teaching electromagnetics via virtual toolspropagation magazine (since feb 2007) and a member of the...

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TEACHING ELECTROMAGNETICS

viavia

VIRTUAL TOOLS

L. Sevgi July 22, 2015

Levent SEVGİOKAN University – Faculty of Engineering & Architecture

Electrical – Electronics Engineering DeptTuzla Campus, AKFIRAT, Tuzla / ISTANBUL http://leventsevgi.net ; [email protected]


Copyright

©The use of this work is restricted solely for academic purposes. The author of this work owns the copyright and no reproduction in any form is permitted without written permission by the author.

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Biography

Prof. Dr. Levent Sevgi

Born in Akhisar / Turkey on 1st January 1958.

He received his BsEE, MsEE and PhD degrees in Electronic Engineering from Istanbul Technical University (ITU) in 1982, 1984 and 1990, respectively. In 1987, while working on his PhD, he was awarded a fellowship that allowed him to work with Prof. L. B. Felsen at Weber Research Institute / New York Polytechnic University York for two years. His work at the Polytechnic concerned the propagation phenomena in non-homogeneous open and closed waveguides.

He was with Istanbul Technical University (1991–1998), TUBITAK-MRC, Information Technologies Research Institute (1999–2000), Weber Research Institute/Polytechnic University in New York / USA (1988–1990), Scientific Research Group of Raytheon Systems, Canada (1998 – 1999), Center for Defense Studies, ITUV-SAM (1993 –1998 and 2000–2002) and with University of Massachusetts, Lowell (UML) MA/USA as a full-time faculty (2012 – 2013) and with Doğuş University (2001-2014). Since Sep 2014, he has been with Okan University.

He has been involved with complex electromagnetic problems and complex communication and radar systems for nearly three decades. His research study has focused on propagation in complex environments, analytical and numerical methods in electromagnetic, EMC/EMI modeling and measurement, communication, radar and integrated surveillance systems, surface wave HF radars, FDTD, TLM, FEM, SSPE, and MoM techniques and their applications, RCS modeling, bio-electromagnetics. He is also interested in novel approaches in engineering education, teaching electromagnetics via virtual tools. He also teaches popular science lectures such as Science, Technology and Society.

He is a Fellow member of the IEEE, an AdCom member of the IEEE Antennas and Propagation Society (2013-2015), the writer/editor of the “Testing ourselves” Column in the IEEE Antennas and Propagation Magazine (since Feb 2007) and a member of the IEEE Antennas and Propagation Society Education Committee (since Jun 2006). He is also a member of several editorial boards (EB), such as the IEEE Antennas and Propagation Magazine (since 2007), the IEEE Access (2017-2019), Wiley’s International Journal of RFMiCAE (since 2002), etc.

He has published many books/book chapters in English and Turkish, over 170 journal/magazine papers/tutorials and attended nearly 100 international conferences/symposiums.

His two books "Complex Electromagnetic Problems and Numerical Simulation Approaches" and "Electromagnetic Modeling and Simulation" were published by the IEEE Press - Wiley in 2003 and 2014, respectively. His third book, “A Practical Guide to EMC Engineering” was published by ARTECH House (Norwood/MA, USA and London, UK) in March 2017. His fourth book “Guided Wave Propagation and Parabolic Equation Modeling” with Gökhan Apaydın will be published by the IEEE Press - Wiley around Oct 2017.

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Abstract


Virtual tool based novel teaching methods in electromagnetic will be discussed. Fundamental concepts, such as modeling and simulation, analytical- and numerical-based modeling, simulation, validation, verification, etc., in relation to the virtual labs widely-covered as parts of engineering education will be reviewed. Sample virtual tools that can be used in basic as well as advanced level courses will be shown.

Index Terms: virtual tool

SummarySummary


We have witnessed a transformation from ENGINERINGENGINERINGELEELECCTRTROMAOMAGGNETICSNETICS to ELEELECCTRTROMAOMAGGNETICNETIC ENGINEERINGENGINEERINGfor the last couple of decades, therefore virtual labs and toolshahavvee becbecoomeme aatttrtractivactivee inin educeducaattionion andand trtrainingaining.

The overall effectiveness is very positive and the impact onstudents is that they are better equipped to understandphysics and use mathematics.

Several user‐friendly electromagnetic virtual tools have beenintroduced toggether with useful tutorials in the IEEE APMagazine.

The IEEE motto “Teach me I’ll forget, show me, I’ll remember,involve me, I’ll understand” is best expressed with thesetools.

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MotivationMotivation

QuestionQuestion‐‐1:1:

How do you teach How do you teach electromagneticselectromagnetics to students to students

well above the average (within top 0.1 %)?

yy gg

within top 10 %?

around the average?

or, well‐below the average?


or, well below the average?

QuestionQuestion‐‐2:2:

Is it possible to teach all using the same methods / approaches?Is it possible to teach all using the same methods / approaches?

Engineering Engineering andand EM TeachingEM Teaching

WE ARE ENGINEERS. WE DEAL WITH

PHYSICSPHYSICS

WE USE WE ALSO USE


MATHMATH COMPUTERCOMPUTER

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RealReal--WorldWorldProblemProblem

EM Teaching and MODSIMEM Teaching and MODSIM

ProblemProblem

ConceptualValidity

Operational Validity

Numerical and physicalExperimentation

Physics-basedAnalytical Modeling

Data Analysis


Code Verification

Computer Programming

A Conceptual A Conceptual ModelModel

A Computer A Computer ModelModel

Antenna and Radiation Problems:Antenna and Radiation Problems:Use Maxwell equations and BCsDefine and Use Auxillary scalar and Vector Potential functions

EM EM Problems & Classical ApproachesProblems & Classical Approaches

yThen derive electric and magnetic fields.

Radar Radar Cross Section (RCS) and Scattering Problems:Cross Section (RCS) and Scattering Problems:Use Maxwell equations and BCsRepresent total fields in terms of incident and scattered fieldsSend an incident field on to the object, satisfy the BCsh l l h d f ld


Then calculate the scattered fields.

Guided Wave Propagation Problems:Guided Wave Propagation Problems:Use Maxwell equations and BCsApply Transverse & Longitudinal decompositionDeal with Eigenvalue and/or Green’s function Problems.

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ModelModel‐‐based Approachbased Approach

GEOMETRY USER DATA

ANALYTICALANALYTICAL NUMERICALNUMERICAL

GEOMETRY

ANALYTICAL

MODEL

GEOMETRY

CIRCUIT

NUMERICAL

COMPUTER CODE

NUMERICAL

MODEL

NUMERICAL

COMPUTER CODE

CIRCUIT


You solve your problem!You solve your problem!

NUMERICAL RESULT

Computer only gives you Computer only gives you a resulta result!!

NUMERICAL RESULT

YouYou discretizediscretize youryour problemproblem

ComputerComputer solvessolves it it forfor youyou!!

leventsevgi.net

EM Virtual ToolsEM Virtual Tools


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More than 20 VToolsin the last decade

EM Virtual ToolsEM Virtual Tools

in the last decade


Teaching ElectromagneticsTeaching Electromagnetics

Basic level Virtual ToolsBasic level Virtual Tools

EM Virtual Tool PurposeD FFT A virtual FFT instrument prepared with the LabVIEW It can generate and

Undergraduate CoursesUndergraduate Courses

EMW ThEMW ThD‐FFT A virtual FFT instrument prepared with the LabVIEW. It can generate anddisplay time and frequency domain behaviors of sinusoids, a rectangularpulse, a pulse train, a Gaussian function, a sine modulated Gaussian function.

1DFDTD A Matlab‐based FDTD simulation of plane wave propagation in time domainthrough single, double or three‐layer media.

TDRMETER A virtual time‐domain reflectometer virtual tool used to locate/identify faultsin all types of metallic paired cable. Fourier/Laplace analysis is also possible.

RAY / MODEHYBRID*

Ray/mode representations inside a parallel plate non‐penetrable waveguide.RAY computes/displays eigenray trajectories between specifiedsource/observer locations. HYBRID displays field vs. range and/or height.

EM Wave TheoryEM Wave Theory Transmission Line TheoryTransmission Line Theory Antennas and PropagationAntennas and Propagation Electromagnetic CompatibilityElectromagnetic Compatibility Computational ElectromagneticsComputational Electromagnetics


/ p y g / gDiSLAB A Matlab package designed to investigate wave propagation through a 2D

dielectric waveguide based on analytical and numerical formulations.ARRAY A simple Matlab antenna array package of isotropic radiators accommodated

with beam forming and beam steering capabilities.MGL‐2D A general purpose 2D FDTD package for both TE and TM type problems. Any

2D scenario may be created by the user by just using the PC mouse.SNELL A simple Matlab package for the visualization of ray contributions between a

source/receiver pair above a 2D ground using the ray shooting technique.

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AdvancedAdvanced LevelLevelEM Virtual

ToolPurpose

WEDGE A Matlab package for the exploration of wave propagation inside a 2D non‐penetrable,homogeneously filled wedge‐waveguide. It investigates line‐source‐excited wave fields in terms of

Graduate CoursesGraduate Courses

EMModeling and SimulationEMModeling and Simulationnormal/adiabatic/intrinsic modes.

DRMIX A Matlab‐based package prepared for the mixed‐path path loss predictions. The effects of thenumber of multi‐mixed paths, path‐lengths, electrical parameters, and the frequency can beinvestigated.

GrSSPE A simple Matlab groundwave propagation package for the visualization of EM propagation over non‐flat terrain through non‐homogeneous atmosphere, for waves radiated by a horizontal antenna overthe ground.

GrMoMPE A Matlab package which modifies MoM method by the application of forward backward spectralacceleration (FBSA) technique and integrate it with the SSPE method. Precise SSPE vs. MoMcomparisons are possible.

MSTRIP An FDTD‐based EM simulator for the broadband investigation of microstrip circuits. The user only

EM Modeling and SimulationEM Modeling and Simulation Diffraction TheoryDiffraction Theory Radiowave Propagation ModelingRadiowave Propagation Modelingand Simulationand Simulation Microstrip Circuit Design and Microstrip Circuit Design and SimulationSimulation


g p yneeds to picture the microstrip circuit via computer mouse on a rectangular grid, to specify basicdimensions and operational needs such as the frequency band, simulation length.

MGL‐RCS An FDTD‐based EM simulator for RCS prediction. The user locates a 3D image file of the target in 3DSgraphics format, specify user parameters. The simulator predicts RCS vs. angle and/or RCS vs.frequency.

MGL‐MTM A general purpose 2D FDTD package for metamaterial structures. Any 2D geometry can be created bythe user by just using the PC mouse.

WedgeDIFFWedgeFDTD

High Frequency asymptotics (GO,GTD,UTD,PO,PTD) and FDTD for the diffraction at an semi‐infinitewedge problem.

RCS Prediction and ReductionRCS Prediction and Reduction Guided Wave TheoryGuided Wave Theory

EM Modeling and SimulationEM Modeling and Simulation


2014

L. Sevgi, “Teaching Electromagnetic Modeling and Simulation as a Graduate‐Level Course,” IEEE Antennas and Propagation Magazine, Vol. 54, No. 5,

pp.261‐269, Oct 2012.

E. Arvas, L. Sevgi, “A Tutorial on the Method of Moments,” IEEE Antennas and Propagation Magazine, Vol. 54, No. 3, pp.260‐275, Jun 2012.


G. Apaydin, L. Sevgi, “A Canonical Test Problem for Computational Electromagnetics (CEM): Propagation in a Parallel Plate Waveguide” IEEE Antennas and Propagation

Magazine, Vol. 54, No. 4, pp.290‐315, Aug 2012.

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Radiowave PropagationRadiowave Propagation

2005 – SSPE_GUIL S i Ç Ul k F Akl "A M tl b b d T di i l P b li E ti


2007 – GrMoMPE

L. Sevgi, Ç. Uluışık, F. Akleman, "A Matlab‐based Two‐dimensional Parabolic Equation Radiowave Propagation Package", IEEE Antennas and Propagation Magazine, Vol. 47,

No. 4, 184‐195, Aug. 2005

2006 – DrMIX_GUIL. Sevgi, "A Mixed‐Path Groundwave Field Strength Prediction Virtual Tool for Digital Radio

Broadcast Systems in Medium and Short Wave Bands", IEEE Antennas and Propagation Magazine, Vol. 48, No. 4, pp.19‐27, Aug 2006


F. Akleman, L. Sevgi, "A Novel MoM‐ and SSPE‐based Groundwave Propagation Field Strength Prediction Simulator", IEEE Antennas and Propagation Magazine, Vol. 49, No.5, pp.69‐82, Oct 2007

2011 – PETOOLO. Ozgun, G. Apaydin, M. Kuzuoglu, L. Sevgi, “PETOOL: MATLAB‐based One‐Way and Two‐Way

Split Step Parabolic Equation Tool for Radiowave Propagation over Variable Terrain,” Computer Physics Communications (CPC), Elsevier, 182, 2011, pp. 2638‐2654.

RCS Prediction and ReductionRCS Prediction and Reduction


2008 – MGL‐RCSÇ. Uluışık, G. Çakır, M. Çakır, L. Sevgi, "Radar Cross section (RCS) Modeling and Simulation:

Part I – Definitions, Strategies, and Canonical Examples ", IEEE Antennas and Propagation Magazine, Vol. 50, No. 1, pp. 115‐126, Feb 2008

G. Çakır, M. Çakır, L. Sevgi, "Radar Cross section (RCS) Modeling and Simulation: Part II – ANovel FDTD‐Based RCS Prediction Virtual Tool ", IEEE Antennas and Propagation

Magazine, Vol. 50, No. 2, pp.81‐84, Apr 2008


2014 – FastRCSG. Cakır, M. Cakır, L. Sevgi, “An FDTD‐based Parallel Virtual Tool for the RCS Calculations of

Complex Targets,” IEEE Antennas and Propagation Magazine, Vol. 56, No.5, pp.74‐90, Oct 2014.

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Diffraction TheoryDiffraction Theory

2011 – WedgeGUIF H li ğl M A U l L S i “A M l b b d Si l f h El i


2012 – WedgeFDTDM. A. Uslu, L. Sevgi, “Matlab‐Based Virtual Wedge Scattering Tool for the Comparison of

High Frequency Asymptotics and FDTD Method,” ACES, Int Journal on AppliedComputational Electromagnetics, Vol. 27, No. 9, pp.697‐705, Sep 2012.

F. Hacıvelioğlu, M. A. Uslu, L. Sevgi, “A Matlab‐based Simulator for the Electromagnetic Wave Scattering from a Wedge with Perfectly Reflecting Boundaries,” IEEE Antennas and Propagation Magazine, Vol. 53, No. 6, pp.234‐243, Dec 2011.

2014 WedgeTOOL


F. Hacıvelioğlu, L. Sevgi, P. Ya. Ufimtsev, “Electromagnetic Wave Scattering from aWedge with Perfectly Reflecting Boundaries: Analysis of Asymptotic Techniques,”IEEE Antennas and Propagation Magazine, Vol. 53, No. 3, pp.232‐253, Jun 2011.

2014 – WedgeTOOLA. Uslu, G. Apaydin, L. Sevgi, “Work in Progress: Teaching EM Diffraction via Virtual

Tools: “The WedgeTOOL,” EDUCON 2015, Mar 18‐20, 2015, Tallinn Estonia

Microstrip Circuit Design and SimulationMicrostrip Circuit Design and Simulation


2011 – FilterDesignerA. Uslu, L. Sevgi, “Matlab‐based Filter Design Program: From Lumped Elements to

Microstriplines,” IEEE Antennas and Propagation Magazine, Vol. 53, No. 1,

2006 – TDRMETER_GUIL. Sevgi, Ç. Uluışık, "A Matlab‐based Transmission Line Virtual Tool: Finite‐Difference time‐

Domain Reflectometer", IEEE Antennas and Propagation Magazine, Vol. 48, No.1, pp. 141‐145, Feb. 2006


pp.213‐224, Feb 2011.

2006 – MSTRIPG. Çakır, M. Çakır, L. Sevgi, "A Novel Virtual FDTD‐based Microstrip Circuit Design

and Analysis Tool", IEEE Antennas and Propagation Magazine, Vol. 48, No. 6, pp.161‐173, Dec 2006

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Guided Wave TheoryGuided Wave Theory


2004 – RAY‐MODE / HYBRID_GUIL. B. Felsen, F. Akleman, L. Sevgi, "Wave Propagation Inside a Two‐dimensional Perfectly

Conducting Parallel Plate Waveguide: Hybrid Ray‐Mode Techniques and Their Visualisations", IEEE Antennas and Propagation Magazine, Vol. 46, No.6, pp.69‐89, Dec 2004 (Kamel‐Felsen paper, IEEE TAP Jul 1981)

2007 ‐WEDGE‐GUIL. Sevgi, F. Akleman, L. B. Felsen, "Visualizations of Wave Dynamics in a Wedge‐waveguide

ith t bl B d i N l Adi b ti d I t i i M d


with non‐penetrable Boundaries: Normal, Adiabatic, and Intrinsic Mode Representations", IEEE Antennas and Propagation Magazine, Vol. 49, No. 3, pp.76‐94, Jun 2007

G. Apaydin, L. Sevgi, “A Canonical Test Problem for Computational Electromagnetics (CEM): Propagation in a Parallel Plate Waveguide” IEEE Antennas and Propagation

Magazine, Vol. 54, No. 4, pp.290‐315, Aug 2012.

The philosophy and TipsThe philosophy and Tips

EMVtools should be useful and give physical insight.

EMVtools should be very user‐friendly (simple‐to‐use).

The user should be able to change some parameters.

Some parameters should be fixed so that the user will nott l t


get lost.

It should be open to non‐physical results to some extendso that the user may commend on them.

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EMVToolsEMVTools: Generic Design: Generic Design

Front Panel

The StructureDiscretizationParameters

Operational Parameters

VISUALISATION


PANEL

VT 1: VT 1: PPlatePPlate


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xPEC

0

222

nk

Postulate the problemPostulate the problem

z

PEC

0y

The Green’s function associated with this problem is:

)'()'()',';,( zzxxzxzxgkzx

22

2

2

2axg ,00 at +

a


0

)',';,( zxzxgLimz

and the Green’s function may be obtained as

a

x'nSin

a

xnSin

n

zzjn

j

e

azxzxg

2

||)',';,(


111m = 1 m = 3 m = 6

Mode solutionMode solution

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Pla

te h

eigh

t (a)


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

Mode profiles

Mode solution is the addition of all excited modes using sourceMode solution is the addition of all excited modes using source‐‐based excitation coefficients. based excitation coefficients.

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VT 1: VT 1: PPlatePPlateRay solutionRay solution


Ray solution is the addition of all the contributions of Ray solution is the addition of all the contributions of eigenrayseigenrays. .

VT 2: ArrayVT 2: Array


Feb 2005

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VT 3: SnellVT 3: Snell


Aug 2004

VT 4: VT 4: GRMoMPEGRMoMPE

L. Sevgi July 22, 2015Oct 2007

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VT 4: VT 4: GRMoMPEGRMoMPE


VT 6: VT 6: FeMixFeMix


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VT 6: VT 6: FeMixFeMix


VT 7: MGLVT 7: MGL‐‐2D2D


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Indoor PropagationMGL‐2D



Outdoor PropagationMGL‐2D



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VT 8: MTMVT 8: MTM‐‐FDTDFDTD

n=‐2

n=‐1


n=2

n=‐3

VT 9: VT 9: WedgeGUIWedgeGUI


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VT 10: VT 10: WedgeFDTDWedgeFDTD


SBC



Total fields Diff fields

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L. Sevgi July 22, 2015Total fields Scattered ields

VT 11: VT 11: MsFilterDesignerMsFilterDesigner


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VT 12: VT 12: FastRCCFastRCC


RCS ModelingRCS Modeling



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=90, =90, =0=0





1. Run FDTD1. Run FDTD

2 R FFT2 R FFT


2. Run FFT2. Run FFT

33.. PlotPlot RCS vs. RCS vs. AngleAngle


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VT 13: MSTRIPVT 13: MSTRIP


FDTD: FDTD: MicrostriplinesMicrostriplines

Port 2



Source+ Port 1

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Power Divider

FDTD: FDTD: MicrostriplinesMicrostriplines



FDTD: FDTD: MicrostriplinesMicrostriplines EBG filters



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[1] L. Sevgi, Electromagnetic Modeling and Simulation, IEEE Press – John Wiley (EM WaveSeries), NJ, Apr 214.[2] L. Sevgi, “Teaching Electromagnetic Modeling and Simulation as a Graduate-LevelCourse,” IEEE Antennas and Propagation Magazine, vol. 54, no. 5, Oct 2012, pp.261-269.[3] L. Sevgi, “Virtual Tools/Labs in Electrical Engineering Education,” ELEKTRIK, Turkish J. ofElectrical Engineering and Computer Sciences (Special issue on Electrical and ComputerEngineering Education in the 21st Century: Issues, Perspectives and Challenges), vol. 14, no.1, 2006, pp., 113-127.[4] Visit http://leventsevgi.net for the virtual tools discussed here.[5] L. B. Felsen, F. Akleman, L. Sevgi, "Wave Propagation Inside a Two- dimensional PerfectlyConducting Parallel Plate Waveguide: Hybrid Ray-Mode Techniques and Their Visualisations,”IEEE Antennas and Propagation Magazine, vol. 46, no.6, Dec 2004, pp.69-89.[6] L. Sevgi, “A Ray shooting Visualisation Matlab Package for 2D Groundwave PropagationSimulations,” IEEE Antennas and Propagation Magazine, vol. 46, no 4, Aug 2004, pp.140-145.[7] L. Sevgi, Ç. Uluışık, “A MATLAB-based Visualization Package for Planar Arrays of IsotropicRadiators,” IEEE Antennas and Propagation Magazine, 47 (1), Feb 2005, pp. 156-163.[8] L. Sevgi, Ç. Uluışık, “A Matlab-based Transmission Line Virtual Tool: Finite-Differencetime-Domain Reflectometer,” IEEE Antennas and Propagation Magazine, vol. 48, no 1, Feb2006, pp.141-145.[9] G. Çakır, M. Çakır, L. Sevgi, "A Multipurpose FDTD-Based Two DimensionalElectromagnetic Virtual Tool,” IEEE Antennas and Propagation Magazine, vol. 48, no.4, Aug2006, pp.142-151.[10] M. Çakır, G. Çakır, L. Sevgi, “A Two-dimensional FDTD-based Virtual Metamaterial -Wave Interaction Visualization Tool,” IEEE Antennas and Propagation Magazine, vol. 50, no.3, Jun 2008, pp.166-175.[11] L. Sevgi, F. Akleman, L. B. Felsen, "Visualizations of Wave Dynamics in a Wedge-waveguide with non-penetrable Boundaries: Normal, Adiabatic, and Intrinsic ModeRepresentations,” IEEE Antennas and Propagation Magazine, vol. 49, no.3, Jun 2007,pp.76-94.[12] F. Hacıvelioğlu, M. A. Uslu, L. Sevgi, “A Matlab-based Virtual Tool for theElectromagnetic Wave Scattering from a Perfectly Reflecting Wedge”, IEEE Antennas andPropagation Magazine, vol.53, no. 6, Dec 2011, pp.234–243.[13] M. A. Uslu, L. Sevgi,“Matlab-based Virtual Wedge Scattering Tool for the Comparison ofHigh Frequency Asymptotics and FDTD Method”, ACES Journal, vol. 27, no. 9, 2012, pp.697–705.[14] F. Akleman, L. Sevgi, "A Novel MoM- and SSPE-based Groundwave Propagation FieldStrength Prediction Simulator,” IEEE Antennas and Propagation Magazine, vol. 49, no.5, Oct2007, pp.69-82.[15] G. Çakır, M. Çakır, L. Sevgi, “A Novel Virtual FDTD-Based Microstrip Circuit Design andAnalysis Tool,” IEEE Antennas and Propagation Magazine, vol. 48, no.6, Dec 2006,pp.161-173.[16] G. Cakır, M. Cakır, L. Sevgi, “An FDTD-based Parallel Virtual Tool for the RCS Calculationsof Complex Targets,” IEEE Antennas and Propagation Magazine, vol. 56, no.5, Oct 2014,pp.74-90.[17] L. Sevgi, “A Mixed-Path Groundwave Field Strength Prediction Virtual Tool for DigitalRadio Broadcast Systems in Medium and Short Wave Bands,” IEEE Antennas and PropagationMagazine, vol. 48, no 4, Aug.19-27.

References

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Engineers should be well equipped in terms of physicalunderstanding, mathematical modeling as well as practicalimplementations.

ConclusionsConclusions

implementations.

With this in mind, lectures of measurement techniques should beimproved accordingly and concepts like accuracy, precision,resolution, error, uncertainty should be well taught.

Within this context, Virtual tools have become attractive / effectivetools in electromagnetic engineering education in addition to the


techniques such as problem‐based learning, or, inquiry‐basedteaching, etc.

The aim of using virtual tools should be understanding the real‐world and physics behind mathematical relations.

teaching electromagnetics via virtual toolspropagation magazine (since feb 2007) and a member of the...

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