# Transmission Line Reflected Waves

#### 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

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#### 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.

#### jasonRF

Gold Member
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
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

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