??? 01/28/05 02:57 Modified: 01/28/05 03:05 Read: times |
#85978 - Series termination methode Responding to: ???'s previous message |
Erik said:
How can a resistor in series with a high impedance input terminate a line? Assume you have two points in space, A and B, which you connect by a pair of wires, let's say a twisted pair. The distance between point A and B shall be 1m, or so. At point A is a voltage source, which drives a constant voltage into the twisted pair cable. At point B is a reciever providing infinite input impedance. If we change very slowly the output voltage of driver A, then we will see exactly the same potential at reciever B. It seems that the potential change at point A can immediately be seen at reciever B. No delay seems to occur. And as we make the changes of potential only very slowly, we will even not be able to see any delay. We are now in the domain of electrostatics. We can arbitrarily change (very slowly, or course) any potential in such a system and will immediately see the reaction at different places, whereever we feed this potential to by our cable. Of course we know from physics courses, that the change will not immediately occur at reciever B, but this will not have any noticable consequences for us. And even if we make one fast change of potential at driver A, we know what the reaction will be at reciever B if we wait for a suited time, the same as if we had made the change very slowly. So, for steady state conditions we can solve all our potential problems by the laws of electrostatics. Our twisted pair is only a piece of wire which transports the potential from driver A to reciever B. The special shape of this cable doesn't play any role, it can be a pair of straight wires of 1m length or a cable turn of 10km length, two chains, parts of the chassis of a car, or whatsoever. Situation totally changes if we make very fast changes of potential at driver A. Then we will notice a certain delay between the change of potential at driver A and the reaction at reciever B. We will notice, that the 'fast change' travels with a certain velocity, which is very high but finite. We will also notice, that the 'fast change' will be reflected, when reaching either end of cable, unless termination impedance at ends of cable shows a very certain value. Physical analysis shows, that the wire is no longer transporting a constant potential, but a wave packet. This wave packet is made from electrical and magnetical fields, which show a certain coupling and which must fullfill certain conditions. We are no longer in the domain of electrostatics, but electrodynamics. And with electrodynamics our twisted pair no longer easily and immediately transports a constant potential from point A to point B, but opposes now a bottle neck for the fast travelling wave packet representing the sudden change of potential at point A. If we put directly at output of driver A a series resistance before the signal goes into the cable, and if we choose this resistance so that total source impedance of driver exactly matches the characteristic impedance of cable, then a voltage dividing of exactly factor 2 will take place. Means, if your sudden change at output of driver A is a transition from 0V to 5V, then a transition from 0V to only 2.5V can be measured at entering point of cable. So, a square wave of only 2.5V amplitude will travel along the cable. If the edge reaches the end of cable and there's an infinite load impedance, then a total reflection occurs. It's the same as if you throw a ball against a wall without having losses due to friction or else. If the ball is totally reflected by the wall, then the wall recieves the double of the momentum the ball had before the reflection. Similar with our transmission line, the total reflection without losses results in a doubling of potential. So, what we see at reciever B is not a square wave of 2.5V amplitude but 5V! We are not able to notice at reciever B, that the signal has travelled along a transmission line. The only we could detect is a more or less slight increase of rise time of edge, if we compare the rise times of signal at point A and B. The signal which is echoed at reciever B travells back to driver A and is totally absorbed because source impedance of driver A exactly matches characteristic impedance of cable. This total absorption results in two things: 1. No further reflection occurs at driver A, and 2. the absorbed portion of wave packet superimposes to original signal, resulting in a change of potential at cable entry to finally 5V. In opposition to situation at reciever B, where no staircase signal can be seen but a true 0V-to-5V transition, at entry of cable (at driver A) a staircase signal can be observed, consisting of two steps, a 0V-to-2.5V transition and then 2.5V-to-5V transition. Transmission line effects, means this echoing stuff, will occur, if the rise time of signal is in the same range as the time period the signal needs to travel from point A to B. If the rise time is very low, then we will not notice this echoing, because there's no distinct sudden change. Or by other words: A smooth edge can be represented by an infinite number of infinitely small sudden changes, where all these infinite separate reflections overlap and smear. No distinct reflection can be seen. Each digital chip family has it's certain maximum cable length, where no cable termination is urgently needed. Normally, the slowlier a chip is the longer the cable may be. For 74HCMOS the maximum cable length is about 20cm, if I remember correctly. Kai |