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Mudcat : JEH, thanks for the reply, but I think you missed my question, what is being referred to when a cable is called 75 ohm? What is 75 ohm, the source sending the signal through the cable or the load at the other end? Or is it 75 ohm per mile (kilometer) or something like that? Like the guy with a gun to his head in one of the Dirty Harry movies - "I gots to know man."
Well, I answered you - 75 ohms is the cable's impedance.
But, let's try to do better than just hanging a name on it.
Impedance in general is a sort of
effective resistance that only applies to alternating current. It is the resistance offered to the flow of AC. It may or may not be different from the DC resistance. For a simple composition resistor, for example, the DC resistance and the AC impedance are the same for most practical uses; but for a wirewound resistor or a coil, the impedance to AC current flow will be higher than the DC resistance.
(By the way, by "AC" here we really mean "time-varying", not necessarily "alternating." A single pulse from 0 to 20 ma and back to 0 is "time-varying" and so is considered "AC" even though it never actually "alternates" its polarity.)
The reason is that a time-varying current induces a time-varying magnetic field, which in turn tries to induce current in the same conductor - but in the opposite direction. The effect of this differs with frequency. Capacitance also contributes to impedance.
In the case of coaxial cable, think about it like this:
Suppose we have a cable of very long length and we connect a battery to it - say positive to center conductor and negative to shield. We leave the far end open for now.
As soon as the battery is connected, it will attempt to charge the cable as a capacitor is charged, positive charge on the center and negative on the shield. This charge takes time to propagate "down" the cable. Incidently the
velocity factor of a cable is simply the fraction of C at which this happens. If the cable has a VF of 0.89, the figure for RG59 coax, then charge - or changes of charge - propagate through the cable at 89% of the speed of light.
(The electrons themselves don't move anywhere near that fast; in fact "electron drift velocity" is at rather ordinary speeds, but that's another discussion.)
Now think about the point of view of the battery. Current is being drawn to charge this very long capacitor. If you measure the current and divide that into the battery voltage, E/I, the answer comes out in ohms. It's the cable's impedance. Z=E/I. Ohm's Law for AC.
The greater the per-foot capacitance of the cable (for example, the closer the conductors are to each other), the faster it will draw current, therefore the
lower the impedance. Conversely, the greater the inductance per foot, the more the "back EMF" fights the charging current, therefore the
greater the impedance.
Impedance does not vary with the length of the cable - it is not "75 ohms per mile" or whatever as resistance would be. The usual formula for impedance is: Z = sqrt (L / C), where L is inductance in henries and C is of course capacitance in farads. A little thought will show you that for a cable, both the inductance and capacitance are quoted per unit length, but the "per unit length" cancels itself out of that formula as it appears on both sides of the fraction bar.
Or - The longer the cable, the more capacitance there is to charge, but also, the
farther away that additional capacitance is. The rate at which charge propagates down the cable doesn't change when you make the cable longer! So making the cable longer doesn't change the impedance.
The impedance of a component usually has a DC resistance component as well. However in the case of cable this is negligible for practical lengths.
You asked about the ends... well, in most audio work, we don't much care about them, or about the cable impedance either. In most line-level analog hookups, your source impedance is around 100 ohms (sometimes as high as 600, sometimes only a few tens of ohms in high end gear), your load impedance is at least 10K ohms, and the cable impedance is whatever it happens to be. This works fine. 75 ohm cable works fine but isn't necessary. Same is true for speakers: Power amplifier outputs are small fractions of an ohm, speakers are eight ohms, cable impedance doesn't matter (series resistance does matter though). Same for microphones, although the differences (source to load impedance) aren't as great.
The reason it doesn't matter is that for audio work your cable is a tiny fraction of the wavelength in the cable. The shortest audio wavelengths are, say, 20 kHz; at 20 kHz with a cable VF about 0.89, wavelength is about eight and a quarter
miles, and at lower frequencies it is even longer. So, telephone system engineers do have to worry about impedance matching, but audio engineers don't. In fact for most sources and loads, if your load impedance actually matched the source, it would try to draw too much current!
If your cable length is a significant fraction of your wavelength, though, impedance mathcing does matter. Let's think about this.
Go back to the battery and very long cable. If the cable is of inifinite length, charge just keeps propagating down the cable forever. If instead we connect an AC signal source, and we go travelling down the cable with a scope with a high-impedance probe, then at any point on the cable (barring attenuation due to distance) we can measure the same signal.
But now instead think what happens with a cable of practical length. Go back to the "battery" model for a moment. What happens when that propagating charge gets all the way to the end?
Well, the current obviously can't keep going. Nor can it just disappear. What happens is that it is "reflected" off the end of the cable, back toward the source.
That's pretty clear. What isn't so clear is that if you short the end of the cable the same thing happens.
The reason is that the impedance of the cable has abruptly changed at the end - whether it's open or shorted. In the case of the "open", what is propagated back to the source is the
stoppage of current flow. In the case of the short, it's an
increased current draw as the short tries to discharge the capacitance of the cable into zero ohms, and this discharge current propagates back up the cable to the source.
If the cable length is short w.r.t. the wavelength this isn't a problem. The voltage is the same "everywhere at once" on the cable, even with the reflections. But if the wavelength is short enough (or the cable is long enough), the reflections cause corruptions of the waveform you're trying to send.
The cure is to ensure the cable is terminated (at both ends) with a source and load that match the cable impedance.
Think about the battery again. Suppose we have a 75 ohm cable. To the end of the cable we connect a 75 ohm resistor. When the charge propagating down the cable reaches this resistor, it continues drawing current at the same rate! We do the same thing at the source, and we have a matched transmission line. The terminating resistors simulate a cable of infinite length.
In digital audio, your max frequency is up around 6 MHz. Wavelength is now down around 145 feet in cable with a VF of 0.89. A cable of just 12 feet, well within the length guidelines for s/pdif or IEC958 as it is now called, is a significant fraction of this. So impedance matching is important. It's also important in baseband video, where your top frequencies are about the same - try using 50 ohm cable instead of 75 ohms, and you will see your images are softened a bit. If your cable is long enough you will even see a "ghost" image on the screen slightly to the right of the real one. You are literally seeing a reflection of the original signal, bounced back down the cable to the source and then back again.
The 50 ohm story (actually it's about all coax impedances, not just 50 ohms)
Velocity factor (VF) of common coaxial cables
Transmission line problems (that is, "class problems" and solutions that help in understanding)
Practical Line-Driving Current Requirements , particularly the section titled "simplifying a complex problem"
Impedance matching for microphones
s/pdif interface
(edit) p.s.: Please let me know if this helps, makes things more or less clear, etc.!</font>
