Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni Narayana Rao Edward C. Jordan Professor of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA Distinguished Amrita Professor of Engineering Amrita Vishwa Vidyapeetham, Coimbatore, Tamil Nadu, India

Lines with Initial Conditions 6.5 Lines with Initial Conditions

Line with Initial Conditions

Example:

Uniform Distribution

t = 0.5 mS t = 1.5 mS

t = 2.5 mS

Bounce Diagram Technique for Uniform Distribution

Energy Storage in Transmission Lines we, Electric stored energy density = We, Electric stored energy =

wm, Magnetic stored energy density =

Check of Energy Balance Initial stored energy

Energy dissipated in RL

System in steady state at t = 0–. Another Example: System in steady state at t = 0–.

t = 0–: steady state

t = 0+:

Solving, we obtain

Voltage G = 0 G = 0 tV = 1

Current G = 0, tC = 1 tCeff = 0.5 G = 0

t = 3 ms + : New steady state

t = 3 ms + :