Need help with calculations for a ribbon speaker cable!

[Peter F. Kelly]

I built a ribbon speaker cable and the sound is wonderful. In retrospect, I wonder about the low ur, permeability, for inductance which seemed to make all calculations agree.

This is for a speaker cable, a trace horizontal pair, which is two films parallel over each other with their wide sides facing and separated by a double stick dielectric tape and the whole assembly covered with single stick tape. (My units are feet and mils)

1. Capacitance Cp (pF/m) = er x eo x (w/d)

Where:
eo = constant, 2.669 10^−12 F/Ft = 2.6pF/Ft
er = rel permittivity, dielectric constant = 2.8
w = area, W width 750 mil of the trace x L (1 Ft length always)
d = conductor separation, 7 mil

Cp (pF/m) = er x eo x (w/d)
= 2.8 x 2.669 x (750/7)
= 801 pF/Ft

Since mils W/D cancel and length is 12 inches and we are dealing with units of per 1 foot, that cancels.

2. Inductance L (nH/Ft)  (uo/3.28 x ur x H) / W

Where:
uo = constant, 1260 nH/m and 1m = 3.28 Ft
ur = relative permeability, 0.55 which is my question.
H = mutual distance, center-to-center, 12.4 mil
T = trace thickness for determining H, 5.4 mil
Tape is 7 mil thick
W = width of traces. 750 mil

L (nH/Ft)  (uo/3.28 x ur x H) / W
= 1260/3.28 x 0.55 x (12.4/750)
= 3.5 nH/Ft

My question is: If I don’t use a low ur permeability (less than one) (and copper is diamagnetic anyway) then the DC (dielectric constant) verified by SQRT [c (FPS) / V (FPS)] or (c^2 * Ls * 10^9 * Cp * 10^12), does not match. Neither does respective velocity. I think it should match.

For example, DC is a velocity ratio to the speed of light.
DC = (c/V)^2 is (c^2 * Ls * 10^9 * Cp * 10^12)
DC = (9.84 * 10^8 FPS)^2 * (3.5 * 10^-9) * (801 * 10^-12)
= 2.71

I built a set of these cables and Capacitance is easy and reliable to measure and agrees with the equation. The inductance is low and it is hard to get a good reading.

When other manufacturers or reviewers test similar ribbon cables, their capacitance is low and sometimes impossibly low ( where v > speed of light) and the inductance is always way higher than mine, sometimes by a factor of 10. Worrisome.

I shot a signal down the line and back and the return time was 35 ns just like a DC of 2.8 predicted in that length. So I know that the DC is right at least.

Getting the dielectric and velocity numbers to agree seems natural. What bugs me is this low er permeability – and huge discrepancy with guys who are professional engineers. I am just a hobbyist, want to do this right and this is driving me nuts. Am I missing something?


Equation References

Shukla, Vikas; Capacitance per unit length; Reference Designer Ch. 4; Section 4.5
http://referencedesigner.com/books/si/capacitance-per-unit-len.php

Wikipedia; Capacitance; Article, December 5, 2014
http://en.wikipedia.org/wiki/Capacitance

Inductance Calculations – Differential Traces (Vertical); The Clemson University Vehicular Electronics Laboratory
http://www.cvel.clemson.edu/emc/calculators/inductance_Calculator/trace-v.html

 

[KrisBlueNZ]

Hi Peter and welcome to Electronics Point

I can't answer any of your technical questions, but I have a question for you.

How do you know that your impression that "the sound is wonderful" is accurate?

My impression is that a length of standard low-cost (but reasonably thick) twin tru-rip ("figure eight") cable is audibly indistinguishable from expensive audiophile products made with oxygen-free copper and other cool-sounding features; that would include your carefully engineered ribbon cable. But I'm just a musician and music appreciator; I don't claim to have golden ears or anything like that.

Have you done a double blind A-B test comparing these cables against generic speaker wires, to verify that you can hear a difference? A fairly reliable test could be done in less than an hour with the help of two people, or one at a pinch. I would even write up a test protocol, if you would be prepared to run the test.

I'm interested in your response. I've asked this question of groups of audiophiles before, and never had any valid responses. Which seems strange, because of the amount of time and money that is at stake!

 

[Arouse1973]

Hi Peter and welcome to Electronics Point

I can't answer any of your technical questions, but I have a question for you.

How do you know that your impression that "the sound is wonderful" is accurate?

My impression is that a length of standard low-cost (but reasonably thick) twin tru-rip ("figure eight") cable is audibly indistinguishable from expensive audiophile products made with oxygen-free copper and other cool-sounding features; that would include your carefully engineered ribbon cable. But I'm just a musician and music appreciator; I don't claim to have golden ears or anything like that.

Have you done a double blind A-B test comparing these cables against generic speaker wires, to verify that you can hear a difference? A fairly reliable test could be done in less than an hour with the help of two people, or one at a pinch. I would even write up a test protocol, if you would be prepared to run the test.

I'm interested in your response. I've asked this question of groups of audiophiles before, and never had any valid responses. Which seems strange, because of the amount of time and money that is at stake!

I will spare you all the swear words that I could use for audiophiles that claim all these things that make a difference to the sound quality, most of which is bollocks
Adam

 

[Arouse1973]

I built a ribbon speaker cable and the sound is wonderful. In retrospect, I wonder about the low ur, permeability, for inductance which seemed to make all calculations agree.

This is for a speaker cable, a trace horizontal pair, which is two films parallel over each other with their wide sides facing and separated by a double stick dielectric tape and the whole assembly covered with single stick tape. (My units are feet and mils)

1. Capacitance Cp (pF/m) = er x eo x (w/d)

Where:
eo = constant, 2.669 10^−12 F/Ft = 2.6pF/Ft
er = rel permittivity, dielectric constant = 2.8
w = area, W width 750 mil of the trace x L (1 Ft length always)
d = conductor separation, 7 mil

Cp (pF/m) = er x eo x (w/d)
= 2.8 x 2.669 x (750/7)
= 801 pF/Ft

Since mils W/D cancel and length is 12 inches and we are dealing with units of per 1 foot, that cancels.

2. Inductance L (nH/Ft)  (uo/3.28 x ur x H) / W

Where:
uo = constant, 1260 nH/m and 1m = 3.28 Ft
ur = relative permeability, 0.55 which is my question.
H = mutual distance, center-to-center, 12.4 mil
T = trace thickness for determining H, 5.4 mil
Tape is 7 mil thick
W = width of traces. 750 mil

L (nH/Ft)  (uo/3.28 x ur x H) / W
= 1260/3.28 x 0.55 x (12.4/750)
= 3.5 nH/Ft

My question is: If I don’t use a low ur permeability (less than one) (and copper is diamagnetic anyway) then the DC (dielectric constant) verified by SQRT [c (FPS) / V (FPS)] or (c^2 * Ls * 10^9 * Cp * 10^12), does not match. Neither does respective velocity. I think it should match.

For example, DC is a velocity ratio to the speed of light.
DC = (c/V)^2 is (c^2 * Ls * 10^9 * Cp * 10^12)
DC = (9.84 * 10^8 FPS)^2 * (3.5 * 10^-9) * (801 * 10^-12)
= 2.71

I built a set of these cables and Capacitance is easy and reliable to measure and agrees with the equation. The inductance is low and it is hard to get a good reading.

When other manufacturers or reviewers test similar ribbon cables, their capacitance is low and sometimes impossibly low ( where v > speed of light) and the inductance is always way higher than mine, sometimes by a factor of 10. Worrisome.

I shot a signal down the line and back and the return time was 35 ns just like a DC of 2.8 predicted in that length. So I know that the DC is right at least.

Getting the dielectric and velocity numbers to agree seems natural. What bugs me is this low er permeability – and huge discrepancy with guys who are professional engineers. I am just a hobbyist, want to do this right and this is driving me nuts. Am I missing something?


Equation References

Shukla, Vikas; Capacitance per unit length; Reference Designer Ch. 4; Section 4.5
http://referencedesigner.com/books/si/capacitance-per-unit-len.php

Wikipedia; Capacitance; Article, December 5, 2014
http://en.wikipedia.org/wiki/Capacitance

Inductance Calculations – Differential Traces (Vertical); The Clemson University Vehicular Electronics Laboratory
http://www.cvel.clemson.edu/emc/calculators/inductance_Calculator/trace-v.html

Hi Peter

Ok you lost me a bit, what are you trying to do measure or calculate? What can't you get to tie up in your calculations. Are you trying to find another diamagnetic material with a lower relative permeability than copper?

Can you draw out your cable with dimensions added so we can see what it looks like and so there is no interpretation. Take some pictures of your cable from different angles so we can see what it looks like in real life.

Thanks
Adam

 

[BobK]

Munching on popcorn for this one.

Bob

 

[davenn]

hey can I share your popcorn ? please

ya gotta love woo woo science

 

[Peter F. Kelly]

 

[Peter F. Kelly]

Hope this helps. The math isn't hard, I just need verification, or if I am not calculating it right, to be corrected. Hence, the references. Capacitance is right on the nose. Inductance is the problem, I cannot verify it as it is so low. Experts measuring VTP (vertical trace pair) ribbon cables appear to be way off. Using better equipment, yet. I am worried about ME being way off instead, overlooking some obvious thing. I have to get it right. Thanks, all.

 

[Peter F. Kelly]

The sonic result is far beyond these cables alone. Many other developments contributed substantially. I am only stuck on this inductance. That is my only concern. Perhaps it is not the problem I thought. Need to be sure. I thought ur should be around 5. Turns out it is about 0.55. How can that be so?

Sorry for my brevity. Currently, the stereo has disappeared from the room. The artists stand 10 feet before you and guests describe the system as "spooky". It is very unnerving to all. But another result was unexpected, it goes far beyond. What is conveyed is their emotional intention deeply piercing your soul, laying you bare, riveting you speechless to your chair and stripping you of your defenses. Listening to the system can be an exhausting experience, it is other-worldly. So, small differences are not my goal, been there many times.

I hope you are still thinking about the inductance equation.

A 16-year project, I have never experienced anything like this. At Axpona I heard two very good systems, but not like this. A-B studies used to interest me in audio, before these staggering results. I used similar comparative studies when publishing development of surgical laser applications to prove the results were valid. For that I needed numbers. For this, I require an "Oh my God.....", jaw dropping, catastrophic, spell-binding difference.

You haven't forgotten about inductance have you?

Audiophilia is more like a religion, so I go my own way, and remain focused. There is a lot of subjective tit-for-tat around. That can get very expensive.

Still, the scientist in me delights in seeing a nearly perfect square wave, with the drivers attached.....not at 2 kHz, or 10 kHz, but at 100 kHz. Besides the enrapturing emotional involvement, this esoteric science demonstrates proof. Never experienced anything like this before. Incredible rewarding hobby.

(Don't forget about the inductance.)

 

[davenn]

Sorry for my brevity. Currently, the stereo has disappeared from the room. The artists stand 10 feet before you and guests describe the system as "spooky". It is very unnerving to all. But another result was unexpected, it goes far beyond. What is conveyed is their emotional intention deeply piercing your soul, laying you bare, riveting you speechless to your chair and stripping you of your defenses. Listening to the system can be an exhausting experience, it is other-worldly. So, small differences are not my goal, been there many times.

Sorry Peter

But that's about as unscientific as anyone could get and gives no credibility to the rest of your approach

I generally find that people that have spent $500+ on OFC speaker cables, swapping all the capacitors in their amplifiers to the fancy blue ones ( or red or yellow ... what ever the current flavour is) are extremely unlikely to come and say " it didn't make any difference"
because that makes them look so foolish for wasting 500 bucks when it could have been spent more wisely

Still, the scientist in me delights in seeing a nearly perfect square wave, with the drivers attached.....not at 2 kHz, or 10 kHz, but at 100 kHz. Besides the enrapturing emotional involvement, this esoteric science demonstrates proof. Never experienced anything like this before. Incredible rewarding hobby.

and significant levels of square waves ( regardless of freq) is the last thing you want to be pumping into any speaker
it tends to destroy them


Dave

 

[Gryd3]

Let's stop for a moment...
The audio signal could be 'perfect' at the input, 'perfect' at the output... but how do you know the 'sound' waves produced match the 'perfect' signal?

The weakest link needs to be evaluated.
-How much can you degrade a perfect sample before the human ear can detect a difference?
-How much error does the speaker introduce in reproducing the sample?
-How much error does the speaker wire introduce?
-How much error does the amplifier introduce?
-How much error does the signal wire introduce?
-Is additional error or degradation being introduced from the environment?

The only test in my opinion that can actually resolve this is to put a collection of people in an anechoic chamber and play various samples to first determine what 'people' can distinguish.
Once some samples are correctly, and repeatedly identified as being of lower quality by different test subjects, then it can be measured.
Once this measurement is made and recorded, then you can then create lab-grade tests in the very same chamber to accurately determine if the output from the speaker is changed any significant degree compared to the previously recorded value by swapping out parts of a 'high-end' audio system. The speaker is an open-loop, system... so the amplifier does not know if the sound being produced actually matches the signal.
Don't get me wrong, I'm sure the double-blind system works, but when you compare high-end $400 Unobtainium to dollar store cables I'm sure there will be enough of a difference to claim one is better.

 

[Peter F. Kelly]

Sorry Peter



and significant levels of square waves ( regardless of freq) is the last thing you want to be pumping into any speaker
it tends to destroy them


Dave

The drivers are Gold Ribbon Concepts which are flat from 400 Hz to 500 kHz. Tested by Rudi Blondia. The cabinets are diffractionless.

 

[Peter F. Kelly]

Back to the subject..

I am glad to have found an answer so soon.
The equation for inductance assumes complete dielectric space filling, and the ur has a linear effect. This first study measures inductance for the model 2 from the Speaker Cable Face off articles (see references). Let’s determine what the ur is:

Lstrace-pair (nH/Ft) = (u0 /3.28 x ur x H) / W

Where:
H = 7.5 mil mutual distance (½ x 3.5 mil t) x 2 + 4.0 mil dielectric
W = 750 mil
L = 19.0 nH/Ft
1m = 3.28 Ft

19.0 nH/Ft = (1260 / 3.28) x ur x (7.5 mil / 750 mil)
4.95 = ur

This result appears out of range for a non-magnetic material. The importance of this derivation is to confirm inductance calculations and Zo are accurate.

Copper is a non-magnetic material. Copper metal is composed of atoms which have no net magnetic moments, that is all the orbital shells are filled and there is one non-paired electrons in the outermost orbital. However, in bulk copper metal the odd electron is sent into the pool of electrons making the metallic bond, thus the metal is diamagnetic.

In the periodic table, the arrangement of d-block elements shows that copper, silver and gold are in the same group due to their similar configuration. All these elements have an unpaired electron, so they are theoretically paramagnetic. But this is negligible by their diamagnetic property.

Diamagnetism is a property of every material which makes some weak contribution to the material’s response to a magnetic field. Materials called diamagnetic are non-magnetic. Copper and heavier elements such as gold with many core electrons, most organic compounds such as petroleum and some plastics. We know these cables act as capacitive devices. Thus, the magnetic contribution is low.

When exposed to a field, a negative magnetization is produced, this acts diamagnetic, and ur is less than one. It also indicates there is very little absorption of the magnetic component.

I found consistent agreement among equations and with my in my scope measuring the reflected waves arrival time, velocity and propagation time calculations, and DC measurement and calculations, when ur <1

A second study confirms these calculations for a diamagnetic material with a low relative permeability and the measurements I obtained.

Measurement of inductance by Hansen (see reference) for a model 1-2 “T” bi-wire cable. This is not the Model M1-2 in the face-off study (see reference). This cable width is 35 mil vs. 750 mil. The inductance should be about double. There are two parallel cables in the bi-wire configuration. This is a four-fold increase. Any separation of the paralleled bi-wires will minimize the mutual inductance between them.

However, the result shows a low relative permeability. Inductance was 18 nH/Ft. This value is purely coincidental as the conductors are different dimensionally. When the conductor thickness is corrected to be 14 mil from 10 mil (from the 1.6 mohms/Ft measured) and the DC taken as 3.2 from the PET dielectric used, a ur < 1 results. This is in agreement with expectations and we have independent verification.

His study is not without limitations. The inductance was measured at 120 Hz and 1 kHz only. This analysis is intended to determine Zo. In cable measurement, Zo references high frequencies and simple DCR is specified for the audio band. Zo cannot be applied. These measurements appear applicable only to the lumped circuit model of the audio band.

This is the reason. In TVP ribbon cables, Zo starts in the transition area (the area from a lumped circuit model to a transmission line model) at around 100 kHz. Inductance also raises further here, even over 10 kHz, but neither of these was measured. We will see later that the ribbons transition into the T-L area a full one decade lower than most other cables, including coax, which is also a TEM mode cable (frequencies are non-dispersive as frequency rises above cut-off). He cited the discrepancy of this much higher value vs. the manufacturer.

One correction should be applied to his otherwise excellent study. The wrong inductance equation was referenced. This was not used. This is inductance for a microstrip rather than for a Vertical Trace Pair, or Plane Impedance calculation.

 

[Peter F. Kelly]

Now we should confirm this as inductance is not really so independent of capacitance after all

Example 2

In a study by Hansen (see reference), the capacitance of the model 1-2 “T” bi-wire cable was in agreement with that calculated. The correct capacitance equation was cited. The measured 697 pF/Ft is close to 756 pF/Ft calculated. This is not affected by the conductor thickness corrected by the resistance measured. Despite 120 Hz and 1 kHz being low frequencies, this is noncontributory, as the capacitance is nearly flat through 100 kHz and the values are high enough to demonstrate good precision.

Determine εr

Given:
W 0.350 in
D 0.004 in

Cp (pF/Ft) = εr x 8.854/3.28 pF/Ft x w/d

697 (pF/Ft) = εr x 8.854/3.28 pF/Ft x 0.350/0.004

εr = 2.95

This is close to my measured DC of 2.8. This synchronizes nicely with the relative permeability of inductance, ur < 1. We can assume the conductor and dielectric combination of this cable is diamagnetic for inductance calculations.

Example 3

There are several on-line calculators you can use, which predict an expected value of Cp. One is at: http://www.daycounter.com/Calculators/Plate-Capacitor-Calculator.phtml, where ε0 is in pF/in. I include this below. This capacitor equation goes by area, and this one simply determines overall C in pF. You must include L x w to just w above, so please include the 12 inch length multiple to determine this in pF/Ft. Thus, the area for one foot of cable would be 0.750 in x 12 in = 9 in2 area of capacitance.

Example 4

This example uses the first of four assembled ribbon cables. I found Cp to be a reliable measurement. I built and measured several cables. My results from these DIY products were in reasonable range of calculations. All four of my DIY ribbon cables predict Cp in the ballpark

The first DIY ribbon cable was a ¾” wide using a 2 x 3.5 mil dielectric tape. The DC was 2.8 as measured by the time of the first echo of a reflected wave. Cp predicts 810 pF/Ft. An average of 4 frequency measurements shows this cable is actually 687 pF/Ft for the 7.0 mil dielectric. I am off by 18% which is quite remarkable for a first assembly at home.


So this is how to get started in designing an impedance matched cable to minimize reflected waves and clean up the signal. T-L and circuit theory has been late to the audio game by about 60 years. It is off to a good start and should occupy a good part of the industry by the end of this decade in the US, followed by Japan and China. Europe is already leading.

Excerpts were from High-End Audio Cables Principles and Projects, Ch. 5 The Foil Ribbon, due out later this year. 300-400 pgs. A one stop source for DIYers. Other ch include Power cables, Interconnects, other speaker cable types, reference equations, etc. Or skip to the cookbook pictorial with step-by-step instructions and source suppliers to precisely build and measure SOTA cables with predictable results.

Not all work and no play, funny sections include
Transmission Lines for Dummies,
Why Single Crystal Copper does not exist (with proof and references for this great farce)
Exposing audio vendors promoting Series Resonance for their $6K cables
Are conductors really slower at low frequencies
Spectrographs of the WTC detonations (in the frequency chapter)
A lot of exposure of fraud in the audio industry, and credit to the good guys too.

And yes, ha ha, I did have my hearing checked. -3 dB@ 18 kHz left ear. (Short fuse on a firecracker one day....)

All done here now. I should really get something to eat.....

 

[pebe]

Peter.
I have read your postings several times in an effort to understand your reasoning, and these are my views.

It appears that you are designing a balanced transmission line between amplifier and speakers. If so, I don’t think you will have much success, for these reasons.

Source and load resistances both need to be the same as the characteristic impedance of the transmission line:-

Source: The output of most amplifiers is effectively a voltage source with an impedance of almost zero.

Load: The load is the loudspeaker, which is a complex of resistive and inductive components in series, and which will be almost impossible to match. I cannot see in your calculations a value for the load for the speaker you are using, and I cannot see any calculations relating to the Zo of the cable.

You give a formula for DC, which appears to be the reciprocal of the established Velocity Factor, Vb, used in cable parlance, but I don’t see why you would need to know that in this application.

The length of the cable would be insignificant compared to the wavelength of the audio signal you are sending down it; it is the equivalent of applying a slowly varying dc voltage to it and there would be no reflections due to mismatching. You would have the equivalent of two wires with current in them flowing in opposite directions, and their magnetic fields would cancel out, leaving no inductance. The capacitance between the wires would effectively be across the amplifier output – not a good idea.

So you may as well just use a pair of wires with minimum capacity between them – which is just what an ordinary figure-of-8 cable is.

 

[Arouse1973]

View attachment 18512 View attachment 18513 View attachment 18514

Ur of copper is 1 it can't be 0.55. How are you calculating this? How are you measuring the inductance, tell me how you have things connected. Your picture is not clear at all. Take a closer picture so we can see how it's put together.
Adam

 

[Arouse1973]

Peter.
I have read your postings several times in an effort to understand your reasoning, and these are my views.

It appears that you are designing a balanced transmission line between amplifier and speakers. If so, I don’t think you will have much success, for these reasons.

Source and load resistances both need to be the same as the characteristic impedance of the transmission line:-

Source: The output of most amplifiers is effectively a voltage source with an impedance of almost zero.

Load: The load is the loudspeaker, which is a complex of resistive and inductive components in series, and which will be almost impossible to match. I cannot see in your calculations a value for the load for the speaker you are using, and I cannot see any calculations relating to the Zo of the cable.

You give a formula for DC, which appears to be the reciprocal of the established Velocity Factor, Vb, used in cable parlance, but I don’t see why you would need to know that in this application.

The length of the cable would be insignificant compared to the wavelength of the audio signal you are sending down it; it is the equivalent of applying a slowly varying dc voltage to it and there would be no reflections due to mismatching. You would have the equivalent of two wires with current in them flowing in opposite directions, and their magnetic fields would cancel out, leaving no inductance. The capacitance between the wires would effectively be across the amplifier output – not a good idea.

So you may as well just use a pair of wires with minimum capacity between them – which is just what an ordinary figure-of-8 cable is.

You don't need TL techniques at these frequencies even with a very broadband amplifier.
Adam

 

[pebe]

Exactly!

 

[BobK]

To a man who can hear 500KHz, it might make a difference.

Bob

 

[Arouse1973]

To a man who can hear 500KHz, it might make a difference.

Bob

That's Bat-man with super sonic hearing then