IEEE TRANSACTIONS ON EDUCATION, VOL. 42, NO. 3, AUGUST 1999 229

Fig. 2. Nyquist plot ofH(s) = (1 + s)=s2: (a) the expected plot and (b)the correct plot, a parabola (there is no asymptote, the distance to both axesincreases as the distance to the origin increases).

Letting x = ReH(j!) andy = ImH(j!) we see, upon eliminating!, that

x = �y2: (9)

This parabola is sketched in Fig. 2(b), whereas Fig. 2(a) depicts theexpected plot.

These discrepancies can be explained easily. IfH(s) is of nonzerotype

H(s) =P (s)

snQ(s)(10)

with n 2 IN. Consequently,

lim!!0

P (j!)

(j!)nQ(j!)= lim

!!0M(!)ej�(!) (11)

where

M(!) =P (j!)

(j!)nQ(j!)(12)

and �(!) is the phase angle of

P (j!)

(j!)nQ(j!): (13)

If P (s) andQ(s) have real coefficients we may assume without lossof generality thatP (0) andQ(0) are nonzero reals, meaning that

lim!!0

�(!) = integer��

2: (14)

The functionM(!) clearly increases without bound as! ! 0.However,M(!) ! 1 and (14) together do not necessarily meanthat the Nyquist plot ofH(s) approaches the real or imaginary axisas! ! 0. The phase angle of a complex points which approachesthe point at infinity may converge to a multiple of�=2 without itsreal or imaginary parts converging to zero.

The converse proposition is obviously true: if the limit point isa point belonging to one of the axes, then the phase angle mustconverge to a multiple of�=2. Thus, when the limit point is not thepoint at infinity, the branches will indeed end on one of the axes.

III. REMARKS

Nyquist plots found in textbooks depict in a clear way the globalbehavior of the functionH(s) infinitely far from the origin, in termsof its magnitude and phase.

For systems of nonzero type, the branches of the plot do notnecessarily have to approach an axis, and for systems of type two and

higher the branches may even deviate infinitely from both of them.This behavior is not readily apparent analytically to the student, butbecomes so with the help of computer software.

Paulo J. S. G. Ferreira was born in Torres Novas, Portugal.He is currently Professor Associado com Agregaccao at the Universidade

de Aveiro, Portugal. His research interests include signal processing, modelingand approximation of signals and systems, and inverse problems such assampling, interpolation, and signal reconstruction.

Dr. Ferreira was the Technical Program Chair and the main organizer ofthe 1997 International Workshop on Sampling Theory and Applications, andis presently a member of the Editorial Board of the IEEE TRANSACTIONSON SIGNAL PROCESSING.

Using Contests to Teach Design to EE Juniors

Peter H. Gregson,Member, IEEE,and Timothy A. Little

Abstract—Most electrical engineering programs have a capstone designcourse, but lack a suitable design experience in the junior year. Thismakes the capstone course very difficult for students and compromisesits pedagogical aims. A good design experience offers opportunities forlearning to identify key operational concepts, to identify and remedyprocedural and factual knowledge deficits, and to exercise judgment.Design problem should be open-ended, moderately difficult, and commonto all groups. We use a design contest as a vehicle for teaching designin the junior-year analog electronics course, in lieu of conventionallaboratories. Students design and build analog circuitry to autonomouslycontrol a small robotic vehicle. The contest culminates in a competitivetournament. Students’ questionnaire responses indicate that the contestis a useful learning tool, increasing interest in electrical engineering andwell worth the time spent. They indicate that contests are preferable toconventional labs for learning and understanding course material, formotivating them, and for providing an engineering experience.

Index Terms—Capstone course, design contest, design course, inte-grated design, juniors.

I. INTRODUCTION

TO GAIN mastery of the discipline, an electrical engineer (indeedany engineer) requires:

1) factual knowledge;2) knowledge of engineering procedures;3) the ability to identify key concepts;4) the ability to acquire new knowledge;5) judgment to use incomplete/contradictory information.

The normal engineering curriculum addresses items 1) and 2) throughdidactic learning. Items 3)–5) are developed largely through designexperience gained on-the-job during co-op and internship placementsor after graduation, not in the classroom. This is in part becauseit is difficult to teach concept identification, knowledge acquisition,and judgment other than through practice. It is also very difficultto assess students’ performance in these areas principally because

Manuscript received October 1, 1997; revised March 31, 1999.The authors are with the Department of Electrical Engineering, DalTech,

Dalhousie University, Halifax, Nova Scotia, Canada.Publisher Item Identifier S 0018-9359(99)06314-1.

0018–9359/99$10.00 1999 IEEE

230 IEEE TRANSACTIONS ON EDUCATION, VOL. 42, NO. 3, AUGUST 1999

the assessment domain is not rigorously defined. There are no “rightanswers” for items 3)–5).

The resulting lack of consistent design experience is a significantdeficit in most programs. Our design contest attempts to address thisproblem.

II. CURRENT DESIGN PROGRAMS

Most programs contain design exposure at the freshman, sopho-more, and senior levels, but not at the junior level. While typicalfreshman design courses include projects that are related to mechan-ical and/or civil engineering, electrical projects have proven difficultto include. Some schools provide freshmen with more in-depth designprojects [7] but this is not common.

Many programs include sophomore design experience throughappropriate design problems found in many modern electronics texts.These problems usually exploit students’ knowledge of physics,mathematics, and chemistry but do not require abstraction or technicalskills. Coursework covering design methodologies is appropriate atthis level also.

In the senior year, most schools have a capstone course whichpermits students to work on either faculty-initiated [1]–[3], [5], [6]or industry-initiated [4] design projects. Students usually work ingroups of two or at most three so as to ensure that all group membersacquire both design and teamwork experience [5]. With faculty-initiated projects, all groups are usually working on the same task [2],[3], [6] whereas courses using industry-initiated projects frequentlyhave a different project for each group.

Open-ended design experience is gained, in most programs, only inthe senior-year capstone course. Students are tremendously insecurewhen faced with this course because they have had little opportu-nity to develop concept identification, knowledge acquisition, andjudgment skills. Further, capstone project evaluation is frequentlyinconsistent because design projects are not usually assessed by acommon panel of assessors, particularly with industrially-initiatedprojects. Industry-initiated capstone courses offer little opportunityfor students to compare their design methodologies with those ofothers working on similar problems. Finally, capstone courses makedisproportionate demands on students’ time [4].

An appropriate junior-year design experience can address theseproblems.

III. PROVIDING A JUNIOR-YEAR DESIGN EXPERIENCE

A good junior-year design experience, employing an open-endedtask common to all groups in the class, permits learning from othersin one’s group and from other groups, and provides for assessmentconsistency. Students see the design methods used by other groupsand can assess their effectiveness. They are exposed to the plethoraof ideas that a large number of people will generate when solvingthe same task, and can assess their suitability. Finally, they have theopportunity to learn group dynamics, albeit in a limited way due tothe small size of each group.

A suitable design task must be scaled to the students’ engineeringsophistication. The task must be structured so as to exploit students’factual and procedural knowledge while simultaneously providingexperience in identifying key concepts, acquiring new knowledge,and exercising judgment. It must also be a strong motivator. In ourelectrical engineering program, we have found that a competitivedesign contest culminating in a tournament provides an ideal designexperience at the junior level. A good contest:

1) is safe;2) requires increasing factual and procedural knowledge;3) requires exercising engineering judgment;

Fig. 1. The maze for the A-MAZE-ing Robots competition of 1995.

4) fosters creativity;5) incorporates significant course material;6) provides success commensurate with care in design;7) permits many strategies with levels of success;8) does not require significant infrastructure;9) is easy to understand, with simple scoring;10) should be a spectacle.

This last item should not be overlooked. The status that studentsfeel when talking to their friends and family about the contest is animportant motivator. A little “glitz” also attracts better students to theprogram and raises the interest of the community.

A. DalTech’s Analog Electronics Design Competition

At Dalhousie University (DalTech), we have mounted the annualAnalog Electronics Design Competition in the junior year for the lastseven years. Students, working in groups of two, are required to de-sign and implement analog controllers for small, autonomous roboticvehicles (about 70 cm in diameter and 60 cm high, Fig. 2). The con-test culminates in a double-knockout tournament on a 3.6 m� 6.7 mplaying field. The tournament challenge is changed every year but thesize of the playing field and the vehicles have remained unchanged forthe last four years. Winners have their names inscribed on a plaqueand of course, they have “bragging rights.”

This contest constitutes the laboratory part of the junior analogelectronics course in lieu of more traditional laboratory sessions. Thecontest requires students to design, implement, and test circuitry forcontrolling motor direction and speed, low-level signal conditioning,sensing light, metal, obstacles, etc., voltage regulation and powersupply conditioning, implementing control strategy, and generatingtiming signals. This supports the course material which includesmultistage BJT and FET circuits, opamp circuits, nonideal opamp be-havior, power amplifiers, voltage regulators, sinusoidal and relaxationoscillators, nonlinear circuits, and motor speed control. Controllercircuitry is constrained to be predominantly analog. Circuits areimplemented from a standard kit of parts which contains a largevariety of analog components and a few digital chips.

To meet academic goals and to provide a basis for assessment,students must submit three progress reports on controller design andimplementation, including test results. The contest is worth 20 termmarks; 15 marks for the reports, and five marks for tournamentperformance.

IEEE TRANSACTIONS ON EDUCATION, VOL. 42, NO. 3, AUGUST 1999 231

Fig. 2. A typical controller mounted on a vehicle. All circuitry must be mounted on the light plywood “controller platform” although sensors may bemounted on the body of the vehicle.

A 135-page design handbook was written to address the dearthof suitable material on systems design. Topics covered include:understanding the problem, identifying the underlying key concepts,generating many candidate solutions, deciding on one solution toexplore further, implementing the solution, evaluating the solution,and time management. The handbook also covers many aspects ofsensing, signal conditioning, motor control, etc.

B. A-MAZE-ing Robots: The 1995 Contest

One of the best contests held in recent years was called A-MAZE-ing Robots, held in the Fall of 1995. Each team designedand constructed a circuit to guide the team vehicle from its startingposition, through a maze to the far end of the 6.7 m� 3.6 m playfield(Fig. 1). The various playfield features provided many strategiesfor winning. Fully autonomous controllers were designed from thestandard kit of electrical and mechanical parts.

Students’ solutions to the task included dead-reckoning, “wall-following,” light-seeking, and stripe-counting using various combina-tions of timers, optical sensing, metal-detection, and touch-sensing.The large number of sensing strategies used in various combinationssuggests that students were not clear as to the “best” way to win.A typical controller is shown in Fig. 2. Students had to designand implement circuitry for sensing, motor control, implementingstrategy, regulating voltage, timing, etc. The contest incorporatedmost components of the course material as is required of a goodcontest.

A-MAZE-ing Robots required little infrastructure (a donated car-pet, halogen lights, and the maze components as well as the smallvehicles; total cost of about $1000). Most of this infrastructure isreused each year. Since students purchase the kit of parts (about Can.$150 per group of two), the contest typically costs about $200 perclass per year. The contest provided a good spectacle, drawing a largeaudience (between 200–300 people) and the local television media.

IV. EVALUATION OF THE CONTEST

The entire class of between 40–60 students participates in thecontest each year. Evaluating the value of the contest is thus difficultbecause there is not a control group. While the class could be divided

into contest and noncontest cohorts, making the contest optionalwould lead to skewed data due to students’ self-selection. Further,the small sizes of the classes would result in very small cohorts,limiting the validity of any conclusions drawn from the data unlessthe cohorts were matched for age, ability, maturity, experience, andmany other variables. For this reason, a questionnaire was used forcontest evaluation.

Questionnaires were administered to both junior and senior stu-dents one week after the contest to acquire their assessments bothimmediately after it and one year later. Completing the questionnairewas voluntary for both groups. We had 24 respondents (65%) in thejunior class and 34 (68%) from the senior year class.

The questionnaire used a five-point Likert scale and consisted oftwo parts. Part 1 (five statements) dealt with the value of the contestas a course component. The statements, and the responses, were: 1)“useful as a learning tool” (very useful); 2) “worth the time spent”(seniors: definitely, juniors: less clearly); 3) “increases interest inelectrical engineering” (very much so); 4) “increases comprehensionof other courses” (no impact); and 5) “increases interest in othercourses” (slightly). Results are shown in Table I.

Part 2 (four statements) dealt with the value of the contest inrelation to more conventional laboratory sessions. Statements andthe responses were: 1) “more effective than labs for learning coursematerial” (very much so); 2) “provides motivation for learning”(juniors: very much so; seniors: somewhat); 3) “provides a goodengineering experience” (overwhelmingly); and 4) “better aids ingaining understanding of theory” (moderately strong agreement).Results are shown in Table II.

V. PROBLEMS WITH CONTESTS

The contest is not without problems, however. The problems thatwe have identified are as follows.

1) The students are overly focused on the demands of the contest,so it is difficult to teach material not directly related to thecontest challenge.

2) Pretournament stress results in students making many im-plementation mistakes in the days immediately prior to thetournament.

232 IEEE TRANSACTIONS ON EDUCATION, VOL. 42, NO. 3, AUGUST 1999

TABLE IRESPONSEDATA FOR PART 1 QUESTIONS. JUNIOR YEAR DATA

IN FIRST ROW OF PAIR, SENIOR YEAR DATA IN SECOND ROW

TABLE IIRESPONSEDATA FOR PART 2 QUESTIONS. JUNIOR YEAR DATA

IN FIRST ROW OF PAIR, SENIOR YEAR DATA IN SECOND ROW

3) Contest-relevant course material must be covered in sufficientdetail to be useful, sacrificing depth in other areas.

4) Toward the end of the contest, students were strongly temptedto skip classes in this and other courses.

5) Contest design and management is much more time-consumingfor the instructor than for conventional labs.

Most of these problems relate to time management and can beminimized by careful course planning. Pacing of the contest workcan be accomplished through requirements for regular submissions,orchestrating the course material so that it both follows a logicalsequence and fits the day-to-day requirements of the contest, andsetting assignments which pose contest-relevant questions.

VI. CONCLUSIONS

The Analog Electronics Design Competition has proven to bea useful, effective teaching tool for presenting analog electronicsdesign. Students agree that it is a good learning tool, that it wasworth the time spent, and that it increased their interest in electrical

engineering. Students were less clear as to the increase in interestand comprehension of other courses as a result of the contest. Thecontest compared favorably with conventional labs with respect tolearning course material, gaining understanding of material, providingengineering experience, and motivating them. From these results, itseems that the contest is an effective pedagogical tool.

The open-ended nature and difficulty of the contest and the widevariety of solutions observed over the years suggests that studentsgain valuable experience in identifying key concepts, opportunities toacquire new knowledge and techniques. They are forced to exerciseengineering judgment. The contest provides an exciting, motivatingmilieu in which this learning takes place.

REFERENCES

[1] J. D. Crisman, “System design via small mobile robots,”IEEE Trans.Educ.,vol. 39, pp. 275–280, May 1996.

[2] R. E. Gander, E. Salt, and G. J. Huff, “An electrical engineering designcourse sequence using a top-down design methodology,”IEEE Trans.Educ.,vol. 37, pp. 30–35, Feb. 1994.

[3] A. S. Hodel and T. A. Baginski, “An interdisciplinary senior designcourse utilizing electronically guided model rockets,”IEEE Trans.Educ.,vol. 38, pp. 321–327, Sept. 1995.

[4] S. R. Hoole, “Engineering education, design and senior projects,”IEEETrans. Educ.,vol. 34, pp. 193–198, May 1991.

[5] S. Lekhakul and R. A. Higgins, “Senior design project: Undergraduatethesis,” IEEE Trans. Educ.,vol. 37, pp. 203–206, May 1994.

[6] R. L. Mertz, “A capstone design course,”IEEE Trans. Educ.,vol. 40,pp. 41–45, Feb. 1997.

[7] R. B. Uribe, L. Haken, and M. C. Loui, “A design laboratory in electricaland computer engineering for freshmen,”IEEE Trans. Educ.,vol. 37,pp. 194–202, May 1994.

Peter H. Gregson (S’73–M’75) received the B.Eng. degree in 1974, theM.Eng. degree in 1977, and the Ph.D. degree in 1988, from the TechnicalUniversity of Nova Scotia, Halifax, Nova Scotia, Canada.

He is a Professor in the Department of Electrical and Compter Engineeringat DalTech, Dalhousie University, Halifax, and is Director of the ComputerVision and Image Processing Laboratory. He founded two companies de-signing and manufacturing data acquisition and control systems, and wasemployed by the Defense Research Establishment. His research is fucused ondevelopment of new theory, architectures, and algorithms for “early” computervision and image processing and on applications of this technology toautomated pathology assesment in medical imaging systems, robot navigation,and industrial control and measurement. He is also developing theory,algorithms, and analog VLSI circuitry for real-time vision-based short-rangerobot navigation, for automated surveillance monitoring and for motiondetection and tracking. He has a major interest in effective relevant teaching.

Dr. Gregson received the Wighton Fellowship in 1996, an annual awardmade to one professor of engineering and applied science in Canada for in-novative and distinctive contributions to undergraduate laboratory instruction.

Timothy A. Little was born in St. John, New Brunswick, Canada. He receivedthe B.Sc.Eng. degree from the University of New Brunswick and the M.Eng.degree from Memorial University of Newfoundland. He received the Ph.D.degree from the University of New Brunswick in the area of wind energyconversion systems.

He has been a Design Engineer for General Electric Co. of Canada andhas taught design courses at Memorial University. He joined the faculty ofDalhousie University, Halifax, Nova Scotia, Canada, in 1993 and has beenteaching power systems and machines courses. His interests include teachingand new and innovative techniques for presenting complex information so thatstudents can easily grasp key concepts.