Electronics > Beginners
Does cable impedance add to source or load impedance?
vealmike:
--- Quote from: Doctorandus_P on February 15, 2019, 12:31:20 pm ---Impedance of a transmission line is a whole other beast, and Richard keeps hammering on it that it is not relevant. But why then bring it up?
--- End quote ---
I suspect, because when someone asks about the impedance of a cable that is what they are referring to. They may be mistakenly using the wrong terminology, but that is the question conveyed by the words used.
To the OP.
At dc or low frequencies (compared to the length of the line), you can use lumped elements to model the cable. Just as we consider a capacitor model to have a small R & L element as well as a C. A cable will have a small C & L as well as a R.
You can draw those in series with the cable's resistance and calculate the effect using standard ac analysis. Or if you're feeling lazy, put it into PSPICE and simulate.
I think the point being made is that these stray inductances and capacitances are usually so tiny compared to the cable and load that they do not need to be taken into consideration.
If you were driving a very high impedance load, then maybe. But it would usually be far simpler to just reduce the impedance of the load.
I challenge the OP to measure the self inductance and capacitance of a 10m length of speaker wire.
1/ Because it's bloody difficult, the values are small, and it will give him a sense of proportion.
2/ Because it will answer his questions in a way that we're not going to be able to and help him understand what's going on.
Dave:
--- Quote from: Doctorandus_P on February 15, 2019, 12:31:20 pm ---Impedance of a transmission line is a whole other beast, and Richard keeps hammering on it that it is not relevant.
--- End quote ---
When we talk about transmission lines, we're usually interested in characteristic impedance.
We simply call it impedance to save us an extra word, but the two are not simply interchangeable.
--- Quote from: Richard Crowley on February 15, 2019, 12:15:15 am ---Remember that series resistance has nothing to do with cable impedance.
--- End quote ---
A bit of a misleading statement.
Characteristic impedance of a cable is:
The resistance, inductance, conductance and capacitance are all specified per unit length.
It is only because resistance and conductance usually have a negligible effect at RF frequencies, that we tend to ignore them and simplify the equation to:
David Hess:
--- Quote from: fonograph on February 15, 2019, 10:27:34 am ---Cable impedance, cable resistance... does it matter? Its almost the same thing. I cant imagine how one part cable impedance, the resistance, adds up to source output impedance but the cable reactance does not. That doesnt make any sense, not saying its wrong, I need explanation why its like that.
--- End quote ---
At high frequencies where the signal does not have time to reach the end of the cable, only the cable's impedance is seen by the source. At low frequencies, the impedance seen is the load plus the cable's series resistance and the cable's parallel capacitance.
In audio applications, both can be relevant. At audio frequencies, the cable impedance is practically irrelevant except for the parallel capacitance which can cause instability however at high frequencies, the source must be designed to handle the cable impedance plus load mismatch to prevent instability.
The above leads to an interesting problem in some poorly designed amplifiers where they work fine with short or long cables but oscillate with medium cable lengths. Look for something like a pi network which includes a pair of Zobel networks to avoid this problem. This also serves to suppress RFI pickup in the output leads.
ArthurDent:
Some of the typical values of inductance and capacitance per foot of speaker wire I've seen are around .2 microhenry and a few picofarad, small enough to be ignored.
If you model speaker wire as an RLC network it will look like a speaker crossover network. A typical speaker crossover network could have around a 10uF capacitor and a 1 mH inductor, many orders of magnitude greater than any speaker wire you could use. So to make a crossover network with just speaker wire you would probably need over a mile of two conductor wire and the resistance of that length of wire could be in the range of 70 ohms. No matter how you look at it, resistance is the major problem with long or smaller diameter wires.
Here are a couple of links that help explain some of the stuff to consider. One concludes with: "The bottom line is the resistive losses are far more a dominant factor to consider when choosing loudspeaker cables. The associated electrical delay of a "long" cable vs a "short" cable is simply not a real issue to concern yourself with."
https://www.audioholics.com/audio-video-cables/speaker-cable-length-differences-do-they-matter
Richard Crowley:
Indeed, over on GearSlutz audio forum cable series resistance and especially parallel capacitance is a very frequent topic of discussion. But cable (characteristic) impedance is only a topic when referring to high-frequency signals. Like digital audio, digital video, or RF like wireless microphones, etc.
Electrified string instruments (guitars, bass, etc.) still use a half-century old connection protocol/standard. High-source-impedance, low-level, unbalanced. Impedances on the order of 100K to 1M ohm. Now, in more modern times some (many?) pickup coil assemblies are lower impedance, and some instruments have battery-powered buffer amplifiers which provide a lower source impedance.
Cable parallel capacitance has the effect of creating a high-cut/low-pass filter (in interaction with the source impedance). For that reason many manufacturers still make "instrument cable" which is specifically designed for low parallel capacitance.
And because the high-impedance nature of the source (and by necessity load impedance), the typically cables tend to be microphonic and sensitive to movement. For that reason many instrument cables have a conductive coating on the outside of the insulation dielectric which attenuates the triboelectric voltages. And sometimes even around the inner conductor.
In order to reduce the capacitance, they frequently use a very small center conductor. But since the signal is such a very low voltage (and low power) the series-resistance of the center conductor is of no practical significance over the relatively short distances (a few meters). For instrument cable, parallel capacitance is the important factor, not series resistance.
OTOH, at the other end of the audio chain, for a connection between a power amplifier and a speaker, we are talking about very low source and load impedance (on the order of 10 ohms) In that scenario, parallel capacitance is of no practical significance. However, series resistance is of very significant importance because it will attenuate the signal at such low (source and destination) impedance. Which is why speaker cables tend to be large gauge for low series resistance.
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