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Short Topical Videos[edit]

Reference Material[edit]

<latex> \documentclass[11pt]{article} \usepackage{graphicx} \usepackage{amsmath} \usepackage{fullpage} \begin{document}


Have you ever taken a rope, tied one end of it to something, and then shaken the other end sent little waves down it? If you haven't, try it. You'll notice that the waves travel up the string, hit the tie-off, and bounce back at you. It turns out the same thing happens when you send a wave down a transmission line. Energy has to be conserved, so if the wave can't dissipate into something at the end, it has to bounce back at you. As anyone who has had to listen to their own voice echo on a phone line knows, this is very annoying.

\begin{figure} \includegraphics[width=1in]{termination.png} \caption{Terminating a transmission line with a resistive load that matches the characteristic impedance.} \end{figure}

All you need to do to solve the problem is properly terminate the transmission line. This means providing a resistor at the far end of the line that closes the circuit with the same value as the characteristic impedance of the cable. Likewise, when trying to launch a signal into a transmission line, in order to avoid reflecting off the input (and to protect against any random waves that might be traveling back up the cable), it is a very good idea to match the output impedance of the driver to the characteristic impedance of the cable.

\section*{Reflection and Transmission Coefficients}

Sadly, impedance mismatches are a fact of life. A reflection coefficient, $\Gamma$, is used to characterize how a wave responds to an interface: \begin{equation} \Gamma=\frac{Z_{load} - Z_{src}}{Z_{load} + Z_{src}} \end{equation}

Likewise, $T$ is used to denote the transmission coefficient. Energy conservation dictates that $T=1+\Gamma$.

You may notice that these coefficients look very much like the coefficients used to describe the transmission and reflection of light from a change in refractive index. Totally not an accident. \end{document}