ieee circuits and systems society · 2008-05-14 · 1. preview activity at iscas 08 panel session...
TRANSCRIPT
IEEE Circuits and Systems Society
Workshop Future directions in Circuits and Systems education
Views, Experience, and Prospects for Education in Circuits and Systems
Seattle May 22, 2008
Organizer Joos Vandewalle, CAS VP Technical ActivitiesElectrical Engineering Department (ESAT)Katholieke Universiteit LeuvenKasteelpark Arenberg 10, PB 2446B-3001 Leuven-Heverlee, Belgiumemail : [email protected]
Table of content1. Preview activity at ISCAS 08 : panel discussion on CAS education2. Workshop schedule3. Motivation4. Outline5. Expected outcomes6. List of speakers and participants7. Papers
http://www.esat.kuleuven.be/sista/CASeducationworkshop2008/
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1. Preview activity at ISCAS 08 panel session on CAS education
May 21, 200817h45-18h45 Panel session on CAS education at ISCAS
Josef Nossek (Technical University of Munich, merger of circuits and systems and design, Region 8 experiences)Paulo Diniz (Universidade Federal do Rio de Janeiro, Latin American experiences)Yong Lian (National University of Singapore, experience in Region 10)Tuna Tarim (Texas Instruments, views of the industry)Mark Yoder (Rose-Hulman Institute of Technology, experience with DSP first)Randy Geiger (Iowa State University, views on design and undergraduate and graduate teaching)
2. Workshop schedule
Thursday May 22, 2008 (day after ISCAS)Room : Willow in ISCAS Sheraton hotel, Seattle
08:30-08:50 Welcome and workshop objectives and outcomesJoos Vandewalle ( Belgium)
08:50-09:30 Viewpoints of industry and of GOLD graduates of the last decadet CAS education : an industry perspective : Tuna Tarim (US) t Viewpoint of Gold – Region 9 : Martin Di Federico (Argentina)t Viewpoint of Gold – Region 10 : Pui-In (Elvis) Mak
09:30-12:00 Experiences with various educational approaches (25 minute presentations)t Turning students on to circuits : Yannis Tsividis (US) t From KCL to class D amplifier : Charles Trullemans (Belgium)t Can we make signals and systems intelligible, interesting, and relevant?: Babak
Ayazifar (UC Berkeley)t Teaching Circuit courses to engineering students: Two decades of ongoing debate
Ljiljana Trajkovic (Simon Fraser University, Vancouver) t DSP from Theory to Tool during the Past Three Decades: Impacts on DSP education
Tapio Saramäki (Tampere University of Technology, Finland) 13:00-14:30 Important issues in CAS education (3 minute presentations)
t Learning is understanding : Raija Lehto (Finland) t Balance between theory and practical experimentation : Robert Rieger (Taiwan) t Vision on an integrated engineering learning environment : Tom Robins (US)t The need for a new pedagogical approach to system modeling and analysis : Soumitro
Banerjee (India,)t Importance of teaching multidimensional Circuits and Systems : Arjuna Madanayake
(Canada) e The pivotal role of design in CAS : Eduard Alarcon (Spain) t Microelectronics Laboratory : Anas A. Harmoui (McGill University)
14:30-16:30 Open brainstorming on specific actions and educational plans and conclusions
3. Motivation
Many questions and open issues are related to the education in CAS : t The role of CAS education has drastically changed with internet, computers, and globalization. New
challenges of environmental issues, energy shortages, globalization offer new opportunities for CAS education
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� Is the link between research and teaching in CAS still important ?t Balance between theory, design, simulation, practice and experimentation. Is the experimentation in
hardware still valuable or is software sufficient ? What is the role of simulation tools like SPICE and MATLAB ?
t Should systems and circuits be taught together or in sequence ? Discrete time systems followed by continuous time systems or vice versa ?
t Can you find good textbooks, reference material (e.g. The circuits and filters handbook by W.-K. Chen) or is there a need for new ones or updates or other ways to bring together knowledge like Wiki's?
t Also several misconceptions circulate about CAS educationt CAS is mature, basic and generic for EEs, so CAS can be taught by any EE professort There is no need to introduce circuits or mathematics of circuits and systems (linear algebra,
differential equations, Laplace, Fourier, z-transforms)t There is no need to study CAS concepts like KVL, KCL, MNA, transfer functions, impedances, Bode
diagrams.. but learn directly to simulate in SPICEt Industry is not interested in concepts and methods of CAS but in electronic products
4. Outline
Main topics, among other:t The core content: what are essential ingredients of CAS education [ e.g. KVL KCL, Thevenin, Norton,
Tellegen, energy, passivity, graph theory, analysis, filter design, impedances, hybrid parameters, ..]t Methodology, dependencies [in 1984 Mac Van Valkenburg wrote:”No common agreement on what
should be taught in a course on circuits” in “Teaching Circuit Theory”, IEEE TCAS, Jan 1984]t Impact of new technologiest Impact of globalization and less developed countriest Impact on educational reforms
5. Expected outcomes
l Conceptual convergence on common approach for CAS educationt Joint report/paper for the CAS Magazine on the education in CAS with intended audience educators in
EEt Actions for making CAS more attractive to students like useful role modelst Common targets benchmarks for courses common experimentation, global competitions, virtual
experimentst Web based learning planst Plans for setting up reference material and wiki materialt CAS concepts, insights, expertise, skills and competences needed by every EE and link with the
criteria for accreditationt Need for more permanent reflection and action on CAS education ?t Ideas for setting up a new Technical Committee on CAS education ?t Links with other IEEE education initiatives and structurest Action towards accreditation bodies like ABET
6. List of speakers and participants
Hoda S. Abdel-Aty-Zohdy,Department of Electrical and Computer EngineeringOakland UniversityRochester MI, 48309-4401
E-mail: [email protected]
Eduard AlarconUniversitat Politècnica de CatalunyaCampus Nord. Modul C-4
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Jordi Girona 1-308034 Barcelona, SpainTel. +34/93/401.56.78Fax. +34/93/401.67.56Email : [email protected]
David J. AllstotUniversity of WashingtonDept. of Electrical EngineeringBox 352500Seattle, WA 98195-2500USATel: +1 206 221 5764Email: [email protected]
Babak AyazifarUC BerkeleyElectrical Engineering and Computer Sciences493 Cory HallUSATel. +1/510/642.99.45Email : [email protected]
Soumitro BanerjeeDepartment of Electrical EngineeringIndian Institute of TechnologyB-173, IIT Campus721302 Kharagpur, IndiaTel. +91/3222/283.030Email : [email protected]
Malgorzata Chrzanowska-JeskePortland State UniversityElectrical and Computer EngineeringUSATel. +1/503/725.5415Email : [email protected]
Martin Di FedericoArgentinaEmail : [email protected]
Pui-In (Elvis) MakUniversity of MacauFaculty of Science and TechnologyAv. Padre Tomas Pereira, TaipaMacau, ChinaTel. 86/853/8397.8796Fax. 86/853/8397.8797Email : [email protected]
Randy GeigerIowa State UniversityDept. Electrical and Computer EngineeringAmes, Iowa 50011USA
Tel. +1/515/294.77.45Fax. +1/515/294.11.52Email : [email protected]
Anas A. HarmouiDept. of Electrical & Computer Engineering McGill University 3480 University Street Montreal, Quebec, Canada H3A 2A7 Tel: 514-398-5466 Fax: 514-398-4470 E-mail: [email protected] http://www.ece.mcgill.ca/~hamoui
Yih-Fang HuangUniversity of Notre DameDept. Electrical EngineeringNotre Dame IN 46556, USATel. +1/574/631.5480Fax. +1/574/631.4393Email : [email protected]
Valencia JoynerTufts UniversityAdvanced Integrated Circuits and Systems Lab.Electrical & Computer Engineering161 College AvenueMedford MA 02155, USATel. +1/617/627.2291Fax. +1/617/627.3220Email : [email protected]
Izzet KaleDirector, Applied DSP & VLSI Research GroupIEEE UKRI CAS Chapter ChairUniversity of WestministerDept. Electronic Systems115 New Cavendish StreetLondon W1W 6UW, UKTel. +44 20 7911 5157Fax. +44 20 7911 5089Email : [email protected];
Raija LehtoDepartment of Signal ProcessingTampere University of TechnologyTampere, FinlandTel. +358/3/3115.3849Fax. +358/3/3115.3857Email: [email protected]
Yong LianNational Univeristy of SingaporeDept. Electrical and Computer Engineering4 Engineering Drive 3Singapore 117576, Republic of Singapore
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Tel. +65/65/16.29.93Fax. +65/67/79.11.03Email : [email protected]
Arjuna MadanayakeMultidimensional Signal Processing Group,Electrical and Computer Engineering, University of Calgary, Canada. Email: [email protected]
Josef NossekTechnical University of MunichLehrstuhl für Netzwerktheorie und SingalverarbeitungArcisstrasse 2180290 Munchen, GermanyTel. +49/89/289.28502Fax. +49/89/289.28504Email [email protected]
Shanthi PavanIndian Institute of TechnologyDept. Electrical EngineeringMadras, India 600 036IndiaTel. +91/44/225.74.437Fax. +91/44/225.74402Email : [email protected]
Robert RiegerNational Sun Yat-sen UniversityDept. Electrical Engineerng, Taiwan ROCEmail : [email protected]
Tom RobbinsNational Technology and Science PressPO Box 13Allendale NJ, 07401, USAEmail : [email protected]
Tapio SaramäkiTampere University of TechnologyFac. Computing and Electrical EngineeringInstitute of Signal ProcessingKorkeakoulnakatu 133720 Tampere, FinlandFax. +358/3/3115.4989Email : [email protected]
Tuna B. TarimTexas Instruments, Inc.12500 TI Boulevard, MS 8729Dallas, TX 75243, USATel: +1 214 480 3384Fax: +1 214 480 7014Email: [email protected]
Ljiljana TrajkovicSimon Fraser University, VancouverSchool of Engineering Science8888 University DriveBurnaby, B.C. V5A 1S6CANADATel: +1 778 782 3998Email: [email protected]
Charles TrullemansDICE, Université Catholoque de LouvainLouvain School of Engineering, Place de l’Université 11348 Louvain-la-Neuve, BelgiumTel. +32/10/47.25.67Fac. +32/10/47.25.98Email : [email protected]
Yannis TsividisDepartment of Electrical EngineeringColumbia University1022 CEPSR, mail code 4712New York, NY, USATel. +1/212/854.4229Fax. +1/212/932.9421Email : [email protected]
Joos VandewalleK.U.Leuven, ESAT/SCD (SISTA)Kasteelpark Arenberg 10, PO 24463001 Leuven, BelgiumTel. +32 16 32 10 52Fax. +32 16 32 19 70 Email : [email protected]
Zushu Yan Beijing Microelectronics Technology InstituteChinaEmail : [email protected]
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Papers
CAS education: An industry perspective
Tuna B. TarimTexas Instruments, Inc.
In the old days, when hiring an electrical engineer into a company, the task of the engineer was clearly defined. The engineer would have a specific responsibility and would be interviewed for knowledge in that specific area: Design engineers would be responsible for designing circuits, test engineers would test the chip when it comes back from manufacturing, product engineers would be responsible for the product, EDA/methodology engineers would be responsible for defining methodologies and flows, system engineers responsible for designing the system, so on so forth. All of these jobs had its boundaries, and in most cases the engineer’s task would be done when they complete their specific task.
Things are quite different these days. Engineering is no longer sitting in a cubicle all day long, isolated from the rest of the team and working on our own specific tasks. Nowadays, it is ever more important to have broader knowledge in circuits and systems, test, characterization, EDA and methodology instead of focusing on a single topic. It is a must to be a team player and to have good communication skills.
Let’s go through these requirements one at a time:
How does all of this translate to circuits and systems education? It all boils down to the “basics”, “flexibility” and “broad knowledge”.
Companies look for engineers who can handle different tasks because the needs of projects constantly change. It is not reasonable to expect an engineer to know “everything”, but it’s reasonable to expect an engineer to know the basics of their discipline. As a personal experience; the best people that I’ve worked with are the ones who learned their basics well in school. It didn’t matter what task they were given, they performed very well because they knew what they had to do and even if they didn’t know too much about the topic at first they learned very quickly, because they knew how to learn. This is one of the main things CAS education should help with: An education should teach students how to think and how to learn, and it should start with teaching the basics. Students should not have to go through graduate school to learn these; undergraduate students should have the perfect opportunity to learn the basics, and learn them well too. To give an example from my own experience, I have interviewed many electrical engineering students who knew that they need to run transient simulations on their circuits and they certainly knew how to run it, but they didn’t know why they were supposed to run it. One of my favorite examples comes from my sister (who is a professor in academia): While a Ph.D. committee was conducting oral exams to recent M.Sc. graduates to determine who will be accepted to the Ph.D. program, one of the students who wrote a M.Sc. thesis on MESFETS couldn’t answer the question “what MESFET stand for?” Till date I have found this to be a very interesting example which shows the difference between “learning the basics” and “learning enough to graduate”.
Now connecting this to flexibility and broad knowledge; you will notice that as we get better in learning the basics, our capability and willingness to be flexible increases because we see learning new topics as challenging opportunities, and we welcome and enjoy the challenge and the opportunity.
The broad knowledge is something related to the basics and flexibility. Imagine we have one opening to hire a design engineer, and there are two design engineers who practically have the same knowledge on the same topics that we’re trying to hire for. They both have the same degree, they’ve both worked on the same type of circuit design, they have the same experience level, and they are both good communicators. What would be the next distinguishing factor? It will be how broad of a knowledge they have on different topics other than design: Spice modeling, manufacturing, device physics, layout, automation, and others. It’s still true that being a good engineer is the starting point to be hired to a job; it’s just that the definition of “good engineer” has changed over the years.
Being flexible and learning new topics makes us well rounded engineers with broad knowledge, and gives us the
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opportunity to understand different aspects to a project. Even now, there are engineers working in companies who think that their job is done as soon as they complete the design of their circuit, and they also only know the specifications of their own circuit and not the system. Clearly, these engineers need to change their mode of operation and adapt to industry’s changing environment.
Over the years, project cycle times have gone from years to months. In addition to this, most companies now have project teams in various countries all over the world and projects are becoming multi-site. The complexity of products has not decreased at the same rate as project cycle times; on the contrary, products are becoming even more complicated, such that every person in the project team needs to understand the different tasks and even perform those tasks when necessary: The design engineer needs to work with the test engineer, the characterization engineer, the system engineer every step of the way, the validation engineer needs to work with the design and test engineer every step of the way, etc. Engineers hear about the importance of “teamwork”. This is not just a cliché; teamwork really is the key for successful products. As project cycle times get shorter and shorter and project teams become more and more multi-site, all team members need to be aligned with regards to the end goal and the project timeline so they can all work in synchronization and complete their tasks on time. Meeting the project timelines depends on the clear communication between multi-site teams and the common understanding of the goals. This is one place where good communication skills play an important role. That is why when hiring managers write the job description, they include a statement similar to “must be able to work in a team environment”. A lot of projects have failed to finish on time, not because the project team was lacking any technical knowledge, but because they simply did not know how to communicate within the project team.
CAS education should not be only about educating students on technical topics. It’s important that our education is aligned with the real world needs (industry and academia) and that the CAS curriculum be up-to-date to prepare the students to their jobs after school.
Most schools in the US offer a reasonable graduate engineering education, however, the undergraduate engineering education is generally too generic, it offers too much flexibility to students in terms of what classes to choose, and doesn’t always require a graduation thesis. Today when the US is debating whether to make a M.Sc. degree the minimum degree in engineering, it should be considered to first try to improve the undergraduate education in its four year format. The fact is, many countries have well established and successful four years of undergraduate engineering education and the US can learn from those countries.
The curriculum of engineering needs to be constantly updated with new classes in new research topics. Academia plays a key role in educating tomorrow’s young minds, successful engineers, and successful engineering managers, and it is therefore very important that academia always stays up-to-date with the required education to meet industry’s needs to design products. Academia and industry need to work together to establish a well defined CAS education. Without academia industry would not have the resources to research new topics that will soon become products, and without industry academia would have no reason to do any research. We are in this together and we need to work together to define a CAS education that meets the needs of both.
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Viewpoint of GOLD – Region 9
Martin Di Federico, GOLD Representative of Region 9, CASS
One of the most important parts of the education on CAS are the Labs. I am a strong believer of an ACTIVE education (passive is a like a master speech, and active is the student doing things.) Lab practices in engineering are one of the best strategies of significant learning. The more the student does, the more he learns.
There are two kinds of labs, the Verification (the student learns something in theory and ensembles a circuit to probe it) and the Design (they learn how does it function and they have to design ensemble and test their own designs)
Its important also the role played by the teaching Assistant (TA).He/she has to: Pay attention to the motivation of the students; Try to imply the students in their own learning process; Orient them toward the prior discussion of the basic concepts; To make aware of the magnitude of the work they are doing; To favor the positive interaction for group work so that group decisions without the constant intervention of
the professor; Visit to each commission carrying out you random questions (to increase its analysis capacity of continuous
improvement, as well as its critical attitude of constructive form); They have to feed-back the student in his own learning process, in order to learn of the experience and to
improve the learning process; Permit the student to frame clearly its work inside the resources and the possibilities of the development of the
practice, to level of idea and of its own capacities, as for effort, commitment and dedication, necessary to increase its autonomy;
It is necessary to stand out that to obtain the better achievements of this strategy is important to make aware the
student on the importance of theory learning, for achieve the synergy and the necessary, positive internal motivation.
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Viewpoint of GOLD – Region 10
Pui-In Mak GOLD Representative of Region 10, CASS
Undergraduate CAS EducationIt has been a long tradition that circuit theory class looks like a “graphical” mathematics class for students.
Students are not easy to find the link to the practice. Experiments are therefore very important and should not be simply replaced by simulations. Students should have the chance to feel the size and shape of different kinds of electronics components. Students also interest in using equipments, all those are fresh to them. However, SPICE in circuit theory class is also very useful, especially for pre-laboratory. For electronics class, SPICE is both useful for learning and experiments.
For textbooks, I prefer those that contain “learning plan for student” and “teaching plan for instructors” before the text. It not only gives the students an overview of the course, but also the instructors a reference in preparing their teaching materials.
“Writing the board” is still very effective in CAS education, in particular the circuit analysis. Students should follow the instructor, step by step, to get familiar with the problem-solving-procedures. On the other hand, PowerPoint is time efficient to show the figures and highlight the key points.
Impact of new technologies and Educational ReformsI trust that cross-discipline education will be very important for CAS education. Nano, biomedical and organic
electronics are some examples. I strongly believe that CAS is not a generic EE course that can be taught by any EE professor. For instance, biomedical CAS should be taught by EE professors with background knowledge of biomedical science. All biomedical-related courses should be well-distributed in each academic year, synchronizing with the electronics courses.
Industrial HelpFor new emerging technologies, the information from company is important to guide the students in course or
major selection. Special class or workshop given by industrial experts is a way, and is believed to be more and more important. Speakers can highlight what combinations of knowledge and skill can best-fit their job, and what is the study roadmap of their employees. All of them can give inspiration to the teaching of professors and learning of students.
Impact of Globalization and Less Developed CountriesLess-developed countries usually lack of latest information about the industrial trends and technologies. Offering
international courses is a way to alleviate this, but should be localized to reduce the traveling cost such that students and professors from less-developed countries can afford. Another way is to make the materials of international courses and conferences to a video that can be shipped with low cost or downloded through the internet.
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Turning Students On to Circuits
Yannis TsividisDepartment of Electrical EngineeringColumbia University New York, NY
From the January 2008 Issue Printed from: http://www.ieee.org/portal/pages/sscs/08Winter/Tsividis.html
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Can We Make Signals and Systems Intelligible, Interesting, and Relevant?
Babak AyazifarUC Berkeley, Department of EECS
The way we teach signals and systems often leaves our undergraduates bored, bewildered, or battered. "We need more practice problems." "This stuff is too abstract!" "Why do I need to learn about op-amps before I even know what `frequency response' is? Shouldn't it be the other way around?" "Somebody, please rescue me from this torturous algebraic grunt work!" "If the professor thinks that we can finish this [lab or exam] in three hours, he must be on crack!" "All right, I can identify a memoryless system from a mile away. So what?" "Where in the world can I apply what you're trying to teach me?" The litany of their grievances is virtually endless, and substantially legitimate.
Most of our lectures and textbooks are short on interesting, relevant, and mind-bending examples. Instead, they're saturated with theoretical minutiae, mathematical pedantries, or rote exercises whose solutions are better suited for a recipe book. Is it that essential to harp on Dirichlet's conditions for the convergence of Fourier series, on a first pass? Perhaps we should broach Fourier series in a context where convergence is ensured-discrete-time periodic signals. More on this point later.
A typical undergraduate curriculum imposes unnecessary prerequisites for the introductory signals and systems course (traditionally in the form of an electronic circuits course). The problem sets we assign drown our students in intractable mathematical manipulations that clutter the main concepts and interfere with learning. The exams we devise are plagued with formulaic problems that interrogate our students for cookbook solutions based on literal recall, rather than stimulate their creativity, gauge the depth of their understanding, or stretch them to the brink of their knowledge. Typically, our focus on applications is narrow and of questionable relevance to the modern, interdisciplinary world. Alas, we often fail to motivate what we teach and this, perhaps, is our greatest failing. Sometimes, I wonder if we even know what we want our students to learn, much less how to teach it to them. When I was an undergraduate, this is how we used to describe our state of affairs: "The problem sets, lectures, and exams form a set of mutually orthogonal basis vectors." In retrospect, we should have added discussion sections, labs, and the textbook to the basis of our lamentations. Since the 1980s, not much has really changed, in terms of how we deliver at the blackboard or on the page of the textbook.
Why is it that the way we teach alienates many of our students? And how do we fix it? I don't think there's a universal formula, an infexible rule, a panacea. But here's a sampling of what I've learnt so far--my report from the trenches, so to speak, tinseled in parts with my vision of the future.
Abstraction from Experience Suppose we want to teach our students to think of signals as vectors. They're already comfortable with the algebraic properties of a space of signals, so they know how to scale and add signals pointwise. But we want to convince them that a signal space can have geometry as well--with all the attractive notions of projection, angle, and magnitude.
Do we begin by listing the axioms of a vector space, and move from there to the properties of a well-defined inner product? I once did this, and I lived to regret it. As I wrote the fifth axiom on the board, I could swear I heard someone snore. My students had tuned out. Some of them had simply dozed off. The classroom's pulse would have caused an EKG monitor to scream, prompting an ICU physician to call the "time of death."
What a terrible way to go: death by axiom overdose!
I've since learnt to begin with a discrete-time signal having a period of two (three, if I feel particularly brave that day). I show how the signal values in one period can be stacked into a two-dimensional Euclidean vector. That vector can be decomposed into a linear combination of the canonical vectors
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Students have no trouble seeing that the coeffcients of this linear combination are x(0) and x(1), the signal values in the period of interest. We've essentially decomposed the signal in terms of shifted Kronecker impulses: x(n) = x(0)t (n) + x(1) t (n - 1) for n = 0,1. Drawing the canonical vectors t 0 and t 1 and the signal vector x on a two-dimensional Euclidean plane drives the point home. Nothing new so far. There are textbooks that discuss this method of decomposing discrete-time signals into a linear combination of canonical vectors (shifted impulses). But I haven't seen it done in the chapter on Fourier series!
Ah! We can also decompose the signal vector x (over one period) into a linear combination of another pair of orthogonal basis vectors (actually, let's not use the word "basis" . . . some students may faint). These vectors are constructed from harmonically-related complex exponentials t 0(n) = exp (i0t 0n) and t 1 (n) = exp (i1t 0n), where t 0= 2t /2 = t is the fundamental frequency of the periodic signal. Our goal is to find the coefficients X0 and X1 in the following decomposition:
I ask the students to draw the new vectors t 0 and t 1 on a two-dimensional Euclidean plane, and verify that they're merely rotated and scaled versions of the canonical vectors t 0 and t 1. This rotation is the crux of Fourier series analysis--best illustrated in discrete time.
The remaining question is how to determine the coeffcients X0 and X1. This, of course, requires that we project x onto each of t 0 and t 1, which in turn requires that we have a well-defined inner product. If the new vectors t 0 and t 1 are orthogonal (which we show in class), then the coeffcients are simply
To project, we simply extend the notion of "dot product" (which the students know by heart) to the more enlightened concept of "inner product," which we define for potentially complex-valued vectors; if f and g are two vectors (signals), then we define their inner product as t f,gt =fTg*. This is where I imitate a stereotypically nasal nerd voice, raise my hand, and ask why we use the complex conjugate of the second signal g; why not leave it intact, like in a dot product of real vectors? To answer this, I ask the students to take the dot product of [1 i ]T with itself and see that it makes no sense. Complex conjugation makes the definition of inner product sensible. Fair enough.
We can consign the rigor of describing the properties of an inner-product space to an appendix or a guided problem on the homework. An introductory lecture is no place for this.
If you feel that going through this exercise in three dimensions will have greater curb appeal in class, I admire your courage and root for your success. There is a strong case for doing this analysis in three dimensions (i.e., for signals whose period is three), because the basis vectors t 0, t 1 and t 2 will not all be real-valued. But please bear in mind that you'll encounter difficulty drawing the vectors on the board, if you try this.
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What I've described is a process of building an abstraction based on the students' geometric experience from elementary Euclidean spaces, which they studied in high school.
The late mathematician Ralph Boas wrote a must-read essay that articulates this process with elegance [4]. His piece Can we make mathematics intelligible? cannot be overrated. It's by far the richest fountain of pedagogical advice that I've ever come across. In fact, it's the inspiration for the title of this document and much of what I have to say. Here's my favorite passage:
Suppose you want to teach the "cat" concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractile claws, a distinctive sonic output, etc.? I'll bet not. You probably show the kid a lot of different cats, saying "kitty" each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience. They should come one at a time; too many at once overload the circuits.
Notice how the paragraph is an ingenious example of its own wisdom! It's regrettable that we often blunt our teaching by doing precisely the opposite of what Boas suggests.
Textbooks Every year, I get up to half a dozen books on signals and systems from publishers eager to promote their latest crown jewels. Almost every copy makes me wonder why the author even bothered to write a book that's hardly more than a cosmetic permutation of examples from yesteryear. The book I grew up on as an undergraduate over two decades ago [16] trumps many of the "new" books on the market.
Most of our textbooks (and lectures) are designed to tell all in one go, as if by religious decree. Let's ask a simple question. Must we discuss mathematical pathologies that defy pointwise convergence of something or another to some other thing or another? Must we invoke Fubini's Theorem every time we reverse the order of two integrals?
In jest, I often say to my students, "The education that we provide you is a process of progressively diminishing lies." To say it with a positive spin, "We educate you based on a process of successive refinement." In short, we don't tell all.
Is it possible (or even wise) to split the discussion of, say, Fourier series, so that elementary concepts are conveyed in an earlier chapter, and the mathematical nuances in a subsequent one, which might be taught even a semester later when our students have greater mathematical maturity and a refined intuition for the basic concepts? Can we do this for all salient concepts in our introductory courses? I don't know the best answers to these questions. But it's no wonder that most books have long chapters well beyond the attention span of our students.
There are exceptions though. Two groups of authors have taken fundamentally novel pedagogical approaches that deserve special mention. McClellan et al. [12, 13] advanced the idea that a course in signal processing, with an emphasis on linear systems, ought to be the first introduction to electrical engineering. Lee and Varaiya [8] concurred that an introductory signals and systems course must stand on its own, largely decoupled from analog circuits. They took the idea a step further by including nonlinearities, such as those inherent to finite-state machines and hybrid systems.
At the time of this writing, I have not seen the second editions of the books by Jim McClellan and his team. At Berkeley, I'm working with my colleagues Edward Lee and Pravin Varaiya on a sequel to their original textbook. One of our main goals is to bring an interdisciplinary flavor to the new version, which we expect to be much revised.
Interdisciplinary Learning and Teaching It's been nearly seven years since Dimitris Anastassiou published his delightful article, Genomic Signal Processing [3]. As he explained:
Genomic information is digital in a very real sense; it is represented in the form of sequences of which each element can be one out of a finite number of entities. Such sequences, like DNA and proteins, have been mathematically represented by character strings, in which each character is a letter of an alphabet. In the case of DNA, the alphabet is size 4 and consists of the letters A, T, C and G; in the case of proteins, the size of the corresponding alphabet is 20 . . . if we properly map a character string into one or more numerical sequences, then digital signal processing (DSP)
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provides a set of novel and useful tools for solving highly relevant problems.
The landscape has been bustling with activity in the past several years, with researchers developing and applying signal processing techniques to unveil information about biomolecular sequences. But this has yet to percolate into our introductory textbooks in signals and systems.
In his extraordinary book, Evolutionary Dynamics: Exploring the Equations of Life [15], Harvard mathematical biologist Martin Nowak makes a statement that I believe we should heed:
The life sciences in general, and biology in particular, are on the brink of an unprecedented theoretical expansion. Every university is currently aiming to establish programs in mathematical biology and to offer its students an interdisciplinary education that spans fields as diverse as mathematics and molecular biology, linguistics and computer science. At the borders of such disciplines, progress occurs. Whenever the languages of two disciplines meet, two cultures interact, and something new happens.
Nowak further points out that
Evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Because of the tremendous advances over the last half century, evolution has become a discipline that is based on precise mathematical foundations. All ideas regarding evolutionary processes or mechanisms can, and should, be studied in the context of the mathematical equations of evolutionary dynamics . . . Wherever information reproduces, there is evolution . . . Mutation and selection make evolution. Mutation and selection can be described by exact mathematical equations. Therefore, evolution has become a mathematical theory.
Every chapter of Nowak's book is a gold mine of application areas that we're well-positioned to learn about and teach our students; examples are Evolutionary Graph Theory, HIV Infections, Evolution of Virulence, Evolutionary Dynamics of Cancer, Language Evolution, etc.
One of my all-time favorite books is Steven Strogatz's Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering [18] -- a respected textbook that translates seemingly complex, intractable systems from a broad array of disciplines into a vernacular that's accessible to a sophomore-level undergraduate. I have a personal affinity for this book for more than one reason. The book is a perfect example of how an author can be careful with mathematics without being pedantic knowing exactly where to tackle nuances and where to let go.
Although I didn't have Steve as my instructor for this particular topic (a cause of personal lamentation), I did have him in another applied mathematics course at MIT in the early 1990s. He's a superb educator, and his influence on my teaching has been profound.
One of my favorite examples from Steve Strogatz's book is the synchronized flashing of fireflies, which I talk about in our introductory signals and systems course almost every semester; the students love it, including a BBC video documentary (narrated by Sir David Attenborough) of fireflies flashing synchronously in the mangrove forests of southeast Asia.
The multidisciplinary nature, the mathematical depth, and the smooth flow of its coverage make Steve Strogatz's book a role model worthy of emulation.
I fear that unless we expand our teaching and textbook design efforts toward a multidisciplinary paradigm, we may come to be regarded as "wooden bridge" engineers in the coming years. I'm convinced that any natural or artificial dynamic system or evolutionary process is fair game for us to probe, tinker with, design, discuss, or otherwise tackle and teach. We need to stake a claim across a wide intellectual space, at the interfaces of multiple disciplines, not to dilute what we teach, but to exploit the common principles underlying the "equations of life."
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I've included several more references in the bibliography, which I hope will be useful. Let's make signals and systems education intelligible, interesting, and relevant by breaking down the artificial walls that separate what is traditionally considered "electrical engineering" from the physical and life sciences, the social sciences, and medicine, and by making an enlightened use of mathematics in our teaching and mentoring of our undergraduate students.
References
[1] Anant Agarwal and Je®rey H. Lang, Foundations of Analog and Digital Electronic Circuits, Morgan Kaufmann, San Francisco CA, 2005, ISBN 1-55860-735-8.
[2] Bruce Alberts, et al., Essential Cell Biology, second ed., Garland Science, New York NY, 2004, ISBN 0-8153-3480-X.
[3] Dimitris Anastassiou, Genomic Signal Processing, in the IEEE Signal Processing Magazine, Vol. 18, Iss. 4, July 2001, pp. 8{20.
[4] Ralph P. Boas, Can We Make Mathematics Intelligible?, in The American Mathematical Monthly, Vol. 88, No. 10, December 1981, pp. 727{731.
[5] Robert L. Devaney, Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics, Addison-Wesley, Menlo Park CA, 1990, ISBN 0-201-23288-X.
[6] Stephen P. Ellner and John Guckenheimer, Dynamic Models in Biology, Princeton University Press, Princeton NJ, 2006, ISBN 0-691-12589-9.
[7] Steven A. Frank, Dynamics of Cancer: Incidence, Inheritence, and Evolution, Princeton University Press, Princeton NJ, 2007, ISBN 0-691-13366-2.
[8] Edward A. Lee and Pravin Varaiya, Structure and Interpretation of Signals and Systems, Addison-Wesley, Menlo Park CA, 2003, ISBN 0-201-74551-8.
[9] Gareth Loy, Musimathics: The Mathematical Foundations of Music, Vol. 1, MIT Press, Cambridge MA, 2006, ISBN 0-262-12282-0.
[10] Gareth Loy, Musimathics: The Mathematical Foundations of Music, Vol. 2, MIT Press, Cambridge MA, 2007, ISBN 0-262-12285-5.
[11] Robert M. May, Simple Mathematical Models with Very Complicated Dynamics, in Nature, Vol. 261, June 10 1976, pp. 459{467.
[12] James H. McClellan et al., DSP First: A Multimedia Approach, Prentice-Hall, Upper Saddle River NJ, 1998, ISBN 0-13-243171-8.
[13] James H. McClellan et al., Signal Processing First, Prentice-Hall, Upper Saddle River NJ, 2003, ISBN 0-13-090999-8.
[14] Pratap Misra and Per Enge, Global Positioning System: Signals, Measurements, and Performance, second ed., Ganga-Jamuna Press, Lincoln MA, 2006, ISBN 0-9709544-1-7.
[15] Martin A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life, Belknap/Harvard, Cambridge MA, 2006, ISBN 0-674-02338-2.
[16] Alan V. Oppenheim et al., Signals and Systems, ¯rst ed., Prentice-Hall, Englewood Cliffs NJ, 1983, ISBN 0-13-809731-3.
[17] Arkady Pikovsky et al., Synchronization: A Universal Concept in Nonlinear Sciences, Cambridge Univ. Press, Cambridge UK, 2001, ISBN 0-521-53352-X.
[18] Steven H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Addison-Wesley, Reading MA, 1994, ISBN 0-201-54344-3.
[19] Jeanette A. Thomas et al. (eds.), Echolocation in bats and dolphins, The University of Chicago Press, Chicago IL, 2004, ISBN 0-226-79599-3.
[20] Arthur T. Winfree, The Geometry of Biological Time, second ed., Springer, New York NY, 2006, ISBN 0-387-98992-7.
[21] William K. Zinsser, On Writing Well, seventh ed., HarperCollins, New York NY, 2006, ISBN 0-06-089154-8.
15
From KCL to class D amplifier
Charles TrullemansFrancis Labrique, Louvain School of Engineering, Louvain-la-Neuve, Belgium
Significant changes have taken place since the end of the 90’s in the undergraduate (bachelor) program at the Louvain School of Engineering (EPL).The traditional program started with a hard core of basic mathematics, physics, chemistry and computer science followed by applied mathematics and physics oriented towards electrical engineering (Laplace transforms, Circuit theory, Electromagnetism, Device physics, etc.) On the supposedly sound basis of these grounds, students were eventually exposed to real electronic circuits. Projects included in the program were merely illustrations, a nice feature but only weakly coupled to the lectures.In the present bachelor program of the EPL, circuits and systems are introduced from the 1st term of the 1st year onwards. Physics and computer science lectures, and a project are organized in close relationship. The students actually 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 teaching of the corresponding theoretical concepts. In departure from most physics textbooks, lectures about electricity are oriented towards modeling basic elements (R, C, L). At the end of this term, students are able to simplify a circuit using equivalent dipoles, and to write and solve the differential equations of a simple first order dynamic circuit (e.g. the relay driver of fig.1).During the 2d term, another project involves the design, building (drawing PCB’s), and testing of a circuit containing an operational amplifier, and reactive elements (e.g. an anti-shoplifting system).During the second year, a Circuit theory course and a related project are run in parallel. During this 2007-2008 academic year, we are testing an ambitious project. The aim is to build a Class D amplifier according to an t � approach. The project is ambitious, because, at its starting up time, the background of the students is all but sufficient. The introduction to the project refers to websites of Bang & Olufsen (Ice Power) and NuForce. The students attend a demonstration of a prototype Class D Amplifier. They see moving waveforms on a scope screen while listening to the sound. They are interested, impressed, and mostly lost.The lectures proceed as follows: Static circuits (linear algebra), Operational Amplifiers, Phasors (complex numbers), Bode plots, Laplace transforms, Feedback and 4-poles.The project proceeds as follows: Spice self-learning, building an Op-Amp based integrator, analyzing an t� PWM modulator, determining components values, simulating and testing the modulator. The next steps are: to design the microphone pre-amplifier and anti-aliasing filter, to design the reconstruction low-pass filter, to build a complete class D amplifier (the power switching output stage is given) and to listen to the sound of his mp3 player through the amplifier. The path from KCL applied at circuit level to an abstract description of the functional structure of the t � , according to fig. 2, covers a four-month- period.The project is due to be completed by mid-May. The statement about CAS education issues will be focused on the outcomes of this learning process.
16
i n t e g r
R 1 8 o h m
V i n
M L I HP
0
0
N U M = 2D E N O M = ( 1 + s / ( 6 . 2 8 * 1 . 8 e 3 ) )
N U M = 0 . 0 6 6D E N O M = 1 + s * 1 e - 7
s ig
G A I N = - 8 . 3 e 3
- 7 . 5
1 e 6
1 5
0
2 . 0
IntegratorHysteresis
triggerReconstruction
filter
Signal in
V i n
0
R f
1 M E G
R i n
1 0 0
C f
1 0 p F
o u t0
-+
+-
O p A m p
E
G A I N = 1 e 5
X0
KCL
Op Amp
fig. 2
i n t e g r
R 1 8 o h m
V i n
M L I HP
0
0
N U M = 2D E N O M = ( 1 + s / ( 6 . 2 8 * 1 . 8 e 3 ) )
N U M = 0 . 0 6 6D E N O M = 1 + s * 1 e - 7
s ig
G A I N = - 8 . 3 e 3
- 7 . 5
1 e 6
1 5
0
2 . 0
IntegratorHysteresis
triggerReconstruction
filter
Signal in
i n t e g r
R 1 8 o h m
V i n
M L I HP
0
0
N U M = 2D E N O M = ( 1 + s / ( 6 . 2 8 * 1 . 8 e 3 ) )
N U M = 0 . 0 6 6D E N O M = 1 + s * 1 e - 7
s ig
G A I N = - 8 . 3 e 3
- 7 . 5
1 e 6
1 5
0
2 . 0
IntegratorHysteresis
triggerReconstruction
filter
Signal in
V i n
0
R f
1 M E G
R i n
1 0 0
C f
1 0 p F
o u t0
-+
+-
O p A m p
E
G A I N = 1 e 5
X0
KCL
Op Amp
V i n
0
R f
1 M E G
R i n
1 0 0
C f
1 0 p F
o u t0
-+
+-
O p A m p
E
G A I N = 1 e 5
X0
KCL
Op Amp
KCL
Op Amp
fig. 2
t < 0 : IS = 0t t� 0 : IS = 100 mA
VDC
fig. 1
IS
L R
t < 0 : IS = 0t t� 0 : IS = 100 mA
VDC
fig. 1
IS
L R
Teaching Circuit Courses to Engineering students : Two decades of an ongoing debate
Ljiljana TrajkovicSimon Fraser University, Vancouver
Topics to be discussed:t General approach: Basic Circuits I and II vs. Digital Signal Processing (DPS) first, experiences from
Georgia Tech and UC Berkeley experiments.t Targeted audience: Design tailored circuit courses for a variety of engineering students such as electronic
engineers, computer engineers, bioengineers, or mechatronics majors.t Choosing the right text: Is the cookbook approach offered by a myriad of textbooks available in our
bookstores (at a hefty price) serving future electrical engineers well?t Software tools: Using SPICE and MATLAB as supplemental tools for better understating of the theory
taught.t Presentation styles and delivery: From blackboard to overhead projectors to PowerPoint sides and back to
the whiteboard.t Laboratories: Exercises designed to illustrate application of the theory taught, reflect modern technological
advances, and are fun for students.t Recruiting future engineers: Reaching-out to high-school students by organizing visits to engineering labs,
engineering days, summer camps, and summer works programs.t Course instructors: Teaching circuits as service courses by unmotivated instructors will hardly generate
students’ enthusiasm.
References:[1] R. Rohrer, “Taking circuits seriously,” IEEE Circuits and Devices Magazine, vol. 6, no. 4, pp. 27-31, July 1990.
[2] Y. Tsividis, “Some thoughts on introducing today's students to electrical engineering,” IEEE CAS Newsletter, vol. 9, no. 1, p. 1, 6-7, March 1998.
[3] Y. Tsividis, “Teaching circuits and electronics to first-year students,” Proc. IEEE Int. Symp. Circuits and Systems, Monterey, CA, May/June 1998, pp. 424-427.
[4] Y. Tsividis, “Turning students on to circuits,” IEEE Solid-State Circuits Newsletter, January 2008.
17
Learning is Understanding
Raija LehtoDepartment of Signal Processing
Tampere University of Technology, Tampere, FinlandEmail: [email protected]
New technology makes it possible to teach in a new way. There are already some attempts to use these new techniques like e.g., web-based teaching etc. Several questions arise, however, when we start to think about learning and teaching vs. the technology available. Are all the changes for the best? Is it wise to let technology decide how to teach? Does a technique know how we learn? Do we really want to outsource these desicions to some outside force like anonymous technology?
My experiencies and ideas arise from several aspects, which are research, teaching basic courses in digital filters for Finnish undergraduate students, my work experience in industry and also my days as a student.
In the physical world there are some rules for the learning process, i.e., how we do learn. This can be compacted into a metaphor I once saw: “You cannot cross the sea by just looking at the water”. This means that you have to take some concrete action yourself. How can this be linked to teaching and learning? In the world of learning, the way of crossing the sea is: do the work and learn to think, and the result is understanding. Therefore, when we teach we should teach the students the basics and teach them how to think.
Now usually the question arises: could not the basics be taught by using new technology, e.g., by using Matlab “builtin” functions or do we really have to learn the algorithms themselves or do the math? Could we not skip some of it because of technology? This is a thought I keep hearing. In my point of view everything around us in our physical world tells us how we function. As an example, if we look at a tree, it does not grow without first growing the roots. The rules for learning are the same. The basics are like a stable foundation, from which it is possible to grow and reach higher levels of understanding and knowledge. Without the basics there is no learning or growth. This is what we do in other areas of our lives e.g., if we build a house, we first build a stable foundation. As we see, there are numerous examples of this rule everywhere around us. So why not follow this rule in teaching and learning?
In old sciences this rule tends to get forgotten and therefore, methods become rules themselves like axioms, which are then learned by memorizing. Like in mathematics we have axioms which nowadays are as a proposition that is considered to be self-evident. Therefore, its truth is taken for granted, and new theory-dependent truths are deduced and inferred from these.
This means that the thinking process of how these truths were created is lost and thereby understanding becomes more difficult. If we lose the basic knowledge of how things have been discovered, how can one build the roots necessary to create a foundation from which to reach for new horizons? It is very important that teaching follows the thinking patterns in research to keep them alive.
What I have also noticed is that by using Matlab tasks in teaching with the intention to visualize basic algorithms and rules, e.g. in digital filter design, students tend to get the misconception that they don’t need to learn the algorithm itself anymore. Using these technical tools in teaching seems to give ground for these kind of misconceptions. How this can be seen is for instance, when having an exam question like “what are the basic steps in Remez algorithm when designing linear-phase FIR filters?”, Matlab-like answers ”first we have to decide the requirements and then we calculate something with mathematical formulas and then we have the filter”, tend to come up frequently. The only thing some students seem to remember and learn is how to create a filter by using Matlab’s “built-in” functions. The question is now, how to make students learn and understand the basic principles and methods? One way of doing this might be using so-called combination tasks whenever possible during the course. This means doing it by hand with pen and paper and then simulating the same in Matlab. In other words, we have to go back to basics.
Still there is the question, how to make students and other instances understand that basic principles have still to be taught and learned, including the math? I often hear people say:”Because of computers, mathematics is not needed anymore”. But as I see it, they are both tools, and thereby needed. Mathematics can be seen as basics and computers as the implementation. In CAS-related areas, as one of my good
friends expressed it: “The basics are mathematical principles and Matlab and Spice are implementations. An implementation can break down, basic principles do not”.
From this follows that new technique could be included in teaching bearing in mind the rule of learning, and not forgetting the basics.
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This could be concluded by saying: “Technology is a good servant but a poor master” and the roots are the breeding ground.
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CAS Education Workshop 2008
Robert Rieger
Teaching of CAS in undergraduate education requires a balance between practical experimentation and theory. When teaching the first-year undergraduate experiment class at National Sun Yat-Sen University (Taiwan), I felt that students’ attention span and interest in circuit design is relatively low. Students appear to expect immediate results from a circuit and want to see it work and produce direct visual output in some form.
Therefore, we implemented several quite simple software routines using National Instrument’s Labview to visualize circuit input and output and put it in direct context with the lecture (Fig. 1). The software is connected to the real circuit students are building on breadboard using a standard DAQ card. A survey among 85 students in the course indicates that such software support in CAS education can be beneficial even if students are not familiar with the underlying software part itself (see part of the survey’s response in Fig. 2).
However, such visual preparation of circuit data must be employed with care. It may lead students to expect immediately clear results from all circuits and it may lead them to give up easily if such a result is not obtained. A too high level of data abstraction results in a situation that a simulator could entirely replace the experiment, so that the actual hands-on experience becomes void.
Fig. 1: Visual preparation of experimental data using a software interface, e.g. in filter design and signal synthesis.
Did Labview help you understand the experiment result? Have you heard of Labview before?
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Fig. 2: Part of the results of a survey amongst 85 undergraduate students taking the experiment course.
21
Prospects for Engineering Education
Armando Valim, National InstrumentsMark Walters, National Instruments
Tom Robbins, National Technology and Science Press
Despite the numerous textbooks available on circuit analysis and what seems to be common agreement over content and organization after almost fifty years of the same teaching model, many students still find the content difficult and come away with only a hazy idea about electrical engineering practice. Worse, after taking a beginning circuit class many decide that electrical engineering is not for them.
Many educators argue that today’s students have lost the ability to work on their own, having been programmed from an early age that watching is better than doing. Listening but not hearing. Many students memorize whatever it is that they have to memorize, and regurgitate it back on an exam. In fact, numerous studies provide abundant evidence that many students emerge from their studies with superficial knowledge of miscellaneous facts and formulas, with little ability to apply what they presumably have learned. Many have almost no laboratory skills or knowledge of hardware concepts when they enter school, and a decreasing number possess intuitive everyday knowledge developed from tinkering and taking things apart.
Is there a better way of teaching to a generation of students who have trouble sitting still and focusing on the sound of one professor's voice for an hour and a half? Can the format or even the narrow definition of textbooks be changed to better match the way current and future generations of students learn?
Some feel the answer to improved student performance is an increased focus on hands-on hardware opportunities that engage students in learning by doing. They envision a rich new learning environment, where information is presented in a more dynamic and interactive fashion to bridge the gap between theory and practice, leading to greater retention and application of acquired knowledge.
This emerging interest in providing students with hands-on, interactive curriculum that is both cost-effective and intrinsically valuable is reflected in a new publishing venture by National Technology and Science Press, or NTS Press. NTS Press is sponsored by engineers for engineering, and is dedicated to the publication of material of intrinsic value on emerging technology and existing subjects, distinguished by a high degree of software and hardware integration, to breathe new life into engineering and science applications.
We will present our vision of an integrated engineering learning environment where students work actively through an integrated design flow to stimulate learning. We will discuss the importance of motivating learning by comparing simulation results with signal measurements to better understand circuit behavior. Finally, we will announce several new tools for educators and students, including the pending publication of introductory circuits textbook that offers a framework for subsequent studies and an inspiring vision of the profession.
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The need for a new pedagogical approach to system modeling and analysis
Soumitro BanerjeeDepartment of Electrical Engineering
Indian Institute of Technology, Kharagpur, India
One important component of CAS education is to impart in the student the abilities to formulate mathematical models of systems and to analyze the behavior of systems based on the mathematical description. In this respect, the current undergraduate textbooks on dynamics and control suffer from a serious deficiency, as they are heavily biased toward linear systems, with nonlinearity treated as oddity. Modeling approaches are generally aimed at deriving transfer functions, and the analysis of stability and other properties is then carried out with the standard tools in the Laplace domain. This restricts the exposure of the students to the behavior of linear systems only.
Over the past few years there has been an increasing realization that most of the physical systems are nonlinear, and linearity is a very special case. This calls for adequate exposure to the techniques of time-domain formulations in addition to those in the Laplace-domain. The student has to learn the techniques of obtaining differential equations for any given physical system, and has to understand the dynamics in terms of the character of the vector field. A linear system description can then be understood as local linear approximation in the neighborhood of an equilibrium point.
In general, the methods of obtaining differential equations follow from the Lagrangian and Hamiltonian techniques of classical mechanics. In contrary to common belief, they are quite applicable to engineering systems: mechanical as well as electrical. For complex electrical circuits, the graph theoretic methods offer a systematic procedure. The bond graph technique is also a very convenient tool in achieving the same end, and is applicable to a wide array of systems: mechanical, electrical, electromechanical, and mechatronic. Unfortunately, these approaches have not yet been adopted in the mainstream EE or CAS education.
In this time-domain viewpoint, one understands dynamics as the motion of a point in the state space, following the vector field. In the neighborhood of an equilibrium point, the character of the orbit is given by the local linear approximation (the Jacobian matrix). Linear dynamics can be taught both through the eigenvalues and the eigenvectors of the linearized differential equations, or equivalently through the poles of the transfer function. But the former has the advantage that it gives a geometric view of the dynamics, and facilitates a smooth transition to the understanding of the possible effects of nonlinearity (including limit cycles, subharmonic oscillations, and chaos).
In view of the variety and complexity of systems that a modern engineer has to deal with, the above pedagogical approach forms a natural grounding. I propose that this workshop should recommend the introduction of a course of such content in the electrical engineering curriculum, at the undergraduate(sophomore) level.
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Multidimensional (MD) Circuits and Systems Education in the 21st Century
Arjuna Madanayake, PhD, Grad Student Member IEEEMultidimensional Signal Processing Group,
Electrical and Computer Engineering, University of Calgary, Canada. Email: [email protected]
Quality education is essential for producing professional electrical engineers who are dedicated to serve the engineering profession and society and provide leadership in general. Primary objectives for teachers of circuits and systems (CAS) would be to promote independent thought, teamwork and develop CAS-related problem-solving abilities in the students in the process of the transfer of knowledge. A participatory learning approach complemented by an introduction to the core concepts, foundational mathematics, and fundamental principles, may potentially be helpful in achieving this in CAS learners.
Linear systems have been part of the foundation of traditional CAS education. Ever since Electrical Engineering (EE) became a formally taught subject, linear systems, albeit one-dimensional (1D) systems, have been part of the main stream curricula. Usually, 1D CAS and signal processing education is built up on fundamentals involving the Laplace and Fourier transforms, Nyquist sampling theorem, basic control systems, KVL, KCL, and Tellegen’s theorem, feedback control, poles and zeros, z-transform, impulse response, transfer functions, etc. However, emerging CAS involving multimedia, digital video, earth-observing satellites, space-science, microwave imaging and radar, audio, ultrasound, and wireless array DSP for communications and navigation, necessitate the natural extension of well-known fundamentals of CAS to 2 or more dimensions. Therefore, I am of the opinion that MD-CAS needs to be part of mainstream CAS education at the undergraduate level.
The importance of MD-CAS is highlighted by some common examples that can relate to the everyday experience of the average undergraduate student, who may typically be in the age group 17-24. Digital video seems a perfect example for introducing students to the fundamentals of 3D spatio-temporal CAS, which means topics such as 2D/3D image processing and 3D Fourier transforms can be taught with exciting examples such as HD Video and 3D Cinema. I think use of modern relevant examples a person of the target age group can relate-to can make CAS education and the class-room active learning much more exciting. For example, Playstation3/Xbox/Wii type of technology can be used for teaching concepts in 2D/3D spectral analysis, image compression, H.264 and other video coding, model based coding, computer graphics, parallel computing for 2D/3D multimedia, object identification, classification, object tracking, 2D/3D noise cancellation, edge detection, Fourier/wavelet transform applications, and 3D space-time video processing etc.
Beamforming is another important aspect of MD-CAS that may potentially be updated in our EE curricula – I notice much of undergraduate EE material is still limited to delay-and-sum beamforming theory which has been taught in classrooms since 1940s! It is time to introduce knowledge generated in MD-CAS and multidimensional signal processing within the last 30 years into the classroom. For example, the 2D/3D spectral properties of far-field plane-waves can be used for broadband beamforming, and can be taught in an exciting and interesting manner to students with examples that relevant to the modern age, such as satellite-based remote sensing, radio astronomy and SETI, radar imaging, GPS, ultra-wideband and cellular communications.
The upcoming generations will increasingly be involved in multi-sensor CAS and array processing, which means a solid background in MD-CAS is a requirement. Textbooks are an important concern as well. From personal experience, Multidimensional Signal Processing by D. Dudgeon and R. Mersereau, and One- and Multi-dimensional Signal Processing Algorithms and Applications in Image Processing by H. Shroeder and H. Blume, are both excellent. However, a structured approach to standardized teaching of MD-CAS would require a thorough study of the MD-CAS area to determine what is important , and then guidelines for a syllabus may need to be designed by the IEEE CAS Society to meet the needs of the 21st century.
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Views, Experience, and Prospects for Education in Circuits and Systems
One-day CAS workshop on future directions of education in Circuits and SystemsIEEE Circuits and Systems Society
Statement about CAS-related education issues
The pivotal role of design in CAS
Our statement focuses in CAS-related learning methodologies, hence complementing the issue of which CAS-related contents should included in engineering curricula. By pointing out CAS-related learning methodologies we are not merely referring to learning tools (such as e-learning, or distance-learning) but (design) methodologies that could benefit education of EE engineers from a CAS perspective. Nowadays the concept of transversal competences and skills to be acquired by EE students is in open debate. It is argued that the competences of design and conceive/innovate naturally come from common practices inherent to the CAS Society.
Keywords: Design, Conceive, model, learning methodologies, design-oriented analysis, CDIO methodology.
Scenario and Rationale:The CAS society is unique in the sense that it combines both solid and thorough fundamental aspects encompassing circuits and systems together with their use in diverse and specialized applications. In all CAS fields, the concept of design plays a pivotal role. Eventually, the ultimate task of an EE engineer is to design. Proper design is a two-fold process, namely:
1) First to appropriately model the interdependencies among a set of performance indexes and the variables that form the multidimensional input design space.
2) Afterwards, appropriate application of optimization tools which lead to a final optimum design.
The second part of the design process can be thus carried out automatically, so that the optimum design process relies on the modeling process. This modeling process can be carried out in two ways:
A) By hand calculation, in which the human designer should derive an intuitive low-order model. To avoid that algebra and analysis clutters the derivations it is proposed to use low-entropy design-oriented analysis, to improve the model intelligibility, following the methodology proposed by Caltech professor David R. Middlebrook [1]. It is argued that by a widespread use of this approach, the way the EE discipline is to be lectured/learned in the future could be benefited from a CAS perspective.
B) By computer-based simulations, which come into play when more sophisticated dependencies and not only intuitive trends are required.
In any case, though this approach yields an optimal design, either the system architecture or the circuit topology is given a priori. Exploring the design space thoroughly can be a way to understand how to circumvent a given circuit or system fundamental limitation, thereby paving the way to conceive and innovative a solution the can outperform the precedent circuit or system, either through simple design-oriented analysis or through thorough but more aseptic and unintelligible design-space explorations. The bottom-line of this approach is hence not to teach/learn the “know-how”, but add the “know why”, which naturally leads to the question “why don’t …?” the answer of which potentially leads to new designs. This approach is connatural to the research activities of the CAS society, in which it is used either explicitly or implicitly, because of the circuits and system broad perspective.
It is proposed to foster the use of these CAS-related methodologies into the learning process of the contents of both current and new EE curricula. This approach is aligned with an initiative that originally comes from aerospace departments, namely the CDIO approach [2] (that comes from a consortium that includes MIT, CU Boulder, KTH, Chalmers, Linköping and Univ. Auckland). This engineering education methodology (which stands for Conceive, Design, Implement, and Operate) considers concepts similar to the aforementioned design-oriented analysis, but they are included in an integral project-based learning methodology that targets Engineering Schools. It has been scarcely
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applied in ECE-centered study programs and curricula (save for instance in Linköping, Sweden). The School I am representing is considering this method, strongly tied to a methodology that is natural to the CAS society, in the reform of the Telecom and Electrical Engineering degrees in the convergence towards the Bologna model in Europe. This complete approach to exercise (and thus to learn) the design of Circuits and Systems, clearly delimits the need for computers and simulations, the need for design-oriented analysis towards optimum designs, and the use of both for conceiving innovative Circuits and Systems solutions. These procedures are widely used in the CAS Society research activity and hence it would be natural to apply them when revisiting study plans and EE engineering curricula. Additionally, note that these methodological concepts being transversal, they could thus be potentially applied to foster the abstract transversal skill of design in a pervasive manner. They come from the different subdisciplines in the CAS Society and could affect different contents of study plans.
An additional last remark is that, in the context of the convergence to the Bologna declaration model in Europe, fundamental CAS-related contents could be challenged when defining shorter 4-year degrees to the detriment of more specialized but shallow vision of applications. This lack of CAS-related fundamentals are difficult to recover at Master level since the student is more motivated to go into in-depth learning of applications than to go back to fundamentals.
References:[1] Middlebrook, R.D.; “Low-entropy expressions: the key to design-oriented analysis “, IEEE Frontiers in Education Conference, 1991. Twenty-First Annual Conference. Proceedings. 21-24 Sept. 1991 Page(s):399 - 403[2] Rethinking Engineering Education: The CDIO Approach”, Crawley, E.F., Malmqvist, J., Ostlund, S., Brodeur, D. Springer, 2007.
Eduard AlarconAssociate Professor, Electronic Engineering departmentAssociate Dean of International Affairs, School of Telecom EngineeringTechnical University of Catalunya (UPC), Barcelona, Spain
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Experiences of McGill University's educational approach in teaching integrated circuits to undergraduate students
Anas A. HarmouiDept. of Electrical & Computer Engineering
McGill University 3480 University Street
Montreal, Quebec, Canada H3A 2A7 Tel: 514-398-5466 Fax: 514-398-4470
E-mail: [email protected] http://www.ece.mcgill.ca/~hamoui
In this course, undergraduate students:
1) design an integrated circuit (IC); 2) layout their IC using a linear-bipolar-array technology: 3) send their layout for fabrication; 4) receive their fabricated and packaged IC in 2 weeks; 5) test their IC prototype before the end of the course term.
This is a core undergraduate course, i.e. all students in electrical & computer engineering have to take this course at McGill University. Thus, undergraduate students gain hands-on experience in the full design flow of integrated circuits.
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