Obviously the nature of quality of speaker cables is and has been hotly debated in forums around the world. Let see if we can establish some perspective.
Generally we want the Resistance of the Cable to be less than 2% of the nominal impedance of the speakers. Some say it can be as high as 5%, others say it needs to be less than 1%. I'll leave you to make up your own mind on that. Generally, I use 2% as the standard.
That leaves Capacitance
to contend with. Those are hard specs to find, but I did find those specs on several cables, and am posting the results below.
I chose a point where the impedance of the cable was equal to
that of an idealized 8 ohm speaker. That would be the point where, ignoring phase, the cable and the speaker would drop HALF the applied signal each.
This started with this link provided in another speaker cable discussion -
Low Inductance DIY HiFi Speaker Cables -
I posted this in another forum because I though some people might be interested in the project. But near the bottom of that link, they posted the Capacitance
of a variety of cable including the DIY Cable.
With that information, I started calculating at what frequency the impedance of the wire was equal to the idealized impedance of an 8 ohm speaker.
But first, here is now the math breaks down -
The Impedance of a Coil -
XL = 2(PI)(f)(L)
The Impedance of a Capacitor -
XC = 1 / (2(pi)(f)(C)
So the frequency at which XL comes into play is -
fL = XL / (2(pi)L)
The frequency at which XC come into play is -
fC = 1 / (2(pi)(XC)(C))
f = frequency
(pi) = mathematical PI (3.14159...)
X = impedance
C = Capacitance
L = Inductance
Cable with specs in capacitance/foot
are for a 10 foot cable
Cable specs with capacitance/meter
are for a 3 meter cable (9.84ft).
The DIY Cable (at the link provided above) -
650pf / 10ft
0.50µH / 10ft
/ (2(pi) x 0.5x10^-6
f = 8 / (6.28 x 0.0000005) = 8 / 0.00000314
fL = 2,546,479 hz
Some one should check that math.
= 1 / (6.28)(XC
f = 1 / (6.28) 8 x 650x10^-12
f = 1 / 50.24 x 650x10^-12 = 1/ 50.24 x 0.000000000650
= 1 / 3.27x10^-8
fC = 30,622,220 hz
As you are about to see, fC
is commonly in the millions of Hertz and the fL
is in the 100's of thousand of Hertz.
Next, using the information provided at the DIY Cable link, we measure some bog-standard 12ga twin-lead speaker wire.
common 12ga twin lead
For 10 feet of common 12ga wire, we have -
f = 8 / ((6.28) x 1.90x10^-6)
fL = 670,120 hz
fC = 1 / (2(pi)(XC)(C))
f = 1 / (6.28) 8 x 180x10^-12 = 1 / 6.28 x 8 x 0.000000000180)
fC = 110,580,326 hz
Just out of curiosity I calculated the fL
for 32 ohms and for 4 ohms, just to see how much difference the changing of the speakers impedance across the frequency range would make.
32 ohms = 2,680,504 hz
4 ohms = 335,063 hz
Still well outside the audio range.
Here is straight forward double insulated Belden speaker wire.
Belden 46381NH 2-conductor 2.5mm²
speaker wire -
Resistance conductor @ 20°C < 8 W/km
Nominal capacitance at 1kHz 76 pF/m
Nominal inductance @ 1kHz < 1.2 uH/m
1.2µH x 3 meters = 3.6µH
fL = 353,677.7hz
76pF x 3 meters = 228pF
fC = 87,255,999.5 hz
Then I decided to try some common but slightly exotic cables - The QED Anniversary XT
and the new QED XT400.
QED Anniversary XT -
Capacitance - 50pF/m
Inductance - 0.47 µH/m
Wire gauge - 16 AWG
Cross-sectional area - 1.50mm²
Dissipation factor - 0.0006
QED XT400 -
Capacitance - 43pF/m
Inductance - 0.50 µH/m
Wire gauge - 12 AWG
Cross-sectional area - 4.00mm²
Dissipation factor - 0.0400
There is a graphic on the QED XT400
page that explains the design concept of this wire. (3 meter cable)
Anniversary XT -
(50pf, 0.47µH) -
fC = 132,629,119 hz
fL = 903,007 hz
QED XT400 -
(43pF, 0.50µH) -
fC = 154,219,906 hz
fL = 848,826 hz
No matter what wire I choose, from basic to exotic, the results are the same. The impedance effects of the Capacitance
are WELL OUT of the Audio Range.
For what it is worth.
PS: Feel free to check my math, or to recalculate using other ratios. For example, rather that X = R, you might want to use X = R/10.