Audio, hi-fi and car audio - TCI Cobra interconnects against Chord Chameleon

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TCI Cobra interconnects against Chord Chameleon

Jim Lesurf wrote:

Out of interest I decided to do a comparison of the simple lumped CRLG
model and the analytical transmission line model for 5 metres of various LS
cables into an 8 Ohm load. The results are shown at

http://jcgl.orpheusweb.co.uk/temp/DiffGain.gif

Top graphs shows the gains (losses) for a set of different cable
measurements. These results use the transmission line method. i.e. use
reflection and transmission coefficients for the amp-cable and cable-load
junctions derived from the cable, source, and load impedances. Then use the
propagation constant to include the cable loss and propagation delay.

The bottom graphs show what you get if these results are subtracted from
the results that simply use the C'R'L'G' values multiplied by the cable
length to get the four lumped CRLG values. Note the vertical scale on these
plots!

For simplicity I assumes the amp o/p impedance was zero.

In general, the difference between the two approaches seems to be well
below 0.01dB over the audio band. In practice it seems doubtful we'd either
have measured values accurate enough to worry about 0.01 dB, or that the
cable values remain stable to that level of precision. I also doubt anyone
would be able to hear such a difference and say, "hey! your result is out
by 0.0001 dB!" ;-

The results were done quickly, but confirm similar checks I've done in the
past, and support my view that there is generally no real need to use the
full transmission line method for computation in such practical cases. The
cable is far too short at audio frequencies to have to employ the
transmission line approach. Simply a matter of which approach you prefer to
get much the same results. However, for other reasons I explain elsewhere,
the lumped CLRG approach is an easier predictor for people to use at audio
frequency. :-)

FWIW I also tend to avoid using series of lumped elements in a line, as
that tends in my experience to simply give rise to computation limitations
causing misleading results. If you wish to use the transmission line
approach it seems better to me to use the simple analytic solution.

Very interesting post Jim. Not being a classic RF man, I'm no expert at the
lumped constant simulation and it's varieties, but I have myself modelled
cables using different numbers of 'lumps' in series and not and been surprised
at the apparent difference (just in amplitude response) particularly with
regard to ripples.

I'd be grateful of any further advice you could offer as regards your thoughts
on the most appropriate simulation and accurate methods.

In passing, it also amazes me how far we have come over the years to be
analysing these topics critically now.

Graham

TCI Cobra interconnects against Chord Chameleon

In article , Don Pearce
wrote:
Jim Lesurf wrote:
In article , Don
Pearce wrote:
Jim Lesurf wrote:
In article , Don
Pearce wrote:

Perhaps you could make a 5 metre length of your "10 Ohm cable with
no insulator - velocity equal to free space light" and send it to
me. I can then test it and compare its properties as a LS cable
with the other types I have measured and analysed. :-)

Ooh - no way to make that and get it to you, but not too much trouble
to make it yourself. Get a couple of metal strips 5 metres by 35mm.
Place them one above the other as near air-spaced as possible about
1mm apart. A matchstick every foot or so should do it.

Your response rather confirms what I thought. The above construction
is rather impractical. It is also unlikely to provide an impedance
that is fairly close to 10 Ohms across the entire audio band...

But the impedance really only starts to matter towards the top end of
the band. At lower frequencies the whole thing is just too short
(electrically) to make a difference. That is why you don't see
unflatness at the bottom end even though the impedance is heading
skywards.

Yet, earlier, you kept insisting that it was the impedance that mattered,
and that any analysis should use this (which you also seemed to presume was
always non-complex) not use the lumped model. Your statements recently in
this thread seem to have been oddly inconsistent...

How thick do you assume the metal strips will need to be to keep the
impedance perfectly uniform at 10 Ohms? Also, are you confident that a
single matchstick per (non-SI) 'foot' will be enough to get accurate
geometry? I must confess that your constructional skills are greater
than mine if you can make the above work. Particularly in terms of
avoiding fringing field effects by keeping the whole things clear of
anything else, keeping it absolutely plane, etc, etc.

I was working on 1mm for the calculations.

Not too fussed about the width as I imagine it doesn't matter about
it being exactly 10 ohms.

Odd. I thought you were saying it *would* be 10 Ohms... :-)

This is all about velocity, remember? My point was that we were in
danger of a "post hoc propter hoc" connection between impedance and
propagation velocity. This was really a gedankenexperiment to show that
they aren't really associated other than by the mechanics of
construction.

So now your "easily made" cable was just a thought-experiment... :-)

Not too flexible, I'm afraid ;-)

Nor, it seems, likely to be very precisely in accord with your initial
description of its performance. :-)

I appreciate that such constructions look nice and simple in undergrad
textbooks. Often because the analysis ignores various aspects to
provide a simple analysis that is easy to examine at the end of a
course. :-)

But when you come to analyse them in more practical detail, or try to
build them, it tends to be the case that they don't quite perform as
you might expect. :-)

I designed one of the first TEM cells for Multitone, a paging company
for testing the sensitivity of pagers. It was eight feet long and
comprised a stripline about a foot above the groundplane, with tapered
feeds down to N-type connectors. It performed exactly to theory.

It is actually much easier to do that at RF than audio. :-)

Bear in mind that most of the approximations and approaches used in
textbooks for transmission lines are chosen on the basis that the main uses
that rely on them are RF.

Note, for example that a 'transmission line' for audio would have to cover
at least three decades in frequency. That isn't common for radio systems.
Although wideband systems do arise, even wideband radars and hopping
comms tend to use far smaller decade ranges. Note also, that the problems
due to R' and G' tend to have larger effects at LF, and that down at such
frequencies details like your assuming 1mm thickness may matter more than
at RF. :-)

Slainte,

Jim

--
Change 'noise' to 'jcgl' if you wish to email me.
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Armstrong Audio http://www.audiomisc.co.uk/Armstrong/armstrong.html
Audio Misc http://www.audiomisc.co.uk/index.html

TCI Cobra interconnects against Chord Chameleon

In article , Eeyore
wrote:

[snip]

Very interesting post Jim. Not being a classic RF man, I'm no expert at
the lumped constant simulation and it's varieties, but I have myself
modelled cables using different numbers of 'lumps' in series and not and
been surprised at the apparent difference (just in amplitude response)
particularly with regard to ripples.

I'd be grateful of any further advice you could offer as regards your
thoughts on the most appropriate simulation and accurate methods.

if you just want to assess things like frequency response in the audio
band, and are using domestic cable lengths, then simply use the CRLG values
for the cable as a set of four lumped numbers, and make that a network with
the load and amp o/p impedance. Then use simple AC circuit theory. As the
results I put up show, with a wide range of real-world cables (some of them
quite exotic!) this will get you the right answers to levels of accuracy
better than you are likely to know the CRLG values. This is in effect just
a single 'section' in terms of the approach of using a series of sections.
Just put the capacitance and leakage at the load end, and the resistance
and inductance between the load and and source. (So in sectional terms, not
even a symmetric arrangement.)

The approach is shown on

http://www.st-andrews.ac.uk/~www_pa/...rt7/page4.html

The previous pages in that part (and part6) deal with cables.

For LS cables, in virtually all cases it will be the series R and L values
of the cable that matter and you can safely ignore C and G. Doing the above
will get you very close indeed to the correct answers in most practical
cases.

For interconnects it may be wiser to consider R, L, and C, and ignore G.
You can generally also ignore L, but the range of impedances is wider for
loads and sources so this is less sure than the LS situation.

Using the analytical transmission line model will be accurate in either
case, provided you accurately know CLRG, etc. But will almost certainly
return results practically indistinguishable from the above 'lumped'
approximations. Advantage will be that it works over a wider range of
frequencies and lengths - provided you really do know the cable properties
over the wider ranges!

Point here is that domestic lengths at audio frequencies are orders of
magnitude smaller than the signal wavelengths. So a simple approximation
generally works exceedingly well. No need for modelling with multiple
'sections' of CRLG. That tends to just throw up quirks in the computational
model, and may give *less* accurate results. The wiggles you get in the
response stem from - as Don said - regarding the line as a high order
filter. Actually, it will be, but only when the physical steps (or
wavelengths) are comparable with the conductor spacing and you have to
worry about the wave being non-TEM00. Alas, that implies so many sections
that getting a result by computation tends to become hopeless for other
reasons.

Of course, if the cables are much longer, or you venture well above 20kHz
then the simple lumped CRLG approach will rapidly break down and give
incorrect results. Horses for courses.

If you prefer the transmission line approach then just use the analytic
method. Work out the answers in terms of the transmission and reflection
coefficients at the source-cable and cable-load boundaries, and use these
with the impedance. length, and propagation constant of the line. But as I
say, there is no real need to do it that way to get satisfactory results
unless you need to extend the frequency range and/or cable lengths well
beyond the simple domestic audio case.

The analytic based method works well in computing terms as it requires less
number-bashing than using a series of sections, and avoids the sectional
approximations. If you use a language that include complex types then
writing the code is easy, and the results appear without you having time to
spare and make a cup of tea whilst you wait. :-)

FWIW I've mainly been driven to using series of sections when there are no
analytic solutions because the line properties are highly nonlinear.
Example being pulse forming lines that use nonlinearity to compress pulses.
But even here there are some 'special case' analytic solutions.

In passing, it also amazes me how far we have come over the years to be
analysing these topics critically now.

A problem is that undergrad texts tend to focus on simple 'special cases'
that are useful for RF applications. The advantage is that the analyses are
easy to examine. Academics and students like to be able to set/do/mark
exam questions. :-) ...and generally works fine for the common examples
like RF coax and twin feed and rectangular waveguide. But not so
appropriate for some other situations.

The above does throw up some quirks. For example, that there are *two*
different common sets of expressions for the properties of twin feed
cables. One is based on assuming the conductors have charge and current
distributions that are circularly symmetric about their centers. The other
does not make this assumption. So one set of results is appropriate for
Litz braided type conductors (or equivalent), and the other for a solid
conductor. But if you look, textbooks generally ignore this distinction.

The second article in the HFN series does touch on this, and give results
for both assumptions.

Fortunately, it doesn't really matter for 300 Ohm twin feeder as the
conductors are spaced so far apart that the expressions give almost the
same result. An example of the behaviour of textbooks, etc, that I mention
above. ;-

Quite a lot of engineering is based on the idea that the cases that are
simplest to analyse are also the best-behaved. Physicsts also like this
thought. But this is a sort of 'selection effect' where people move towards
what works well and agrees with the simple analysis. Possibly then
forgetting what else can happen in other cases.

It occurs to me when writing this that I can't recall a simple text that
goes though the analytic model for situations where both load and source
mismatch the cable. Maybe I should go though it and add the physics and
math to the 'Scots Guide' somewhere... It is easy to work out for a
physicist as it is equivalent to a 'Fabry Perot' resonator or a set of
material discontinuities. So is a familiar situation for me. But is it
commonly encountered by electronic engineers? Be interested in your
comments and Don's on that.

The other side of this, of course, is that in audio people often get hold
of the wrong end of the stick and try to make mountains out of molehills.
This means you have to explore the details to determine when this is
occuring... or when they have a valid point. From the POV of someone with
an 'academic' turn of mind this is fine, as you can investigate and find
out all kinds of curious features which allow you to learn more about the
physics. But that does not mean they matter much in practice a lot of the
time. More likely, it allows you to conclude that they don't - despite
adverts, etc, claiming they do. :-)

Slainte,

Jim

--
Change 'noise' to 'jcgl' if you wish to email me.
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Armstrong Audio http://www.audiomisc.co.uk/Armstrong/armstrong.html
Audio Misc http://www.audiomisc.co.uk/index.html

TCI Cobra interconnects against Chord Chameleon

Jim Lesurf wrote:
In article , Don Pearce
wrote:
Jim Lesurf wrote:
In article , Don
Pearce wrote:
Jim Lesurf wrote:
In article , Don
Pearce wrote:
Perhaps you could make a 5 metre length of your "10 Ohm cable with
no insulator - velocity equal to free space light" and send it to
me. I can then test it and compare its properties as a LS cable
with the other types I have measured and analysed. :-)

Ooh - no way to make that and get it to you, but not too much trouble
to make it yourself. Get a couple of metal strips 5 metres by 35mm.
Place them one above the other as near air-spaced as possible about
1mm apart. A matchstick every foot or so should do it.
Your response rather confirms what I thought. The above construction
is rather impractical. It is also unlikely to provide an impedance
that is fairly close to 10 Ohms across the entire audio band...

But the impedance really only starts to matter towards the top end of
the band. At lower frequencies the whole thing is just too short
(electrically) to make a difference. That is why you don't see
unflatness at the bottom end even though the impedance is heading
skywards.

Yet, earlier, you kept insisting that it was the impedance that mattered,
and that any analysis should use this (which you also seemed to presume was
always non-complex) not use the lumped model. Your statements recently in
this thread seem to have been oddly inconsistent...

This has got a bit disjointed. Let me try and spell out what I think.
The cable, being a rather short item, only starts to become significant
in determining frequency response (whether you are considering lumped or
distributed models) towards the upper reaches of the audio band. That is
why the effects only manifest themselves there. If you think in a
distributed fashion you say that it is because the cable is electrically
much shorter (ie compared to a wavelength) at low frequencies. What this
means is that it really doesn't matter what the cable is doing at 100Hz
- it is too short a discontinuity to make any difference. At 20kHz that
is no longer so true, although the effects are still small as we know.

Now I know that in those lower frequency regions (where R and G start
appearing) the cable is complex, but up towards 20kHz - the region we
are talking about - the imaginary term has dropped to the point where it
can be safely ignored, and a simple R term will describe the cable
adequately. Have a look at this; it is the impedance of my notional 10
ohm air-spaced cable from 100Hz to 100kHz

http://81.174.169.10/odds/10ohmcable.gif

You can see that it is substantially 10 ohms by the time it has reached
1kHz - far too low for any capacitance or inductance discrepancies to
matter.

This is why I am saying that it this characteristic impedance term (the
10 ohm asymptote) that matters - the rest of that stuff does nothing,
because it is in a frequency range where it can do nothing.

How thick do you assume the metal strips will need to be to keep the
impedance perfectly uniform at 10 Ohms? Also, are you confident that a
single matchstick per (non-SI) 'foot' will be enough to get accurate
geometry? I must confess that your constructional skills are greater
than mine if you can make the above work. Particularly in terms of
avoiding fringing field effects by keeping the whole things clear of
anything else, keeping it absolutely plane, etc, etc.

I was working on 1mm for the calculations.

Not too fussed about the width as I imagine it doesn't matter about
it being exactly 10 ohms.
Odd. I thought you were saying it *would* be 10 Ohms... :-)

This is all about velocity, remember? My point was that we were in
danger of a "post hoc propter hoc" connection between impedance and
propagation velocity. This was really a gedankenexperiment to show that
they aren't really associated other than by the mechanics of
construction.

So now your "easily made" cable was just a thought-experiment... :-)

No it really is easily made. Just chop up some copper strip. Actually
the use of matches is probably not the best idea as you say. What you
would do is get some plastic of the right diameter and sort of snake it
along between the plates to hold them the right distance apart. Cable
ties would hold it all together in a handy unit.

Why I say it is a thought experiment is because I wasn't actually
expecting you to make one - I was just showing you that cable impedance
and propagation velocity are independent variables. The one does not
cause the other.

Not too flexible, I'm afraid ;-)
Nor, it seems, likely to be very precisely in accord with your initial
description of its performance. :-)

I appreciate that such constructions look nice and simple in undergrad
textbooks. Often because the analysis ignores various aspects to
provide a simple analysis that is easy to examine at the end of a
course. :-)

But when you come to analyse them in more practical detail, or try to
build them, it tends to be the case that they don't quite perform as
you might expect. :-)

I designed one of the first TEM cells for Multitone, a paging company
for testing the sensitivity of pagers. It was eight feet long and
comprised a stripline about a foot above the groundplane, with tapered
feeds down to N-type connectors. It performed exactly to theory.

It is actually much easier to do that at RF than audio. :-)

No it isn't. The effect of any discontinuity is directly proportional to
the frequency, so it all gets harder, not easier as you go up. In
microwaves even surface finish starts to become a factor.

Bear in mind that most of the approximations and approaches used in
textbooks for transmission lines are chosen on the basis that the main uses
that rely on them are RF.

Note, for example that a 'transmission line' for audio would have to cover
at least three decades in frequency. That isn't common for radio systems.
Although wideband systems do arise, even wideband radars and hopping
comms tend to use far smaller decade ranges. Note also, that the problems
due to R' and G' tend to have larger effects at LF, and that down at such
frequencies details like your assuming 1mm thickness may matter more than
at RF. :-)

I designed signal generators and vector network analysers so I know all
about broadband work (how about an amplifier that covered 10kHz to
4.5GHz flat to 1dB?).

Now I see where we are at cross purposes. Yes indeed the effects of R
and G are bigger at LF, but I don't agree that they cause problems at
low frequencies, because the cable runs that contain them are too short
to have an effect. Can you show a cable frequency response plot that
shows LF unflatness? I bet you can't. They only wander off at HF,
despite the fact that they have just about attained their stable HF
impedance.

d

TCI Cobra interconnects against Chord Chameleon

In article , Don
Pearce
wrote:
Jim Lesurf wrote:

Now I know that in those lower frequency regions (where R and G start
appearing) the cable is complex, but up towards 20kHz - the region we
are talking about - the imaginary term has dropped to the point where it
can be safely ignored, and a simple R term will describe the cable
adequately. Have a look at this; it is the impedance of my notional 10
ohm air-spaced cable from 100Hz to 100kHz

http://81.174.169.10/odds/10ohmcable.gif

The difficulty here is the assumptions you made for the 'notional' cable
and how well they would describe reality. Did you, for example, include
both internal impedance (skin effect) and non-uniformity of charge and
current distributions to ensure that the boundary conditions for the fields
were self-consistent? It is quite common for analyses to ignore such
effects.

You can see that it is substantially 10 ohms by the time it has reached
1kHz - far too low for any capacitance or inductance discrepancies to
matter.

This is why I am saying that it this characteristic impedance term (the
10 ohm asymptote) that matters - the rest of that stuff does nothing,
because it is in a frequency range where it can do nothing.

Yet when you do an analysis using a number of examples of real cables you
find that you can get a close correlation between HF droop at 20kHz and the
cable inductance, close correlation between LF loss and resistance - and no
real correlation of either with characterisic impedance. :-)

Thus the cable 'impedance' turns out to be a much poorer predictor of
behaviour at audio for typical domestic cases than do the simple lumped
approximations. Thus showing that in practice - as distinct from theory
based on matched examples - the cable impedance as a parameter is of
secondary interest.

This is all about velocity, remember? My point was that we were in
danger of a "post hoc propter hoc" connection between impedance and
propagation velocity. This was really a gedankenexperiment to show
that they aren't really associated other than by the mechanics of
construction.

So now your "easily made" cable was just a thought-experiment... :-)

No it really is easily made. Just chop up some copper strip. Actually
the use of matches is probably not the best idea as you say. What you
would do is get some plastic of the right diameter and sort of snake it
along between the plates to hold them the right distance apart. Cable
ties would hold it all together in a handy unit.

I'd suggest that you make some. Then try measuring its ZcGamma properties
across the audio band. You might be surprised by the results. :-)

Why I say it is a thought experiment is because I wasn't actually
expecting you to make one - I was just showing you that cable impedance
and propagation velocity are independent variables. The one does not
cause the other.

Indeed. Nor do the other variables 'cause each other'.

In effect CRLG and ZcGamma are just the same four values in a different
form. In each case you just need four values (at a given frequency) to
specify the basic line behaviour.

However in physical reality, it is the stored/guided E and H fields that
determine the behaviour, and we then come along and describe this in terms
of CRLG or ZcGamma as we prefer.

I designed one of the first TEM cells for Multitone, a paging company
for testing the sensitivity of pagers. It was eight feet long and
comprised a stripline about a foot above the groundplane, with
tapered feeds down to N-type connectors. It performed exactly to
theory.

It is actually much easier to do that at RF than audio. :-)

No it isn't. The effect of any discontinuity is directly proportional to
the frequency, so it all gets harder, not easier as you go up. In
microwaves even surface finish starts to become a factor.

....and the behaviour of such systems tend to be affected by the relevant
physical sizes, etc, in terms of *wavelength*. So *being used over three
decades of wavelength* tends to be rather harder than you might expect *if*
you wish to keep thinking in terms of a specified impedance like saying
"this is a 10 Ohm line".

Bear in mind that most of the approximations and approaches used in
textbooks for transmission lines are chosen on the basis that the main
uses that rely on them are RF.

Note, for example that a 'transmission line' for audio would have to
cover at least three decades in frequency. That isn't common for radio
systems. Although wideband systems do arise, even wideband radars and
hopping comms tend to use far smaller decade ranges. Note also, that
the problems due to R' and G' tend to have larger effects at LF, and
that down at such frequencies details like your assuming 1mm thickness
may matter more than at RF. :-)

I designed signal generators and vector network analysers so I know all
about broadband work (how about an amplifier that covered 10kHz to
4.5GHz flat to 1dB?).

Alas, an amplifier isn't a transmission line or a guide. It can also be
made relatively 'small' wrt the wavelengths involved. Not many 10kHz to 4.5
GHz amps are 5 metres long.

FWIW I've also designed systems and devices going up to 3THz. Some of them
metres long. Some working over a range like 30Ghz to 3THz. But these didn't
use conventional guides. I also should confess I won the UK National
Metrology Prize in the 1980s for my design for a VNA covering the 60Ghz to
150 Ghz band. The instrument was then build by my old research group for
use by the NPL for primary standards measurements of impedances in that
band. But I didn't use conventional guides for this as that would have
limited the performance. :-)

Now I see where we are at cross purposes. Yes indeed the effects of R
and G are bigger at LF, but I don't agree that they cause problems at
low frequencies, because the cable runs that contain them are too short
to have an effect. Can you show a cable frequency response plot that
shows LF unflatness? I bet you can't. They only wander off at HF,
despite the fact that they have just about attained their stable HF
impedance.

I agree that R and G need not 'cause problems' at LF in terms of *use*. But
they do rather spoil the idea that you just need to work in terms of an
impedance value since the result is a complex number for both the impedance
and and wave velocity which varies a great deal across the audio band. My
interest here is in what it the most appropriate and convenient way to
think of, and analyse, the audio arrangements we have been discussing. Not
on ideal thought experiments, etc.

In matched situations then ZcGamma make good sense. But that simply doesn't
turn out to be the situation with practical domestic LS cables.

So in general for domestic LS cables, in practice the choice is between
using CLRG as four values, or variable Zc and gamma complex values. In
effect by moving from CLRG to ZcGamma you introduce frequency dependacies
into your four values that then tend to dissapear again later in the
calculations. (Indeed, in practice, just using RL is likely to be fine in
most cases as the errors will usually be small compared with other
sources.)

The results only differ by amounts tiny compared with the probably accuracy
with which you knew any of the values in the first place. :-) The choice
then is to use either 4 constants (CLRG) over the audio band, or use them
to create two frequency-dependent complex ones (ZcGamma) whose
dependencies are related in such a manner that they essentially correct to
give much the same outcome as if you'd used CLRG.

And of course in reality all four CRLG values will be frequency dependent,
but by amounts that generally don't show much effect for domestic LS
applications.

BTW the latest HFN arrived here today. The 'investigation' in that issue
is by Barry Fox. Have no idea when the cables articles will appear. Up to
the editor. I usually don't know what issue an article is in until it
hits my doormat! :-)

Slainte,

Jim

--
Change 'noise' to 'jcgl' if you wish to email me.
Electronics http://www.st-and.ac.uk/~www_pa/Scot...o/electron.htm
Armstrong Audio http://www.audiomisc.co.uk/Armstrong/armstrong.html
Audio Misc http://www.audiomisc.co.uk/index.html

TCI Cobra interconnects against Chord Chameleon

On 2008-07-19, Jim Lesurf wrote:
In article , Don
Pearce
wrote:
This is why I am saying that it this characteristic impedance term (the
10 ohm asymptote) that matters - the rest of that stuff does nothing,
because it is in a frequency range where it can do nothing.

Yet when you do an analysis using a number of examples of real cables you
find that you can get a close correlation between HF droop at 20kHz and the
cable inductance, close correlation between LF loss and resistance - and no
real correlation of either with characterisic impedance. :-)

Thus the cable 'impedance' turns out to be a much poorer predictor of
behaviour at audio for typical domestic cases than do the simple lumped
approximations. Thus showing that in practice - as distinct from theory
based on matched examples - the cable impedance as a parameter is of
secondary interest.

Let me disagree a bit and see the result :-) In theory I agree but in
practice (for a lossless line) not only do we have:

Z = sqrt(L/C)

but also I think we have (at the risk of exposing my superficial knowledge
of transmission lines):

L * C = permeability * permittivity.

For LS cables with real-world dielectrics that seems to introduce a
constrained, if not perfect, relationship between L and Z. So a low
inductance cable is, generally speaking, a low impedance cable.

I agree it's not sufficient for adequate modelling purposes but is useful
for qualitative purposes (e.g. choosing a low impedance cable for a
"difficult" loudspeaker when you can't go into the maths).

I agree that the impedance is a (much?) poorer predictor of audio
behaviour. And I agree with your point about HF droop. But I think
it is nevertheless fairly well correlated with the inductance.

--
John Phillips

TCI Cobra interconnects against Chord Chameleon

In article , John Phillips
wrote:
On 2008-07-19, Jim Lesurf wrote:

Thus the cable 'impedance' turns out to be a much poorer predictor of
behaviour at audio for typical domestic cases than do the simple
lumped approximations. Thus showing that in practice - as distinct
from theory based on matched examples - the cable impedance as a
parameter is of secondary interest.

Let me disagree a bit and see the result :-) In theory I agree but in
practice (for a lossless line) not only do we have:

Z = sqrt(L/C)

The snag being that for most real-world LS cables the effect of the series
resistance means the actual impedance varies across the audio band and may
orders of magnitude different in modulus to the above 'approximation'. Thus
in practice for most cables it is a hopelessly bad appoximation

but also I think we have (at the risk of exposing my superficial
knowledge of transmission lines):

L * C = permeability * permittivity.

Equivalent to saying that the L'C' product is related to the wave
propagation velocity.

Snag here is parallel to the above. The real-world values turn out *not* to
be all close to 'c', and tend to be frequency dependent.

In free space and with lossless media you'd be spot on. But we are
considering guide structures whose cross-sectional sizes are 'small' in
wavelength terms, etc. So geometry, R', etc change the velocity as well as
the characteristic impedance.

For LS cables with real-world dielectrics that seems to introduce a
constrained, if not perfect, relationship between L and Z. So a low
inductance cable is, generally speaking, a low impedance cable.

The measured results tend to show that 'constrained' is an interesting word
to use above. :-)

Yes, the wave velocites are all = c.

But their actual values vary with frequency, and are often well away from
being close to 'C'. Partly for geometric reasons the simple textbook
analysis ignores. Partly for various other reasons. TBH I was quite
startled by the level of variations I measured in wave velocities. I did
wonder at one point if the results were wrong. But cross-checking using
another method, and comparision with some other people's data confirmed the
variations. So your phrase 'not perfect' rather understates what I found.

Fortunately, for typical (unmatched) LS situations all the above doesn't
matter a great deal as the end-result is as I have described previously,
and re-state below.

I agree it's not sufficient for adequate modelling purposes but is
useful for qualitative purposes (e.g. choosing a low impedance cable for
a "difficult" loudspeaker when you can't go into the maths).

I agree that the impedance is a (much?) poorer predictor of audio
behaviour. And I agree with your point about HF droop. But I think it
is nevertheless fairly well correlated with the inductance.

Yes. That was my main point, and a finding backed by both measurement and
the theoretical analysis I did. :-)

For nearly all LS cables, the outcome was that R tells you the series loss
at LF, and the inductance tells you the droop. You can then apply these two
values to get good predictions of the behaviour into complex loads.
Provided you stick with the audio band up to 20kHz and don't make the cable
vastly longer than 5 metres or so.

You can certainly set out to find some extreme or special cases where the
above isn't a reliable guide. But the bulk of domestic LS cable
arrangements look like they won't be such extreme or special cases. :-)

BTW I do now have some commercial 'copper tape' type LS cable similar in
broad terms to what Don proposed. Been measuring it today, and hope to have
some results from the measured values over the next few days. This may well
show a better correlation between use of impedance as a predictor and
performance as it seems well made, and I have reason to think the maker
knows what he is doing. But I haven't yet analysed the results.

Slainte,

Jim

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TCI Cobra interconnects against Chord Chameleon