[August Karlstrom]

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?


/August

[Arny Krueger]

"August Karlstrom" wrote in message


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 chased the footnotes for this paper, and found that it was heavily based
on this paper:

http://procosound.com/download/white...r%20Cables.pdf

Proco Sound is a well-known supplier to the professional audio and in
particular the live sound industry. In general the acccuracy requirements
for live sound are somewhat relaxed as compared to high-accuracy home or
mastering/mixing room audio. The Wikipedia article wire length
recommendations seem to be based on maintaining a damping factor of about 20
which again is somewhat relaxed as compared to the requirements for high
performance audio. I would recomment using a criteria of maintaining the
damping factor between 50 and 100.

I have also heard that output power and damping factor
should be considered as well - a high power amplifier
needs a thicker cable.

Generally speaking, sizing wire for a good damping factor will result in
adequate capacitor for the kinds of power amps generally used for home
audio.

Are there any studies made about the wire length contra
output power and damping factor?

Yes. The Greiner JAES paper is a classic and covers other issues. If the
speakers being used have unusually variable and low impecance curves then
the resistance and inductance of the speaker cable become more signficant.

[August Karlstrom]

On 2010-10-15 21:41, Arny Krueger wrote:
In general the acccuracy requirements
for live sound are somewhat relaxed as compared to high-accuracy home or
mastering/mixing room audio. The Wikipedia article wire length
recommendations seem to be based on maintaining a damping factor of about 20
which again is somewhat relaxed as compared to the requirements for high
performance audio. I would recomment using a criteria of maintaining the
damping factor between 50 and 100.

That's interesting. I read the article with the impression that they
were talking about home audio. The Wikipedia article probably needs to
be updated then. If we would make a similar table applicable to high
performance audio, what would it look like?

I have also heard that output power and damping factor
should be considered as well - a high power amplifier
needs a thicker cable.

Generally speaking, sizing wire for a good damping factor will result in
adequate capacitor for the kinds of power amps generally used for home
audio.

Sorry, I'm not sure what that means in a practical sense. To take a
concrete example, let's say I have two 2x1.5 mm^2 (approx.15 AWG) OFC
cables, each of length four meter. Is there a high performance system in
which these cables would be insufficient?

Are there any studies made about the wire length contra
output power and damping factor?

Yes. The Greiner JAES paper is a classic and covers other issues. If the
speakers being used have unusually variable and low impecance curves then
the resistance and inductance of the speaker cable become more signficant.

OK, thanks for the reference Arny.


/August

[Trevor Wilson[_3_]]

"August Karlstrom" wrote in message
...
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

**Like all such cliams, the Wiki article over-simplifies things. They ignore
the very real effects of inductance, when using long cable runs and speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.


I have also heard that output power and damping factor should be
considered as well - a high power amplifier needs a thicker cable.

**Again, it depends on the speakers and the length of the cable.


Are there any studies made about the wire length contra output power and
damping factor?

**It's just maths. There's no real mystery here. The problem with the term
'damping factor' is that it relates to (usually) an 8 Ohm impedance. Hardly
any loudspeakers present an 8 Ohm impedance. A far better term for amplifier
manufacturers to use is output impedance vs. frequency. IOW: The output
impedance should always be specified from 20Hz ~ 20kHz. Many SET and Class D
amplifier manufacturers carefully avoid citing this data for some very good,
albeit cynical, reasons. The output impedance of such amplifiers can easily
reach several Ohms at 20kHz.


--
Trevor Wilson
www.rageaudio.com.au

[August Karlstrom]

On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge

**Like all such cliams, the Wiki article over-simplifies things. They ignore
the very real effects of inductance, when using long cable runs and speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.

To take my example again, let's say I need a pair of cables, each four
meters long. Is there a system in which a 2x1.5 mm2 (approx.15 AWG) OFC
wire would be insufficient?

Several people in this newsgroup believe that all wire sounds the same
provided it is of the "correct type". What I'm trying to find out here
is what the correct type is. I am not so interested in general claims
that cannot be used in practice to make decisions.

Thanks for the input.


/August

[Audio Empire]

On Sun, 17 Oct 2010 06:54:25 -0700, August Karlstrom wrote
(in article ):

On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge

**Like all such cliams, the Wiki article over-simplifies things. They ignore
the very real effects of inductance, when using long cable runs and speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.

To take my example again, let's say I need a pair of cables, each four
meters long. Is there a system in which a 2x1.5 mm2 (approx.15 AWG) OFC
wire would be insufficient?

Several people in this newsgroup believe that all wire sounds the same
provided it is of the "correct type". What I'm trying to find out here
is what the correct type is. I am not so interested in general claims
that cannot be used in practice to make decisions.

Thanks for the input.


/August

All wire sounds exactly the same. Copper zip cord, 14 Gauge or bigger should
be sufficient for any 4-meter run for any domestic amplifier or speaker
setup. If you have a really big amp (say 700 watts/channel or more), you
might want to increase that size to something like the bulk cable used in
industrial-sized extension cords (12 -10 Gauge). Forget everything else, it
doesn't matter.

[isw]

In article ,
Audio Empire wrote:

On Sun, 17 Oct 2010 06:54:25 -0700, August Karlstrom wrote
(in article ):

On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge

**Like all such cliams, the Wiki article over-simplifies things. They
ignore
the very real effects of inductance, when using long cable runs and
speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.

To take my example again, let's say I need a pair of cables, each four
meters long. Is there a system in which a 2x1.5 mm2 (approx.15 AWG) OFC
wire would be insufficient?

Several people in this newsgroup believe that all wire sounds the same
provided it is of the "correct type". What I'm trying to find out here
is what the correct type is. I am not so interested in general claims
that cannot be used in practice to make decisions.

Thanks for the input.


/August

All wire sounds exactly the same. Copper zip cord, 14 Gauge or bigger should
be sufficient for any 4-meter run for any domestic amplifier or speaker
setup. If you have a really big amp (say 700 watts/channel or more), you
might want to increase that size to something like the bulk cable used in
industrial-sized extension cords (12 -10 Gauge). Forget everything else, it
doesn't matter.

Why is the wire size used to feed the speakers so much more important
than the wire used *in* the speaker -- for crossovers and more
importantly, for the voice coil? Clearly, the *length* of the latter two
far exceeds the former.

Isaac

[Audio Empire]

On Mon, 18 Oct 2010 07:12:18 -0700, isw wrote
(in article ):

In article ,
Audio Empire wrote:

On Sun, 17 Oct 2010 06:54:25 -0700, August Karlstrom wrote
(in article ):

On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge

**Like all such cliams, the Wiki article over-simplifies things. They
ignore
the very real effects of inductance, when using long cable runs and
speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.

To take my example again, let's say I need a pair of cables, each four
meters long. Is there a system in which a 2x1.5 mm2 (approx.15 AWG) OFC
wire would be insufficient?

Several people in this newsgroup believe that all wire sounds the same
provided it is of the "correct type". What I'm trying to find out here
is what the correct type is. I am not so interested in general claims
that cannot be used in practice to make decisions.

Thanks for the input.


/August

All wire sounds exactly the same. Copper zip cord, 14 Gauge or bigger
should
be sufficient for any 4-meter run for any domestic amplifier or speaker
setup. If you have a really big amp (say 700 watts/channel or more), you
might want to increase that size to something like the bulk cable used in
industrial-sized extension cords (12 -10 Gauge). Forget everything else, it
doesn't matter.

Why is the wire size used to feed the speakers so much more important
than the wire used *in* the speaker -- for crossovers and more
importantly, for the voice coil? Clearly, the *length* of the latter two
far exceeds the former.

Isaac


It isn't. In any case, "more than sufficient for the task" is just being
pretentious.

[August Karlstrom]

On 2010-10-17 23:53, Audio Empire wrote:
All wire sounds exactly the same. Copper zip cord, 14 Gauge or bigger should
be sufficient for any 4-meter run for any domestic amplifier or speaker
setup.

OK, so you mean that the resistance in a four meter wire of gauge 15 or
more may be too high. Do you base this claim on some resistance
percentage similar to the Wikipedia article where 5% is mentioned?

According to the Wikipedia article I could even use a wire as thin as 20
AWG for a four meter run. On the other hand Arny Krueger suspects that
the 5% value is a recommendation for live sound rather than for critical
listening in a domestic environment. So what is the maximum resistance
percentage for critical listening?


/August

[Audio Empire]

On Mon, 18 Oct 2010 07:47:42 -0700, August Karlstrom wrote
(in article ):

On 2010-10-17 23:53, Audio Empire wrote:
All wire sounds exactly the same. Copper zip cord, 14 Gauge or bigger should
be sufficient for any 4-meter run for any domestic amplifier or speaker
setup.

OK, so you mean that the resistance in a four meter wire of gauge 15 or
more may be too high. Do you base this claim on some resistance
percentage similar to the Wikipedia article where 5% is mentioned?

I base it on the fact that 14-Ga Zip cord is less than 0.006 Ohm/foot. A
meter is a hair over three feet (3.37 inches over to be exact). You figure it
out.

According to the Wikipedia article I could even use a wire as thin as 20
AWG for a four meter run. On the other hand Arny Krueger suspects that
the 5% value is a recommendation for live sound rather than for critical
listening in a domestic environment. So what is the maximum resistance
percentage for critical listening?

Just buy 14-Ga zip cord and forget about it. Your are counting angels on the
heads of pins here.

[Arny Krueger]

"August Karlstrom" wrote in message

On 2010-10-17 23:53, Audio Empire wrote:
All wire sounds exactly the same. Copper zip cord, 14
Gauge or bigger should be sufficient for any 4-meter run
for any domestic amplifier or speaker setup.

OK, so you mean that the resistance in a four meter wire
of gauge 15 or more may be too high. Do you base this
claim on some resistance percentage similar to the
Wikipedia article where 5% is mentioned?

According to the Wikipedia article I could even use a
wire as thin as 20 AWG for a four meter run. On the other
hand Arny Krueger suspects that the 5% value is a
recommendation for live sound rather than for critical
listening in a domestic environment. So what is the
maximum resistance percentage for critical listening?

The maximum resistance percentage for critical listening is between 1 and 2%
of the lowest impedance of the speaker. That ensures that the effect of the
wire is less than from 0.1 to 0.2 dB, and thus inaudible in all cases.

[Trevor Wilson[_3_]]

"August Karlstrom" wrote in message
...
On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge

**Like all such cliams, the Wiki article over-simplifies things. They
ignore
the very real effects of inductance, when using long cable runs and
speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.

To take my example again, let's say I need a pair of cables, each four
meters long. Is there a system in which a 2x1.5 mm2 (approx.15 AWG) OFC
wire would be insufficient?

**Without knowing the impedance curve (20Hz ~ 20kHz) of your speakers, I
cannot say. In all probability, yes, it would be OK.


Several people in this newsgroup believe that all wire sounds the same
provided it is of the "correct type". What I'm trying to find out here is
what the correct type is. I am not so interested in general claims that
cannot be used in practice to make decisions.

**There are three characteristics of speaker cable that are of interest.
They a

* Resistance. The lower the better.
* Inductance. The lower the better.
* Capacitance. Largely unimportant, when using a competently designed
amplifier.

That leaves resistance (R) and inductance (L). The significance of the two
paramaters depends on the impedance of the speaker and the length of the
cable. 4 Metres is a modest cable run and SHOULD present few problems in any
system.

Resistance is governed by the amount of conductive material in the cable.
Indutance is much more complicated. Standard 'zip' type speaker cables
(basically any parallel pair of conductors) exhibits pretty much the highest
possible inductance. The wider the spacing of the cable conductors (see:
Naim speaker cable), the higher the inductance and less desirable the cable.
As the conductor spacing is made smaller, the inductance falls. Some
manufacturers use multiple conductors, closely bound together to reduce
inductance still further. Others (Goertz, et al) use flat conductors, in
intimate proximity to reduce inductance to extremely low levels. For my
part, I suggest the use of RG213/U coax cable, which exhibits quite low
resistance and very low inductance, at reasonable cost.


--
Trevor Wilson
www.rageaudio.com.au

[Audio Empire]

On Sun, 17 Oct 2010 16:08:37 -0700, Trevor Wilson wrote
(in article ):

"August Karlstrom" wrote in message
...
On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge

**Like all such cliams, the Wiki article over-simplifies things. They
ignore
the very real effects of inductance, when using long cable runs and
speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.

To take my example again, let's say I need a pair of cables, each four
meters long. Is there a system in which a 2x1.5 mm2 (approx.15 AWG) OFC
wire would be insufficient?

**Without knowing the impedance curve (20Hz ~ 20kHz) of your speakers, I
cannot say. In all probability, yes, it would be OK.


Several people in this newsgroup believe that all wire sounds the same
provided it is of the "correct type". What I'm trying to find out here is
what the correct type is. I am not so interested in general claims that
cannot be used in practice to make decisions.

**There are three characteristics of speaker cable that are of interest.
They a

* Resistance. The lower the better.
* Inductance. The lower the better.
* Capacitance. Largely unimportant, when using a competently designed
amplifier.

I practice, none of these things have the slightest effect on the sound.
Resistence/foot is less than a 0.006 Ohm for 14 Ga. zip.

That leaves resistance (R) and inductance (L). The significance of the two
paramaters depends on the impedance of the speaker and the length of the
cable. 4 Metres is a modest cable run and SHOULD present few problems in any
system.

Capacitance is around 12pf/foot or about 144pf for 4 meters of 14 Ga zip
cord. It has been found that capacitive loads of up to 20,000 pf (.02 mfd)
have no audible or visible effect on audio signals. That means that 4 meters
of 14 Ga zip cord would need 100 times more capacitance/foot to have any
effect whatsoever on a an audio signal passing through it. Inductance is
likewise negligible.

One can run 80 ft of 14 Ga zip as speaker cable for 8 Ohm speakers before it
is recommended that one increase the wire size to 12 Ga.

IOW, as long as the zip cord is 14 Ga or larger and your runs are less than
80ft, don't sweat it. just buy what you like and cheap hardware store zip
cord is FINE.

[Trevor Wilson[_3_]]

Audio Empire wrote:
On Sun, 17 Oct 2010 16:08:37 -0700, Trevor Wilson wrote
(in article ):

"August Karlstrom" wrote in message
...
On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge

**Like all such cliams, the Wiki article over-simplifies things.
They ignore
the very real effects of inductance, when using long cable runs and
speakers
which exhibit a falling impedance at HF (like ESLs). In those
cases, the inductive effects of cable can become quite significant.

To take my example again, let's say I need a pair of cables, each
four meters long. Is there a system in which a 2x1.5 mm2 (approx.15
AWG) OFC wire would be insufficient?

**Without knowing the impedance curve (20Hz ~ 20kHz) of your
speakers, I cannot say. In all probability, yes, it would be OK.


Several people in this newsgroup believe that all wire sounds the
same provided it is of the "correct type". What I'm trying to find
out here is what the correct type is. I am not so interested in
general claims that cannot be used in practice to make decisions.

**There are three characteristics of speaker cable that are of
interest. They a

* Resistance. The lower the better.
* Inductance. The lower the better.
* Capacitance. Largely unimportant, when using a competently designed
amplifier.

I practice, none of these things have the slightest effect on the
sound. Resistence/foot is less than a 0.006 Ohm for 14 Ga. zip.

**Incorrect. Both resistance and inductance can affect sound quality,
depending on the length of the cable and the impedance of the speaker.
Capacitance, as I have already stated many times, is irrelevant with any
properly designed amplifier.


That leaves resistance (R) and inductance (L). The significance of
the two paramaters depends on the impedance of the speaker and the
length of the cable. 4 Metres is a modest cable run and SHOULD
present few problems in any system.

Capacitance is around 12pf/foot or about 144pf for 4 meters of 14 Ga
zip cord. It has been found that capacitive loads of up to 20,000 pf
(.02 mfd) have no audible or visible effect on audio signals. That
means that 4 meters of 14 Ga zip cord would need 100 times more
capacitance/foot to have any effect whatsoever on a an audio signal
passing through it.

**As I carefully pointed out, capacitance is irrelevant.

Inductance is likewise negligible.

**No. Inductance is not negligible. It *may* be irrelevant, depending on the
length of the cable and the speakers used, however.

One can run 80 ft of 14 Ga zip as speaker cable for 8 Ohm speakers
before it is recommended that one increase the wire size to 12 Ga.

**Just a reminder: There is no such thing as an "8 Ohm speaker". All
speakers, with the possible exception of Maggies, exhibit varying
impedances. SOME speakers, like ESLs, which may present a relatively high
impedance over most of the audible range, can often present very low
impedances at high frequencies. Here is one such example:

http://www.rageaudio.com.au/index.php?p=1_12

Click on 'Accustat'.

With a 25 Metre length of standard 'zip' type speaker cable, a serious and
very audible problem at HF can be expected. Low resistance and low
inductance cables are absolutely essential with such speakers and such long
cable runs.


IOW, as long as the zip cord is 14 Ga or larger and your runs are
less than 80ft, don't sweat it. just buy what you like and cheap
hardware store zip cord is FINE.

**I have no issue with cheap, but misleading people by suggesting that they
can connect very long cables to speakers and expecting no problems is just
wrong.


--
Trevor Wilson
www.rageaudio.com.au

[Sebastian Kaliszewski]

Trevor Wilson wrote:
"August Karlstrom" wrote in message
...
On 2010-10-17 03:17, Trevor Wilson wrote:
"August wrote in message
http://en.wikipedia.org/wiki/Speaker_wire#Wire_gauge
**Like all such cliams, the Wiki article over-simplifies things. They
ignore
the very real effects of inductance, when using long cable runs and
speakers
which exhibit a falling impedance at HF (like ESLs). In those cases, the
inductive effects of cable can become quite significant.
To take my example again, let's say I need a pair of cables, each four
meters long. Is there a system in which a 2x1.5 mm2 (approx.15 AWG) OFC
wire would be insufficient?

**Without knowing the impedance curve (20Hz ~ 20kHz) of your speakers, I
cannot say. In all probability, yes, it would be OK.

4m of zip cable will do on any home-use speakres, Kappa 9 included.


Several people in this newsgroup believe that all wire sounds the same
provided it is of the "correct type". What I'm trying to find out here is
what the correct type is. I am not so interested in general claims that
cannot be used in practice to make decisions.

**There are three characteristics of speaker cable that are of interest.
They a

* Resistance. The lower the better.
* Inductance. The lower the better.

At 4m cable length inductance is unimportant.

* Capacitance. Largely unimportant, when using a competently designed
amplifier.

That leaves resistance (R) and inductance (L). The significance of the two
paramaters depends on the impedance of the speaker and the length of the
cable. 4 Metres is a modest cable run and SHOULD present few problems in any
system.

I would say no problems in any home system.

Resistance is governed by the amount of conductive material in the cable.
Indutance is much more complicated. Standard 'zip' type speaker cables
(basically any parallel pair of conductors) exhibits pretty much the highest
possible inductance. The wider the spacing of the cable conductors (see:
Naim speaker cable), the higher the inductance and less desirable the cable.
As the conductor spacing is made smaller, the inductance falls. Some
manufacturers use multiple conductors, closely bound together to reduce
inductance still further. Others (Goertz, et al) use flat conductors, in
intimate proximity to reduce inductance to extremely low levels. For my
part, I suggest the use of RG213/U coax cable, which exhibits quite low
resistance and very low inductance, at reasonable cost.

It's an overkill unless you use 20m cable together with extremely low
(broken by design?) impedance (1.5ohm) speakers.


rgds
\SK
--
"Never underestimate the power of human stupidity" -- L. Lang
--
http://www.tajga.org -- (some photos from my travels)

[August Karlstrom]

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

[August Karlstrom]

On 2010-10-19 17:23, August Karlstrom wrote:
Here is my calculation of the minimum cross-sectional area of speaker
wire. Please tell me if you spot any errors.

***

Unfortunately, some strange characters seem to have creped into the
text. Here is a corrected version:

***

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 1.68E-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 = 1.68E-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 ohm. 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 8.4E-07 m^2 so a 2x0.50 mm^2
wire should be enough.


/August

[August Karlstrom]

On 2010-10-19 18:41, August Karlstrom wrote:
On 2010-10-19 17:23, August Karlstrom wrote:
Here is my calculation of the minimum cross-sectional area of speaker
wire. Please tell me if you spot any errors.

Well, I spotted an error myself. In equation (1) the constant should of
course be 1.68E-06 rather than 1.68E-10. The rest of the calculation
should be correct however. Sorry about that.

Here is the corrected version:

***

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 1.68E-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 = 1.68E-06 * 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 ohm. 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 8.4E-07 m2 so a 2x0.50 mm2
wire should be enough.


/August