A couple of thoughts, probably ill-founded:
I was thinking about “damping factor” (DF ∝ ZLOAD / ZOUT) and how relatively small additions of (ZWIRE) might substantially change damping factor. … This chain of reasoning lead me to again question just how much various DF numbers might impact actual speaker output. Yes, yes, going from quantitative to qualitative in one fell swoop.
Remembering back to other threads, I remember various sage conclusions that having DF >> 20 or so seems to be the edge of diminishing returns. Yet, if DF = 20, and a speaker might (nominally) have an 8 Ω rating, then
kind of tells me that a nominally very nice piece of 10 foot cable, having a pair of 16 gauge pure copper conductors …
Now see? This is perhaps a few hundredths-of-an-Ω. But I'm interested in the effect on damping factor. Putting that back into the DF equation:
Its clear that the DF has dropped from “diminishing returns” (20) to something modestly lower. In the 'audible' region?
This doesn't even take into account linear capacitance or inductance afforded by cable length and gauge-of-wire. (and physics: separation of conductors, thickness of insulation, geometry of insulation, proximity to other dielectrics, parasitic inductors, yada, yada, yada…)
There are endless snake oil-and-bear grease theories (and entire businesses capitalizing on the same) for making endlessly expensive speaker cables. While most of the “theory” is absolute bûllsnot, I do think in the end this: if DF matters substantially, then added cable resistance matters markedly.
Additionally, one can see from (ZLOAD / (ZOUT + ZRES)) formula that the effect of linear resistance increases with higher nominal damping factors. As examples (same 10 foot 16 GA wire):
now try
Again, a substantial change in DF. IS the change acoustic? I don't know. Others might tho'.
______
GoatGuy
¹ R = L/10000 × 10gauge/10 is not an equation you'll find anyplace common. It is in fact the derivation from this: 10 gauge solid-core 99.99% copper wire has a resistance of 1 Ω per 1000 feet.
Wire gauge is an exponential scale… 20 gauge is 10× the resistance of 10 gauge. 30 gauge, is 10× that of 20 gauge, or 100× that of 10 gauge. And so on. Each gauge is 10¹/₁₀ power different from either neighbor. 25.9% more going up, or 20.6% less, going down.
There is a trick tho' with that (L/10000) term. The actual term is L/(1000 × 10), which is to say, the length in thousandths-of-a-thousand-feet times a correction-factor of 10. The correction factor is scaling the fact that (10¹⁰/₁₀ = 10¹ = 10) which is "10× too much". So, L/10000 multiplicatively removes that 10× without changing the underlying exponentiality of equation.
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Metrics make things easier:
Resistance = Metal resistivity x Length / Cross section area.
Copper resistivity is 17 x 10-9
From tables: AWG #14 is 2.09 square millimiter.
#10 5.27mm2
#12 3.3mm2
#14 2.09mm2
#16 1.31mm2
#18 0.82mm2
#20 0.52mm2
Don't foget that the wire lenght is double the cable lenght.
Resistance = Metal resistivity x Length / Cross section area.
Copper resistivity is 17 x 10-9
From tables: AWG #14 is 2.09 square millimiter.
#10 5.27mm2
#12 3.3mm2
#14 2.09mm2
#16 1.31mm2
#18 0.82mm2
#20 0.52mm2
Don't foget that the wire lenght is double the cable lenght.
Wow... cool 
Yes. It does As I and a number of members have already mentioned earlier - the "closer" the speaker to the amplifier's output - the better.
Some recent researches indicate that too tight control of the speaker (remarkably high DF) is not always a good thing - the speaker's measured distortion increases with very high DF values. But anyway, in my opinion, it's better to control the DF in the amplifier (less global FB, etc.), than having it noticeably increased because of the cable.
Yes. It does
As I and a number of members have already mentioned earlier - the "closer" the speaker to the amplifier's output - the better.Some recent researches indicate that too tight control of the speaker (remarkably high DF) is not always a good thing - the speaker's measured distortion increases with very high DF values. But anyway, in my opinion, it's better to control the DF in the amplifier (less global FB, etc.), than having it noticeably increased because of the cable.
Actually, old bean, using Metric doesn't in any way improve the little formula that I posted. Note if you will … that you had to FIND the above information. Then note that in so finding, you didn't actually convert mm² to Ω-per-meter. You could, had you explored the math!
If “№ 10 is 1 Ω per 1000 feet” and its also 5.27mm², then you can convert that to metric with
1 / (1000 × 0.3048) = 0.003281 Ω/m (for № 10 at 5.27mm²)
0.003281 × 5.27 = 0.01729 Ω-mm² per meter
0.003281 × 5.27 = 0.01729 Ω-mm² per meter
Now you could then go on to fill out the rest of your table.
№ 10 = 5.27 mm² = 0.01729 ÷ 5.27 mm² → 0.003281 Ω/m
№ 12 = 3.30 mm² = 0.01729 ÷ 3.30 mm² → 0.005239 Ω/m
№ 14 = 2.09 mm² = 0.01729 ÷ 2.09 mm² → 0.008273 Ω/m
№ 16 = 1.31 mm² = 0.01729 ÷ 1.31 mm² → 0.013198 Ω/m
№ 18 = 0.82 mm² = 0.01729 ÷ 0.82 mm² → 0.021085 Ω/m
№ 20 = 0.52 mm² = 0.01729 ÷ 0.52 mm² → 0.033250 Ω/m
or, we could use MY formula… (let's try for a 1 meter = 1 ÷ 0.3048 → 3.28 foot hank):
№ 10 = 3.28 ft ÷ 10,000 × 1010 ÷ 10 → 0.003281 Ω/m;
№ 12 = 3.28 ft ÷ 10,000 × 1012 ÷ 10 → 0.005198 Ω/m; (–0.81%)
№ 14 = 3.28 ft ÷ 10,000 × 1014 ÷ 10 → 0.008239 Ω/m; (–0.42%)
№ 16 = 3.28 ft ÷ 10,000 × 1016 ÷ 10 → 0.013058 Ω/m; (–1.04%)
№ 18 = 3.28 ft ÷ 10,000 × 1018 ÷ 10 → 0.020695 Ω/m; (–1.83%)
№ 20 = 3.28 ft ÷ 10,000 × 1020 ÷ 10 → 0.032810 Ω/m; (–1.33%)
Just saying.
The “Metric is better” argument is painfully thin.
GoatGuy
In Europe we don't mess with AWG.
When we buy electric wires, they are specified in square millimeter.
I know… “we don't use any inventions other than European ones…” Its a very European point of view. I've often found myself both irritated and bemused by the consequence of all that European pro-individualism pro-nationalist pro-Metric thinking: in the most recent Granger catalog, there are nearly 7 pages of hexagonal fasteners in ASME sizes. 3 different kinds of threads, 30+ general sizes, variations on materials, anodizing, hardnesses. Yet these 7 pages cover 100% of American Standard of Mechanical Engineering fasteners and threads. By comparison, in the very same Granger catalog, it takes nearly 85 pages to cover the European, Japanese and other Asian fasteners. You think that that's an improvement? I don't. There are over 18 variations on thread pitch; at any given nominal diameter, at least 8. There are over 70 nationally important “standards” for diameter size. There are more variations (but huge holes in representation) of different anodizing, plating, hardness levels of fasteners and bolts.
In the end? I'm sorry but there's no call except “total confusion”. The not-European-but-American system is SO much easier. 3 thread pitches. 30 diameters. You can tell by “picking up a nut and screw” whether they're right for each other or not. Not so with France's 11.5 thread/cm pitch compared to Germany's 12 thread/cm.
But go ahead: be as individualistic, nationalist, protectionist as you like. We - in the Americas - don't order wire by an obscure sequence of square-millimeter gauges (which in the end are just translations of AWG), but rather an easy to remember sequence of numeric gauges. 0, 2, 4, 6, … 16, 18, 20… 28, 30, 32, … to about 42 or so. Covering every wire from 250 horsepower 576 V mains wiring to the very finest high voltage Tesla coil magnet wire. Can't do THAT in Metric, lad.
LOL! Please feel free to defend Metric if you like. You simply can't overlook the silliness tho' of the truth in that last paragraph, permuted to the present day. You don't have to admit the truth, but you might sit back and laugh at the silliness.
PS: all the above notwithstanding, I - as a career scientist - think Metric is The Bomb. The Max. Awesome in most of its scientific consequences. I am old enough to remember what was before, a bewildering unit-system of drams, minims, grains, pounds, ounces and scruples. Tuns, hogsheads, rods and chains. Cwt (hundredweight), grosses, gills and knots. I remember that stuff, in the scientific mode. By comparison, tho' it is definitely an imperfect system², the Metric system, specifically the MKS system is pretty darn good. CGS is good too - if you like reading older German literature. But MKS is now essentially the only practicing Metric system.
The only “imperfect system” aspect is this: who had the bâhlls to prevent the ultimate unification of the Metric system?
A system where “1 m³ = 1 liter”?
A system where “1ℓ of H₂O = 1 gram”?
A system where “1 m² = 1 are”?
THAT would have been a truly unified system. Its units tho' unfortunately don't cluster - in the human world - around “human objects and distances” very nicely. The only way is to make a smaller meter, for at least some of it to be useful. If the longitude from North Pole-thru-Greenwich to the Equator is 100,000,000 meters instead of 10,000,000 meters (so that a unified meter is about 10 cm in today's measure) then 1 m³ = 1ℓ (as today). Your weight tho - say 75 kg in todays measure - would be 75 g in the unified measure. In a way, easier, no? Just saying. Someone really had big balls.
GoatGuy
This is only theory, in practice you need a micrometer to measure correctly the small ohm values of wires.
To calculate the induction of the wire you need a high voltage generator and an oscilloscope. I measure this daily for factories building high power electric motors.
I always use this type of models: AEMC 6240 Micro-Ohmmeter 10A - AEMC Instruments
With the option to ground the return shield you can remove inductance from the equation or ground induction. I send the equipment to the calibration professionals every month. I doubt this has any application or importance for the small voltages in audio... 0.1 ohm or 0.003 has no meaning in audio cables. So many wires in XO and coils, it doesn't matter.
To calculate the induction of the wire you need a high voltage generator and an oscilloscope. I measure this daily for factories building high power electric motors.
I always use this type of models: AEMC 6240 Micro-Ohmmeter 10A - AEMC Instruments
With the option to ground the return shield you can remove inductance from the equation or ground induction. I send the equipment to the calibration professionals every month. I doubt this has any application or importance for the small voltages in audio... 0.1 ohm or 0.003 has no meaning in audio cables. So many wires in XO and coils, it doesn't matter.
Well, that is the question, isn't it? I have shown, using (I hope) uncontested math, that a relatively small addition of resistance can change the damping factor as “seen” at the speakers, by a substantial amount. A quantitatively substantial amount. 250 → 93, as one example above, and 100 → 50 in another. In the original example (20 → 17), the difference isn't so large.GABDX said:
I proposed rhetorically that high damping factors may have little-to-no audible effect for most amplifier-speaker combinations. Yet and still, there are those amongst us who insist that they are able to hear differences in damping-factors between either adjustable amplifiers (using active negative feedback) or just different amplifiers (much more subject to actual amplifier differences apart from damping factor!)
So that's a long winded way of my saying “I don't think you're right, there bud.” Perhaps you are, and perhaps we should not worry about an extra 10 feet of modest-gauge speaker cable. Empirically, this may be so: at our church we ran a hundred feet of 12 gauge to a large "Bag End" brand speaker at the back of the church in the Choir Loft. Our RA–100 amplifiers had no problem driving it. The sound was excellent. Not a good experiment for sure, but clearly nothing acoustically impressive was lost.
Just saying,
GoatGuy
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A definition for the best amplifier in the world is a straight wire with gain.Finding a piece of cable to connect a speaker will become more complex than designing the best amplifier in the world!
So there is still a cable in the circuit.
Yes, I'm thinking about it - this exercise requires some time for preparation. My studio microphone and the mic preamp are stored in the external warehouse - I hope I will pick them up next week.
We don't even care about the absolute distortion values at this point - it would be really interesting to see the difference
It's possible to create a reasonably good model of the complex impedance of the speaker, but unfortunately, it's rather difficult to simulate the non-linearities caused by the mechanical (suspension, cone deformation) and electromagnetic (magnetic field degradation away from the center position, back EMF). So seems to be easier to practically measure the live prototype
Wolfgang Klippel from Klippel Gmbh is a guru of simulating the speaker distortion (see the links in the post #151), my knowledge and modeling "instrumentation" are not that good in this area.
Absolutely.
And, anyway, it will not be correlated with any other aspects than the behavior of the specific amplifier you will use (stability margin with the added capacitance of the cable) and the ones of your specific speaker ( change of its distortion and response curve with the damping factor modified by the added resistances of the cable).
There is no need to do such work because your results will have no overall value and cannot be generalized.
Butler Audio
I don't know what it is about damping factor that causes people to put their brain in neutral! Sometimes I feel I want to scream when reading never ending drivel on the subject.
The elephant in the room is the voice coil resistance. Current due to the back EMF has to pass through this as well as the wire resistance and amplifier output resistance for damping of the cone motion to occur.
George Augspurger (a one time editor of the AES Journal) explains it very well in the linked article. Be sure to read the gag at the bottom of the page.
Keith
I don't know what it is about damping factor that causes people to put their brain in neutral! Sometimes I feel I want to scream when reading never ending drivel on the subject.
The elephant in the room is the voice coil resistance. Current due to the back EMF has to pass through this as well as the wire resistance and amplifier output resistance for damping of the cone motion to occur.
George Augspurger (a one time editor of the AES Journal) explains it very well in the linked article. Be sure to read the gag at the bottom of the page.
Keith
Hi, Keith. A very simple thing to do to figure out how important it damping for your speaker is to power your amp. Once able to play music (all protections out) hit your bass speaker with your finger to make-it resonate. Then unplug the speaker and do the same. The difference is huge at resonance frequency.
And, when the voice coil is well controlled by the amp's feedback, the membrane is a lot more prone to fractionate (IE distortions). The amp itself will produce more distortion too, because the feedback signal is the sum of the amp signal and the back EMF of the speaker.
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