# EM Waves on TL

Discussion in 'General Electronics Chat' started by Mazaag, May 9, 2008.

1. ### Mazaag Thread Starter Senior Member

Oct 23, 2004
255
0
Hey guys...

I am trying to understand how voltage and current exist on a TL.

Lets say we have a coaxial cable, that is terminated with a load (matched , for now)

Say we have a voltage out (say a sine wave) from a circuit like an amplifier or something... so say the core of the coax is connected to the output, and the outer conductor of the coax is connected to ground...

If our output is of high enough frequency, ( ? ) our coax no longer acts as a simple wire, and behaves as a TL .. ie: lumped analysis no longer applies ( when exactly does is this the case ?)

Now.. the voltage is no longer the same along the length of the coax.. and as a result, the current also varies.... HERE lies the confusion....

when we talk about voltage and current (say across a resistor) , we talk about the voltage being ACROSS the resistor, and the current is THROUGH the resistor...

In the case of the TL .. what is the potential difference across? isn't the voltage variation with respect to ground ? (outer conductor) ? and where/how does the current flow ? does it travel through the dielectric ? I understnad that the Voltage over the Current is the Characteristic Impedance... what exactly does it represent ?

Thanks guys

2. ### Papabravo Expert

Feb 24, 2006
12,212
2,697
The behavior of a transmission line is described by a partial differential equation with boundry conditions. The derivation of that partial differential equation for an ideal transmission line assumes that the conductors have no DC resistance. Then think of a large number of sections consisting of a series L and a shunt C. Put a resistor Zo at the other end from the source.

In the solution there are two parts. In one of the parts the votage and current do not depend on time, only on distance along the transmission line. This solution is called the standing wave; it does not depend on time. The other part of the solution does not depend on distance along the tranmission line it is only a function of time. This solution is called the traveling wave.

You can think of these two solutions being superimposed on each other. Now depending on the frequency of the source and the length of the terminated transmission line the two solutions will interact in various ways.

At some frequency your terminated trnasmission line will have a standing wave only with no traveling wave. I believe this happens when the length of the transmission line is a quarter wavelength.

With respect to voltages and currents. Current flows back and forth on the center conductor, this is AC remember, and it also flows back and forth in the shield. Voltages can be measured at various points usually with respect to the source or with respect to the load.

For a complete treatment I recommend:
Gonzalez, G., Microwave Transistor Amplifiers Analysis and Design, Prentice Hall, 1997, pp.4-22

http://www.amazon.com/Microwave-Tra...bs_sr_1?ie=UTF8&s=books&qid=1210363222&sr=1-1

3. ### Caveman Senior Member

Apr 15, 2008
471
1
For some good pictures of what happens for a more intuitive feel, also look at Howard Johnson's books. They are a bit expensive, but are very good. My Barnes & Noble has it, so I can just go flip through it over some Starbucks...

4. ### Mazaag Thread Starter Senior Member

Oct 23, 2004
255
0
...but if the voltage changes as a function of distance, that means the current is different at different points on the coax? but how does that make sense if the current flows through the core ? i mean... isn't current related to the flow of charge THROUGH something ? in other words , how can the water flow be different everywhere along the pipe?

5. ### Papabravo Expert

Feb 24, 2006
12,212
2,697
The answers to all of the questions in your last post are yes. Water flow, like current, is a vector field. That means that at each point there is a vector with both magnitude and direction. The way it happens is that the effects of forces like pressure or voltage are not instantaneous. They propagate along a pipe, or a channel, or a transmission line. If the voltage is changing and the impedance is constant then Ohm's law requires a change in the current.

In fluid flow if you change the diameter of a pipe certain things happen to pressure and velocity. Check out Bernouli's principle. Also remember that in a smooth (not turbulent) laminar fluid flow the velocity of a fluid at a boundry is zero! At every other point away from the boundry the velocity has a profile.

6. ### Caveman Senior Member

Apr 15, 2008
471
1
Various parts of the current are going through the capacitances that exist between the core and shield. So some of the current is not making the full trip down the cable.