# Transmission Line Reflected Waves

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1. Aug 6, 2015

### jendrix

Hi ,

I'm studying transmission lines and how waves move through the device , so far I haven't delved into the maths behind it as I have been trying to get an overview of it.So far I have seen the effects when there is an open circuit , shorted and matched impedance loads.

The example I saw said that with a short circuit :

Reflection coefficient =-1

Phase 180 Degrees

It then says how the incident and reflected waves will interfere to create a standing wave. Is this correct? I thought that if the incident wave and reflected wave (which will be in anti-phase) combined it would be destructively giving no resultant wave?

Thanks

2. Aug 6, 2015

### Dorian Black

Imagine the two waves as they travel opposite each other; one incident and one reflected. This would bring about a different sum of the amplitudes at different times and at different locations along the line. Two sine waves running in opposite directions; neither would they cancel everywhere, nor would they add up to higher values everywhere. Whether the reflection coefficient is -1 or +1 it doesnt really matter. Both will yield standing waves, though with different null-locations.

3. Aug 6, 2015

### jasonRF

Yes, it is correct, as Dorian Black indicated. For me it is hard to visualize the sum of two waves traveling in opposite directions. I actually think the math helps here. Let the short circuit be at $x=0$. If the incident wave is traveling in the positive x direction, then a simple voltage wave can be written as $v_i = v_0cos(\omega t - k x)$. The reflected wave is then $v_r= -v_0cos(\omega t + k x)$. The total voltage is then $v = v_r + v_i$. If you use trig identities you can turn this into the standing wave pattern you are looking for.

jason

Last edited: Aug 6, 2015