Electromagnetic Field Theory: A Problem Solving Approach Part 62. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Transmission Line Transient Waves 585 r0 v v_ Vp 2 T 1 2T Y0V0 YqVq 2 Short circuited line. Rl 0 ï z t 2D 0 i z t 2D Yo Vo v 2 t Vp Ko Vo Vp 2 - z t Vo V - V_ M T t 2T c t T Open circuited line RL vl d Figure 8-9 rov_ 1 clt - D 2D Vo i z t 2D 0 ii Open Circuited Line When Rl 00 the reflection coefficient is unity so that V V_. When the incident and reflected waves overlap in space the voltages add to a stairstep pulse shape while the current is zero. For t 2T. the voltage is Vo everywhere on the line while the current is zero. iii Short Circuited Line When Rl 0 the load reflection coefficient is 1 so that V V_. When the incident and reflected waves overlap in space the total voltage is zero while the current is now a stairstep pulse shape. For i 2T the voltage is zero everywhere on the line while the current is V0 Z0. 8-2-3 Approach to the de Steady State If the load end is matched the steady state is reached after one transit time T l c for the wave to propagate from the source to the load. If the source end is matched after one 586 Guided Electromagnetic Waves round trip 2T 21 c no further reflections occur. If neither end is matched reflections continue on forever. However for nonzero and noninfinite source and load resistances the reflection coefficient is always less than unity in magnitude so that each successive reflection is reduced in amplitude. After a few round-trips the changes in V and V_ become smaller and eventually negligible. If the source resistance is zero and the load resistance is either zero or infinite the transient pulses continue to propagate back and forth forever in the lossless line as the magnitude of the reflection coefficients are unity. Consider again the de voltage source in Figure 8-8a switched through a source resistance Rs at t 0 onto a transmission line loaded at its z Z end with a load resistor RL. We showed in 10 that the V wave generated at the z 0 end is related to the source and an incoming V_ wave as r - 1I .
