the end of this course, the students solution V(t) by following the arrows along the path should be able to analyze a first order dynamic circuit from the starting point Vstart to the equilibrium value. as suggested in Figure 2. They should know how to The plot shows the derivative of the voltage V(t) across isolate a subset of the sources and resistances in or- the capacitor of Figure 2. The derivative at a point (V, der to replace them by a 2-terminal equivalent, how to t) is easily computed from the differential equation for derive the first order differential equation of the sim- the circuit: plified circuit, how to solve it in a transient case, and 1 dV 5 2 1 V 2 Veq 2 , how to calculate any voltage or current in the comt dt plete circuit. In an equivalent circuit, all the internal details of the complete circuit are hidden. An exact where t is the time constant, and Veq the equilib description of its behavior as seen from the outside rium value. These two examples illustrate the early introduction of basic methods suitable for many application fields. This is especially welcome as the course is intended for V all first-year engineering students, whichever their future specialization. Table 2. Summary of element modeling.
Equilibrium
Veq
t
Vstart
Figure 4. Link between mathematics and physics: Slope field plot for a first-order system.
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First Year Projects During the first term of the first year, lectures in physics and computer science are closely coordinated with a project. Using Lego parts, groups of six students design, build and test a small computer controlled vehicle driven by electric motors. According to the principles of active learning, solving problems may come before the corresponding theoretical concepts are taught: an unusual situation that leaves the students quite confused. This is also their first experience of a large team project that lasts for about ten weeks, and their first experience of written and oral reporting on technical topics. A Master’s or PhD engineering FIRST QUARTER 2009
student is assigned to tutor each project group, but his or her job is mainly to take care of non-scientific skills, while the course tutors act as consultants in their own scientific fields. The second-term project is related to electromagnetism, circuits, and the electrical properties of materials (i.e. topics addressed in the physics and chemistry courses). After a few introductory laboratory sessions, the students are asked to design a simple electrical system. They converge towards a good solution by testing it on a breadboard in the lab, and by debating the results and new tests with the rest of their team. An important detail is that the debate takes place in a separate room at a different time. This increases the need to take accurate notes about the experimental conditions and the measured values, as the lab bench is not available during the discussion. It also deters the students from adopting a trial-and-error design methodology, as the reflection time and the experimentation time are clearly separated. Eventually they build the final version on a PC board. A new project theme, linked to everyday life, is chosen every year. Some examples are: a high voltage unit for a flash from a disposable camera; a DC-DC converter driving a small electrical motor (a real motor for a car window); the driver for a brushless DC motor (built from cheap parts by the students themselves); the detector circuit associated with an anti-theft device (similar to the tuned circuits found in shops); and a simple pushpull amplifier for a loudspeaker (build by the students from a Petri box and a neodymium magnet). During this project, the students are still being trained in teamwork, written and oral communication, time management etc., but progressively more stress is put on individual knowledge and skill acquisition, still within the scope of a progressive learning process. For example, the push-pull amplifier is built from op amps and bipolar transistors. The students use highly idealized models, but these are sufficient to develop a good understanding of the amplifier operation. The evaluation of the first-year projects is based partly (2/3) on a group rating and partly (1/3) on the results of an individual examination. Different rules are applied in special cases, when a student’s individual performance or contribution to the team work is abnormally low. What the Students Can Do at the End of Year One Almost all the groups end up with successful working devices. The students greatly appreciate the contextualization of scientific topics from the very beginning of the curriculum. Most of them realize that their individual performance as an engineer will be in vain if it is not expressed in interaction with a team. They realize that FIRST QUARTER 2009
nobody can become a task leader by reading a textbook, and that the projects provide the necessary training. Changes in the behavior of many students are observed from the end of the first project onwards, and more significantly at the end of the second one. The examiners report oral communication skills which are not usually expected in first year students. On the other hand, only a few of the students really perceive the necessity for deep and meaningful learning. Their favorite problemsolving technique is a kind of pattern matching to select the appropriate formula, followed by the application of the formula as a magic trick. To some extent, this could be due to the fact that the problems they are faced with during this first year are often quite simple. Unfortunately, in many cases, the magic trick works well. 3. Second Year: The Class D Amplifier The Class D amplifier project started in February 2008, when the students attended an introductory talk. They expected a starting point not too far from something they already knew, such as Kirchhoff’s Current Law. But the talk immediately refers to the Bang & Olufsen (Ice Power) and NuForce websites. They hear that Class D amplifiers, once restricted to bass drivers and low quality audio, are now entering the audiophile market. The project will deal with the underlying principles of this kind of new, high-end application. The speaker explains the ideas behind a Class D amplifier using a block diagram (Figure 5), and states that a PWM modulator delivers, as its output, a rectangular waveform whose mean value follows the input signal. This cryptic statement is clarified in a simple way on the blackboard. The students then watch a demonstration of prototypes of Class D amplifiers. They even listen to the sound produced by the amplifiers while live waveforms from an oscilloscope are dancing on the screen. At the end of the show, they are interested, impressed, and mostly lost. If motivation is the keystone for learning, then the basis for an efficient curiosity-driven learning is established from the first day onwards.
Loudspeaker
MP3 Player
Preamp + Anti-aliasing
PWM Modulator
Class D Driver + Reconstruction
Figure 5. Introductory talk: Class D amplifier block diagram.
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Managing the Challenge The idea of asking second year students to design and to build a Class D amplifier based on an analog modulator was born from a brainstorming session during a preparatory meeting of the teaching staff. At that time, this kind of circuit was actually unknown by several members of the teaching staff. Later on, it turned out that discovering this technique had been a source of motivation for the staff too, as had the challenging nature of the project. A prototype of the expected amplifier was built using the same components as the ones that would be available to the students. The prototype was tested before any further discussion took place. We took advantage of the fact that the same teachers were in charge of this project, and of the circuit theory course that was scheduled during the same term. As an additional advantage, they had complementary backgrounds: IC design, and power electronics. We set up a unique twelve-person teaching staff group which was
aware of the possible two-way interactions between the course and the project. A one-hour staff meeting was held almost every week, and frequent communications between the staff members allowed short-term modifications of the content of the activities, and last minute calendar adjustments to be made, according to the students’ actual progress. The actual scheduling, as recorded after the project completion, is summarized in Table 3. It is not easy to design an interesting project for second year students, as a project related to circuits has to start with very little background knowledge. Common sense can be a useful starting point in mechanics (even if it is unreliable), but no-one can develop an intuitive perception of electrical circuits without some practical experience. We decided to provide just enough support to make the project feasible within the workload limits and time constraints set by the program, while maintaining a good level of active learning.
Table 3. The project calendar. Week 1 2
Lectures
Support
Temporal domain 1st order circuit 1 ideal op amp Phasors Impedance and admittance Sinusoidal steady state
Preliminary Presentation Paper and pencil exercise and spice demo: Hysteresis trigger Web site: spice tutorial
3
Fourier domain Frequency effect on circuit behavior Bode plot Frequency spectrum
6
7 8 9
Laplace domain 1st and 2nd order circuit transient response Feed back Op amps offset voltage, limited bandwidth
10 11 12 13 14
68
Spice simulation of a compensated attenuator Spice simulation of a lossy integrator
Paper and pencil exercise: lossy integrator
4
5
Product
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Laboratory notice: PWM oD modulator Spice: Question and answer session Web site: Lab equipment manuals Sigma delta modulator Laboratory notice: oD PWM modulator Consultancy
Assembly of a lossy integrator, amplitude and phase measurements oD PWM modulator: comparison between hand calculations, simulations and measurements Preliminary report
Just-in-time lecture based on the preliminary reports Spice ABM library. Input and output amplifier Power output stage and reconstruction filter
Comparison between oD and carrierbased PWM modulators
Preamplifier
Microphone or MP3 input Final report Demonstration for the examiners
Characterization of the complete amplifier
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The Circuit Theory Course The circuit theory course starts from the students’ background by revisiting circuit analysis in the time domain. The main novelty is the concept of the transformation of the circuit description into different domains, from the phasor representation to the Laplace transform. Additional topics, such as 3-phase circuits, quadripole equivalent circuits, and electrical measurements, are omitted from Table 3, as they do not have a direct relationship to the project. The coverage of the subject in a second year course is necessarily limited: it explains for instance what a Fourier spectrum is; the Spice simulation program and FIRST QUARTER 2009
the oscilloscope allow students to visualize the spectrum of a signal; they are helped to understand how a reconstruction filter can recover (with some additional noise) the input sinusoidal waveform hidden in the pulse-width modulation (PWM) signal at the amplifier output. But this course does not tell students how to calculate the Fourier spectrum of the PWM signal. The rule is that we should not oversimplify the answer to a complex question that beyond the students’ grasp. It is much more fruitful to stress the question by leaving it open as an intriguing point to be cleared up in subsequent courses. Phase I: Apprenticeship The agenda of the project, as seen by the students, is listed in the third column of Table 3, under the heading ‘Product’. The first five-week period is a kind of apprenticeship before the core of the project is tackled. This apprenticeship concerns theoretical concepts, tool mastering, and circuit design methods. The difficulty is to elevate the students from the level evoked by the voltage divider loaded with a capacitor in Figure 2 to the level of the oD modulator (Figure 6) required by the intermediate milestone. We knew from previous experience that this gap was too wide to be crossed within such a short period in the open and free context of a pure project. We thus chose to use a mix of activities: formal lectures (D: directed activity), paper and pencil exercises in a classroom (S: supervised activity), and team or individual work in the lab, in a computer room or at home (A: autonomous learning). Our choice was a compromise that delivered a fast, dedicated training in the basic concepts, and an active acquisition of problem-solving skills. The supervised activities are listed in the second column, ‘Support’, of Table 3. Additional support is provided by a website on iCampus, a UCL e-learning platform similar to Moodle (see http://moodle.org/). Copies of the lecture slides, and solutions to exercises were posted on the site after the corresponding session. The students were told that they should actively participate in the exercise sessions in order to benefit from the supervised activity.
R1
VCC
R12 R2 VEE
Op Amp
+ −
R11 A C1
R3
R20 1kΩΩ
With regard to the project credibility, and to the students’ motivation, we felt that it was important to keep our promises by guaranteeing that it was feasible to build a complete amplifier within the time available. As the aim of the project was not really to demonstrate the students’ ability to assemble a complete amplifier, we decided to supply the switching Class D power stage, the preamplifier and most of the anti-aliasing filter as ready-to-use modules (although we initially intended only to supply the power stage). The students then only had to build the central part (i.e. the analog PWM modulator, Figure 5) by themselves. In a real project, the initial exploration of the solution space is not normally limited to a single point. Exploring a large number of solutions was obviously outside the scope of this project. Nevertheless, we decided that each group would have to build two different PWM modulators: a oD modulator, and a carrier based modulator. The aim of the project is to help students learn. We felt that a comparison between the characteristics of two different solutions would trigger good learning opportunities. We also wanted to implicitly suggest that, when dealing with design choices, looking for the maximum on a curve is not the whole story. For reasons external to the project, the availability of the laboratory was limited to two hours a week for each group. While foreseeing strong time-constraints during the unavoidable rush of the last few weeks, we felt that this would also be a good opportunity to force experimental planning instead of promoting a trial-and-error approach. It would also be a way of making students aware that time is a resource in engineering; lab time should not be wasted. On the other hand, the simulator was permanently available. We decided to ask for an intermediate report on the project at the end of Week 8, just before the Easter vacation. Staff comments on the reports, delivered just after the holiday, should help the students refine their projects. At that time, five weeks were left to build and test the amplifier according to a revised scheme.
+ −
B
Comparator
Vin Figure 6. During the project: An analog oD modulator at the circuit level.
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Otherwise, they should adopt a consistent attitude, stay at home, and obtain the solutions from the website (to their own disadvantage). We also knew from experience that it only takes a classroom demonstration, a manual and a few tutorials posted on the website to support Spice self-training. The tutorials, prepared in the scope of the project, do more than list basic Spice commands. They are organized according to the calendar, and they give examples of circuits similar to the building blocks of the class D amplifier. Above all, they situate the simulator in the context of the recommended design methodology. The calendar shows that successive subjects are introduced in a tiling way. For instance, the sequence of activities related to the integrator is: ■ Week 1, D: integrator schematic introduced during a lecture about op-amps; ■ Week 2, S and A: calculation of the ideal integrator equation in the time domain; extension to the lossy integrator left for homework; ■ Weeks 2, 3, D: phasors, steady state solution of a 1st order differential equation for sinusoidal signals; ■ Week 4, A: mission, with the help of a Spice selflearning notice: (1) to sketch the output waveform of a lossy integrator driven by a sinusoidal input, (2) to run a simulation, and (3) to compare the simulator output to the predictions of the sketch; ■ Week 5, A: mission: (1) to determine the component values for a lossy integrator from a given specification, to assemble the circuit; (2) to measure the amplitude and the phase of the output signal as compared to the input at various frequencies. The short-term result is training in a design methodology based on a back-and-forth trajectory between reasoning, simple hand calculations, simulations and measurements. The long-term objective is for students to become accustomed to autonomous, lifelong learning. A problembased learning approach is well suited to that objective as it has the potential to prepare students effectively for future learning because it is constructive, self-directed, collaborative and contextual [5]. The apprenticeship also yields some familiarity with the hysteresis trigger and the integrator, two main components of the oD modulator that will be used from Week 6 onwards. Phase II: The SD Modulator We obviously did not expect the students to invent the schematic of a oD modulator by themselves. They would have had a good chance of finding a suitable schematic on the web or in a library but the timetable was too tight to enable them to undertake such a time-consuming task. It was not mandatory to include bibliographic research 70
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here as it is practiced in other parts of the curriculum. We thus decided to give the students the schematic of the modulator (Figure 5) as a starting point, along with the specifications of the input and output interfaces. However, the only resistor value supplied was that of the comparator pull-up resistor. The task for each group was to understand the operation mode of the circuit, to determine the resistor and capacitor values according to the specifications, to simulate the circuit, to build and test a prototype, and to produce a preliminary report. At first sight, this may look like a simple routine task. However, from the students’ point of view, given their level at Week 6, it was a tough, creative challenge. To design, build and test a carrier-based modulator was also part of the final brief. Several groups asking for staff comments had already made suggestions in the intermediate report. They had noticed that the oD modulator could be used to produce the triangular waveform that was needed, and that a comparator (well known to them at that time) could do the job. The most striking impression from the intermediate reports was that, at the time of writing, the students were still stumbling around in the dark. What they did was basically to write down as many equations as possible from the equations of the element models, and from Kirchhoff’s laws (mainly from their preferred voltage law). Then, by manipulating these equations, they derived the values of the elements. In several cases, the students seemed to be happy with the values found in the particular case of a null input signal, losing sight of the fact that an amplifier was supposed to handle other signal values as well. For instance, group G wrote: The integrator output voltage will be a triangular signal. The rising and falling edge will have exactly opposite slopes. We are looking for a ratio between R1 and R2. If the voltage at the common node is 0, we get VB 2 R1 IR1 5 0 and 215 1 R2 IR2 5 0. We also want the current through C1 when VB .. 15 V to be exactly opposite to the current at the same place when VB 5 0. This gives: IR1 2 IR2 5 IR2. Hence R2 5 2 R1 … The tutor commented: “Is the purpose of the circuit to produce a symmetric triangular wave?” This approach does not allow the students to answer questions such as: “If the value of C is changed, what is the effect on the amplitude of the triangle?” When trying to answer questions like this, the only way they can think of is to run a lot of simulations for different FIRST QUARTER 2009
Phase III: The Class D Amplifier The debriefing session on the intermediate report actually turned into a just-in-time lecture. The main mistake in the students’ approach was that they had not paid attention to the block structure of the modulator. Hence the lecture pushed them to begin the analysis of a complex circuit by applying the following steps: ■ find the borders of the functional blocks ; ■ identify the interface signals; ■ derive the circuit details from the overall structure. Looking at Figure 7, the students easily recognized the integrator and the hysteresis trigger. However naming the set of resistors R1, R2 and R3 “the summing block” was new to them. The main point they had missed was looking at the current as the interface signal between the summing block and the integrator. The key equation is then VA 5
1 t 1 1 1 VEE 1 Vin bdt. 3 a VB 1 C1 0 R1 R2 R3
Written in this form, the equation is not only a formal equation but also a description conveying useful information about the circuit behavior. Finally, the lecture pointed out that the description of a circuit has to be driven by its overall structure in a top-down way. Starting from the overall function, specifications are then derived for the internal blocks, going into more and more detail until all the design decisions can be justified. After the painful experience of writing the intermediate report, many students readily understood this point. In the final report, group G rewrote the paragraph quoted above as follows: When the input signal is null, the mean value of the PWM signal must be null too. The integrator is intended to obtain a mean error voltage from an error current. … The basis of their explanation was now correct: the mean value of the PWM signal has to be equal to the input signal value, and the integrator input current must FIRST QUARTER 2009
R1
Vin Signal
VEE
R12
VCC
R2
Op Amp
R3
C1 A
B Comparator
Integrator
Hysteresis Trigger
Summing Block
+ −
R11
+ −
R20
values of C. The correct answer, stemming from a clear understanding of the circuit operation, is that the high and low thresholds of the hysteresis trigger set the triangle amplitude, not C. In this case at least, the magic trick of applying meaningless formulae does not work. The intermediate reports are apparently a mess, but … people walking in darkness are in a good position to see a great light as soon as it appears. Making mistakes is an integral part of the learning process. For that reason, there was no formal evaluation of the intermediate report.
PWM
Figure 7. After project completion: Structured view of the oD modulator schematic.
be interpreted as an error signal. They produced a diagram showing the frequency of the PWM signal as a function of the input signal amplitude. In their final report, the tutor wrote: “Sound reasoning”. What is expected is that students get the opportunity to experience the power of an abstract model as a tool in a top-down design trajectory. They should at least realize that such a model may be of great help when trying to structure the description of the circuit shown in Figure 3. They learn that Spice can simulate a modulator described at the level of analog block models (ABM, available in the Cadence OrCad demo version), even in the Laplace domain; they also learn that the idea is to assess the concept of the system before going into the details of the circuit schematic. This was the missing step in their first approach. During the demonstration, all 14 groups were able to demonstrate at least one working Class D amplifier playing a 440 Hz A note from a signal generator. A few groups took the amplifier input signal from their own MP3 player. Thanks to them, this highly appreciated project ended with the sound of music! 4. Examination and Survey Evaluation of Students’ Performances The criteria applied to the groups’ productions require the ability to write a clearly structured top-down description of the amplifier, and a good correspondence between theoretical, simulation, and experimental results. The criteria applied to the individual evaluation can be inferred from the following question from the written examination: The system given by Figure 8 produces an output signal yout from an input signal xin . The function of the blocks are described by the following equations: ysum 5 a sum xin 1 yout t
yint 5 kint3 ysum dt 0
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yout
xin
ysum
yint
∫ Summing Block
Integrator 1/s
Hysteresis Trigger
Figure 8. Examination question.
yout can take 2 values : 210, or 110, and the threshold of the trigger is (a yout ); asum , kint, and a , 0.2 are constants. What is the function of the system ? Show that the frequency of yout is f= kint/4a when xin 5 0. The criteria are in line with the project’s objectives. The marking shows that notable objectives were well met. It has often been suggested that this project was far too difficult for second year students. This turned out not to be true. People do not all learn in the same way. Some are intuitive, others are cerebral; some are self-confident, others are worried, etc. We used a variety of teaching methods: controlled, supervised and autonomous. This could explain why many students obtained good marks. During this term, most of the students made significant progress in mastering circuits. As well as the competences which were formally evaluated, the project aimed to develop transverse competences, among which was the ability to work efficiently in a team. The students who used the team primarily for sharing tasks missed the real power of teamwork. A group is a natural place for debate, which is especially helpful in problem solving. It fosters the development of communication skills. Even the best students benefit from the challenging effect of debate on a misconception. In this project, a group of six students worked at two lab benches on two different breadboards, and, simultaneously, on the simulator. Because the tasks were not easy, and because they were closely related, the groups were almost forced into debating their problems and solutions. Survey A survey was conducted among the students a few weeks after they had started the third year of the course. The results of this survey are in some way a conclusion to this paper written by the students themselves. The reasonably high participation rate (45 responses from the 84 students involved in the project) is an indicator of their interest. The questionnaire contained, in a random 72
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order, 32 statements which the students were asked to rate on a Likert scale, from 22 (I strongly disagree) to 12 (I strongly agree). Table 4 summarizes the most important results of the survey. The questions have been sorted into 5 topics related to the objectives of the project, and the histograms show the answers to all the items relating to each of the first four topics, along with the average scores on some of these items. Taking all the answers into account, the average agreement level for the objectives of the project is 0.9. The last topic, covering organizational issues, is not reported here. It is quite difficult to assess the effects of such a learning activity, especially in the long term. This was the task of the Impact Group at the beginning of the EPL curriculum change. There is however an extensive literature on this topic. For instance Gijbels et al. [6] reviewed 43 articles to assess the main effects of problem-based learning on three levels of the knowledge: (1) the understanding of concepts; (2) the understanding of the principles that link concepts together; and (3) the linking of concepts and principles to conditions and procedures for applications. They found that students in problem-based learning programs acquired slightly less knowledge than students in lecture-based programs, but they remembered more of this knowledge. There was a positive effect on their ability to understand the principles that link concepts, and their paths towards expertise were accelerated. The students that answered the survey about the Class D amplifier project were not aware of this study. Their spontaneous answers were, however, consistent with the effects reported by Gijbels et al. 5. Conclusion Unusual demands came along with the Candis 2000 project. Many opponents argued that it was not sustainable in the long term in its original form. Its basic requirements were however not questioned: teaching with a research spirit, favoring questioning and selfquestioning over established course material, exercises, and solutions; and seeking to develop long-term skills and knowledge instead of simply trying to pass the next exam. A major contribution of Candis 2000 was to show that large-scale curriculum reform was possible. The Class D amplifier project described in this paper, and more generally the context in which it is embedded, are an example of a learning environment designed according to the same principles. Although they mix different learning styles, they are characterized by a large element of active learning. In this context, the students have shown that the journey from a lamp and FIRST QUARTER 2009
Table 4. Results of the survey conducted in Year Three. Team working (11.2) • It has been quite useful to explain what I had understood to other group members so as to get a clear understanding of the theoretical concepts myself (1.4). • Team working is not wasting time; the training is more efficient than when working alone (1.4). • Other group members often helped me in understanding the behavior of a Class D amplifier (1.0). • I think I’ve put a lot of myself into this project (1.0). Learning issues (11.0) • I developed better engineering skills (1.2). • What I learned during the project will outlast what I learned during lectures (1.0). • The project has been an opportunity to use previous knowledge in order to gain new knowledge (0.9). • The students had to discover and to learn a lot by themselves thanks to this project (0.8). Better view of circuits and systems (10.9) • I think I know how and why a sine wave can be recovered from a PWM signal (1.1). • This project makes me want to learn more about and design electronic circuits (1.1). • This project makes me want to learn more about and design signal processing applications (0.9). • Although there is still a lot to be learned, I have grasped that describing and simulating a circuit at a functional block level, possibly in the Laplace domain, is a good and efficient method (0.8). Support to courses (10.8) • The project has provided good support for tackling the electronic circuits course next year (1.0). • The project has provided good support for tackling the signals and systems courses next year. (0.8).
Best of free comments • A project is an opportunity to understand the way other people look at the theory and the way they apply theory to analysis or design situations. This results in an in-depth understanding. It is an opportunity to develop problem solving skills. • A project is an experience in team working, including conflict resolution. • It has been a very rewarding project. I feel such a project is a must in an Engineering curriculum. I caught sight of the profession. • Thank you for this nicely packaged project!
battery circuit to an analog PWM modulator can be accomplished within a two-year period, while meeting demanding learning objectives. Acknowledgment The authors are indebted to the members of the teaching staff (François Baudart, Olivier Bulteel, Thierry Daras, Jonathan Denies, Julien Devos, Thibaut Labbé, Christophe Mouvet, and Christophe Vloebergh) for their enthusiastic contribution. We also wish to thank the students, although the list of their names is too long to be included here. By taking part in the project, they actively helped to shape its final form. Charles Trullemans received his master degree (1969) and his Ph.D. (1974) in electrical engineering from the Université catholique de Louvain, Belgium. He joined then ITT Bell Telephone, Antwerpen, as a research engineer. From 1980, he has worked at the Microelectronics Laboratory of the Louvain School of Engineering as an assistant professor and then as a full professor. His reFIRST QUARTER 2009
search interest evolved from device physics to ASIC design and eventually to implanted active prostheses. He is a cofounder of NeuroTECH S.A. (Louvain-la-Neuve) that is developing products for the stimulation and monitoring of the nervous system. Charles Trullemans has been Head of the Microelectronics laboratory from 1990 to 1995, Dean of engineering from 1995 to 2000, and Chairman of the EPL undergraduate curriculum commission during the realization phase of the “Candis 2000” project, from 2000 to 2004. Laurent De Vroey was born in Brussels, Belgium, in 1979. He graduated in Electromechanics Engineering in 2002 and received the PhD in Engineering Science in 2008 from both the Université catholique de Louvain, Belgium, and the Ecole Normale Supérieure of Cachan, France. Since July 2008, he works for the Belgian competence center Laborelec as Specialist Sustainable Process & Energy Audits, after six years as Research Assistant at the Université catholique de Louvain. IEEE CIRCUITS AND SYSTEMS MAGAZINE
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Stanislas Sobieski received the electrical engineering degree from the Université catholique de Louvain, Louvain-la-Neuve, Belgium, in 2006 and is currently working at the microwave laboratory, at the Université catholique de Louvain. His research interest is in the design and analysis of magnetic sensors, the thermal effect on microsystems and the optical characterization of MEMS. Francis Labrique was born in Maurage (Belgium) in 1946. He received the degrees “Ingénieur civil électricien” (1970) and “Docteur en Sciences appliquées” (1983) from the Université catholique de Louvain (UCL). From 1970, he has been with the Laboratory of Electrotechnics and Instrumentation of the Louvain School of Engineering of the same university successively as Assistant, Lecturer and Professor. From 1987 to 1993, he has been head of the laboratory. He has also been invited professor at the Technical University of Lisbon from 1985 to 1990. His research activities are in
the pole of power electronics and design of high performance electromechanical actuators. F. Labrique is co-author of several books on power electronics (in english, in french, and in portuguese) and author or coauthor of more than 150 journal or conference papers. F. Labrique is Doctor Honoris Causa of the University of Craiova (Romania). References [1] B. Raucent, “What kind of project in the basic year of an engineering curriculum,” J. Eng. Des., vol. 15, pp. 107−121, 2004. [2] F. Dochy, M. Segers, P. Van den Bossche, and D. Gijbels, “Effects of problem-based learning: A meta-analysis,” Learn. Instruct., vol. 13, pp. 533−568, 2003. [3] M. Frenay, B. Galand, E. Milgrom, and B. Raucent, “Project- and problem-based learning in the first two years of the engineering curriculum at the University of Louvain,” in Management of Change: Implementation of Problem-Based and Project-Based Learning in Engineering, E. de Graaff and A. Kolmos, Eds. Rotterdam: Sense Publishers, 2007, pp. 93−10. [4] G. B. Thomas, R. L. Finney, M. D. Weir, and F. G. R. Giordano, Thomas Calculus, 10th ed. Reading, MA: Addison Wesley, 2001, p. 445. [5] D. H. Dolmans, W. De Grave, I. H. Wolfhagen, and C. P. Van Der Vleuten, “Problem-based learning: Future challenges for educational practice and research,” Med Educ., vol. 39, pp. 732–741, 2005. [6] D. Gijbels, F. Dochy, P. Van den Bossche, and M. Segers, “Effects of problem-based learning: A meta-analysis from the angle of assessment,” Rev. Educ. Res., vol. 75, no. 1, pp. 27–61, 2005.
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