Wednesday, August 10, 2011

Transmission Line Effect: Bouncing Voltages

It's 4am on black Friday at Walmart. A single door opens and millions of people including yourself run to the entrance as one mob. You're running as fast as everybody around you. As the people near the building, those who luckily made it to the door enter the building. However, you, being at the front of the mob and having not run close enough to the door, smash into the outer walls of the building. The people behind you don't see the wall yet and keep running, pushing you into the wall even more. Soon enough, you have the collective force of thousands of people squishing you. 

The same thing happens with voltage. When entering a high impedance load (narrow doorway) from a low impedance cable (wide parking lot), voltage (pain) can spike up as you can see in the simulations below (Line C, top trace). The input voltage is only 100V, but the voltage at the load jumps up to 160V.


When you push back, the people behind you push the people behind them, and a wave of shoving propagates down the mob of people. When this wave reaches the end of the mob (the people at the very back) they push forward and that wave propagates back to you. This phenomenon is called ringing as demonstrated in the oscillation seen in the top trace.

Below are models of cabling. The inductor keeps the current going, just like you want to run at the same speed as the people behind you (to stay alive). The capacitor is like the space infront of you; it's somewhere to run to. Almost all conducting cables can be modeled this way, a chain of infinitesimally small units of L, R, and C. All cables have parasitic inductance and capacitance. Line D and the top trace demonstrates how doubling the cable length (double length of Line C) doubles the amount of time for the voltage to hit the load. This is just like having the parking lot double in length. It takes twice as long for you to run into the wall.
 Moral of the story:
  • Walmart on black fridays is dangerous. 
  • Unexpected voltage spikes fry parts when cables are too long or impedances are not matched.