Seems like soldered bananas or spades would take care of connection issues. But I agree it is worth paying more for copper.
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Degradation of sound quality by speaker cables with high loop resistances?
- Thread starter oal
- Start date
charleski
Major Contributor
For best accuracy when measuring low resistances you really want to hook up the sense inputs (labelled 4WΩ here) as well. ADCMT sell a special 4-wire cable for this, but you can get the same result with another set of leads clipped onto the ends of the wire and plugged into the sense sockets. Not sure how much difference this would make here, though.
CCA gets tricky because you have a thin layer of copper reducing resistance. How much depends upon how thick the copper layer and the signal frequency, among other things. Going up a size or two (numerically lower AWG) is the usual fix for attaining CCA equivalent to copper resistance.
No matter how many times the OP said that the wire isn't pure copper, people kept posting charts and rules of thumb that are specific to copper and using this to argue that the OP's measurement of the cable resistance couldn't be correct. The OP's measurement might not be correct, but in order to apply charts and tables that are specific to copper to figure out whether his value is or isn't correct, you'll need to factor in the ratio of the resistivity of aluminum to the resistivity of copper. You can do it this way, however it is surely more direct to calculate the resistance for 1 meter of 16-gauge aluminum wire, which will give you a worst-case value for the actual resistance of the copper-clad aluminum.
Or you can use an online calculator. Even if you intend to do the calculation yourself, the value returned by the online calculator will give you a sense of whether your calculation is correct. According to an online calculator I found with no effort, the resistance of 16-gauge aluminum wire is approximately .02 ohms/meter.
Resistivity has units of ohm x meter. If you divide a resistivity value by the cross-section area of wire expressed in m^2, the units of the result will be ohms/meter. Since the units will be correct, it is virtually certain, given that this is a simple thing, that this must be the correct way to do the calculation. You can figure out a whole lot just by paying attention to the units of measure.
So I need to convert the cross-section area of the wire in mm^2 to m^2. Based on information I found on the Web, the cross-section area of 16-gauge wire is 1.3 mm^2. To convert this to m^2, I use the fact that 10^3 mm = 1 m. By simply squaring both sides of this equation, I find that 10^6 mm^2 = 1 m^2.
To convert the cross-section area of the wire from mm^2 to m^2, I need to multiply by a conversion factor that has m^2 in the numerator and mm^2 in the denominator. Thus, I multiply: 1.3 mm^2 x 1 m^2 / 10^6 mm^2. The result is obviously 1.3 x 10^-6 m^2.
I need to divide the resistivity of aluminum by this value. Looking up the resistivity of aluminum, the value I find in several places is 2.65 x 10^-8 ohm x m. The division:
2.65 x 10^-8 ohm x m / (1.3 x 10^-6 m^2) =
2.65/1.3 x 10^-8 x 10^6 ohm/m =
2.04 x 10^-2 ohm/m =
.0204 ohm/m
Rounding this off to two significant digits, the value matches the value returned by the online calculator. I am therefore confident that the resistance per meter of 16-gauge aluminum wire is .02 ohm/m. The round-trip length of the wire is 4 m. The resistance of 4 m of 16-gauge aluminum wire is thus .08 ohm. The OP's value was .2 ohm, which is greater than the theoretically correct value by a factor of 250%. If his result had been less than the theoretically correct value, the difference could be chalked up to the benefit of the wire being clad with copper. But his resistance value is higher, and since the wire does have some copper, the true resistance will be something less than .08 ohm.
The resistivity of copper is 1.7 x 10^-8 ohm x m, which is less than the resistivity of aluminum by a factor of roughly .64. This means that if the wire were made of pure copper, the resistance should be .64 x .08 ohm = .05 ohm. The actual resistance value of the 2 meter (round trip 4 meter) 16-gauge CCA wire is most likely about .07 ohm. Coincidentally this is the upper limit of what Revel recommended. For various reasons, any recommendation of this sort is based on multiple assumptions, specifically assumptions about the amplifier output impedance and the listener's tolerance threshold for peaks and dips in the response. Ordinarily a recommendation of this sort will also make assumptions about the speaker's nominal impedance and the impedance peaks and dips, but in this case the recommendation is given for one specific speaker.
You can find rules of thumb and online calculators for the maximum value for speaker cable impedance and for amplifier output impedance. It is not smart to do either of these separate from the other, because if you are going to fuss over either one of them, the analysis necessarily involves the other one, so it only makes sense that you should fuss over them together.
No matter what rule of thumb you use or what formula or calculator you use, the answer will come down to your personal notion of what amount of effect in decibels is acceptable. No calculator or rule of thumb can answer this for you. If you think the threshold of acceptability should be .1 decibel, you will get one value for the tolerance threshold of speaker cable impedance; if you think the threshold of acceptability should be .5 decibel, you will get a different value for the tolerance threshold of speaker cable impedance. And I will say once again that it depends on the amplifier output impedance. You need to do both in unison. Many people find this calculator useful:
https://benchmarkmedia.com/blogs/application_notes/audio-myth-damping-factor-isnt-much-of-a-factor
While I find this calculator somewhat useful, I would approach it by calculating the approximate allowable value for amplifier output impedance, then subtracting the actual amplifier output impedance from the calculated value, to obtain the allowable impedance for the speaker wire. I wrote this up here:
https://www.audiosciencereview.com/...standing-of-amplifier-output-impedance.22380/
The gist of it is:
OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit _dB x NI)
In this inequality, Limit_dB is your chosen threshold of acceptability. The other variables are:
OI : the amplifier Output Impedance
NI : the Nominal Impedance of the speaker (i.e., the mean value over the full audio spectrum)
PI : the Peak Impedance of the speaker
You use NI (nominal speaker impedance), PI (peak impedance of speaker) and your personal value for Limit_dB to calculate the maximum allowable output impedance of the amplifier, such that the response peak coinciding with the speaker's impedance peak will not exceed Limit_dB. Whatever value you get for OI, you can subtract your actual amplifier output impedance from this value to obtain the allowable speaker cable impedance.
Or you can use an online calculator. Even if you intend to do the calculation yourself, the value returned by the online calculator will give you a sense of whether your calculation is correct. According to an online calculator I found with no effort, the resistance of 16-gauge aluminum wire is approximately .02 ohms/meter.
Resistivity has units of ohm x meter. If you divide a resistivity value by the cross-section area of wire expressed in m^2, the units of the result will be ohms/meter. Since the units will be correct, it is virtually certain, given that this is a simple thing, that this must be the correct way to do the calculation. You can figure out a whole lot just by paying attention to the units of measure.
So I need to convert the cross-section area of the wire in mm^2 to m^2. Based on information I found on the Web, the cross-section area of 16-gauge wire is 1.3 mm^2. To convert this to m^2, I use the fact that 10^3 mm = 1 m. By simply squaring both sides of this equation, I find that 10^6 mm^2 = 1 m^2.
To convert the cross-section area of the wire from mm^2 to m^2, I need to multiply by a conversion factor that has m^2 in the numerator and mm^2 in the denominator. Thus, I multiply: 1.3 mm^2 x 1 m^2 / 10^6 mm^2. The result is obviously 1.3 x 10^-6 m^2.
I need to divide the resistivity of aluminum by this value. Looking up the resistivity of aluminum, the value I find in several places is 2.65 x 10^-8 ohm x m. The division:
2.65 x 10^-8 ohm x m / (1.3 x 10^-6 m^2) =
2.65/1.3 x 10^-8 x 10^6 ohm/m =
2.04 x 10^-2 ohm/m =
.0204 ohm/m
Rounding this off to two significant digits, the value matches the value returned by the online calculator. I am therefore confident that the resistance per meter of 16-gauge aluminum wire is .02 ohm/m. The round-trip length of the wire is 4 m. The resistance of 4 m of 16-gauge aluminum wire is thus .08 ohm. The OP's value was .2 ohm, which is greater than the theoretically correct value by a factor of 250%. If his result had been less than the theoretically correct value, the difference could be chalked up to the benefit of the wire being clad with copper. But his resistance value is higher, and since the wire does have some copper, the true resistance will be something less than .08 ohm.
The resistivity of copper is 1.7 x 10^-8 ohm x m, which is less than the resistivity of aluminum by a factor of roughly .64. This means that if the wire were made of pure copper, the resistance should be .64 x .08 ohm = .05 ohm. The actual resistance value of the 2 meter (round trip 4 meter) 16-gauge CCA wire is most likely about .07 ohm. Coincidentally this is the upper limit of what Revel recommended. For various reasons, any recommendation of this sort is based on multiple assumptions, specifically assumptions about the amplifier output impedance and the listener's tolerance threshold for peaks and dips in the response. Ordinarily a recommendation of this sort will also make assumptions about the speaker's nominal impedance and the impedance peaks and dips, but in this case the recommendation is given for one specific speaker.
You can find rules of thumb and online calculators for the maximum value for speaker cable impedance and for amplifier output impedance. It is not smart to do either of these separate from the other, because if you are going to fuss over either one of them, the analysis necessarily involves the other one, so it only makes sense that you should fuss over them together.
No matter what rule of thumb you use or what formula or calculator you use, the answer will come down to your personal notion of what amount of effect in decibels is acceptable. No calculator or rule of thumb can answer this for you. If you think the threshold of acceptability should be .1 decibel, you will get one value for the tolerance threshold of speaker cable impedance; if you think the threshold of acceptability should be .5 decibel, you will get a different value for the tolerance threshold of speaker cable impedance. And I will say once again that it depends on the amplifier output impedance. You need to do both in unison. Many people find this calculator useful:
https://benchmarkmedia.com/blogs/application_notes/audio-myth-damping-factor-isnt-much-of-a-factor
While I find this calculator somewhat useful, I would approach it by calculating the approximate allowable value for amplifier output impedance, then subtracting the actual amplifier output impedance from the calculated value, to obtain the allowable impedance for the speaker wire. I wrote this up here:
https://www.audiosciencereview.com/...standing-of-amplifier-output-impedance.22380/
The gist of it is:
OI < PI x NI x (1.122^Limit_dB -1) / (PI - 1.122^Limit _dB x NI)
In this inequality, Limit_dB is your chosen threshold of acceptability. The other variables are:
OI : the amplifier Output Impedance
NI : the Nominal Impedance of the speaker (i.e., the mean value over the full audio spectrum)
PI : the Peak Impedance of the speaker
You use NI (nominal speaker impedance), PI (peak impedance of speaker) and your personal value for Limit_dB to calculate the maximum allowable output impedance of the amplifier, such that the response peak coinciding with the speaker's impedance peak will not exceed Limit_dB. Whatever value you get for OI, you can subtract your actual amplifier output impedance from this value to obtain the allowable speaker cable impedance.
OP
- Thread Starter
- #26
Good suggestion. I will try the 4 wire testing on Saturday (as I can use the ADCMT Digital Multimeter only in weekend at a fab lab). I think the fab lab has another set of leads for another Digital Multimeter (Keysight's).
A lot of people seem to doubt the results of my cable measurements. I will double check them in this weekend.
By the way, do you remember that Amir tested many 12 AWG speaker wires in 2016?
When 12 Gauge Wire is Not 12 Gauge
At that testing, Belden's 12 AWG wire was 1.15 DCR/ft. While BestBuy's 12 AWG was 4.82 DCR/ft - 418% of Belden's. So, it is not surprising that the Amazon Basic's 16 AWG was 52 mili-ohm/m and Belden's 16 AWG was 11.5 milli-ohm/m by my testing.
Anyway, as I wrote before, I use 14 AWG copper cable for my speakers. I bought Amazon Basic's CCA cable just for testing because I was merely curious - what happens if I use it for low impedance speakers? I want to be at the safe side here because speaker cables are cheap compared to speakers.
OP
- Thread Starter
- #27
I agree with you. Changing listening position is noticeable too. Room Gain is much bigger than FR changes by cables.
This is a fair point. However, aluminum material does not explain this. If there is a 4X difference then it would be interesting to get at the reason.
But note that your FR plots, where measured resistance difference was 7X, don't show a corresponding FR degradation. So this also makes me suspect a problem with the resistance measurements. One suggestion: solder some terminals on the ends of the cable to make sure you are not seeing connection issues.
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OP
- Thread Starter
- #29
I too am interested in the reason. Pure aluminum does not explain the 4x difference. However, about 20 types of aluminum alloys are commonly used for electric wires. Conductance of some type of alloy is much lower than pure aluminum’s.
Calculation of area in the AWG table is also too simple. (pi * D/4) Actual speaker cable consists of many thinner wires (either strait or leaning). The total cross-sectional area will be smaller than pi * D/4. I suspect that the actual area of a same AWG wire varies from manufacturer to manufacturer.
A 7x difference in DCR does not produce a 7x difference in SPL. High DCR (i.e. 0.42 ohm) of cable just drops driving voltage (thereby, SPL) a few percent.
Look at my table. Let us ignore 200Hz and below as room gain is big. At 1000Hz, the FR Magnitude drops by -0.51 dB with the Amazon cable. -0.51 dB is 94% (or -6%). At 10kHz, it drops by -0.22 dB. -0.22 dB is 97.5% (or -2.5%). I think these are not so strange values even if the Amazon cable’s DCR is 0.42 ohm.
Good suggestion. I will solder terminals when testing the cable again.
OP
- Thread Starter
- #31
Thank you. But, don't you need frequency-impedance chart of my speaker to calculate the differences?
OP
- Thread Starter
- #33
Oh, actually, I measured the FR with another speaker which I have not measured its impedance yet. Then, I will measure FR with Revel M105 too in this weekend. My rough hand-calculation says the diff will be about -0.35dB at 1kHz, -0.8dB at 500Hz with 1W power.
EDIT: Sorry but I do not have output impedance curve of my amps. Please use AHB2 curve, I do not have such a good amp though.
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Below are some measurements I took when I was doing a double blind amp test between a tube amp with ~0.7 ohms of output impedance and a Neurochrome SS amp with vanishing low output impedance. I then added in a 0.9 ohm resistor to the SS amp speaker cable to simulate the output impedance of the tube amp and you can see that the FR of the SS amp with the resistor almost perfectly matched the tube amp. For the purposes of this thread look at the red and purple lines, red is no resistor and purple is with the resistor. This will give you some perspective on how much and how the FR changes with added speaker cable resistance. The speaker measured was a Sonus Faber Concerto. For what it's worth I could not ABX with and without the 0.9 ohm resister.
OP
- Thread Starter
- #35
Because a lot of people doubted the results of my cable measurements, I have measured the cables again. I apologize that my initial measurements were not accurate. DCR of the Amazon 16AWG cable was 27.4 milli-ohm/m, not 52 milli-ohm/m.
As charleski suggested, I used the 4-Wire Measurement method this time. I used 1m cables to test, then shorted and clamped one end of each cable (so, a 2m loop). I used terminals at the other end so that I can clip leads of the digital multimeter easily. The digital multimeter I used was ADCMT 7451A and its accuracy is 100 micro-ohm or 0.1 milli-ohm.
Following table shows the results. In the 4-Wire Measurement (4WΩ), DCR values are displayed smaller, and they are more accurate than 2WΩ.
So, I was comparing 0.22 ohm and 0.06 ohm, not 0.42 ohm and 0.06 ohm. DCR ratio of Amazon 16AWG and Belden 16AWG are 1.6 times. Typical OFC and CCA can explain this result. Many people were right at this point.
There is still a 3.4x difference between Amazon cable and Audio-Technica cable. So, I used the Revel M105 too to measure the difference in FR between the two cables, just in case.
The largest gaps (diff) above 200Hz are around 500Hz and 3kHz. But they are less than 0.4 dB.
Despite of this result, I continue using 14AWG copper cable for my speakers as cost saving by CCA cables is small. Good OFC cables are cheap as well.
As charleski suggested, I used the 4-Wire Measurement method this time. I used 1m cables to test, then shorted and clamped one end of each cable (so, a 2m loop). I used terminals at the other end so that I can clip leads of the digital multimeter easily. The digital multimeter I used was ADCMT 7451A and its accuracy is 100 micro-ohm or 0.1 milli-ohm.
Following table shows the results. In the 4-Wire Measurement (4WΩ), DCR values are displayed smaller, and they are more accurate than 2WΩ.
So, I was comparing 0.22 ohm and 0.06 ohm, not 0.42 ohm and 0.06 ohm. DCR ratio of Amazon 16AWG and Belden 16AWG are 1.6 times. Typical OFC and CCA can explain this result. Many people were right at this point.
There is still a 3.4x difference between Amazon cable and Audio-Technica cable. So, I used the Revel M105 too to measure the difference in FR between the two cables, just in case.
The largest gaps (diff) above 200Hz are around 500Hz and 3kHz. But they are less than 0.4 dB.
Despite of this result, I continue using 14AWG copper cable for my speakers as cost saving by CCA cables is small. Good OFC cables are cheap as well.
Thanks for redoing this. The spec on the AT6158 is 6.8 millohms/meter so about 13AWG. I find that interesting; maybe I would choose 13AWG if they had it on reels at my local Ace store. Like you, I use 14AWG copper, about 16 ft round trip. This with 8 ohm speakers (6 ohm minimum).Because a lot of people doubted the results of my cable measurements, I have measured the cables again. I apologize that my initial measurements were not accurate. DCR of the Amazon 16AWG cable was 27.4 milli-ohm/m, not 52 milli-ohm/m.
As charleski suggested, I used the 4-Wire Measurement method this time. I used 1m cables to test, then shorted and clamped one end of each cable (so, a 2m loop). I used terminals at the other end so that I can clip leads of the digital multimeter easily. The digital multimeter I used was ADCMT 7451A and its accuracy is 100 micro-ohm or 0.1 milli-ohm.
View attachment 138842
Following table shows the results. In the 4-Wire Measurement (4WΩ), DCR values are displayed smaller, and they are more accurate than 2WΩ.
View attachment 138843
So, I was comparing 0.22 ohm and 0.06 ohm, not 0.42 ohm and 0.06 ohm. DCR ratio of Amazon 16AWG and Belden 16AWG are 1.6 times. Typical OFC and CCA can explain this result. Many people were right at this point.
There is still a 3.4x difference between Amazon cable and Audio-Technica cable. So, I used the Revel M105 too to measure the difference in FR between the two cables, just in case.
View attachment 138844
View attachment 138845
The largest gaps (diff) above 200Hz are around 500Hz and 3kHz. But they are less than 0.4 dB.
Despite of this result, I continue using 14AWG copper cable for my speakers as cost saving by CCA cables is small. Good OFC cables are cheap as well.
OP
- Thread Starter
- #38
AT6158 is the cable with the lowest DCR that I have. But there is one thing to note about the AT6158. It is a thick cable, a wire diameter of 2.5mm (with OFC φ0.12mm x 238 strands). For its diameter, I think 6.8mΩ/m is a high DCR. Because my speaker connector plugs accept up to 2.0mm diameter, I use the 14 AWG cables.
pogo
Major Contributor
- Joined
- Sep 4, 2020
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You are forgetting the time domain, i.e. the swing-out behavior of a speaker at different damping factors, where the cable also makes its contribution. From my listening experience, the FR Magnitude drops plays a subordinate role. A speaker must be guided and must not develop a life of its own by reproducing sound components that are not present in the source signal.
OP
- Thread Starter
- #40
Did you mean "the damping of driver motion" by "the swing-out behavior of a speaker"? If so, I do not believe it is a big factor with amplifiers these days and even with the CCA cables.
MrPeabody quoted an excellent pager:
In short, DAMPING IS NOT AN ISSUE, BUT THERE IS AN ISSUE (another issue). Output impedances of amps these days are 80 mili-ohm at the largest, usually 40 milli-ohm or less (dumping factor is 200 with an 8 ohm speaker, much larger than 10) even by an entry class integrated amp:
https://usa.yamaha.com/products/audio_visual/hifi_components/a-s301/specs.html#product-tabs
Just in case, I analyzed FR + Distortion from the first impulse (0ms) to +12ms with the 2 cables, but could not see big differences in distortion. There is a small difference in distortion between 50 Hz and 70 Hz, but I think it is not audible (too low in dB).
