# Need help with calculations for a ribbon speaker cable!

Discussion in 'General Electronics Chat' started by kelpf, Feb 5, 2015.

1. ### kelpf Thread Starter New Member

Apr 11, 2013
20
2
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 = 2.669 pF/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

2. ### MikeML AAC Fanatic!

Oct 2, 2009
5,450
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A double blind study comparing your wire to bell wire?

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3. ### Alec_t AAC Fanatic!

Sep 17, 2013
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Given that any connected speaker has an inaccurately known (except under stringent lab test conditions) impedance which varies wildly with signal frequency and amplitude, why is a ribbon cable with carefully calculated characteristics supposed to be beneficial?

4. ### MrChips Moderator

Oct 2, 2009
12,622
3,451
and at audio frequencies... just like oxygen free cables.

5. ### Alec_t AAC Fanatic!

Sep 17, 2013
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So does the ultimate audiophile use oxygen-free copper for the ribbon cable construction?

6. ### GopherT AAC Fanatic!

Nov 23, 2012
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Those are just two of many requirements to be called an "audiophile".

7. ### GopherT AAC Fanatic!

Nov 23, 2012
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Double blind studies are a complete violation of the Audiophile culture.

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8. ### kubeek AAC Fanatic!

Sep 20, 2005
4,686
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Or a coat hanger wire for that matter.

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9. ### Papabravo Expert

Feb 24, 2006
10,338
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It's all just a steaming pile.

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10. ### Kermit2 AAC Fanatic!

Feb 5, 2010
3,838
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O, can you hear that? Here, let me play it again.
There, there, right there after the cymbal crash. Did you hear it that time.
Yeah, yeah, I heard it.
( please god, don't let him play it again. How can I get out of here without pissing him off)

so it goes with my experience with audiophiles. do you hear that?

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11. ### kelpf Thread Starter New Member

Apr 11, 2013
20
2
We can standardize say at 100 kHz as inductance result rises with frequency, but is so low across the board nonetheless with VTP (vertical trace pair) ribbon cables. I find velocity and dielectric constant equations agree with a ur of 0.55 which puts it in the "diamagnetic". Well filled orbital metals fall in that category, as does some plastics, and the film dielectric is predominantly acrylic adhesive. The DC checks out well at 2.8, and was verified by the reflected wave time, 35 ns. Capacitance is nailed down. OK, that's nice, but it just seems like I should be in the ur (rel permeability) up around 5 or so. I cannot find reliable expert studies that do not self-conflict. So, I provided an example dimensions. Any feedback is very much appreciated.

12. ### kelpf Thread Starter New Member

Apr 11, 2013
20
2
Oh yeah, I got it.

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 350 mil vs. 750 mil. The inductance should be about double. Next, there are two parallel cables in the bi-wire configuration. This makes it at least a four-fold increase. Any separation of the paralleled bi-wires will minimize the mutual inductance between them. So instead of agreeing with the first study, it lowers that ur by at least a factor of four.

Ls (nH/Ft) = (u0 /3.28 x ur x H) / W

Where:
H = 18 mil mutual distance (½ x 14 mil ) x 2 + 4.0 mil dielectric
W = 350 mil
L = 18.0 nH/Ft
1m = 3.28 Ft

18.0 nH/Ft = (1260 / 3.28) x ur x (18 mil / 350 mil)
0.91 = ur

Reverse calculating his result confirms that suspicion of this low relative permeability. Inductance was 18 nH/Ft. This value is purely coincidental with the other study as the conductors are completely different dimensionally. When the conductor thickness is corrected (equivalent cross-area) to be 14 mil from 10 mil (from the 1.6 mohms/Ft measured) and the DC taken as 3.2 specified from the PET dielectric used, a ur < 1 results. This is in agreement with expectations and it’s so nice to have independent verification.

Excerpts above 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.

Closing out now....time for a snack...

13. ### crutschow Expert

Mar 14, 2008
13,462
3,353
You won't appreciate mine.
You are expending a great deal of energy generating a exotic cable that, from a engineering/technical point-of-view is no different than a zip cord (with oxygenated copper wires) in driving a low impedance speaker at audio frequencies.

If you want to expend your time in doing that, you're welcome to, but don't expect much support from this forum, which follows engineering principles.
You will need to find a pseudoscience audiophile forum for that.

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14. ### kelpf Thread Starter New Member

Apr 11, 2013
20
2
Moved to: Why engineers are not wealthy or interesting.

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15. ### Kermit2 AAC Fanatic!

Feb 5, 2010
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but engineers are practical and knowledgeable. Interesting? Well anyone can be interesting, depending on whether one is interested in deeds, or stunts. I find both equally interesting but I have pity for the fools.

16. ### #12 Expert

Nov 30, 2010
16,655
7,293
I used to go down rabbit holes like this when I was a teenager. I thought if I worked the math to death it would improve my mind...or something. I was wrong. I got very good at low level math (algebra) but the bigger picture is so big that I might as well have been picking fleas off the monkey next to me. That's what college is for. They throw the accumulated knowledge of centuries at you so fast that speaker cables become child's play, a "thirty minutes at the most" kind of calculation. And then, you realize it doesn't matter. Humans can't hear the propagation speed of a pulse in a wire.

17. ### BobTPH Active Member

Jun 5, 2013
806
121
Sorry, but I am a counter example to that, and there are many others.

Bob

18. ### MikeA Member

Jan 20, 2013
125
17
I once out of curiosity hooked up my left speaker with a pair of 24awg twisted pair pulled out of a CAT5 cable, and the right speaker with some decent 12awg "speaker" grade cables. The run was about 40 feet, the amp is at the opposite side of the room.

Hooked up Channel1 of the o-scope to left speaker, Channel2 to right. The signals were identical to a T.

19. ### kelpf Thread Starter New Member

Apr 11, 2013
20
2
True. Also valid with most (99%+) audio systems. Then there are the snake oil audio vendors out there, very frustrating. The audio boards are very bad. By impedance matching the HF energy on the cable is lost into the load. This minimizes repeated reflected waves which gradually erode audio frequency transients. It works. I understand your algebra point, but if after measuring Cp, Ls and DC, the math (for example velocity) should be in the ballpark and generally agree. That's all. I discovered my ur resultant to be too low I think. It took months to iron out other problems, this ur remains. What is a reasonable value for these diamagnetic materials? Just under 1? Thanks for any input.
Pete

20. ### kelpf Thread Starter New Member

Apr 11, 2013
20
2
I did too. The CAT5 is about half the impedance of twin lead. Still way too high a match for the load. Very little difference on the scope @ 100 kHz.