Cable Theory

Apr 3, 2010
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#1
This was posted by Gary in another thread. I am simply moving it, not endorsing it. So any stones get thrown at Gary. Ditto for compliments. :D

Would be a good thread to discuss plausible reasons for why we may be hearing differences in cables.

Cable engineering is a well-understood science. That is why engineers are able to design cables to pass higher and higher speeds for computer networking, and higher and higher current for power transmission. For example, a Cat7 cable allows 10 Gigabit Ethernet over 100m, and is rated for a transmission speed of 600MHz. That is far, far above any frequency needed for audio.

No cable is perfect, and any loudspeaker cable or interconnect can be modeled as follows.


Loudspeaker designers will recognize this as a low-pass filter. However, the filter effect at audio frequencies is negligible with the values that are encountered in cable design.

There are three key electrical parameters that are all easily understood.

1) Resistance (R1 and R2)
Resistance can be determined by size and material. 12 awg stranded copper wire has a resistance of 5.3ohm per kilometer (1.6ohms per 1,000ft). Go up to 10awg and it falls to 3.3 ohm/km, go down to 14awg and it rises to 8.5 ohm/km. Purity makes a miniscule difference to the resistance above about 99.5% pure. Silver has about 5% lower resistance than copper all else being equal.

Pure resistance causes a voltage drop, and does not affect frequency response and phase characteristics of the signal. The resistance needs to be sufficiently low that the voltage drop from one end of the cable to the other is negligible when terminated into the expected impedance.


2) Inductance (L1 & L2)
Whenever electrons flow through a conductor, a magnetic field will develop around that conductor. The more current that flows, the stronger the magnetic field. This magnetic field stores energy, and when the current stops, the collapse of the field returns energy to the conductor. Since this occurs between the amplifier and the loudspeaker, the sonic result is a smearing of detail.

The measure of this effect is inductance, and high inductance causes a cable to store and release current. Thus, a cable with high inductance can be regarded as “powerful” and “full bodied”. Intuitively, we can understand that this store and release of energy also causes a smearing of the signal.

When we build a cable, the two wires that carry current in opposite directions can be placed close one another so that the inductance can almost cancel out. The closer the two wires are to each other, the greater the cancellation effect and loop inductance can approach zero.


3) Capacitance (C1)
Whenever a voltage exists between two separated conductors, an electric field will exist between those two conductors. The two conductors with the insulator in between will act as a capacitor which stores and releases energy.

Capacitors tend to resist changes in voltage between the two conductors. Hence, when the voltage is increased or decreased (as when a musical signal flows), the capacitor resists the change by drawing current from, or supplying current to the source of the voltage change in opposite to the voltage change. Since this is in parallel between the source and the destination, the capacitance acts as a shunt across the cable and the sonic result is the blunting or softening of transients and dynamics.

This effect can be measured in a cable as capacitance. A cable with higher capacitance can be said to be “sweeter” or “smoother” as a result. The closer the two conductors are together, the higher the capacitance.


While the range of inductance (micro-Henrys) and capacitance (pico-Farads) are sufficiently small that they should not result in significant frequency response distortion, we can hear the store and release of energy as distortion in the soundstage, a smearing of micro-dynamic detail and a loss of focus.

Some cables are optimized for the lowest possible inductance at the expense of high capacitance. It is easy to recognize these cables as they will have multiple insulated conductors that are tightly braided or spiraled together. The more expensive they are, the more conductors there are, and the higher the capacitance!

Other cables are optimized for the lowest possible capacitance at the expense of high inductance. These easily identified as they will have two conductors that are widely spaced and held apart. In these cables, a larger conductor results in lower inductance, but not by enough that it matters much.

Loudspeaker Cable Design
If we then believe that we can hear this inductance and capacitance in a cable (and I know that I can hear it), then we need to balance between inductance and capacitance. Since current matters to inductance, and voltage matters to capacitance, we start to have a clue.

High current loudspeakers should have cables optimized for lower inductance, and high efficiency loudspeakers should have cables optimized for capacitance. To give some numbers, I have three designs:

i) a high-current loudspeaker cable that has a loop inductance of 0.06uH/ft and a capacitance of 43pF/ft;
ii) a high-efficient loudspeaker cable that has a loop inductance of 0.11uH/ft and a capacitance of 24pF/ft;
iii) one in between that has a loop inductance of 0.10uH/ft and a capacitance of 32pF/ft

... all measured at 1kHz.

What about Teflon/Air used as a dielectric?
There is much hay made by marketing people about Teflon being the best insulator because it makes the cable “faster” due to the low dielectric constant. However, in terms of transmission speed of the signal from one end of the wire to the other, it doesn’t make much sense.

Nevertheless, the dielectric constant is an essential factor in the design of a capacitor. A higher dielectric constant would be used to increase the capacitance of a particular design. Hence, when we design a cable to minimize inductance and capacitance, using an insulator of lower dielectric constant decreases the capacitance of a particular design. All things being equal, with the same distance between the two wires to keep inductance constant, going from a PVC insulator to a Teflon insulator would halve the capacitance of the cable.

A second reason to use Teflon is that it has the lowest dielectric soakage. This is the capacitor’s propensity to regain charge after a short circuit. Intuitively, the dielectric soakage is also a form of storage of energy, hence, looking for a material that would not do this would result in a cable that would have better micro-dynamic detail.
 
Jun 8, 2010
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N. California
#3
Thanks, Amir.

I'm ready to be stoned.... or fried in snake oil :)
Very nice elucidation, Gary.

When I have done estimates like this and put in numbers the results are what I would have guessed were beyond human ability to detect. (I've never estimated phase-shift, though, cause I didn't think of it.) Can you put in your own numbers and show how anyone has a chance of hearing this? Do the estimates agree with electrical measurements?

Also, do people really hear differences (between "competently" built cables). I mean really, really. I won't mention the D-word here but...Is there some form of objective, published evidence that shows people really can distinguish between cables?
 

c1ferrari

Member Sponsor & WBF Founding Member
May 15, 2010
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#4
Hi Gary,

What type of instrumentation would you suggest to evaluate speaker cable/IC performance? :confused: Thanks!
 
May 30, 2010
15,212
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Portugal
#5
Also, do people really hear differences (between "competently" built cables).... ?
Could you write down all the physical values of a " " competently" built cable" ?
I mean quantitative values for all of them. And then we would know what we are discussing.

Because if the definition of a " competently" built cable" is "one such that people do not hear differences" or "zip cord" we are not going anywhere...
 

garylkoh

WBF Technical Expert (Speakers & Audio Equipment)
Sep 6, 2010
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Seattle, WA
www.genesisloudspeakers.com
#7
Very nice elucidation, Gary.

When I have done estimates like this and put in numbers the results are what I would have guessed were beyond human ability to detect. (I've never estimated phase-shift, though, cause I didn't think of it.) Can you put in your own numbers and show how anyone has a chance of hearing this?
Thanks, Smokester.

You are on the right track. We have to first establish that the science is correct and I believe that there are enough EE's, physicists, and mathematicians here to correct me if I'm straying - and then establish that it is within the range of audibility.

The first is easy - the electrical model of a conductor is well established, and I don't think that there is a dispute there. So, to run some numbers:

Take for example a 6-foot speaker cable:

Inductance will be 0.6uH and capacitance 192pF.

Inductive Reactance (Impedance) at 1kHz is Angular Frequency X Inductance = 0.377 X 10^ -2 ohms.

Capacitative Reactance (Impedance) at 1kHz is 1/(Angular Frequency x Capacitance) = 0.829 X 10^6 ohms.

Say a loudspeaker has an impedance of 6 ohms, the inductance of the cable is in series with the loudspeaker and is a factor of is 0.628 X 10^ -3 lower than the loudspeaker impedance - 0.000628: extremely small.

The capacitance of the cable is in parallel to the loudspeakers and is a factor of 0.72 X 10^ -5 lower than the loudspeaker impedance - 0.0000072: even smaller.

You should not hear this, right? Well, the ear is more sensitive than that.

The threshold of hearing is generally regarded as 4dB at 1kHz.

If we regularly listen to music at say 74dB, then the threshold of hearing is 70dB lower than the music we are listening to - in other words the sound intensity of the music is 10,000,000 above the threshold of hearing. Then, let's take the numbers above where the inductance of the cable is 0.000628 below that of the loudspeaker, and the capacitance is 0.0000072 below that of the loudspeaker.

Compared to the threshold of hearing against normal listening level, the inductance of the cable is 6,280 times and the capacitance is 75 times higher. Does this make sense at all?

The phase shift equations are very much more complex - this is because the crossover within the loudspeaker makes the phase angles of the two leads different, and as a result you need to look at the complex sum of the phase of the +ve lead, the crossover, and the -ve lead.

Do the estimates agree with electrical measurements?
The loop inductance of a 6ft pair of widely separated 12awg conductors (no insulation) is 5.94uH, and the capacitance the 6ft pair separated by 3mm of air is 109pF. Because the inductance is such a large factor over capacitance, reducing inductance seems to me more beneficial than reducing capacitance. The theoretical calculations and the actual measurements are close - within 10%, and well within the tolerance of what we can hand-build.

Measuring manufactured cables (zip cord, lamp cord, etc.) they are extremely close. Measuring computer networking cables (CAT 5, 6, 7) is almost spot on - as they have to be.

Also, do people really hear differences (between "competently" built cables). I mean really, really. I won't mention the D-word here but...Is there some form of objective, published evidence that shows people really can distinguish between cables?
I think that the jury is still out here. There haven't been objective, published evidence. However, comparing high-capacitance loudspeaker cables and high-inductance cables and balanced capacitance/inductance cables, I can identify each in a DBT.

...... but you would have to define "competently" built cables - because while there is an established specification and standard for computer networking cables, I have not been able to find a published standard for loudspeaker cables.
 

garylkoh

WBF Technical Expert (Speakers & Audio Equipment)
Sep 6, 2010
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Seattle, WA
www.genesisloudspeakers.com
#8

garylkoh

WBF Technical Expert (Speakers & Audio Equipment)
Sep 6, 2010
5,431
21
38
Seattle, WA
www.genesisloudspeakers.com
#9
Actually, that would be a great addition to where it was originally posted. Maybe I'll copy it back to there when I'm ready if nobody minds.

--Ethan
I'll be happy to respond anywhere...... however, I may not be able to respond over the next 10 days or so. I have a family friend fly in from Singapore, and the two families are going to spend some time hanging out.
 

garylkoh

WBF Technical Expert (Speakers & Audio Equipment)
Sep 6, 2010
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www.genesisloudspeakers.com
#10
The physics department of Georgia State University has a very nice website with about all the calculators that you will ever need. Enter here:

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Here's the capacitance reactance calculator:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/accap.html

and the inductance reactance calculator:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/acind.html

Then, I'm out of here. Cooking beef bourguignon tonight, and listening to:
http://www.amazon.com/Amelie-Soundtrack-Recording-Yann-Tiersen/dp/B00005O6PA
 

FrantzM

Member Sponsor & WBF Founding Member
Apr 20, 2010
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#11
Gary

We may have to compare apples with apples ...
Let's have a more meanigful modelization, since our perceptions tend to be logarithmic or quasi-logarithmic. In what way do you think the cable you have mentioned would impact the FR of the speaker at 1 KHz? I will grant you that our ears can detect level changes of 0.1 dB.
 
Apr 3, 2010
15,820
1
0
Seattle, WA
#12
Take for example a 6-foot speaker cable:

Inductance will be 0.6uH and capacitance 192pF.
I plugged this into trusty spice (circuit) simulator without the speaker load and this is what popped up. Green is the signal from the output of the amp, the amber, what is seen at the speaker terminals.

 

c1ferrari

Member Sponsor & WBF Founding Member
May 15, 2010
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#13

Orb

New Member
Sep 8, 2010
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#14
...... but you would have to define "competently" built cables - because while there is an established specification and standard for computer networking cables, I have not been able to find a published standard for loudspeaker cables.
I think that is crucial in these discussions, because I have identified problems using Chord Cables but others may say they are competently built and they are popular over here in Europe.
Two bad experiences with Chord Cables for me were:
1) Interconnect - The noisefloor was too loud on their RCA and even noticable on their XLR, when using mute it would cause a moderately loud buzz to be generated using their XLR version.
The preamp and amp were from a respected pro and consumer based company (Chord Electronics) and working with the dealer they could replicate the problem, also Chord Electronics could replicate the issue but the problem was not their equipment they felt as this did not happen with other cable manufacturers or even for their same gear in the pro world.

2) Speaker cable - We originally thought that the "false" sound generated by some music tracks was an issue with the speakers/gear setup.
Basically if a track had subtle reverb/echo/church hall effect, then this would be amplified/higher energy for that subtle effect to cause it to be heard to be very false or wrong and also affected the imaging/possibly phase only for this reverb-echo type affect.
Trying different equipment and speakers (including different driver-cones implementation) did not resolve this, only changing to a different cable make improved the situation.

Again this is a popular cable model by Chord Cable, and yet for these tracks it was noticable and annoying how it affected a portion of the sound.
For most these are "competently built", but in this context it could be argued they are poorly engineered, but that could be a too harsh accusation.

Also as I raised in another thread with Amir, engineers feel part of the problem relating to cables must include the powered device (source/pre/power) as these also mut be considered when dealing with cables.
My first example is a case in point with the buzz and using mute, but for audio the consideration is galvanic isolation and signal-chassis ground.
The galvanic isolation has raised its head in this months HifiNews relating to USB DACs, they have looked at various USB DACs and can point to problems associated with the galvanic isolation.
Now this is interesting because this is something Charles Hansen is very vocal on with USB and implemented in his USB DAC, and one area that firewire is also strongly defined (specifically implementing galvanic isolation) with IEEE1394.
Whether manufacturers follows those standards is another debate and point.
On firewire and isolation:
http://www.thefreelibrary.com/IEEE+1394+Bus+Galvanic+Isolation+Issues.(proposed...-a057778456
I thought this was worth mentioning as a notable publication in HifiNews has this month commented on their own experience of USB and the affect of no isolation.

Also here is the discussion summary about interconnect cables and active devices such as source/pre/power:
orb said:
I am quoting one of my posts at Stereophile where I am also a member (and also DIYAudio) that touches briefly on the conclusion and summarised pretty nicely by Bruno Putzeys (he was involved along with several other highly respected engineers in working out what JC identified).
Bruno Putzeys said:
Blast from the past! SE wrote me to ask if I would come here. So:

My goodness is this thing still going on?!!

Unbalanced cables are notoriously sensitive to contact noise in connectors (what with the same connection being responsible for equalising ground potentials and providing a reference for the signal), and RCA connectors are notoriously liable to develop such trouble.
What I remember John explaining during our chat was that somehow his setup highlighted these.
The unbalanced I/O of the AP test sets are floating so such problems would not ordinarily arise.

During my measurements in 2004 -done by request of SE who wanted a second opinion whilst being embroiled in a discussion with John- I still occasionally got distortion but when that happened I always checked solder joints and cleaned the connectors which invariably solved it.
Again, in a system with non-floating I/O this might still not cut it.

So where John and I agree is that these (and some other) problems are real.
His test setup was not so much different from the kind of condition under which these cables would be normally used.
The worst thing you could say is that it did not allow proper control of all variables involved.
After all, a layer of oxide on the connector shell belongs neither to the cable, nor to the test equipment.
Same for a circulating current.
But that does not mean the readings are meaningless.
The same problems arise whenever an RCA cable (and occasionally XLR, see "pin 1 problems") sits between two boxes.

Where John and I take different routes is not in the physics but in emphasis on where to start working the problem.
I'll first try to address it electronically (design circuits which are minimally sensitive to anything a nonideal cable might throw at it).
His is first to attack the connection (use cables & connectors that don't cause problems for most circuits).
This is as literally as I can remember what we said.

Both go a long way, but for perfect results you need to do both of course.
You can't design an input that'll successfully recover an audio signal transmitted along two parallel wires, and you can't design cable that will prevent hum in an unbalanced connection with a ground loop and stamped sheet-steel pcb-mounted RCA connectors.

Now note that I didn't bother reading much of this thread. The lone fact that nearly 6 years after all this I could still suddenly be yanked back into the same discussion says something.
I hope you'll understand that I'm not going to follow up on this thread, but I hope that this reply will be helpful/
Just to clarify Bruno's points, from a technical perspective oxidisation, truly floating input/output -isolation transformer, joints-contacts issues,etc are not actually part or integral to the cable even if they do affect results that may vary depending upon the rca cable.

I tend to agree with the view that the HP setup due to not having the same isolation as the APs managed to replicate the behaviour caused between two seperate audio products connected by RCA cables.
In other words cables may have different subtle affects, but they should not if audio circuit design was modified.
Of course this is just theory and as I mentioned earlier no-one has bothered to investigate further this possibility, or any of the others.

Thats my take on it anyway and I am sure many will have a different perspective.

Cheers
orb
Ah, I read on Stereophile site that the Nordost investigation with a 3rd party has some results, but IMO they do not show anything beyond slight changes.
The mistake IMO is that they are solely focusing on the cables, instead of also the potential of active products they connect and interract with, until they do this their results will always be marginal IMO.
Of course the difficulty is that audio products are not alike in terms of implementation and isolation, but that is the point of why interraction may be possible, and why "competently built" needs to be expanded to include the system chain (source/pre/power) the cables also connect with.
However as Gary rightly points out, what are the defined standards for implementation of audio products, unfortunately there are recommendations but not true standards, and this makes determining correctly a "competently built" product difficult when taken out of a lab-controlled environment and put into the real world.

Cheers
Orb
 
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DonH50

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Jun 23, 2010
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#16
Amir, you could fairly easily add the amp's output impedance (R+series L should do initially) and a typical speaker response curve to add a little realism. IMO, the you are likely OK without the amp's output impedance (if SS), but the lack of a load seriously skews the results. I was thinking of doing something along those lines a few weeks ago but got side-tracked.

Also IMO, the biggest variation perceived in listening trials is due to amp/speaker interaction through the cable's transfer function. In other words, I believe differences in cables can be heard, but it is very system-dependent, and feel it is unlikely significant differences can be heard among similar cables. Whatever that means. ;)
 
Apr 3, 2010
15,820
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Seattle, WA
#17
Hi Don. Great minds think alike. There is a series resistance of .01 ohms for the voltage source (you can see that on the schematic). It is a placeholder for whatever the consensus is. I thought about output but that is a wildcard with different speakers. What equiv. circuit do we want to use? Dynamic nature of crossovers+speakers is kind of complex to model.
 

DonH50

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Jun 23, 2010
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#18
Dunno' how "great" mine is, but thanks!

For the amp's output, a damping factor of 100 and 8-ohm speakers yields 0.08 ohms. I'd start with 0.1 ohms -- connections probably add a few tens of milli-ohms. You could throw in a series L to take it up to maybe 1 ohm (DF ~ 10) at 20 kHz.

For the speakers, I had thought to look up the impedance curves for a couple or three and use simple RLC circuits to model them. I had found some for my old Maggies, and Stereophile had smaller bookshelf and larger dynamic system's curves to play with. I didn't think it would take too much to model e.g. a LF and HF peak/dip just to provide something a little more realistic. How's your network theory? (Mine ain't the best -- I'd take a stab then dial in empirically like any good hairy-knuckled engineering type; chain matrices give me the pip). I was thinking the goal is to see what kind of effects (response) we might see at the speaker, not to nail each and every little wiggle. Of course, ideally we'd model the acoustic transfer function via an electrical (impedance) analogue, but I was going to start simple, just get an idea what the response going into the load looks like and provide a feel for the amplitudes we're talking about. So, I'd start with an 8-ohm R (only) load, then a few simple models based upon measured curves for some loudspeakers.

Seem reasonable? - Don
 

JackD201

[WBF Founding Member]
Apr 21, 2010
11,269
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Manila, Philippines
#20
I find myself thinking almost exactly along Orb's line of reasoning.
 

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