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Integrating Electrical Machines and Antennas Via Scalar and Vector Magnetic Potentials; an Approach for Enhancing Undergraduate EM Education

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Integrating Electrical Machines and Antennas Via Scalar and Vector Magnetic Potentials; an Approach for Enhancing Undergraduate EM Education Integrating Electrical Machines and Antennas via Scalar and Vector Magnetic Potentials; an Approach for Enhancing Undergraduate EM Education Seemein Shayesteh Maryam Rahmani Lauren Christopher Maher Rizkalla Department of Electrical and Department of Electrical and Department of Electrical and Department of Electrical and Computer Engineering Computer Engineering Computer Engineering Computer Engineering Indiana University Purdue Indiana University Purdue Indiana University Purdue Indiana University Purdue University Indianapolis University Indianapolis University Indianapolis University Indianapolis Indianapolis, IN Indianapolis, IN Indianapolis, IN Indianapolis, IN [email protected] [email protected] [email protected] [email protected] Abstract—This Innovative Practice Work In Progress paper undergraduate course. In one offering the course was attached presents an approach for enhancing undergraduate with a project using COMSOL software that assisted students Electromagnetic education. with better understanding of the differential EM equations within the course. Keywords— Electromagnetic, antennas, electrical machines, undergraduate, potentials, projects, ECE II. COURSE OUTLINE I. INTRODUCTION A. Typical EM Course within an ECE Curriculum Often times, the subject of using two potential functions in A typical EM undergraduate course requires Physics magnetism, the scalar magnetic potential function, ܸ௠, and the (electricity and magnetism) and Differential equations as pre- vector magnetic potential function, ܣ (with zero current requisite courses and continues the study on electrostatics, restriction when applying ܸ௠), is a source of confusion. When magnetostatics, and Maxwell's Equations. The course also gives using an analogous approach between the electric and magnetic introduction to electromagnetic waves, transmission lines, and potentials within an undergraduate Electromagnetic (EM) radiation from antennas. Some of the learning objectives cover course, students usually raise the issue of dissimilarities between students’ ability to work with electrostatic fields and to be able the electric and magnetic field equations when referring to their to find electric and potential fields from charge distributions potential functions. Textbooks [1-3] usually do not emphasize including the presence of dielectric materials. They should also the importance of using the vector magnetic potential, ܣ, in be able to work with magnetostatic and time varying fields and magnetism and its role in modifying the field equations in the find magnetic fields from current distribution, and solve wave dynamic domain. equations to understand the wave propagation in dielectric and Three lecture periods, extended over one and a half week, lossy media. The students learn how to use analogy between were dedicated to address the analogies between the electric plane waves and transmission lines (TL) and use the transmission line analytical and graphical methods for proper field ܧ and magnetic field ܪ equations, with applied EM examples. Three sets of applications were incorporated into and improper impedance matching in time and frequency these extended lectures. These applications are electrical domains. Table I summarizes the course contents for a typical Electromagnetic course. machines for the scalar magnetic potential function ܸ௠, antennas for the vector magnetic potential function ܣ , and electronic Within the above content, the analogy between ܧ and ܪ devices for the (scalar) electric potential function ܸ. Since the fields may raise some issues that would need more illustration traditional EM undergraduate course serves as a pre-requisite for in the course. Table II shows an example of these concerns. both Electrical Machines and Antennas courses, these extended Three lectures are added to enhance the integration of the course lectures were found to be important not only for understanding components (Lectures 1, 15, and 27). An attached project was the EM field equations but also for integrating them into the next also given as a bonus project. upper level courses within the EE curriculum. This paper details the applied examples from both areas, for better understanding B. Elaborations on the Updated Course of this section of the course, and for preparing the students for Three lectures are added to enhance the integration of the the upper level courses. This work also reports the impact of course components (Lectures 1, 15, and 27). An attached project using examples from electrical machines to show the importance was also given as a bonus project. of applying the magnetic potentials into electrical machines. This better comprehension of the magnetism section of the In lecture 1 (new), students, from prior electronic devices course was assessed by comparing students’ performances and physics classes, can see the importance of the electrostatic within the EM course over two successive offerings of the EM fields in solid state characteristics such as charge, electric fields, Integrated Nanotechnology Development Institute (INDI). ____________________________________________________ This is the author's manuscript of the article published in final edited form as: Shayesteh, S., Rahmani, M., Christopher, L., & Rizkalla, M. (2018). Integrating Electrical Machines and Antennas via Scalar and Vector Magnetic Potentials; an Approach for Enhancing Undergraduate EM Education. 2018 IEEE Frontiers in Education Conference (FIE), 1–4. https://doi.org/10.1109/FIE.2018.8658826 potentials, I-V characteristics, breakdown characteristics in PN Continuity Equation. (The lectures on Coulomb and Gauss laws junctions and in BJT and FET devices. It is important to solve are combined to save one lecture from this section). partial differential equations to find the potentials within channels or base regions, etc. A few diagrams from a previous Lectures 10 to 14 cover Magnetostatics where Static electronics class are used. Magnetic Fields, Lorentz Force, Ampere's Law, Vector Magnetic Potential, Biot-Savart Law, Magnetic Dipole, Magnetization; Magnetic Circuits & Magnetic Materials, TABLE I. TYPICAL EM COURSE CONTENTS Boundary Conditions, Inductance, Magnetostatic Energy, and # of Torque are taught. Analogy between Electrostatic and Topic Lectures Magnetostatic fields has been used as an effective approach to Introduction: Charge; Electric and Magnetic Fields; Units; learn the material. 4 Vector Analysis; Coordinate Systems; Line, Surface and Volume Integrals; Derivatives Lecture 15 (new) covers the following - applications of Electro Statics: Static Electric Fields; Gauss' Law; Magnetostatics in electrical machines and transformers, Coulomb's Law; Superposition; Applications of Gauss' Law applications of the scalar magnetic potentials inside (Continuous Distributions of Charge); Electric Potential; transformers cores, magnetic circuits, and the concept of DC 4 Conductors; Dielectrics; Displacement Field; Boundary Conditions; Capacitance; Electrostatic Energy; Force; machines. Poisson's Equation; Laplace's Equation; Method of Images; Lectures 17 to 19 cover Time Dependent Fields where Electric Currents; Continuity Equation Magneto Statics: Static Magnetic Fields; Lorentz Force; Faraday's Law, Transformers, Generators, Maxwell's Equations, Ampere's Law; Vector Magnetic Potential; Biot-Savart Potential Functions and Boundary Conditions for Time Varying 4 Law; Magnetic Dipole; Magnetization; Magnetic Circuits & Fields, Wave Equation, and Time Harmonic Fields in spherical Magnetic Materials; Boundary Conditions; Inductance; fields of antennas are discussed. Magnetostatic Energy; Torque Time Dependent Fields: Faraday's Law; Transformers; Lecture 20 to 26 covers Uniform Plan Waves and Generators; Maxwell's Equations; Potential Functions and 6 Transmission Lines. Uniform Plan Waves lectures teach the Boundary Conditions for Time Varying Fields; Wave following topics - Uniform Plane Wave (UPW), TEM Waves, Equation; Time Harmonic Fields. Examples from Antennas. Polarization, UPW in Lossy Media, Power flow, and UPW Uniform Plan Waves: Uniform Plane Wave (UPW); TEM 6 Waves; Polarization; UPW in Lossy Media; Power flow; Normal Incidence on Plane Boundary. Transmission Lines UPW Normal Incidence on Plane Boundary lectures cover the following topics – Intro to Using Parallel- Transmission Lines: Intro Using Parallel-Plate Transmission Plate Transmission Line, General Transmission Line Properties, 4 Line; General Transmission Line Properties; Finite Length Finite Length Transmission Lines, Transient Behavior, and Transmission Lines; Transient Behavior; Pulses Pulses. 3 Exams Lecture 27 (new) covers applications of vector and scalar TABLE II. ANALOGY BETWEEN ܧ AND ܪ FIELDS magnetic potentials in radiating systems as well as in electrical machines such as AC machines. Electric Field and Magnetic Field Analogy Electric Field (ࡱ) Magnetic Field (ࡴ) There is also a suggested project as bonus points where students use COMSOL software. Typical project examples are ܸ௠, ܣ Scalar: ܪൌെ.ܸ magnet design and solutions of wave equations over Static ܸ ௠ Only scalar potential, (conditionally, ) Potentials ܬൌͲ microfluidics. The project goes in parallel with the lecture ܧൌെ.ܸ (unconditional) Vector Potential, ܣ , materials. No lecture session was reserved for the project. where ܤൌ. ൈܣ Laplace ܸ satisfies both ܸ satisfies Laplace, and Laplace within conducting ௠ III. THE DETAILED NEW LECTURES while satisfy Poisson’s materials, and Poisson’s ܣ Poisson’s equations equations within dielectrics A. The
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