I think it is best to think transmission lines as just transmission lines
LC-analogy is somewhat misleading, since evenly distributed capacitance and inductance behave quite differently to lumped components. One of the most striking feature of a correctly terminated transmission line is that the line input impedance is resistive (assuming that losses can be neglected), not inductive or capacitive, regardless of the line length. Even unterminated line looks equal to characteristic impedance resistance at first, until the reflection comes back. Another important one is that a transmission line behaves just like a delay, there is no distortion on the waveshape.
A common mistake is to substitute the transmission line with a "LC-lowpass filter", where L is equal of line "DC-inductance" and C is equal to line "DC-capacitance" which gives completely wrong picture of the operation. One would need infinitely many LC-sections composed of infinitesimally small L and C to mimic the transmission line behavior. In fact, one needs only the characteristic impedance and time delay imposed by the lossless transmission line to describe it completely. For most casual digital stuff, ordinary short-length coaxes (few meters) or low-impedance pcb traces can be assumed to be lossless without making a huge error.
With logic circuits, one can't usually source-terminate the line perfectly, because most logic gates have different output impedances in high and low-states. This can be seen from the following scope trace, which is a measurement from 74AHC1G125 driving a 2 meter long RG-58 connected to Agilent MSO6034A, in 1 Megaohm input impedance, so only termination is only at the source end. Note that the frequency used was just about 200 kHz, but the same effect is seen even if the frequency is dropped to 10 Hz or so, naturally as the reflection is due to edges, not repetition frequency. One does not need very high performance scope to see this effect. Longer coax makes the effect easier to see.
As you can see, the termination on the rising edge is quite good, but falling edge has a "ringing" feature. It is not ringing in sense that it does not follow sinusoidal shape, but it is just an echo of the same edge bouncing back and forth in the cable. As the line becomes shorter, the bouncing rate increases, and eventually rises above the measuring equipment bandwidth, and it obtains apparent sinusoidal shape. The rise time suffers somewhat eventually due to losses in the cable and connectors. This "ringing" means that driver output impedance in low-state is lower than in high-state.
One interesting effect happens if we make the source termination resistor value much higher (150 ohms here) than the characteristic impedance of the cable (50 ohms):
One would expect (in sense of previously mentioned LC-lowpass filter) that the edges would become less steep due to cable capacitance, but no, they retain their shape, but instead there are multiple reflections until the signal rises its full height. This can be explained by that the driver output impedance forms a resistive voltage divider initially with the cable impedance. If the input impedance of the transmission line would be inductive or capacitive as seen by the line driver, the edge would not be just a simple step.
A compromise something like this is usually quite acceptable:
I think that with just a basic understanding of the transmission line properties, one can make quite long digital pathways, but of course, there are other practical issues than just managing the signal integrity to make long distance stuff, like coupled noise and such.
Regards,
Janne
Home
Help
Search
Login
Register
