ceived the B S degree from the California State. Polytechnic University, Pomona, in 1983, the M S degree from the University of Illinois in 1986, dnd the Ph D ...
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Scott W. Wedge (S’S2-M’85-S’87-M’90) received the B S degree from the California State Polytechnic University, Pomona, in 1983, the M S degree from the University of Illinois in 1986, dnd the Ph D from the California Institute of Technology, Pasadena, in 1991, all i n electrical engineering From 1983 to 1991 he was with Hughes Aircraft Company, Ground Systems Group, Fullerton, CA, and is now with EEsof, Westlake Village, CA. His interests and experience from industry and academia include RF and MMIC circuit design, computational electromagnetics, microwave measurement systems, and high-frequency CAD Dr. Wedge is a member of Tau Beta Phi and Eta Kappa Nu, a registered professional engineer in California, and was a Hughes Doctoral Fellow at Caltech He is coauthor of the educational microwave CAD program, PUFF, which has over 10.000 users worldwide
David B. Rutledge (M’75-M’77-S’78-M’80SM’89) received the B A degree in mathematics from Williams College, Williamstown, MA, in 1973, the M.A degree in electrical sciences from Cambridge University, Cambridge, England, in 1975, and the Ph.D degree in electrical engineering from the University of California at Berkeley, in 1980. In 1980 he joined the faculty at the California Institute of Technology, Pasadena, where he is now Professor of Electrical Engineering. His research is in developing millimeter and submillimeter-wave monolithic integrated circuits and applications, and in software for computer-aided design and measurement, He is coauthor of the CAD program, PUFF, which has over 10.000 users worldwide
A Hands-on Practical Approach to Teaching Engineering Design S. M. Miri, Member, IEEE, and R.J. Fu
Abstract-A hands-on practical approach to teaching design in engineering courses is presented. This approach is based on the philosophy that students learn the fundamental laws and their applications to design most effectively through design practices which result in demonstrated success. Through such practice, they learn that success in engineering requires understanding the fundamentals and attention to details, they learn the science/art of the iterative design process, and they gain a great deal of self confidence. Students must learn that to be innovative means having a deep understanding of fundamentals and being able to work out details, and that nothing, not even computers, can replace these two ingredients of excellence.
I. INTRODUCTION
T
0 prepare the engineering graduates for the challenges of today’s very competitive industrial world, we must provide them with a strong foundation upon which they could build further engineering knowledge on their own. Such a foundation consists of a deep understanding of the fundamentals of engineering and the ability to deal with the degree of details required in developing new technologies and competitive products. Today, too many engineering students believe they can get by without understanding the fundamentals, and without paying attention to details. To change this attitude, we must demonstrate to them the necessity of having a deep understanding of fundamentals and of being able to work out “tedious” details in order to be innovative and succeed as engineers. An approach to teaching design is presented in this paper which, we believe, can change the students’ attitudes Manuscript received June 1992. The authors are with the Department of Electrical Engineering, University of North Carolina at Charlotte, Charlotte, NC 28223. IEEE Log Number 9205772.
about learning fundamentals and dealing with details, and thus, can help produce future engineers who will be more innovative than many of today’s practicing engineers. 11. THETEACHING PROCESS
A . Selecting a Suitable Design Project
The first step in planning is to select a suitable design project. Careful attention must be paid in selecting the design project if we are to make the design experience a meaningful one for the students. A design project can be considered to be suitable for the proposed teaching approach if a) the instructor has completely worked out the design beforehand; either in conjunction with a previous research project or just for the sake of the class, b) it is relevant to the course material, c) it can be done by the students in a relatively short period of time, d) a prototype can be built or ordered, inexpensively, before the end of the semestedquarter, and e) all the required manufacturer’s catalogues can be made available. Our experience with the proposed teaching approach has been in a senior level required course on electromagnetic devices offered in the Electrical Engineering Department. Usually, this class has an average of forty students. The design project discussed in the following section was assigned as the first take-home test and the students were given nine days to complete the project. All students were given the same design project.
B. The Design Specifications The design requirements should be specified unambiguously. In the professional world, the design requirements are seldom unambiguous and it is left to the engineer to
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work out the details of the requirements. However, we are teaching students to become professionals. The following design specifications were given to the students in our class: In a high precision electronic instrument, it is required to have two isolated power sources. This requires the power supply transformer to have two secondary windings. The design requirements are for one primary winding at VI = 120V and two secondary windings each at V2 = 1OV while delivering I 2 = 0.5A at 60 Hz. The maximum space available for the transformer on the power supply board is, in inches, 2 x 1.5 x 1. Design this transformer in enough detail such that a prototype can be constructed directly from your design. That is, you must provide design information such as core material, lamination type and size, standard bobbins to be used, number and thickness of laminations (this determines the core cross-sectional area), wire sizes for the primary and secondary windings, and the primary and secondary number of turns. Make sure the flux leakages (i.e., the fluxes not confined to the core) are minimized. Analyze your design using the finite element program provided, and discuss the results. Your analysis must include the calculation of the core and leakage average flux densities. C. The Discussion of Fundamentals
To teach students the importance and power of fundamentals, and to prepare them for the design project, the relevant fundamental laws should be discussed in class with enthusiasm. In our class, we discussed the following inspiring fundamentals related to the assigned project; The Faraday’s law of induction can be used to derive the simple, but powerful design equation given by [l].
IEEE TRANSACTIONS ON EDUCATION, VOL. 36, NO. 1, FEBRUARY 1993
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Fig. 1. A shell-type transformer core.
but core real losses are. Equation (1) confidently states that the flux linking a winding, excited by voltage E , does not depend on the permeability of the magnetic medium. That is, for a given whding, the flux linkage is determined only by the ratio ( E l f ) .Then what changes when the magnetic medium is changed? The answer is current. If p is increased we get the same flux linkage with smaller winding current (think of B - H curves for magnetic materials). The reduced current is due to a reduction in the left-hand side of (2), the Ampere’s law,
This is why the unwanted air gaps generated by the core stacking process result in a higher exciting current than that predicted by (2). While (1) indicates that we need a larger NA, for higher operating voltages, (2) indicates that lower 1 may require a larger wire size for the primary winding. To further prepare the students for the project, the following design concepts were also discussed in the class. D. Low-Leakage Design Considerations
The objective of a low-leakage design is to maximize the percentage of the magnetic flux confined to the core. This E = 4.44fNACB,,. (1) objective can be achieved through maximization of a) the effective permeability of the core, In (l), E is the winding’s induced voltage in rms, f is the b) the coupling between the primary and the secondary power frequency, N is the number of turns, A, is the core windings, and cross-sectional area, and B, is the peak of the sinusoidal c) the coupling between the windings and the core. flux density in the core. Although this equation is quantitaProper selection of the core material and the peak of tively valid only in the absence of saturation, it provides a the operating flux density allowed are crucial in achieving wealth of design information far more than evident at the first objectives a) and c) above. Maximizing the bobbin height, and glance. Equation (l),along with circuit equations, can be used in an thus the core window height, and minimizing interwinding and iterative process to determine A,, the primary number of turns, winding-core insulations are crucial in achieving objectives N I , and the secondary number of turns, N2, for given design b) and c). The use of concentric design is necessary for values of B,,,, f and the terminal voltages. To excite the achieving objective b). students, practical implications of this fundamental equation were discussed as follows. The product NA,, and thus the E. Selection of the Core Type transformer size and weight, can be reduced by increasing For a given design, the location and orientation of the the operating frequency (e.g., airborne applications). Low power supply transformer determine the level of the leakage frequency and dc components resulting from asymmetrical flux density detected at a given location. The location of fault currents, asymmetrically triggered SCR’s, etc., can drive the transformer is often dictated by other instrument design the core into deep saturation and adversely affect the trans- considerations. The optimum orientation is the .one which former performance. On the other hand, the presence of higher minimizes the linkage of the transformer leakage fluxes with frequency contents (e.g., harmonics) in the exciting voltage the sensitive circuitry. A shell-type core can be oriented to does not contribute to the core flux significantly. Equation (1) provide “free” shielding in two directions, the positive and explains why ferrite cores are used in high frequency (e.g., negative z directions in Fig. 1, along which sensitive circuitry RF) applications. At high frequencies, the core flux density will be least affected by the transformer leakage fluxes. The does not attain a large value and saturation is not a problem, students were told to use a shell-type core in their designs.
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IEEE TRANSACTIONS ON EDUCATION, VOL. 36, NO. 1, FEBRUARY 1993
18-Tes1a
(49%
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Ft. 49% Co. 2% V)
2.21-
C (50% Fe, 50% Nil
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Fig. 2. Typical B-H loops for magnetic materials used for transformer cores.
Fig. 3. 60 Hz magnetization curve for M-6.
F. Core Material Selection
The core material used is an important design consideration influencing the core effective permeability ( p ) , size, weight, efficiency, and cost. Fig. 2. shows the B-H loops for typical core materials used in transformer design [ 2 ] . To meet our design objectives, we should select a material having high p, high saturated flux density, Bsat,and low cost. The transformer size limitation requires the use of a material with large Bsat such as the material whose B-H loop is shown in Fig. 2-A (49% Fe, 49% CO, 2% V), Fig. 2-B (M-6: grainoriented silicon steel, 97% Fe, 3% Si), or in Fig. 2-C (50% Fe, 50% Ni). If the size limitation allows, the material with higher p (50% Fe, 50% Ni) should be selected for a low-leakage design. However, if minimizing the cost is a major requirement for being competitive, M-6 should be selected. A material such as the one characterized by Fig. 2-A is about 60-75% and that characterized by Fig. 2-C is about 20-25% more expensive than the M-6. In addition to being the least expensive, M-6 is also the lightest among these three materials. It has a large B,,, (1.4-1.8 tesla) and a high p. The students were told to assume that minimizing cost is a requirement and that they should select M-6 for the core material in their designs. Having selected the core material, one can use the peak of the operating flux density waveform to determine the effective p of the core from the p-curves provided by the manufacturers. G. Selection of the Lamination Type and Size
To select the lamination type and size in constructing a shelltype core, one must a) consider the space available, b) try to maximize the core window height, and c) make sure standard bobbin sizes can be used. Most U.S. manufacturers do not use the SI units. For practical reasons, we use the same units as used by the manufacturers in our discussions. The following conversion factors are given for convenience: 1 in = 2.54 cm, 1 Gauss = 10-'TT,and 1 Oersted = 79.577 A / m . H. Selection of the Core Peak Flux Density
approximations.
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To obtain high permeabilities in both, the parallel and normal orientations to the grain directions, while using the core efficiently, we will allow a maximum core flux density of B,,,, = 12,000 Gauss. It can be seen from Fig. 3 that, with this value of B,,,, the transformer core will not saturate at any time during a 60 Hz cycle. Note that while in a lowleakage design saturation is to be avoided, economical designs of transformers require their cores to operate with some degree of saturation. I. The Analysis Programs
The students should be provided with computer analysis and graphics capabilities to analyze and optimize their designs, and most importantly, to deepen their understanding of the underlying fundamentals through analysis. In our example, the students were provided with a finite-element analysis program, along with a detailed user's manual, developed by the authors for magnetostatic problems. Also provided was a graphics package called Coplot'. The students were provided access to high speed PC's, on which the software packages had been installed, about two weeks before the design project was assigned. They were asked to use the menu-driven analysis programs for calculating and plotting core flux density in 3-D, and core and leakage flux equipotential lines in 2-D. Also, they were asked to calculate the average flux densities in the
' CoHort Software, Berkeley, CA.
IEEE TRANSACTIONS ON EDUCATION, VOL 36, NO. 1, FEBRUARY 1993
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CORE.
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C. The Wire Size for the Secondary Windings Fig. 5.
Flux density due to a current-carrying conductor in a plane normal to the conductor.
conductor are calculated and plotted in a plane normal to the conductor (Fig. 5). The students were asked to prepare themselves for the design project by running this example. Referring to Fig. 5 and starting at the center of the conductor and moving away from it, we note that, because of Ampere’s law, the flux density starts from zero at the center and increases to a maximum at the surface of the conductor. And that it decreases as we move away from the conductor. At the corners of the solution domain, where we are farthest from the center of the conductor, the flux density attains its lowest value outside the conductor, as predicted by (2). In teaching the students the fundamentals of electrical engineering, this exercise is just as important as the design project itself. It serves to help students a) develop a good understanding of a fundamental law and its practical implications, b) learn how to use finite-element (FE) analysis and plotting programs, and c) develop a trust in the FE program.
The design. specifications require two isolated secondary windings each providing a maximum of 0.5 amperes at 10 volts. The smallest wire size which can be safely used for the secondary windings is AWG-28 which has a diameter of 0.321 mm [2] D. The Bobbins and the Core Cross-Sectional Area
To begin the iterative design process, we select two 375E1 x 318 bobbins3 having the dimensions, in inches, of 1 x w x h = 0.39 x 0.39 x 0.737, one for each secondary winding. Further, to fill the bobbins with laminations, we design for a square core cross-sectional area. For the selected laminations, the manufacturer gives stacking factor of 0.95, that is, A , = 0.375 x 0.375 x 0.95 = 0.1136 in2. E. Secondary Number of Turns
Using the Faraday’s law of induction given by (1) and the design specifications, the required secondary number of turns can be determined. To calculate N2 using (l), we first need to determine the secondary no-load voltage E2
b
E2
111. THE DETAILSOF
THE
DESIGNPROCESS
A. Instructor Preparations
For the proposed teaching approach to achieve its objectives, it is crucial that at least one student carries out the design successfully. To assure that this happens, the instructor should carry out the design, in all details, before challenging the students to do the design. This will allow the instructor to help the class as much as it takes for the best students to succeed. In our example, the design of the transformer was carried out beforehand. The following iterative design procedure was used to carry out the design. B. Selection of the Lamination Type and Size
V2
+ R212
(3)
where V2 is the secondary rms voltage at the load current I2. R2 is the secondary winding resistance, and the secondary winding leakage inductance has been assumed to be negligible. This assumption is valid considering the wire size involved and the fact that we are designing for low leakages. The resistance per inch of AWG-28 at 20°C is 5.4425 ma. Assuming an operating temperature of 4OoC, this resistance is increased by a factor of 1.09 (read from a resistancetemperature chart [2]). An estimate of R2 in (3) is given by [21
R2 = 1.09 x 5.4425 x
x M L T x N2
(4)
where MLT is the mean length turn for the secondary winding. For the given bobbin and-assuming the secondary winding will be wound over the primary occupying half of the total winding area available, the secondary MLT can be estimated by inspection M L T = 4 [l 2 ( b ~ wW1 i ~ i ) W W ~ ] (5)
Among the standard lamination types and sizes available, the EE lamination made using two E laminations taken from 375-E1 laminations’ is the most suitable choice for our design. The resulting EE lamination (Fig. 6) has an overall dimension, in inches, of 1.875 x 1.375 with a window height of L = 1.5. where, in inches, bw = 0.031 is the bobbin wall thickness, To reduce eddy-current losses without significantly reducing ww1 and ww2 are the widths of the primary and secondary the stacking factor, a lamination thickness of 0.014 is chosen. windings, and iwi = 0.02 is the interwinding insulation thickness. The winding width ww = ww1 = ww2 can be
+
2Magnetic Metals Co., Camden, NJ. “Transformer Laminations Catalog.”
+
+
+
3Plastron Corp., Bensenville, IL. “Engineered Bobbins Catalog.”
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estimated by inspection UJW = 0.5[N - (1 - C ) - b w - I W I - cc] = 0.1033
(6) where cc = 0.04 is the required secondary winding-core clearance. Thus, ( 5 ) gives M L T = 3.2, and (4) gives R, = 0.019N2 ohms. From (3), E2 x 10 0.0095N2 which can be substituted in (1) to give N2 = 554 turns per secondary. We must now determine if there is enough window area available for the number of secondary turns calculated. For each winding, the bobbin height is b h = 0.735 - 2 x 0.031 = 0.673, and the available window area is A , = bh x U J U J = 0.0695 in2. Using an empirical formula, the maximum number of AWG-28 turns which would fit in the area A,, can be shown to be NmaX= 380. Thus, the design value of N2 = 533 will not fit in the available winding area. To reduce the design value of N,, while maintaining B,,,,, at 12,000 Gauss, we will allow a larger core cross-sectional area. We choose our next standard bobbin size to be the 375-E1 x 112 having the dimensions 0.39 x 0.515 x 0.735. To fill this bobbin with 0.014-inch thick laminations, we let A, = 0.375 x 0.504 x 0.95 = 0.1796 in2. Applying the design equations once more, we get N2 = 374 turns which is less than Nmax.This value of N2 results in E2 = 13.6V at 0.5A.
+
F. Primary Number of Turns
On the primary side, we can have one winding per bobbin connected either in series or in parallel. To use larger wire sizes and thus to reduce manufacturing costs, we choose the series arrangement. To determine the primary number of turns N I we assume a primary winding voltage drop equal that of the two secondaries combined, that is
Vi - E1
N1
2 - (E2 - V2)
(7)
N2
Solving (1) and (7) simultaneously for El and N I , we get N I = 2140 or 1,070 turns per bobbin. Applying an empirical formula, we determine the largest wire size filling the available area to be AWG-33. Now we must determine if AWG-33 can carry the primary current. The primary rated current can be estimated by
where the exciting current I,,, pere’s law
can be calculated from Am-
Bmax
Bmax
fibLp
Jzp,,
N ~ I e x= c -I p + -
171
(9)
where p p and pTL are the core permeabilities, and 1, and I , are the core mean lengths along the grain direction and normal to the grain direction, respectively. From Fig. 4 at B,,, = 12,000 Gauss, p p z 8.000 and p, = 4,000. From Fig. 6, 1, = 1.689 and 1, = 0.5. The exciting current can now be calculated from (9) and substituted in (8) to solve for the primary rated current. This gives I,,, = 7.6mA and Il,rateci = 0.182A. Thus, AWG-33 can be used for the primary. This completes the design.
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Solution domain for the FE analysis.
While these design details were not discussed in the class, enough hints were given to the students to be certain that at least the best of them could complete the design. G, Finite-Element ~
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To obtain a measure of the core and leakage flux densities prior to ordering a prototype, the students were asked to use the provided finite-element program to analyze the transformer’s magnetostatic operation for maximum flux conditions (i.e., maximum flux density point on the B-H curve). Because of the existing symmetry, only half of the solution domain, as shown in Fig. 7, was considered in the analysis. Fig. 7 represents one half of the transformer of Fig. 6 rotated 90’; that is, the core center leg now coincides with the Y-axis. The outer lines define the solution domain boundaries. The shaded area represents sensitive circuitry susceptible to magnetic interference. Two cases were studied: a) the loaded case where one secondary is loaded to 0.5A while the other is loaded to 0.1A, and b) the no-load case where the primary is energized at 120 V and both secondaries are left open. The first case is assumed to simulate the field operating conditions, while the second case is considered to be the worst case for leakages. In both cases, the winding currents are estimated using the given operating conditions and the transformer model. The winding current densities required for the FE analysis are estimated using the winding currents, number of turns and window areas. The Loaded Case: Fig. 8 shows the surface plot for the core flux density. The average leakage flux density in the shaded area of Fig. 8, at the center of which the sensitive circuitry is assumed to be located, is calculated to be 0.492 Gauss. This flux density can induce a voltage of 0.0085 mV in a loop area of one square inch where sensitive circuitry might reside. The core average flux density is calculated to be 12,196 Gauss, a value close to the design value of 12,000 Gauss. The No-Load Case: The average leakage flux density in the shaded area of Fig. 7 is calculated to be 0.595 Gauss, a higher value as expected. This flux density can induce a voltage of 0.0102 mV in an area of one square inch. The core average Aux density is calculated to be 14,170 Gauss, a value higher than the design value. This is due to the fact that there is a smaller voltage drop in the primary winding at no load.
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IEEE TRANSACTIONS ON EDUCATION, VOL. 36, NO. I , FEBRUARY 1993
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Fig. 8. Core flux density for the loaded case.
IV. THEDESIGNPROTOTYPE
7
Among the designs submitted by the students, a few designs were similar to ours; we had made sure this would happen. The core operating flux density and the noise levels calculated above were considered to be acceptable and it was decided to build a prototype according to the design carried out in Section I11 (and by some of the students). A prototype was ordered which was received within a few days for a cost of under $100. A group of students were assigned to test the prototype and report the results. They were instructed to a) measure the physical dimensions of the transformer, b) excite the primary at 120V and measure the no-load primary current, the no-load secondary voltage, and the full-load secondary voltage, c) insert a few turns around one of the outer legs and measure the induced voltage at no load, d) use a search coil to observe the leakage flux densities all around the transformer, and e) estimate the maximum core flux density fr2m the measurement in part c). The following test results were reported: a) the maximum dimensions are, in inches, 1 . 9 1~ . 5 1;~ the design requirements were 2 x 1.5 x 1 maximum, b) at no load, the primary current and the secondary voltages are measured to be I,,, = 15mA and V, = 16.2V,c) at full load, the secondary voltages are measured to be 1OV as required, d) the leakage flux densities are negligible except around the areas where the E laminations are butted together to form EE laminations; this was attributed to the resulting air gaps at these areas, and e) the core maximum flux density is estimated to be B,, = 13.884 Gauss. The exciting current of 15mA measured is much larger than the calculated value of 7.6mA. Again, this was attributed to the resulting air gaps which were not accounted for in the design calculations. The maximum core flux density of 13,884 Gauss measured is smaller than the 14,032 Gauss which can be calculated using (1) and the no-load secondary voltage measured in part b). This was attributed to the fact that, in a concentric design, the flux linking the secondary is larger than the core flux. V. CONCLUSIONS We have made the argument that in engineering education nothing can replace the teaching of fundamentals and attention
to details. The engineering students are not educated unless they have developed a deep understanding of fundamental laws and are able to work out complex details. We have presented an approach to teaching engineering design which can achieve these educational objectives. We tried this approach in a senior level course on electromagnetic devices with success. In this course, students were assigned a design project, were exposed to the relevant fundamental laws and were asked to apply the fundamentals to develop a complete design using manufacturer’s component catalogues. The students were helped as much as it took for the best of them to carry out the design successfully. This was done because of our belief that students learn most ewectively through design experiences which result in demonstrated success. A prototype of the best student design was built and tested. Since most engineering courses are already packed with materials, one might find it difficult, as we did, to fit a design project as discussed here in a given course. Obviously, we sacrificed the teaching of some specific subjects for the sake of the design project. However, in our opinion, teaching fundamentals through design is far more valuable than teaching any specific subject. Any specific subject is based on some fundamental laws and students who gain a deep understanding of these laws can self-educate themselves about any given subject. The finite-element analysis program along with its user’s manual we have developed and used are available, for educational use, through the first author.
REFERENCES [1] A. E. Fitzgerald, C. Kingsley, and A. Kusko, Electric Machinery, 3rd ed. New York, McCraw-Hill, 1971. [2] Wm. T. Mclyman, Transformer and Inductor Design Handbook. New York: Marcel-Dekker, 1978. [3] S. R. H. Hoole, Computer Aided Analysis and Design of Electromagnetic Devices. New York: Elsevier, 19x9.
S. Mehdi Miri (M’87) was born in Tehran, Iran, on Dec. 13, 1953. He received the B.S.E.E. degree from Western Michigan University, Kalamazoo, MI, in 1981, the M.S. and Ph.D. degrees in electrical engineering from Ohio State University, Columbus, OH, in 1983 and 1987, respectively. In 1987, he joined the electrical engineering faculty at the University of North Carolina, Charlotte, where he is currently an Assistant Professor. His current research interest is in computer-aided design of high precision electromagnetic devices.
Ren-Jie Fu was born in Shanghai, China, on Dec. 13, 1963. He received the B.S.E.E. degree from Shanghai University of Technology, in 1986. He is currently working on his M.S.E.E. degree. Mr. Fu is a member of phi kappa phi.
