Transmission Line Characteristic Impedance

08/11/2001

This is an area that really does mystify a lot of folks, but if we look at it in the right light it becomes understandable and quite interesting besides. There is a special reason why this is also called "Surge Impedance". Keep that thought in mind as we proceed.

• To begin with, we need to remember that radio signals do not travel instantly from one end of a wire or transmission line to the other. Secondly, these same signals travel even slower down various conductive mediums (wire, coax, etc.), compared with that of free space.
• For our example, we will use a nice long coax that we are told represents a 50 ohm "Characteristic Impedance". For the moment, this long coax will be open on both ends. You cannot measure this "50 ohms" with an ohmmeter, because this is not a simple "DC circuit" here.
• We all know that if we place a 50 ohm resistance across a power supply with an output voltage of 50V, we will by ohms law, expect to see a current flow of 1 Amp into and through that 50 ohm resistive load.
• We also would expect that if we place that so-called 50 ohm coax with the other end still open across that power supply of 50V, that there would be no current flowing through that coax.
• Ah, but here's the secret and a mystery: There's a strange thing that happens that can be demonstrated with the right test equipment and know-how.
• It just so happens, that for the first split second that the power supply sees that coax by it's characteristic impedance of 50 ohms, and will actually deliver 1 Amp into that coax! Believe it or not! But remember that this 1 Amp will travel down that coax at less than "light speed". It's this first surge of current as to why it's called this is also called "Surge Impedance".
• Now, when that 1 Amp quickly flows to the end of that coax and discovers that there is an open end there, another interesting phenomenon now happens. A "contrary signal of an inverted 1 Amp" travels backwards in that same coax, canceling the 1 Amp at the source, when it gets back there!
• But remember, this does take a bit of time, however short a time it may be, depends on the length and some other characteristics of that coax.
• With the right equipment and know-how, this "time-domain" can even be used to determine how long that coax actually is. In fact, the power companies use this technique to determine very closely where one of their power lines are down. Their equipment is called a "Time-Domain-Reflectometer". It can even be used to tell if the line-fault is a open or a short.
• So what happens if that long coax has a dead short at the end? Well, first of all that same "characteristic impedance" of the coax will present itself to that 50V source as before, and 1 Amp will zip down to the end. Fast, but not at the speed of light.
• When it gets to the end of the coax it finds that short circuit and bounces back (non-inverted this time) to the source to report that there's a short circuit out there. Now, the power supply will try to deal with that issue accordingly. Remember though that for the first instant of time that the power supply only delivered that 1 Amp, until the returning signal told it otherwise.
• Now obviously, we would not want to present a dead short, even at the end of a coax, to a good husky 50V power supply. Goodbye coax!
• The secret to our system here though is to have special test equipment that would deliver a very short pulse to the coax, and monitor that initial pulse and the echo of the return pulse. Depending on whether the return echo is inverted or not, will tell us whether the end of the coax is open or shorted.
• What happens though if we have a pure resistive load that "matches the characteristic impedance" of that coax? What we will find is that first of all there is no bounce-back echo of any kind! In fact, we will discover that when we adjust the resistive load to above and below the characteristic impedance of the coax, disregarding the power source pulse voltage, we will observe that the return echo will ether invert, non-invert, or disappear altogether. We can actually use this method to determine what the characteristic impedance of our coax actually is by when the return echo disappears.
• A last consideration is that there will be normal losses in that length of coax, so we will find that our return echo will not return in full strength.