FYI: % Signal Loss for Speaker Wire Length - AVS Forum | Home Theater Discussions And Reviews
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post #1 of 25 Old 02-25-2015, 09:05 PM - Thread Starter
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FYI: % Signal Loss for Speaker Wire Length

I made these charts and thought I might as well post them here.

I've determined the length of wire for a Percent of Signal Loss in Speaker Wire. Some people might find it handy.

The first chart is for 1% Resistive signal loss in the wire, the second is for 2%, and the third for 3%. I was going to calculate 5%, but the wire lengths were so long it seemed a bit pointless.

It is generally recommended that you don't run any wire longer than 50ft. The Inductance per Foot begins to accumulate and cause problems down in the audio range.

As an example, here is the result for -

50ft (15.25m)of QED 79 Strand 2.5mm² (~13ga) Twin Lead Speaker Wire -

Here is a very straight forward QED 79 Strand (2.5mm²) -

Capacitance - 58pF/m
Inductance - 0.66 µH/m


Multiply that out to 50 ft (actually 15.25 meters) -

C = 58pF/m x 15.25m = 884.5pF

L = 0.66µF/m x 15.25m = 10.065µH

I'm going to calculate the frequency at which the cable loss is 1/35th of an idealized 8 ohm speaker. That is about 2.286% signal loss in the cable -

First the Inductance as it is usually the lowest -

fL = (R/35) / (2(pi)L)

fL = 3,614 hz

Clearly well in the audio range.

Now let's calculate the frequency associated with 10% Signal loss -

fL = (R/10) / (2(pi)L)

fL = 12,650 hz

2.86% loss in 50 ft of speaker wire at 3,614hz due to inductive impedance.

10% signal loss in 50ft of speaker wire at 12,650hz.

Just so we have it documented, let's determine the frequency at which Capacitive Impedance is 10% of the idealized 8 ohms speaker -

fC = 1 / (2(pi)(R/10)(C))

fC = 224,922,192 hz

Clearly Capacitance is not a problem with longer cables.

This seemed like information that people would appreciate knowing.

And people might want to give some extra thought to they type of speaker cable they use for longer runs.

Make of it what you will.

Steve/bluewizard
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post #2 of 25 Old 02-25-2015, 09:12 PM - Thread Starter
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1% Resistive Loss in Speaker Cable -



2% Resistive Loss in Speaker Cable -



3% Resistive Loss in Speaker Cable -



5% Resistive Loss in Speaker Cable -



Graphics released into public domain.


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post #3 of 25 Old 02-25-2015, 09:35 PM
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Based on your knowledge of what you know so far, can you make me best speaker cables you can make 3 FT?
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post #4 of 25 Old 02-25-2015, 09:44 PM - Thread Starter
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Quote:
Originally Posted by NAIM101 View Post
Based on your knowledge of what you know so far, can you make me best speaker cables you can make 3 FT?

3 feet? 3 feet is no problem, just about any wire will work for 3 feet.

But on the other hand, knowing you have speaker cable costing hundreds, I can't take your question as genuine.

I'm simply establishing cable length for various fixed cable losses - 1%, 2%, 3%. Don't try to make it out to be more than it is.

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post #5 of 25 Old 02-26-2015, 11:19 AM - Thread Starter
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Originally Posted by NAIM101 View Post
Based on your knowledge of what you know so far, can you make me best speaker cables you can make 3 FT?
I also thought it was worth knowing to see just how much cable Inductance affect the audio range when the cable lengths are very long.

Even I didn't expect 50ft to be that significant. That seems like something people would like to know.

The cable I used in the example, is a very basic twin lead wire in the UK at about 13ga (2.5mm²).

http://www.audiovisualonline.co.uk/p...speaker-cable/

While I didn't show the work, I showed the formula so any person can determine the inductive impedance of any given wire for which they have specs at whatever length they desire.

For Front and Center Speakers, Inductance is not a problem, but for longer runs to Surround Speakers, it could potentially be a problem.

Seems like these are things worth knowing.

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post #6 of 25 Old 02-26-2015, 11:42 AM
 
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A bit late to this party you are.
http://www.bcae1.com/images/swfs/spe...rassistant.swf

With cables of standard construction and average length capacitance and inductance are not an issue. They can be with high priced exotic constructions, which is just one more reason not to waste your money on them.
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post #7 of 25 Old 02-26-2015, 12:37 PM - Thread Starter
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Quote:
Originally Posted by Bill Fitzmaurice View Post
...

With cables of standard construction and average length capacitance and inductance are not an issue. They can be with high priced exotic constructions, which is just one more reason not to waste your money on them.
If you look at my other thread, I analyze Capacitance and Inductance from every conceivable angle, and for typical 10ft/3m cable, Capacitance and Inductance are well outside the audio range.

Speaker Cable Debate in Perspective
https://www.avsforum.com/forum/89-spe...rspective.html

However in this thread here, I have demonstrated that in some cases for longer Surround speaker runs, cable Inductance could potentially be a problem.

3% loss at 3,614hz and 10% loss at 12,650hz.

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post #8 of 25 Old 02-26-2015, 12:53 PM
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Sigh...
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post #9 of 25 Old 02-26-2015, 02:13 PM - Thread Starter
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Quote:
Originally Posted by Elihawk View Post
Sigh...
Sigh what?

You don't think - 3% loss at 3,614hz and 10% loss at 12,650hz - from Inductive Impedance for 50ft of common 13ga wire are worthy of consideration?

It doesn't matter to me because I've got a Stereo, but for those with long run Surround speakers, knowing how much signal you are losing seems worthwhile.

From what I've determined Inductive loss is much greater for long runs than Resistive loss. That just seems worth knowing.

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post #10 of 25 Old 02-26-2015, 02:39 PM
 
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Quote:
Originally Posted by bluewizard View Post
Sigh what?
You don't think - 3% loss at 3,614hz and 10% loss at 12,650hz - from Inductive Impedance for 50ft of common 13ga wire are worthy of consideration?
How much is that in decibels? BTW, the correct term is inductive reactance.
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post #11 of 25 Old 02-26-2015, 05:26 PM - Thread Starter
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Here is the final table -

5% Resistive Cable Loss -


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post #12 of 25 Old 02-27-2015, 05:47 AM
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Quote:
Originally Posted by bluewizard View Post
3 feet? 3 feet is no problem, just about any wire will work for 3 feet.

But on the other hand, knowing you have speaker cable costing hundreds, I can't take your question as genuine.

I'm simply establishing cable length for various fixed cable losses - 1%, 2%, 3%. Don't try to make it out to be more than it is.

Steve/bluewizard
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post #13 of 25 Old 02-27-2015, 05:49 AM
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Quote:
Originally Posted by bluewizard View Post
Sigh what?

You don't think - 3% loss at 3,614hz and 10% loss at 12,650hz - from Inductive Impedance for 50ft of common 13ga wire are worthy of consideration?
If it's less than a decibel of change, than it's not.
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post #14 of 25 Old 02-27-2015, 06:20 AM
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Quote:
Originally Posted by bluewizard View Post
i analyze
lol
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post #15 of 25 Old 02-27-2015, 11:12 AM - Thread Starter
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Quote:
Originally Posted by Transmaniacon View Post
If it's less than a decibel of change, than it's not.
My math skills in this particular area are not that great, but from what I can determine -

3% = ~ 0.3db

10% = ~ 0.92db

db = 20 * log (Vout/Vin)


Though I'm more than willing to let others check my Math.

Still I posted tables from 1% to 5%, people are free to choose for themselves which works best for them.

But the point is that Inductive Reactance is having an effect down in the audio range. Whether it is enough for any given person to be concerned about is up to that person to determine.

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Quote:
Originally Posted by bluewizard View Post
My math skills in this particular area are not that great, but from what I can determine -
3% = ~ 0.3db
10% = ~ 0.92db

db = 20 * log (Vout/Vin)

Though I'm more than willing to let others check my Math.
Still I posted tables from 1% to 5%, people are free to choose for themselves which works best for them.
But the point is that Inductive Reactance is having an effect down in the audio range. Whether it is enough for any given person to be concerned about is up to that person to determine.
So you did all that work and pontificating without first making sure that there was any audible difference?
Sigh...
I think you should find better use for your time.
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post #17 of 25 Old 02-27-2015, 12:11 PM
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Originally Posted by RickJames View Post
So you did all that work and pontificating without first making sure that there was any audible difference?
Sigh...
I think you should find better use for your time.
What a refreshing idea!
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post #18 of 25 Old 02-27-2015, 04:37 PM - Thread Starter
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Originally Posted by RickJames View Post
So you did all that work and pontificating without first making sure that there was any audible difference?
Sigh...
I think you should find better use for your time.
There was no pontificating. I simply did the math and pointed out the results. Others are free to make of those results what they will.

So, are YOU willing to accept a 10% loss in your speaker cables? Do you? Do you have a 10% loss? Why not, you can't hear it?

I didn't think so.

Though it is clear from the charts that most people will have no problem making 1% or less for their Front speakers.

Also keep in mind that the Inductive Reactance is an ADDITIONAL 3% to 10% on top of the existing 3% loss for the Resistive aspect of the wire (50ft, 14ga). So, disregarding phase, we have a total of 6% to over 13% depending on the frequency. That adds up to 1.21db or more, depending on the frequency and the accuracy of my math.

But it is worthwhile to analyze and understand the wire at its extremes.

Knowledge is Power.

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post #19 of 25 Old 03-01-2016, 10:13 AM
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Quote:
Originally Posted by Bill Fitzmaurice View Post
A bit late to this party you are.
http://www.bcae1.com/images/swfs/spe...rassistant.swf

With cables of standard construction and average length capacitance and inductance are not an issue. They can be with high priced exotic constructions, which is just one more reason not to waste your money on them.
Which is more accurate? Your calculator or the chart? With your calculator I am ok at .51 dB, but with the chart I am at 6-7% loss...
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post #20 of 25 Old 03-01-2016, 11:03 AM
 
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Which is more accurate? Your calculator or the chart? With your calculator I am ok at .51 dB, but with the chart I am at 6-7% loss...
And that's why engineers don't use a percentage loss figure. What's OK? What isn't? OTOH we've known since roughly 1920 that a loss of less than 1dB is inaudible. Once again the reinvention of the wheel has been found to be unnecessary.
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post #21 of 25 Old 03-01-2016, 11:59 AM
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One aspect of speaker cable that I have not seen discussed: twisted-pair construction. It is available in a few plenum-class (firecode) cables suitable for in-wall wiring.

I mention this as I have been experiencing RF interference from a nearby 50 kW AM broadcast station. Twisted-pair cable would have helped here.

(I eventually was able to eliminate the RFI by wrapping the offending audio lines around a small toroid core.)
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post #22 of 25 Old 03-01-2016, 12:54 PM
 
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One aspect of speaker cable that I have not seen discussed: twisted-pair construction.
Twisted pairs are common with interconnects, especially balanced lines. They're seldom used, or needed, with speaker cables, since the transmitted signal is not subsequently amplified.
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post #23 of 25 Old 03-03-2016, 03:57 PM
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What rules apply with subwoofer coaxial rca cables?
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post #24 of 25 Old 03-03-2016, 07:10 PM - Thread Starter
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Originally Posted by Wolfgheist View Post
What rules apply with subwoofer coaxial rca cables?
That is a completely different subject. But if you search Google you will get links to speculation on the common limit to RCA Coaxial Cable.

Relative to the RCA cables themselves, is the resistance of the internal wire and the degree of shielding. Many of the ultra-thin ultra-cheap RCA cable would be luck to have 10% shield coverage. Many of the better RCA wire has about 95% coverage. Many decent acceptable cables have about 55% shield coverage.

The less coverage the more likely they are to pick up external noise.

I've seen 15m (50ft) mentioned and I've seen 5m (16ft) mentioned. But since it is very cable dependent, it is hard to lock down one definitive answer.

Here is a link that say 30m (100ft) MAX, but that is making a lot of assumptions.

http://www.cablechick.com.au/blog/cable-length-guide/

Perhaps a better question is - How far do you need to go?

As the cable gets longer the signal starts to deteriorate, how much can you handle?. Typically signal deteriorate in the high end first because of cable Inductance. That's less of a problem for a Subwoofer Cable.

The mating impedance of the Sub input is relatively high, in the range of 10k ohms to perhaps 50k ohms, so you can tolerate pretty substantial Resistance in the cable before it become a significant signal loss.

To lose 1% of the signal into a common 47k ohm input, the wire resistance would have to be 470 ohms.

22 ga wire is 16.14 ohms per 1000 feet.

24ga wire is 25.67 ohm per 1000 feet.

So ...

How long does the wire have to be?

What quality of wire are you buying?


I would say, though extremely variable, you could probably tolerate up to 50 feet for a Subwoofer. I would be more inclined to say about 20 feet for a full range cable, but that is just an intuitive guess.

Steve/bluewizard
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post #25 of 25 Old 03-04-2016, 08:43 AM
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Quote:
Originally Posted by bluewizard View Post
That is a completely different subject. But if you search Google you will get links to speculation on the common limit to RCA Coaxial Cable.

Relative to the RCA cables themselves, is the resistance of the internal wire and the degree of shielding. Many of the ultra-thin ultra-cheap RCA cable would be luck to have 10% shield coverage. Many of the better RCA wire has about 95% coverage. Many decent acceptable cables have about 55% shield coverage.

The less coverage the more likely they are to pick up external noise.

I've seen 15m (50ft) mentioned and I've seen 5m (16ft) mentioned. But since it is very cable dependent, it is hard to lock down one definitive answer.

Here is a link that say 30m (100ft) MAX, but that is making a lot of assumptions.

http://www.cablechick.com.au/blog/cable-length-guide/

Perhaps a better question is - How far do you need to go?

As the cable gets longer the signal starts to deteriorate, how much can you handle?. Typically signal deteriorate in the high end first because of cable Inductance. That's less of a problem for a Subwoofer Cable.

The mating impedance of the Sub input is relatively high, in the range of 10k ohms to perhaps 50k ohms, so you can tolerate pretty substantial Resistance in the cable before it become a significant signal loss.

To lose 1% of the signal into a common 47k ohm input, the wire resistance would have to be 470 ohms.

22 ga wire is 16.14 ohms per 1000 feet.

24ga wire is 25.67 ohm per 1000 feet.

So ...

How long does the wire have to be?

What quality of wire are you buying?


I would say, though extremely variable, you could probably tolerate up to 50 feet for a Subwoofer. I would be more inclined to say about 20 feet for a full range cable, but that is just an intuitive guess.

Steve/bluewizard
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