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Originally Posted by linuxworks /img/forum/go_quote.gif
I'm trying to understand that last part. if a reflection is the wave traveling forward, hitting the remote end point and then a portion returning - then isn't 'longer' going to give a progressively weaker reflection?
I'm also trying to remember from my old ham radio days (30+ yrs ago, literally) that even if we got the swr down to a reasonable level, we would still like to have our transmission lines be in multiples of 1/2 wavelength (or something like that). I wonder why no one talks about 'magic lengths' of cable, then?
or maybe I just invented a new boutique market? lol! for 44.1, use this length or multiple. for 48k, use this. for 96, use this.
'god knows' what to use for dd5.1 or dts.
lol?
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Hi again,
You said a lot of things and I do not have time to answer them all. I think you missed some of my points. Separate the format from the hardware. Then XLR is a 3 pin connector so it can accommodate 2 wires and a shield.
An RCA can not accommodate 2 wires and a shield. Also, yes, a transformer will, to a large extent convert a single ended signal to a balanced signal, but it is not perfect, especially when the wire itself is not balanced. So the differential receiver is an ADDITIONAL measure. In fact, the AES standard calls for one transformer, but the AES/EBU calls for 2 transformers (one at each end), and on top of it there is a BALANCED DIFFERENTIAL RECEIVER. Also, note that a shield should be connected only at the driver end, not at the receiver end.
Regarding reflections:
We are talking about digital signals. So lets just take a step, say 0V to 1V. When the driver is “looking” at the cable, it does not see the end, only the input side. The driver “sees” an impedance. Initially the cable looks like a resistor but impedance is not a resistor, you can not measure it with a DC ohm meter. (The impedance is a characteristic that is due to cable capacitance and cable inductance). So a sudden rise of 1V step divided by 100 Ohm means we are sending 10mA wave into the cable.
That wave front propagates at around 1/3 to 2/3 the speed of light. The speed is determined by the one over the square root of the dielectric constant of the insulating material (such as polypropylene or similar). Given that most of the used materials have a dielectric constant range of 3-6, say we take 4, then square root of 4 is 2 and the wave speed is around half the speed of light. Just figure around 1.5 nano second per foot (pretty close value to most cables).
Now, the 10mA current wave front is moving" towards the cable end. There are 3 cases here:
1. The cable end is terminated by 100 Ohms (same value as the cable impedance). Given that Ohms law always applies, when the current wave get to the termination, the voltage developed on the termination is 1 V, because 10mA times 100 Ohms equals 1V. Sounds simple enough until you read point 2 and 3:
2. Say the termination is 200 Ohms. Now we have 10mA times 200 Ohms, and the voltage step is too large. In fact say the cable is opened (no termination). In such extreme case, the step will double to 2V. That is not a stable condition, because there is now a 2V at the end and only 1V at the beginning of the cable. So a current wave is now going backwards. What will happen when that wave gets back to the driver? It depends on what termination (source impedance) it will see. In most cases the source impedance is much lower then the cable impedance and that will cause an inverted reflection…. Such as in point 3:
3. The case where the termination is lower then the cable impedance: The 10mA wave sees a lower resistor say 80 Ohms. The voltage step is too low. Forget 80Ohms, lets go for broke - a shorted end. In such a case, that 10mA current step must go back. The voltage step is 100% reflected… The driver will not "know" that the end of the cable is shorted until twice the propagation delay of the cable. It sends a step, and all looks fine until the wave goes all the way to the end and all the way back. The electrons are not any smarter then we are, they must get there to see what is going on
The original first step does not lose amplitude until it goes to the end. At the end there is a reflection coefficient which can be calculated by (ZL-Z0)/(ZL+Z0). ZL is load (termination), and Z0 is the cable impedance. For example, a 100Ohm cable and 80 Ohm termination yield (80-100)/(80+100) = -.11 thus a negative reflection of 11%. When the termination is higher then the cable, the reflection coefficient is positive.
Of course, the first reflection, be it positive or negative eventually gets back to the source, and that same formula applies. You now have a reflection of a reflection. Typically, the reflection at the source is close to -1 because the source is low. Say a 10Ohm source and 100Ohm cable then you have (10-100)/(10+110) = -82% reflection. The second reflection is now traveling to the end, where it will make for a reduced third reflection and so on…
Note that the round trip time is twice the cable propagation time length. For example, 100 feet length, and 1.5nsec per foot, the reflections are spaced by 300nsec. That rate has noting to do with sample rate or anything other then the cable.
It is most important to realize that we are talking about a step. This is the opposite case to DC. At DC, there are no reflections and cable impedance is a non issue. Let’s raise the voltage very slowly from 0V to 1V, say over 1 minute. Is that almost DC? Yes, we do not worry about reflections. But what about say 10nsec “sudden step”? Well, rule of thumb is to pay attention to reflections when the rise time of the step is shorter then the cable propagation time (thus length).
An audio signal, say 1V at 20KHz, has a reasonably slow slop. The would cycle is 50usec. Say a 10usec rise is still very slow with respect to say 100 feet (only 300nsec).
The alternative way to look at it all is with standing waves. A distance much lower then the wave length is different then a distance that contains many wave length. I prefer the reflection coefficient view for digital analysis.
The point is: When dealing with slower signals such as audio analog, we do not think about reflections, so we do not terminate our analog cables at 75Ohms or so. Typically we terminate at 10Kohms or higher. There are no cables with impedance that high, in fact there is no 300Ohm cable around, they all range in the 30-180Ohms and that is at the extreme cases…
But for faster changing signals, such as 10nsec digital audio steps, when the cable length is long enough, we need to terminate properly to avoid reflections. At 1 foot, we have 3nsec round trip which is still shorter then 10nsec rise. At 10 feet, we have a 30nsec round trip which is 3 times longer then the rise time, thus reflections count and termination matters.
I can not write such long post often, I hope it helped. Short cable is the way to go. Don’t let anyone tell you otherwise.
Regards
Dan Lavry
Lavry Engineering