Applied Electromagnetics For Engineers

By Prof. Pradeep Kumar   |   IIT Kanpur
Learners enrolled: 1319
Applied electromagnetics for engineers is designed to be an application oriented course while covering all the theoretical concepts of modern electromagnetics. It begins by an in-depth study of transmission lines which play an important role in high-speed digital design and signal integrity of PCBs. After a brief review of necessary mathematics (coordinate systems, vector analysis, and vector fields), the course covers analytical and numerical solution of Laplace's and Poisson's equations, quasi-static analysis of capacitors and skin effect, inductance calculations, and Maxwell equations. Wave propagation in free-space, ferrites, and peroidic media are covered along with waveguides (rectangular, planar dielectric, and optical fibers) and antennas. The course includes a balance between theory, programming, and applications. Several case studies will be discussed.

Intended Audience :UG 2nd, 3rd Year

Prerequisites : Electricity and magnetism at the level of high-school, Vector analysis, Differential and integral calculus, programming using Matlab (preferable)

Industries that will recognize this course :Core UG course that is necessary for follow up courses on high speed digital design, RF and microwave, fiber optics, antennas. Companies/Industry such as Sterlite, Analog Devices, GE, Comsol India, Matlab, Texas Instruments, Defense labs etc will be interested.

Course Status : Completed
Course Type : Core
Duration : 12 weeks
Start Date : 26 Jul 2021
End Date : 15 Oct 2021
Exam Date : 24 Oct 2021 IST
Enrollment Ends : 09 Aug 2021
Category :
  • Electrical, Electronics and Communications Engineering
  • Photonics
Credit Points : 3
Level : Undergraduate

Page Visits

Course layout

Week 1: 

  • Introduction to Applied EM theory
  • Lossless Transmission line equations
  • Frequency-domain behavior: Characteristic impedance of T-line
  • Reflection and transmission coefficients
  • Complete solution for sinusoidal propagation

Week 2: 

  • More general T-lines
  • Attenuation and propagation coefficients
  • Transmission line techniques: Standing wave ratio (SWR) and line impedance
  • Visual aid: Smith Chart derivation
  • Smith chart applications: Impedance to admittance conversion, SWR and impedance calculation

Week 3: 

  • Impedance matching techniques - Part 1
  • Impedance matching techniques - Part 2
  • T-lines in time-domain: Reflection from mismatched loads
  • Lattice diagram calculations
  • Pulse propagation on T-lines

Week 4: 

  • Case study: High-speed digital signals on PCBs
  • Transients with reactive termination
  • Application: Time-domain reflectometry
  • Review of Coordinate Systems
  • Review of Vector analysis -1

Week 5: 

  • Review of Vector analysis -2
  • Vector fields -Part 1
  • Vector fields - Part 2
  • Overview and importance of Maxwell's equations
  • Boundary conditions between two media

Week 6: 

  • Solution of Laplace's and Poisson's equation -- Analytical techniques
  • Solution of Laplace's and Poisson's equation in two dimensions
  • Numerical solution of Laplace's equation: Finite difference method
  • Numerical technique: Method of moments
  • Quasi-statics: Does an ideal capacitor exist?

Week 7: 

  • Magnetostatic fields: Biot Savart and Ampere's laws
  • Magnetic field calculations
  • Inductance and inductance calculation
  • Quasi-statics: Fields of a wire
  • Quasi-static analysis of skin effect

Week 8: 

  • Uniform plane waves - one dimensional wave equation
  • Uniform plane waves: propagation in arbitrary direction, phase velocity, polarization
  • Plane waves in conductors an dielectric media
  • Reflection and transmission of plane waves at a planar interface
  • Oblique incidence and reflection of plane waves - s and p polarization

Week 9: 

  • Total internal reflection and Snell's laws
  • Application: Multilayer thin films
  • Application: Fabry-Perot cavity
  • Waveguides - General introduction
  • Rectangular metallic waveguide modes

Week 10: 

  • Dispersion and attenuation
  • Dielectric planar waveguides
  • Case study: Optical fibers
  • Application: Fiber-optic communications
  • WDM optical components

Week 11: 

  • Wave propagation in crystals and index ellipsoid
  • Wave propagation in Ferrites
  • Wave propagation in periodic structures: Diffraction
  • Vector potential and wave equation
  • Radiation by dipole

Week 12: 

  • Fundamental Antenna parameters
  • Half-wave dipole
  • Antenna array and diffraction
  • Application: RFID
  • Looking ahead

Thanks to the support from MathWorks, enrolled students have access to MATLAB for the duration of the course.

Books and references

Electromagnetics with applications, 5th ed, J. D. Kraus and D.  Fleisch, McGraw Hill, 1999

  • Engineering Electromagnetics, Hayt and Buck, 7th    edition, McGraw Hill.
  • Electromagnetic waves, D. Staelin, A. Morgenthaler, and J. A. Kong, Pearson, Pearson, 1993.
  • Applied Electromagnetics: Early Transmission Line Approach, S. M. Wentworth, Wiley, 2007.
  • Practical Electromagnetics, D. Misra, Wiley, 2007.

Instructor bio

Prof. Pradeep Kumar

IIT Kanpur
Dr. Pradeep Kumar K. obtained his PhD from IIT Madras specializing in quantum cryptography. He joined the Department of Electrical Engineering at IIT Kanpur in 2009. He is also associated with the Centre for Lasers & Photonics. At IIT Kanpur he and his students work in the fields of quantum key distribution, nonlinear fiber optics for signal processing, mitigation of linear and nonlinear impairments in coherent optical communications, mode locked fiber lasers and chaos, fiber-optic sensors for undersea applications, and fiber-optic modeling. He is also actively involved in the LIGO-India effort under IndiGO umbrella. His lab develops single-photon detectors, single- and subcarrier RF transceivers, and is currently working on true random number generators. He has published over 40 papers in peer reviewed journals and conferences. He also holds three patents (one granted and two pending). His MOOC courses on NPTEL has been very popular with more than 15000 enrollments from across the country.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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