Interesting read about Cables

[Feanor]

By dropping large sums of cash on cables there is the expectation of improved sound yet that expectation can be a contaminating effect upon one's judgement of actual performance.

Who'd have guested? New purchase bias?

[E-Stat]

By dropping large sums of cash on cables there is the expectation of improved sound yet that expectation can be a contaminating effect upon one's judgement of actual performance.

I find a great solution to that effect: don't buy stuff until you hear it - ideally in your own system. That's the way I've purchased most all my components, cables certainly included.

rw

[poppachubby]

With cables, I have found that the best evaluation is to listen to your new cabling for several weeks, THEN put back the old cables. This will infact reveal the differences much more aptly than a few days of your new cables.

[Ajani]

The problem I have with just about any discussion of cables is that both sides of the argument are generally not based on proper application of science...

View # 1 - I auditioned XYZ Cables for $$$ and they lifted a veil off my music, so now I'm a hardcore believer in cables making a difference...

View # 2 - Based on specifications and some DBT, I state with authority that NO differences are possible and what anyone heard is in their imagination...

Neither view is scientific...

A simple sighted audition is not enough to prove that differences really exist OR that if they do, that they are because the new cable is better quality, based on all the reasons the maufacturer claims... Faulty connector, gauge size etc can all legitimately affect cable performance, so the comparison might not have been expensive cable VS cheaper cable but 16 gauge vs 12 gauge or good connection versus bad connection etc...

The other view that it must be in the person's imagination is equally ridiculous, as it requires making definitive conclusions from tests that don't definitively prove anything... The statistical failure of most participants in a DBT does NOT prove that there are no audible differences in cables. What is does prove is that differences (if they do exist) are far more subtle than many audiophiles claim... A major difference would be easily identified under DBT conditions... For example, I might not be able to tell the difference between 2 wines under DBT, but no matter how stressed I am, I could tell the difference between water and orange juice... Water versus Orange Juice is a NIGHT & DAY difference...

[E-Stat]

The problem I have with just about any discussion of cables is that both sides of the argument are generally not based on proper application of science...


For example, I might not be able to tell the difference between 2 wines under DBT..

You've identified a third non-scientific approach: the use of unsupported assumptions concerning the very test procedure used to "prove" the question. First of all, do you ever switch interconnects between say a source and pre or power amp while both are powered up and set to normal listening gain levels? Of course not! Why? Well, the noise or huge POP! can potentially damage downstream gear or at least open a fuse. Performing a double blind test of cabling necessarily requires connecting both cables to a switch box between the components used. Naturally, the use of external uncontrolled variables is not required for comparing wines! The non-experiential theorists reason that since the switch contact impedance, inductance and capacitance is low, they assume that the box does not influence the test. Such incomplete thinking completely misses the point! Preventing the POP! requires the use of common grounds. So, now you are comparing the combined electrical characteristics of both cables. Or feedback loops between two amplifier so wired.

Is it any wonder then that listeners are unable to hear the difference between using both cables and - both cables? Frank Van Alstine made that observation long ago. Some folks attempt to defend their position cloaked in the mantle of engineering using fallacious assumptions like this.

rw

[Ajani]

You've identified a third non-scientific approach: the use of unsupported assumptions concerning the very test procedure used to "prove" the question. First of all, do you ever switch interconnects between say a source and pre or power amp while both are powered up and set to normal listening gain levels? Of course not! Why? Well, the noise or huge POP! can potentially damage downstream gear or at least open a fuse. Performing a double blind test of cabling necessarily requires connecting both cables to a switch box between the components used. Naturally, the use of external uncontrolled variables is not required for comparing wines! The non-experiential theorists reason that since the switch contact impedance, inductance and capacitance is low, they assume that the box does not influence the test. Such incomplete thinking completely misses the point! Preventing the POP! requires the use of common grounds. So, now you are comparing the combined electrical characteristics of both cables. Or feedback loops between two amplifier so wired.

Is it any wonder then that listeners are unable to hear the difference between using both cables and - both cables? Frank Van Alstine made that observation long ago. Some folks attempt to defend their position cloaked in the mantle of engineering using fallacious assumptions like this.

rw

Certainly... That is another problem with talking about science... Getting agreement on whether the test procedures are appropriate for the conclusions drawn...

Adding a switch box to cable test makes no sense simply because it is highly unlikely that persons who claim to hear differences in cables, will just accept the idea that the switch box makes no audible difference... If they accepted that then they would just as likely accept the notion that cables make no audible difference...

My view on cables is simply that a lot more research needs to be done... as so far no one has definitively proved that cables make an audible difference (connection, gauge, etc excluded), but also no one has definitively proved that cables don't make an audible difference...

[rightaway]

kinda of a weird read. i'm confused. i thought the thickness of the cable was the most important?

[JohnMichael]

The thickness of the wire is just the beginning. There are plenty of graphs that determine the gauge needed depending on the distance of speakers from the amp. Some buy larger guage cables for low resistance and as often claimed stronger bass.

Now to further complicate things some of us hear a difference in types of cables. I hope you are not one of them. Life would be easier if you can be happy with generic stranded cables.

After gauge you have cable geometry and your choice of copper or silver as two popular conductors. Then the choice of stranded or solid core conductors. Various types of insulations are uses and then often placed inside a jacket.

My preference to my ears, in my system and in my room is a solid core minimal insulation jacketless 12 gauge design.

[frenchmon]

OK, lets start with some visual illusions:

Visual Illusions

Now lets move on to aural illusions:

Shepard Tones

Tri-Tone Effect





Yep.

-Bruce

FLZapped...what took you so long?

[frenchmon]

I'm starting to wonder if we all hear the same.

[Poultrygeist]

"It is almost impossible not to hear what you think you are going to hear" - Siegfried Linkwitz

[frenchmon]

Point being...some hear better than others...especially if one thinks a zip cord is all is needed.

[E-Stat]

"It is almost impossible not to hear what you think you are going to hear" - Siegfried Linkwitz

What a perfect example of one with expectation bias. He definitely doesn't hear the cumulative effect of over a dozen op amps in the Orion crossover. He definitely doesn't hear the mediocre sound of the generic amps he recommends.

Here's a visual as to the distortion added by zip cord and various coaxials. Note the added high frequency hash. Also, high dielectric constant cables store energy and create smear in the time domain which affects clarity and soundstaging.

rw

[Poultrygeist]

"As far as I am concerned a transaction where one guy sells a Quantum purifier cable to another should result with the buyer in the crazy house and the seller behind bars"

- Dan Lavry ( Lavry Engineering )

[E-Stat]

"As far as I am concerned a transaction where one guy sells a Quantum purifier cable to another should result with the buyer in the crazy house and the seller behind bars"

I confess this is the first time I've seen someone combine two logical fallacies - that of Argument from authority and Reductio ad absurdum in a single argument. Congratulations!

BTW, he was talking about Bybee products.

rw

[JohnMichael]

What exactly is a "quantum purifier cable" and how does this relate to audio cables?

rw

Thank you, I was going to ask.

[JohnMichael]

http://www.essex.ac.uk/csee/research...bles_1985).pdf

The Essex Echo
Malcolm Omar Hawksford
Audiophiles are exited. A special event has occurred that promises to undermine
their very foundation and transcend "the event sociological": a minority group now
cite conductor and interconnect performance as a limiting factor within an audio
system. The masses, however, are still content to congregate with their like-minded
friends and make jokes in public about the vision of the converted, content to watch
their distortion factor meters confidently null at the termination of any old piece of
wire. Believing in Ohm's law, they feel strong in their brotherhood.
But the revolution moves forward. . .
This article examines propagation in cables from the fundamental principles of
modern electromagnetic theory. The aim is to attempt to identify mechanisms
that form a rational basis for a more objective understanding of claimed sonic
anomalies in interconnects. Especially as I keep hearing persistent rumours
about the virtues of single-strand, thin wires (John, is it OK to mention thin,
single strand in HFN/RR yet? . . .)
Inevitably, the path towards an objective understanding depends upon both
the correctness and completeness of the model selected. We shall establish,
therefore, a theoretic stance initially and commence with the work of Maxwell
(even though he could not avail himself of a distortion factor meter.) The
equations of Maxwell concisely describe the foundation and principles of
electromagnetism; they are central to a proper modelling of all electromagnetic
systems. The equation set is presented below in standard differential form,
where further discussion and background can be sought from a wide range of
texts(1, 2, 3).
Maxwell's Equations:
Faraday's Law Ampere's Law
curl E = -
¶t
¶B
curl H = J +
¶t
¶D
Gauss's Theorem No magnetic monopoles
div D = r div B = 0
The constituent relationships that define electrical and magnetic material
properties are,
bD = e0erbE bB = μ0μrbH
bJ = s bE (if s is constant then this equation represents
Ohm's law)
However, it is common to write e = e0er and μ = μ0μtrhus bD = ebE and
bB = μbH
where,
bE, electric field strength, (volt/m)
1
bB, magnetic flux density, (tesla)
bD, electric flux density, (coulomb/m2)
r, charge density, (coulomb/m3)
s, conductivity, (ohm-m)-1 (conductivity is the reciprocal of resistivity)
bH, magnetic intensity, (ampere-(turn)-m)
bJ, current density, (ampere/m2)
e0, permittivity of free space, (farad/m)
er, relative permittivity
μ0, permeability of free space, (henry/m)
μr, relative permeability
t, time, (second)
(The bar over some parameters indicate vector or directed quantities.)
It is relatively straightforward to show that the Maxwellian equation set is able
to support a wave equation that governs the propagation of the electric and
magnetic fields in both space and time. However, for those more interested in
the sociological behavioural patterns of the ethnic minority of audiophiles,
allow me a moment to describe the circumstances in which this article is being
prepared.
The date is April 1st 1985 (honest). I have freed myself of the conservative
British climate (political, weather and audio) and undertaken a transposition to
the red-walled town of Marrakech in Morocco. The sky is clear and blue, the
sun warm, yet the snow lies dormant on the Atlas mountains. The sound of a
distant Arabic chant of the Koran sets a background, while the birds sing,
watching the blossom develop on a multitude of orange trees, awaiting the
fresh living fruit that matures in hours of endless sunshine, ready for my
breakfast! There may yet not be a length of large crystal copper within a
thousand mile radius. I shall check out the market place this afternoon,
disguised with black beard and djelaba . . . ! That's strange. the snake
charmer's snake has Snaic written on its side . . . ?
Let formal study commence. The wave equation describing a propagating
electric field bE in a general lossy medium of conductivity s, permittivity e and
permeability μ is derived as follows:
Operating by curl on the Faraday equation,
curl(curl E) = - curl( ¶t
¶B ) = - μ ¶t
¶
curl H
Substitute for curl bH from Ampere's law,
curl(curl E) = - μ ¶t
¶J
- μ
¶t2
¶2D
Substitute also the Ohm's law relationship, bJ = s bE and the vector identity,
curl(curl E) = grad(div E) - Ñ2E
2
where, assuming a charge-free region, div bD = 0, (i.e. div bE = 0), the
generalised wave equation follows directly,
Ñ2E = ms
¶t
¶E + me
¶t2
¶2E
Consider a steady-state, sinusoidal electric field bE, propagating within a
medium of finite conductivity. The travelling wave must inevitably experience
attenuation due to heating, so let us examine a possible solution to the wave
equation, that has the form,
E= Eoe–az sin(wt –bz)
z
Figure 1 Electric and magnetic fields, mutually at right angles and
propagating in z direction.
E
H
The field E is shown here to propagate in a direction z, where the direction of E
is at right-angles to z, as shown in Figure 1. The attenuation of the wave with
distance is chosen to be exponential, e–az, where a is defined as the
attenuation constant, while the distance travelled by the wave is determined by
b, the phase constant,
b=
2p
l
and l (metre) is the wavelength of the propagating field. The frequency at
which the wave oscillates is defined by w, (2pf) rad/s. Thus, for constant z, E
varies sinusoidally, while for constant t, E varies as an exponentially decaying
sinewave. An exponential decay is a logical choice, as for each unit distance
the wave propagates, it is attenuated by the same amount.
3
To check the validity of our chosen solution, the function for E must satisfy the
wave equation. This validation usefully enables the constants a and b (see
expression for E) to be expressed as s, e, μ and w. However, the substitution
although straightforward is somewhat tedious, so I will state the
commencement and show the conclusion:
Substitute, E= Eoe–az sin(wt –bz) into,
¶z2
¶2E
= μs
¶t
¶E
+ μe
¶t2
¶2E
Yes, the function for E is a solution, providing that
b2 - a2 = mew2
ab =
2
wms
Solving for a and b,
a2 =
2
mew2
(1 + (
ew
s )2 )0.5 - 1
b=
wms
2a .
Sometimes a and b are written in terms of the propagation constant g, where
g = a + jb. Thus the constants a, b that govern the propagating field are
expressed as a function of the supporting medium, where the parameters (μ, e,
a) are readily available for many materials.
OK, so you may not have followed the detail of the mathematics, but do not
worry. It is really only important here to follow the philosophy of the
development, that is,
(a) Commence with the established Maxwellian equation set, from which
the generalised wave equation for propagation in a lossy material is
derived.
(b) Guess at a logical solution for a sinusoidal plane wave, knowing the
Fourier analysis allows generalisation to more complex waveforms (at
least for a linear medium).
(c) Show that the chosen solution satisfies the wave equation, where the
constants a and b follow as functions of μ, e, s and w.
4
(d) The velocity of propagation v metre/second also follows from w and b,
where the velocity is the "number of wavelengths" travelled in one
second, thus
v = fl = 2pf (
2p
l ) =
b
w
At this juncture, it is now possible to classify materials into good conductors
(metals) and poor conductors (lossy dielectrics), though it is important to note
that this demarcation is frequency dependent.
(i) Poor conductor: (i.e.. dielectric materials with very low conductivity) s is
small such that, s << ew, whereby the expression for the attenuation
constant shows a o 0, and the wave experiences minimal attenuation.
This condition applies to propagation in both free space and low-loss
dielectrics, where the velocity of propagation can be shown to be,
v =
(me)
1
=
(mr er)
300 . 108
m / s
and μr and er, are the relative permeability and permittivity of the
supporting medium (μr= 1, er = 1 for free space), that is for free space, v
= c, the velocity of light. This is the "fast bit" and results in the comment
that for audio interconnects, the velocity of propagation within the
dielectric is so high that signals respond virtually instantaneously across
the length of the cable. OK, we will not argue, will we John? John
Atkinson smiled, his Linn bounced happily with the platter remaining
horizontal.
(ii) Good conductors: (e.g. copper). Here we assume, s >> ew i.e. w <<
s/e which for copper implies f < 1.04 . 1018 Hz.
s = 5.8 . 107 (ohm-m)–1
e = 8.855 . 10–12 farad/m
μ = 4p . 10–7 henry/m
at audio frequencies, copper is a good conductor, where the
expressions for a and b approximate to,
a = b = [mws/2]0.5
values for a and b are identical for a
good conductor
and the velocity, v =
w
b , whereby
5
v =
ms
2w
very much less than for a material with
low conductivity
For copper a, b and v are given by,
a = b = 15.13 f and v = 0.415 f
Note the frequency dependence of a,
b, v
!All significant at audio !
(i.e. at 1 kHz the velocity is 1/25 of the velocity of sound in air . . . )
Skin depth
A parameter often quoted when discussing propagation within a conducting
medium is skin depth, d (metre). d is defined as the distance an
electromagnetic wave propagates for its amplitude to be attenuated by a factor
e–1, i.e. 8.69 dB (where e is the same e as in an exponential, e = 2.718282,
therefore e–1 = 0.3679).
Recall, E = Eoe-az sin(wt – bz), thus, for z = d, then e-ad = e-1
d =
a
1 =
mws
2
i.e. the skin depth d is simply the reciprocal of the attenuation constant a. It is
strictly a convenient definition (see later: "Digression"). but note, the field still
exists for z > d, even though it is attenuated e.g. for z = 3.5 d, just over a 30 dB
attenuation is attained.
For copper, it follows, d = (15.13 f )–1
. It is also interesting to note that the
phase of E, (bz) has changed by 1 radian at z = d, a far from negligible figure.
The following table gives example calculations of skin depth and velocity
against frequency.
Table of d and v for copper against frequency f
frequency
f hertz
skin depth
d, mm
velocity v
m/s
6
50
100
1,000
10,000
20,000
9.35
6.61
2.09
0.66
0.47
2.93
4.15
13.12
41.50
58.69
Note the low value of velocity, which is directly
attributable to the high value of conductivity of
copper, s = 5.8.107 (ohm-m)–1
Note also, for information:
s (silver) = 6.14 . 107 (ohm-m)–1
s (aluminium) = 3.54 . 107 (ohm-m)–1
These results suggest a copper wire of 0.5 o 1 mm diameter is optimum (see
also later "Digression"). However, the story is far from complete: an electric
field travelling within copper has a low velocity and experiences high
attenuation, that results in skin depths significant to audio interconnect design.
The frequency dependence of d (also a and b) should not be underestimated;
the copper acts as a spatial filter, the field patterns within the conductor, for a
broad-band signal, exhibit a complex form (see Figure 3, for example). Now
introduce either/both a spatially distributed non-linearity or discontinuous
conductivity, as previously discussed in HFN/RR (4), and the defects of cables
become more plausible. The distortion residues (linear and/or non-linear)
would exhibit a complex, frequency interleaved structure, that could well play
to an area of our ear/brain detection process, especially when monitoring an
optimally projected stereophonic field. After all, the ear is both non-linear and
a Fourier analyser; it would seem strange if we had not evolved a matched,
intelligent detector to exploit the complex, possible non-linear, time smeared
patterns that must inevitably result. I believe Gerzon, Fellgett and Craven have
researched the application of bi-spectral processes as an augmentation to
Ambisonics. Is it here that the final, almost hidden, link in our fundamental
understanding of audio systems is to be found?
OK, so those who become bored with my earlier analysis may begin again with
a new aroused interest. The rest of us will have a Gin and Martini, on crushed
rocks (rocket fuel), while you complete your revision. Shaken not stirred,
please, Ivor.
Let us proceed with the model development. Electromagnetic theory shows a
cable to be a wave guide, the conductors acting as "guiding rails" for the
electromagnetic energy that propagates principally through the space between
the conductors, where the currents in the wires are directly a result of the field
boundary conditions at the dielectric/wire interface. This may prove a difficult
conceptual step for those more accustomed to lumped circuits and the
retrogressive 'water pipe' models. However, a wave guide model is correct,
irrespective of cable geometry, only the field patterns vary depending upon the
conductor shape and their spatial relationship. This theory is not new, it has
been widely accepted and practised by engineers for many years.
A propagating electromagnetic wave consists of an oscillation of energy back
and forth between the magnetic and electric fields, the energy in the electric
and magnetic field must therefore be equal. Think of space (both in general
and within the dielectric of the cable) as a distributed LC (oscillator) network.
7
Note: the energy propagates
in an axial direction in the region
between the two conductors
Outer
conductor
Inner
conductor
E, electricfield
H,magneticfield
v, velocity showing
showingaxial direction
of propagation
H
E
v
Fig. 2 Cross section of coaxial cable showing radial E field
and circumferential H field.
E
H
axial
direction
For example, examine the coaxial cable shown in Figure 2. The electric field is
everywhere radial, while the magnetic field forms concentric circles around the
inner conductor (Ampere's circuital law). It is important to note that the bE
and bH fields are both spatially at right angles to each other and to the
direction of propagation, which is along the axis of the cable. This is a direct
result of Maxwell's equations.
In an electromagnetic system, the power flow is represented as a density
function bP (watt/metre2), called the Poynting vector, where
bP = bE x bH
For the coaxial cable, bP is directed axially. Integrate bP over a cross section
of area and the total power carried by the cable results. The expression for bP
can be compared with power calculations in lumped systems, where P = VI
(i.e. V o bE field, I o bH field).
If we assume the two conductors of the coaxial cable are initially ideal, where
s o ¥, then all the electromagnetic energy flows in the dielectric. The bE field
does not penetrate the conductors, the skin depth is zero (check with
expression for d) and the conductors act as perfect reflectors (that's why
mirrors are coated with good conductors). In this case, there is only a surface
current on each conductor to match the boundary condition for the tangential,
magnetic field bH, at the dielectric/conductor interface(2).
8
OK, so in your mind you should now visualise a radio wave travelling within the
dielectric, being guided by the conductors, where the electric and magnetic
fields are both at right angles to each other and to the direction of propagation
along the axis of the cable.
However, this example is unrealistic as practical cables have conductors of
finite conductivity, s. Experience shows that such conductors exhibit signal
loss, where at a molecular level, friction-like forces convert electrical energy
into heat.
As the wave front progresses through the dielectric, the boundary condition is
such that the electric field, bE, is not quite at 90° to the conductor surface,
which is a direct consequence of the finite conductivity. The wave, in a way,
no longer takes the shortest path along the dielectric of the cable and appears
to travel more slowly. However, at each dielectric-conductor interface, a
refracted field now results within the conductor which proceeds to propagate
virtually at right angles to the axis of the cable, into the interior of the
conductor. This is the loss field. In other works, the majority of the
electromagnetic energy propagates in a near axial direction, within the
dielectric, but a much reduced loss field propagates almost radially into each
conductor, with the electric field Es oriented axially along the length of the
conductor. It is this component that is controlled by the internal parameters
(μ, s, e) of the copper and is ultimately attenuated by conversion to heat. It is
here that the story becomes more relevant to audio.
A conductor of finite conductivity causes electromagnetic energy to spill out
from the dielectric into the conductor. We should also note that although the
main component of energy propagates rapidly within the dielectric along the
axis of the cable, the energy spilling out into the conductor propagates much
more slowly (see earlier table) and the parameters a, b, that govern the loss
wave are frequency dependent, a significant complication. It is the loss wave
within the conductor that results directly in current within the copper. We
would, therefore, expect a complex current distribution throughout the volume
of the conductor, and that is precisely what we get, see Figure 3.
9
V
e
conductor
ZL
VL Vg
E directionof
propagation of
dielectric mainfield
V
e
conductor
E E E E E E E
V
g generator voltage
V
e
error voltage across
conductor length
E
s
loss field in conductor
E external electric field
VL
load voltage
radial direction of
propagation of loss field
r
Fig. 3 Basic field relatioships and direction of propagation of main
external field and internal loss field.
r
E
s
E
s
r
r
r
Meanwhile, back at the Maxwellian equation set,
bJs = sbEs (this is Ohm's law)
That is, a conduction current density bJs is induced axially within the
conductors due to the internal electric field, bEs, of the loss wave. This axial
current is the current we normally associate with cables: the model is
compatible with more usual observations of cable behaviour.
Since the electromagnetic energy of the loss wave propagates principally in a
radial direction, entering the conductor over its surface area, the current
density (which is proportional to bEs) is greatest at the surface and decays as
the field propagates into the conductor interior. It is this reason why a
conductor experiences a skin effect, rather than the converse with the current
concentrated near the centre of the conductor.
One of the more instructive parameters is the time Td, for the sinusoidal loss
field, Es, to traverse a distance d within a good conductor, where since,
v =
b
w =
a
w = wd
then
T
d
= v
d =
w
1
| s >> we
For example, consider a copper bar where the diameter is greater than the
skin depth,
10
d = 0.66 mm at 10 kHz : Td = 15.9 μs
d = 2.09 mm at 1 kHz : Td = 0.159 ms
d = 6.61 mm at 100 Hz : Td = 1.59 ms
i.e., the lower the frequency and the larger the conductor diameter, the longer
Td. There is energy storage, it is a memory mechanism.
Observe the importance of discussing principally a time domain model. Our
thesis is attempting to demonstrate that a (copper) conductor exhibits
significant memory, that influences transient behaviour by time smearing by a
significant amount a small fraction of the applied signal.
Consider the cable construction shown in Figure 3. Allow the generator to
input a sinewave for a time >> Td, to enable the steady-state to be established.
The bE field between the conductors responds rapidly to the applied signal, as
the velocity in the dielectric between the conductors is high. We are assuming
here a terminating load to the cable, so there is a net energy flow through the
dielectric. Remember as the wave front progresses, so a radial loss wave
propagates into each conductor, where the bEs field is aligned in an axial
direction.
Now allow the applied signal to be suddenly switched off. The field between
the conductors collapses rapidly, thus cutting off the signal energy being fed
radially into the conductors. However, the low velocity and high attenuation of
the loss wave represents a loss-energy reservoir, where the time for the wave
to decay to insignificance as it propagates into the interior of the conductor, is
non-trivial, by audio dimensions.
The bEs field within the conductor can be visualised as many "threads" of bE
field as shown in Figure 3. The voltage appearing across the ends of each
thread, De, is calculated by multiplying the bEs field by the cable length, L,
though more strictly, this is an integral, where
De = ò
l=0
L
E . dl
However, the macroscopic voltage across a conductor, Ve (i.e. that measured
externally) is the sum of all these many elemental voltages. Because the field
propagates slowly, this summation is actually an average taken over a time
window, extending over a short history of the loss field. Consequently, when
the generator stops, the error signal across each conductor does not collapse
instantaneously, the conductor momentarily becomes the generator and a
small time-smeared transient residual results as the locally stored energy
within each conductor dissipates to insignificance.
Assuming the two conductors are symmetrical, then the total error voltage is
2Ve, whereby the load voltage VL is related to the generator voltage Vg, by VL =
Vg - 2Ve. Clearly, Ve << Vg, however, Ve takes on a complex and time-smeared
form that in practice is both a function of the conductor geometry, cable
characteristic impedance, generator source impedance and load impedance,
as all these factors govern the propagation of both the main electric field, bE
and the electric loss field bEs. In practice, unless the cable is terminated in its
characteristic impedance, the main field bE will traverse the length of the
11
cable, rapidly back and forth, many times, before establishing a pseudo-steady
state. Of course, an optimal load termination unfortunately implies a
significant loss field in the conductors.
This argument would suggest that for non-power carrying interconnects, it is
better to terminate the generator end of the cable in the characteristic
impedance, leaving the load high impedance. The bE field is then rapidly
established in the dielectric, without either multiple reflection along the cable
length, or a finite power flow to the load spilling out a loss wave into the
conductors.
Oh! I see these last comments have raised a question from the floor, from the
dark haired Moroccan lady almost wearing a 'belly dancer's costume in the
front row: she want to know what happens to the electromagnetic field
propagating through the copper conductor when it encounters an abrupt
discontinuity in conductivity, and if this has a correlation with defects in
copper, attributable to crystal boundary interfaces. (No, Ken, this is not the
appropriate time to recommend the use of Gold Lion KT77s.)
Consider for a moment a long transmission line terminated in its characteristic
impedance. Electromagnetic energy entering the line will then propagate in a
uniform manner, finally being totally absorbed in the load (just as a VHF aerial
cable which is terminated in 75 W). If, however, the termination is in error,
then a proportion of the incident energy will be reflected back along the cable
towards the source. In extreme cases, where there is either an open or a
short-circuit load, then all the incident energy is reflected, although with a
short circuit the sign of the bE field is reversed on reflection, thus cancelling
the electric field in the cable and telling the source there is a short circuit
termination. The point to observe, is that a discontinuity in the characteristic
impedance results in at least partial reflection at the discontinuity, which will
distort the time-domain waveform. This reflective property of a change in
characteristic impedance can be used, for example, to locate faults in long
lengths of cable, by using time domain reflectometry, that is, a pulse is
transmitted along the cable and the returned partial echoes from each
discontinuity are measured, their return times then locate the fault. It is the
same principle as radar, though the universe is a narrow cable.
Similarly, for a wave travelling in copper, a discontinuity in impedance leads to
partial reflection centred on the discontinuity. This effect must therefore be
compounded with an already dispersive propagation, i.e. different frequencies
propagate at different velocities thus time smearing the error signal or loss
wave in the conductor. OK, let's now play to the gallery . . .
This observation certainly gives some insight into the effects of crystal
boundaries within copper, where each boundary can be viewed as a
discontinuity in s and corresponds to zones of partial reflection for the radial
loss field. Note however, that this property is not necessarily non-linear. We do
not have to invoke a semiconductor type non-linearity to identify a problem, we
are talking probably of mainly linear errors. So we would not necessarily
expect a significant reading on the distortion factor meter or modulation noise
side-bands on high-resolution spectral analysis, for a stead-state excitation.
However, just as with loudspeaker measurements, amplitude-only response
measurements do not give a complete representation of stored energy and
time delay phenomena. We would require very careful measurements directly
of the errors with both amplitude and phase, or of impulse responses in the
time domain. Following the comments on the error function in an earlier Essex
Echo(5), direct measurements of the output signal will yield, in general,
12
insufficient accuracy to allow a true estimate of the system error. This point is
worth thinking about, re-read my earlier comments in the first Echo (5). Ideally,
we need to assess the actual current distribution in the conductors, or at least
to measure the conductor error directly.
A smile now appeared on the young lady's face, it was Alice through the
Looking Glass all over again - she now understood the subtle distortion in
John Atkinson's reflection. As she relaxed, her large crystal diamond of high
permittivity fell to the floor.
The final stage in the development of our model, is to account for copper
conductors of finite thickness, where the thickness may well be much less than
the skin depth. Just as a wave travelling in air when confronted by a shortcircuit
is reflected, so a wave travelling in a conductor, that encounters an
open circuit (e.g. copper-air boundary) also undergoes reflection and therefore
passes back into the conductor, undergoing further attenuation. However, the
boundary condition requires a reversal of the magnetic field, thus providing the
thickness of the conductor is much less than the skin depth, the incident and
reflected bH fields nearly cancel and the conductor exhibits a lower internal
magnetic field. Consequently, there is predominantly an axial electric field and
corresponding conduction current, the conductor behaves nearly as a pure
resistor, i.e. the magnetic field hence, effectively, inductive component, is
reduced to the pseudo-static case. The current distribution is nearly uniform.
The conductor has lost its memory.
Digression
For completeness, let us now take a more conventional look at skin depth, to
demonstrate that our model is consistent (OK John, not running out of time
yet?)
A direct effect of skin depth is the well-known phenomena that the current in a
conductor resides near the surface at high frequency, where this notion is
perfectly consistent with our model.
A reason for specifying d as the distance travelled whereby the field has
decayed a fraction e–1 is as follows:
Let the current density be given by: Js = Jo e-az sin (wt – bz)
The total instantaneous current, I, in a strip of conductor of width DY but of
infinite extent in z is then,
I = DY ò
z=0
¥
J0 e-a zsin(v t - ßz) dz
Evaluating the integral, putting a = b = d–1 gives,
I = d DY J0 sin(v t - p/4)
The result above shows that the amplitude of the total conduction current is {d
DY Jo}, it is as if a uniform current density existed only for z = 0 to d, but was
13
everywhere else zero for z > d. This leads to our colloquial notion of skin
depth, but observe how the -p/4 phase shift (-45 degree) with respect to the
surface-current density, disguises the propagation of the conduction current
that is internal to the conductors. So we see there is a logical foundation for
our definition of skin depth.
This convenient but approximate view-point of the current distribution being
concentrated in the skin depth allows us to estimate an approximate
impedance for the conductor, based upon the principle that the conductor is
now only of thickness d. Note however, that this approximation completely
removes the more subtle structure of our model.
Imagine a cylindrical conductor of diameter D metre and length L metre where
d < 0.5 D. Picture the skin depth as an annulus as shown in Figure 4. We
may write the modulus of the dc and ac impedances |Zdc|, |Zac| measured
across a length of L of this conductor, as
d
Figure 4 Cylindrical conductor showing approximation to skin depth.
D
approximation to skin depth
|Zdc| =
s pD2
4 L
and, |Zac| =
s pd (D - d )
L
but substituting for d from our earlier result.
d =
a
1 =
mws
2
then for the case where d << 0.5 D,
14
|Zdc|
|Zac|
=
4 d (D - d )
D2
»
4 d
D »
4
D
2
mv s
Returning to Maxwell, we could also show that when the impedance is
proportional to Ö(frequency). that there is a 45° phase shift between voltage
and current, but when d approaches D/2 and ultimately, d > D, then Zac is
substantially resistive with zero phase, which is our usual low frequency model
of a piece of wire.
Hence, where d = D/2, we expect to observe a transitional region in the
effective conductor impedance, i.e.. |Zac| » |Z dc|. This critical frequency fc
follows approximately from our expression for a by putting a = 1/d = 2/D,
whereby
f c =
4
pmsD2
e.g. for a diameter of 0.8 mm fc = 27 kHz. However, this is only approximate
as the cylindrical geometry has not been fully accounted for in the analysis.
Hence, thin conductors behave more like resistors over the audio band,
whereas thick wires have a complex impedance, rather like the "square root of
an inductor" i.e. the impedance modulus is proportional to Öf, the phase – 45°.
In this latter discussion, we have interpreted our model in the steady-state, and
as a lumped impedance. However, we should not lose sight of the timedomain
model and the generalisation to a discontinuous or granular
conductivity. Again, as observed in the earlier Echo(5), steady-state analysis
though correct, can limit our appreciation of a system. We would not expect
to observe anomalies on steady-state tests easily as in the main they are
hidden from view, the test is insensitive. The observations should be made
when the signal stops, at the end of a tone burst for example, and the error
signals displayed by using decay spectra, following loudspeaker measurement
practice.
In developing our model, we have concentrated on the loss mechanisms
inherent in the conductors. We have not discussed the characteristic
impedance observed at the input of the interconnect. This is a direct result of
the amount of energy in the electric and magnetic field needed to "fill" the
cable i.e. the propagating energy within the cable system. Ultimately, the
energy loss in the interconnect is a function of the characteristic impedance
and the length and load termination as these directly influence the loss field,
hence conductor current, hence voltage across the cable length. The load
impedance that terminates the line is mapped into the interconnect error
mechanisms which is particularly relevant with loudspeaker loads.
The detailed characteristics of the dielectric material are also important as the
model shows that the dielectric supports the majority of the signal during its
transportation across the cable (which can take many passes if the cable is not
optimally terminated). Dielectric-loss has been cited as a contributory factor,
which can be modelled as an equivalent frequency dependent, but low
conductivity sd where
sd = we (Power factor), and power factors vary(2) from typically ~0.0005 to
15
0.05. The attenuation and phase constants then follow as ad = 0.05wÖ(μe)
(Power factor), bd = Ö(μe). However, it is difficult to see how these results
affect audio cables from this simplistic appraisal. A more detailed study of the
permittivity of dielectrics is required. Directional wave characteristics could
well affect the loss wave launched into the conductors. But times is running
out . . .
Conclusions
The basic elements of our model are now complete, where we propose the
internal loss fields that propagate within the conductors are at least partially
responsible for some claimed anomalies. The points to emphasis are as
follows:
(a) The loss component propagates at right angles to the axis of the cable i.e.
radially into the conductors.
(b) The loss field gives rise to the corresponding internal current distribution
along the axis of the conductor (bJs = sEs). Note for the loss
component, that although the direction of propagation is radial, the bEs
field is at right-angles to the direction of propagation of the radial loss
wave and is along the conductor axis. This induces an axial conduction
current and is the component of current normally experienced.
(c) The velocity of propagation within the conductor (copper) is both very
slow and frequency dependent, consequently, different frequencies
propagate at different velocities i.e. the material is highly dispersive and
acts as a spatial filter.
(d) The velocity of the loss field is directly dependent upon the conductivity
s and pemeability μ, which should be noted for magnetic materials.
Usual analysis assumes s to be a smooth and continuous function.
However, crystal boundaries suggest discontinuities in s, such that the
conductors appear more like stranded, though disjointed, wire where
such discontinuity represents a point of at least partial reflection and
field redistribution.
(e) There is a problem even if s is a linear but discontinuous function.
However, non-linearity due to partial semiconductor diode boundaries
would lead to a very complex, frequency interleaved intermodulation that
could be governed by bi-spectral processes, to which the ear/brain may
have a significant sensitivity; such residues would of course be at low
level.
(f) Stranded conductors appear to be a poor construction, when viewed by
this model. The loss component propagates against the strands and will
experience discontinuities of air/copper that are inevitably random. This
is comparable to a large-scale granularity, where crystal boundaries
represent possibly a similar structure but within the copper. A single
strand of large crystal copper will behave more as a simple impedance
as outlined in the "Digression". Normal simplified theory and actual
conductor performance merge, where at a diameter circa 0.8 mm the
conductor becomes closer to a low-valued ideal resistor, at audio
frequencies.
16
(g) Irregularities in cable construction and directional wave properties in the
dielectric could well lead to differences in the bEs field patterns, hence
current distribution within the conductors, depending upon which end is
the source. (I wonder if current vortices can result, like whirlpools in a
stream of water?) The exact nature of the loss field (error field) would, in
principle, exhibit differences and thus allow the cable to have a
directional characteristic in that the error is not mirror symmetric. For
example, slight variations in diameter, or indeed internal crystal
structure, may well occur in manufacture due to stress fields. Such
effects however, would appear to be in the domain of error of errors, and
of an extremely subtle nature, where steady-state measurements would
exhibit poor measurement sensitivity, yet the residues from impulse
testing would contain low energy. In other works, very difficult to
measure.
(h) Since all materials within the cable construction, including surface
oxidisation of the conductor indirectly affect the boundary conditions,
hence loss field, we would expect each element to contribute to
performance.
(i) The time taken for the field to propagate to the skin depth d, is longer at
low frequency. Thus, thick conductors would appear more problematic
at low frequency, showing a greater tendency for time dispersion (overhang).
(j) d = [2/(wms)]0.5, magnetic conductors have μ-dependent skin depths and
μ is partially non-linear. This needs investigation; it suggests magnetic
conductors should be avoided. (Of course, I would never admit to
checking passive components with a magnet . . . )
(k) The ear-brain sensitivity to particular complex, high-order frequencydependent
intermodulation distortion requires careful research, using
possible interconnect defects as a basis for identifying classes of error
and of error correlation mechanisms.
(l) Stepping back and observing the problem macroscopically, it appears
cable defects have their greatest effect under transient excitation rather
than within the pseudo steady-state of sustained tones. Transient edges
are effectively time smeared or broadened albeit by a small amount,
where this dispersion is a function of both the signal and the properties
and dimensions of the conductors. Amplitude frequency response
errors in the steady-state are at a level that is insignificant when listening
to steady-state tones. Their significance however, when mapped via the
error function onto transient signals may well be of greater concern,
particularly when the errors are monitored optimally in stereo. In this
sense, we support the Editorial comments recently made by John
Atkinson on the importance of maintaining transient integrity at the
beginning and end of sequences of sound, rather then worrying about
slight relative level errors in the pseudo steady-state of a sustained tone,
or a slight change in harmonic balance. It's the old story of measuring a
frequency and phase response with insufficient accuracy to extract the
true system error and then misinterpreting the significance of that error:
check out the error function(5).
(m) At audio frequencies, axial propagation within the dielectric is usually
not considered important as interconnects are generally much shorter
than a wavelength, even at 20 kHz. However, we have directed our
17
attention to the loss field within the conductors, where, due to the slow
velocity, cable dimensions comparable to wavelength are significant. It
is suggested that this viewpoint is usually not considered, where skin
depth is rarely appreciated in audio circles to be a propagation
phenomena.
From these observations, we conclude that conductors should be sufficiently
thin that only a fraction of a wavelength at the highest audio frequency is
trapped within the conductors. The external propagating fields should be
distributed as uniformly as possible over the whole surface of the conductor.
The composite cable should be tightly wrapped, to prevent external
mechanical vibration from modulating the characteristic impedance (shaking
wires, coils and interconnects in loudspeaker systems, for example). (Thinks:
could the crystal boundaries be vibration dependent? . . . time to stop. Oh,
everyone but the Moroccan girl and Ken has left!)
This article has tried to describe a more rigorous model (finely etched with a
little speculation) for cable systems by reviewing some fundamental
electromagnetic principles. It is important not to make engineering
simplifications too prematurely when evolving a model. Clearly, we have made
some approximations as field patterns can be highly complicated, depending
on cable geometry's and internal material behaviour at a molecular level (and I
keep thinking of current vortices). Nevertheless, there is sufficient evidence to
suggest a cable's performance is not as simple as it first appears, often
because the operation is viewed too approximately and our notions of lumped
circuit elements (discrete Rs, Cs, Ls etc) warp our thinking, especially with
respect to skin depth. To me, the most striking observation is the slow,
frequency dependent velocity of a wave travelling in a conductor; it's rather like
launching a sound wave into a room and waiting for the reverberant field to
decay. Also, a high conductivity and permeability makes the conductor appear
much larger on the inside and crystal boundaries act as partitions within that
space. TARDIS o Transient And Resistance DIStortion. Now, who said that?
Famco of France have just send me some Vecteur cable(6), conductor
diameter 0.8 mm, large crystal copper, immaculate screening, little arrows . . .
Now Ken, what was that about KT77s? So you've heard that all
electromagnetic waves are discrete packages of energy and mercury has a
non-crystal structure. OK, OK . . . I'll turn up the volume and use only mercury
capillary interconnects.

[Poultrygeist]

Here's the PWB Red Pin sound upgrade that some may find interesting :

The P.W.B. Red 'x' Co-ordinate Pen.