Introduction to Time - Varying Electrical Networks

By Prof. Shanthi Pavan   |   IIT Madras
Learners enrolled: 892
The course is intended as a gentle introduction for analog, mixed-signal and RF circuit designers to the area of time-varying circuits and systems. The pre-requisites are minimal. After a refresher and building background in linear-time invariant networks, it introduces linear time-varying (LTV) and linear periodically time-varying (LPTV) circuits. The applications of the theory are illustrated with practical examples.

M.Tech/M.S/Ph.D students, advanced undergraduates
PREREQUISITES : Engineering mathematics, a basic course on electric network analysis at the UG level, signals and systems.
INDUSTRIES  SUPPORT     : Companies engaged in analog, mixed-signal and RF design
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Start Date : 18 Jan 2021
End Date : 09 Apr 2021
Exam Date : 25 Apr 2021 IST
Enrollment Ends : 01 Feb 2021
Category :
  • Electrical, Electronics and Communications Engineering
  • VLSI design
Credit Points : 3
Level : Postgraduate

Course layout

Week 1:Motivation for the topics covered in the course, review of linearity and time-variance;Review of electrical network basics, incidence matrix, Tellegen's theorem;Tellegen's theorem (cntd), its use to prove reciprocity in bilateral networks, reciprocity in networks with controlled sources
Week 2:Reciprocity in networks with controlled sources (contd), inter-reciprocal networks;Modified Nodal Analysis (MNA) formulation to write network equations;MNA formulation (contd), MNA stamps of circuit elements, Reciprocity and inter-reciprocity revisited
Week 3: Reciprocity and inter-reciprocity (contd), the adjoint network.;Introduction to noise in electronic circuits;Noise in RLC circuits, Nyquist's theorem, Bode's Noise Theorem
Week 4:Bode's noise theorem (contd), input referred noise sources in networks;Input-referred noise sources (contd) - equivalent noise voltage and current sources;Equivalent noise sources, noise factor
Week 5:Need to study time-varying circuits and systems;Linear time-varying (LTV) system basics;Linear Periodically Time-Varying (LPTV) systems basics
Week 6:Harmonic transfer functions, the Zadeh expansion;MNA equations in LPTV networks with Harmonic transfer matrices;LPTV circuit example : the sampling mixer
Week 7: Impedance and admittance in LPTV networks, Norton and Thevenin equivalents;The N-path principle;N-path circuits (contd) - the time-interleaved ADC
Week 8:N-path circuits (contd) - the multiphase dc-dc converter, introduction to the N-path filter;N-path filters (contd) - input impedance and gain;N-path filters (contd)
Week 9:Reciprocity and inter-reciprocity in LPTV networks - time-reversal to generate the adjoint;Inter-reciprocity (contd), transfer-function theorem;Inter-reciprocity (contd), the frequency-reversal theorem
Week 10:Inter-reciprocal signal-flow graphs. Example : chopped amplifiers;Chopped-amplifiers with sinusoidal and square-wave modulation;Adjoint networks - the switched-RC kernel example; time-domain implications of adjoint networks
Week 11: Time-domain implications of the adjoint - example of a switched-RC network. Sampled LPTV networks;Equivalent LTI filter of a sampled LPTV system; derivation of the equivalent impulse response, switched-RC network example ;Cont. time delta-sigma as a sampled LPTV system
Week 12:Response of LPTV systems to modulated inputs; equivalent LTI filter;Introduction to noise in LPTV networks, noise in switched-RLC networks, the Bode noise theorem applied to LPTV networks;Course summary and recap

Books and references


Instructor bio

Prof. Shanthi Pavan

IIT Madras
Shanthi Pavan obtained the B.Tech degree in Electronics and Communication Engg from the Indian Institute of Technology, Madras in 1995 and the doctoral degree from Columbia University, New York in 1999. Since 2002, he has been with IIT-Madras, where he is now a Chair Professor of Electrical Engineering. His research interests are in the areas of high speed analog circuit design and signal processing.Prof.Pavan is the recipient of several awards, including the IEEE Circuits and Systems Society Darlington Best Paper Award and the Shanti Swarup Bhatnagar Award. He is the author of Understanding Delta-Sigma Data Converters (second edition), with Richard Schreier and Gabor Temes. Prof.Pavan has served as the Editor-in-Chief of the IEEE Transactions on Circuits and Systems:Part I - Regular Papers, and on the technical program committee of the International Solid State Circuits Conference. He has been a Distinguished Lecturer of the Solid-State Circuits and Circuits and Systems Societies. He is a fellow of the Indian National Academy of Engineering, and an IEEE fellow.

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: 25 April 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 Madras .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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