Reflections at a short-circuit

freddyfish

Hey

I wounder why an approaching electrical impulse is completely reflected if you short-circuit the conductor. I have read some explanations suggesting it is because Kirchhoffs law must be satisfied, but that argument falls badly when the conductor is long and the pulse short, such that there will be no constructive interference and doubling of amplitude. According to the formula z_c=(z₁-z₂)/(z₁+z₂) there should be no reflection, since the characteristic impedance of the two parts of the conductor have the same characteristics.

If the above z₁ instead is the impedance/resistance (instead of the characteristic impedance) of the first part of the conductor, this would mean that a resistor inserted between the two conductors that earlier composed the short-circuit would cause reflections even though its impedance matches the characteristic impedance of the conductor.

Thanks

nsaspook

Think about where the energy is when moving on the transmission line.
http://www.tpub.com/neets/book10/41h.htm

sophiecentaur

The reflection coefficient is given by
ρ = (z_term-z₀)/(z_term+z₀)
(Your formula is not dimensionally correct.)

If z_term =0
the reflection coefficient becomes -1, which is what you get, isn't ti?

freddyfish

Oh, that was a typo. I meant to write coefficient of reflection.

Thanks you for your answers. :)

freddyfish

The formula has, everywhere I have seen it, been given by your termination impedance exchanged for the characteristic impedance of the leader which the signal leaves at the joint. According to your formula all you have to do is match the termination impedance to the characteristic impedance of the second conductor, which is not the case.

sophiecentaur

I don't understand that comment. If you terminate the line with Z₀ you will get a ρ value of zero. If you put a shunt of Z₀ across the line you will be effectively terminating with Z₀/2, which will be a mis-match with ρ of -1/3. Are we confusing the action of terminating with the action of adding a parallel element?
When you short the line out, of course, it makes no difference whether the short is at the end of a line or at some point on the line; the ρ is -1, in that case.

freddyfish

I interpreted your reply as if the characteristic impedance of the termination between two conductors (not necessarily with the same characteristic impedance) was denoted by Z_term. If you by Z_term mean the extra circuitry at the joint And the second conductor, then the formulas are identical.

sophiecentaur

Hopefull my subsequent post will have cleared that up. I used the word 'terminate' in the literal sense - i.e. what is connected to the 'end' of the line in question. This could be a resistor, another line or a dead sheep (antenna engineer's term for any load you care to think of but not an entirely fictional idea, I believe).
But there seemed to be some doubt about the formula producing the right answer - it does.

freddyfish

I really appreciate your help I must add before taking this further. :)

Why is z_term zero at the short-circuit? Would not the stuff connected to the end of the conductor have a characteristic impedance that is not zero?


Talking about all these reflections - if you have an open circuit which is subjected to alternating voltage, wouldn't this mean the circuitry before the point of breach(?) is constantly causing energy to be lost/dissipated to the surroundings?

sophiecentaur

A short circuit in parallel with another value of impedance (the downstream bit of line) is still a short circuit. No signal will propagate past a short, will it? It will all be reflected. Nothing can be dissipated in a short - that's why all the energy is reflected. This all assumes that your transmission line is not radiating (ideal). Sort out those basic issues before talking about a leaky line.

freddyfish

Yes, I am aware of that. Still, at the short circuit there are at least two ends - one through which the incident signal propagates and one through which the signal could possably return, assuming that we don't already know that 100 % of the signal is reflected. Hypothetically removing the second one and measuring its characteristic impedance will leave us with a nonzero result. Reconnecting it, this will cause the characteristic impedance of the termination to be nonzero as well. Right?

That an ideal transmission line does not cause any loss of energy is indeed intuitive, but I was looking for confirmation that this is not the case for a real line and implicitly wondering to what extent this loss is a consern, i.e., the magnitude of the loss (which of course is different for different constructions). Voltage differences in a line --> current. Current + resistance --> power...

sophiecentaur

I am completely confused now. What arrangement are you actually trying to describe? You quoted a formula, earlier on, and I assumed that this was a simple transmission line question (two parallel wires or a co-axial arrangement) and that you were familiar with it. A Google search will show you many hits which will relate that formula to a a practical transmission line. See this link
How are you actually relating this theory to your practical setup?
Can you give us a diagram, please?

f95toli

I wonder if the source of confusion is that the OP is thinking that characheristic impedance is a property of a SINGLE conductor; whereas in fact it is always a property of a PAIR of conductors. This is easier to understand if you realize that we are (nearly) always assuming that you have a TEM wave propagating along the line, and that much of the energy is actually travelling in-between the conductors (which is why the speed of light in a coaxial line is set by the dielectric).

Hence, it does not make sense to talk about the impedance of a short circuit, this would always be a single conductor that connects the signal conductor to ground; in the case of a coaxial cable you could make short by simply bending the inner conductor and soldering it to the outer conductor (and if you wanted to terminate a coaxial line you could solder a 50 ohm resistor between the centre conductor and ground).

Also, when talking about ideal short circuits it is implied that you are talking about something much shorter than the wavelength with zero resistance and reactance. Now, this could obviously never happen in real life, but it is not difficult to make a short with almost perfect reflectivity.

sophiecentaur

You could be right there. Let's wait for a reaction from ff.

freddyfish

Okay, this should clarify my thoughts:

I have attached a picture of a simple circuit. In the original circuit there is no blue line, but then there is a short circuit introduced, represented by the blue line. The length of the blue line has, of course, nothing to do with the "length of the short circuit", but rather we are talking about an ideal short circuit. If the equation for the reflection coefficient ρ is applied at the point which is contradictory represented by the blue line, then Z_term=Z₃ and Z₀=Z₁.

On the other hand, this would mean that if Z₃=Z₁ there would be no reflection at all, which is not the case. This reasoning would imply that the reflection is caused by the point of connection alone. Then the term Z_term would somewhat loosely be the characteristic impedance of only the point of connection, and the termination is completely independent of what the return path, which for that matter could be more than just a wire, has in store.

Attached Thumbnails

 

sophiecentaur

You clearly haven't read f95toli's last post. He was right about your fundamental misconception about transmission lines and what is meant by 'characteristic impedance'. Rather than try to give you the 'right' version, I will suggest you look at this link and many others, in which the term is defined and used correctly.
It amazes me that you haven't already looked up the term. You clearly were having difficulty yet you seem to be using PF as your sole source of information. We have all (you included) been talking at cross purposes and wasting our and your time. What would you have done in the past, when all that was available was a good text book ?

nsaspook

I just remembered this classic video about wave reflections.
http://www.youtube.com/watch?v=DovunOxlY1k