A while ago there was some discussion about loudspeaker cables and the
relative merits of analysis using the transmission line and AC lumped
element approachs. I've now done a page on this which people may find
interesting. It is at

http://www.st-andrews.ac.uk/~www_pa/...g/howlong.html

Note that I decided to put this on the Scots Guide not AudioMisc. This is
because the page shows a fair bit of 'hard sums' - i.e. the algebra for the
two approaches. However even if hard sums make your head ache, the results
may be of interest. :-)

Slainte,

Jim

--
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Audio Misc http://www.audiomisc.co.uk/index.html

Jim Lesurf wrote:
A while ago there was some discussion about loudspeaker cables and the
relative merits of analysis using the transmission line and AC lumped
element approachs. I've now done a page on this which people may find
interesting. It is at

http://www.st-andrews.ac.uk/~www_pa/...g/howlong.html

Note that I decided to put this on the Scots Guide not AudioMisc. This is
because the page shows a fair bit of 'hard sums' - i.e. the algebra for the
two approaches. However even if hard sums make your head ache, the results
may be of interest. :-)

Slainte,

Jim


Thanks for that, Jim. Pretty much what I expected, with the (for many
counter-intuitive) result that the high capacitance cable had the
flattest response - the expected result of having a better
characteristic impedance match. Doing the usual maths on your table of
cables

A = 8.5
B = 176
C = 153
D = 59
E = 211
G = 48.76

So as far as top end flatness goes, characteristic impedance is the best
predictor of performance. Despite high capacitance, which might be
thought of as predicting a sagging top end, the high cap cable (A) at
8.5 ohms impedance is the only cable which is actually flat. And of
course a further implication of this is that this cable does not
present a capacitive load to the amp - it connects the speaker almost
invisibly, presenting the speaker impedance to the amp essentially
unchanged.

Cable A is also interesting in comparing the transmission line and
lumped models. The lumped model, at the top end, actually climbs away in
the wrong direction - this is part of the initial rise in the lowpass
filter model it uses, before the final plunge at the turnover frequency.

And of course this is for cables of 5 metres. There are many audio apps
that use cable considerably longer than this, which makes it important
to think about the applicability of models. For much longer lines it is
clearly necessary to use either the proper transmission line model, or
subdivide the lumped model into many smaller sections. Making that
breakpoint decision needs careful thought, and probably several
calculations to make sure you have it right. As you know, for myself I
say to hell with it and use the transmission line model which I know
will be right every time - no decisions necessary.

Finally, also as predicted, the rise in impedance at low frequencies
brought about by the resistive terms in the lumped cable impedance makes
absolutely no difference to the low frequency flatness of the cable. It
merely changes the overall loss.

Thanks for taking the time and trouble to do all the sums.

d

Don Pearce wrote:

Thanks for that, Jim. Pretty much what I expected, with the (for many
counter-intuitive) result that the high capacitance cable had the
flattest response - the expected result of having a better
characteristic impedance match.

You could also say that it is the low inductance cable that has the
flattest response.
That's not at all counter-intuitive.

--
Eiron.

Eiron wrote:
Don Pearce wrote:

Thanks for that, Jim. Pretty much what I expected, with the (for many
counter-intuitive) result that the high capacitance cable had the
flattest response - the expected result of having a better
characteristic impedance match.

You could also say that it is the low inductance cable that has the
flattest response.
That's not at all counter-intuitive.



So which are you going to pick, and under what circumstances? Go with
the characteristic impedance and you will be right every time, because
it contains both L and C in the correct proportions.

d

Jim Lesurf wrote:

A while ago there was some discussion about loudspeaker cables and the
relative merits of analysis using the transmission line and AC lumped
element approachs. I've now done a page on this which people may find
interesting. It is at

http://www.st-andrews.ac.uk/~www_pa/...g/howlong.html

Note that I decided to put this on the Scots Guide not AudioMisc. This is
because the page shows a fair bit of 'hard sums' - i.e. the algebra for the
two approaches. However even if hard sums make your head ache, the results
may be of interest. :-)

Yes, always been interested in this. I will peruse. Thanks for doing the hard
work.

Graham

Eiron wrote:

Don Pearce wrote:

Thanks for that, Jim. Pretty much what I expected, with the (for many
counter-intuitive) result that the high capacitance cable had the
flattest response - the expected result of having a better
characteristic impedance match.

You could also say that it is the low inductance cable that has the
flattest response.
That's not at all counter-intuitive.

Interesting. I just selected a low inductance cable for a certain job over
one where some attempt had been made to make it 'an impedance' by having
the cores kept further apart.

Graham

"Don Pearce"
Jim Lesurf wrote:

http://www.st-andrews.ac.uk/~www_pa/...g/howlong.html

Doing the usual maths on your table of cables

A = 8.5

** Cable "A" would be a woven multi-strand cable like "Tocord" - it was
sold under other names too.

So as far as top end flatness goes, characteristic impedance is the best
predictor of performance. Despite high capacitance, which might be thought
of as predicting a sagging top end, the high cap cable (A) at 8.5 ohms
impedance is the only cable which is actually flat. And of course a
further implication of this is that this cable does not present a
capacitive load to the amp - it connects the speaker almost invisibly,
presenting the speaker impedance to the amp essentially unchanged.


** Jim got the results he did because of the *artificial* way he set up the
model.

1. The amplifier has no output impedance at any frequency.

2. The speaker load is an 8 ohm resistor.

In the real world, NEITHER of these is EVER the case.

Cable "A" ( which is an 8.5 ohm transmission line) WILL in fact present a
severely capacitive load to the drive amplifier when used with real
speakers, virtually all of which have a steadily rising impedance above
20kHz.

Also, if the cables are ever attached at the amplifier end but not at the
speaker end the load is a pure capacitance.

Some hi-fi amplifiers are highly allergic to capacitive loads in the ranger
of 5nF to 30nF and immediately break into supersonic oscillation - thence
overheat and self destruct.

Most NAIM models were famous for this and the power amps made by Phase
Linear.

Due to its penchant for amplifier destruction, dealers became reluctant to
stock it and Tocord was soon pulled off the market. Other 8 ohm
transmission line cables have exactly he same problem.



...... Phil

"Jim Lesurf" wrote in message
...
A while ago there was some discussion about loudspeaker cables and the
relative merits of analysis using the transmission line and AC lumped
element approachs. I've now done a page on this which people may find
interesting. It is at

http://www.st-andrews.ac.uk/~www_pa/...g/howlong.html

Note that I decided to put this on the Scots Guide not AudioMisc. This is
because the page shows a fair bit of 'hard sums' - i.e. the algebra for
the
two approaches. However even if hard sums make your head ache, the results
may be of interest. :-)


**Nice work Jim. It backs up what I've been telling people for a couple of
decades. As Phil has stated, what would be interesting would be to do the
same analysis with real-world speakers. Particularly ESLs. I've measured one
pair which has a response that falls to less than 1 Ohm at about 17kHz. Low
inductance cables tend to be essential with such speakers.


--
Trevor Wilson
www.rageaudio.com.au

"Phil Allison"

Jim Lesurf wrote:

http://www.st-andrews.ac.uk/~www_pa/...g/howlong.html

Doing the usual maths on your table of cables

A = 8.5

** Cable "A" would be a woven multi-strand cable like "Tocord" - it was
sold under other names too.


** I have placed a pic of a " Tocord " speaker lead on ABSE - since I
could not find one on the net.

There are 72 green and 72 copper coloured strands - each enamel coated so
are all insulated. There is a central clear plastic core ( not visible in
the pic) of about 4mm diameter which the 144 strands are woven around. The
outer sheath is only 7mm diameter and so the cable is quite flexible.

In order to fit a termination like the banana plugs shown, one must first
burn off the enamel coating with a hot soldering iron and lots of solder.
Quite easy really.



...... Phil

Phil Allison wrote:
"Phil Allison"

Jim Lesurf wrote:
http://www.st-andrews.ac.uk/~www_pa/...g/howlong.html
Doing the usual maths on your table of cables

A = 8.5
** Cable "A" would be a woven multi-strand cable like "Tocord" - it was
sold under other names too.


** I have placed a pic of a " Tocord " speaker lead on ABSE - since I
could not find one on the net.

There are 72 green and 72 copper coloured strands - each enamel coated so
are all insulated. There is a central clear plastic core ( not visible in
the pic) of about 4mm diameter which the 144 strands are woven around. The
outer sheath is only 7mm diameter and so the cable is quite flexible.

In order to fit a termination like the banana plugs shown, one must first
burn off the enamel coating with a hot soldering iron and lots of solder.
Quite easy really.



Goertz also make similar cables.

The real danger with these cables comes when they are mistreated - a
heavy table leg stood on them, for instance. When that happens it is
possible for the enamel to rub through between two strands; you then
have an instant short circuit which can't be fixed. A new cable is the
only option.

d