On 2010-10-15 20:38, August Karlstrom wrote:
I have read more than one article where the recommended maximum length
of loudspeaker wire is presented as a function of the wire gauge and
the impedance of the speakers, e.g. in the Wikipedia article
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge
I have also heard that output power and damping factor should be
considered as well - a high power amplifier needs a thicker cable.
Are there any studies made about the wire length contra output power and
damping factor?
Here is my calculation of the minimum cross-sectional area of speaker
wire. Please tell me if you spot any errors.
***
The resistance R of a wire can be computed as
R = rho * l / A
where l is the length of the conductor in meters, A is the
cross-sectional area in square meters and rho is the electrical
resistivity in ohm meters.
Now, if we want the resistance of a wire of a specified length to be no
more than a percentage p of the lowest impedance of the speaker R_L we
have the relation
rho * l / A = p * R_L
which is equivalent to
A = rho * l / (p * R_L)
For copper wire the resistivity is 1.68Eˆ’8 ohm meters. If we choose p to
be one percent, which according to Arny Krueger ensures that the effect
of the wire is less than 0.1 dB and thus inaudible, we have the relation
A = 1.68Eˆ’10 * l / R_L (1)
Example:
Let's say we need two runs of four meter speaker wire. The lowest
impedance of our speaker is 8 Ω. Which cross-sectional area should a
copper wire have for maximum performance? By applying formula (1) we
have that the total area should be at least 8.4Eˆ’07 m^2 so a 2x0.50 mm^2
wire should be enough.
/August