propagation of pulses in transmission lines

Here, we examine the theoretical behavior of pulse propagation in transmission lines under different transient conditions. Our focus is on how pulses interact with various combinations of resistors (R), inductors (L), and capacitors (C) in both series and par- allel configurations. We base our analysis on the transmission line theory outlined in the chapter “Transients in Transmission Lines” from the book Fundamentals of Applied Electromagnetism. Our study starts with a review of the telegrapher’s equations and the wave equation, which describe how voltage and current travel along a line. We then examine how a voltage pulse reflects and transmits when it meets loads made up of pure resistance, RL, RC, and RLC circuits, both in series and parallel setups. We’ll take a closer look at important factors like characteristic impedance, reflection coefficient, and time constants for each arrangement. By taking this approach, the report showcases how various terminations affect the shape, amplitude, and delay of reflected and transmitted pulses. The inclusion of reactive elements leads to complex transient behaviors, including overshoot, ringing, and waveform distortion. These effects are crucial in high-speed digital and analog systems, where signal integrity is a top priority. By offering a unified theoretical view of these cases, this work lays the groundwork for future research on pulse behavior in real-world transmission line systems.