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Headphone wire resistivity

post #1 of 15
Thread Starter 
Hey guys,

some days ago I tried to calculate the resistivity of wires to determine the possible influence on the sound. Also did a comparison between copper / silver. I'm not sure if everything's correct but I'd say it is from taking a look at the results.

Stranded copper has a resistivity of 0.0178 ohm mm² / m and
silver's a bit lower/better: 0.0159 ohm mm² / m.
(based on the values from the CRC Handbook of Chemistry and Physics / Wikipedia)

AWG 24 wire has a diameter of 0.511 mm and cross-area of 0.205 mm².
-->
AWG 24 stranded copper wire has a resistivity of 0.086962431 ohm / m.
AWG 24 stranded silver wire has a resistivity of 0.077679925 ohm / m.

----

Resistivity can have a big influence on the sound because speakers don't have a flat impedance. In fact speaker impedance changes with frequency. For example if you add resistors between your hp-out and headphones, you'll most likely hear a 'bass boost' and probably also some increased treble depending on the model. (see HeadRoom impedance charts)
For the calculations I took the following extreme values:
low: 32->64 ohm (e.g. PX 100) and
high: 320->640 ohm (e.g. HD 800).

Because the per-meter values were so low, I decided to calculate the maximum wire length up to the point where the wire resistivity could, in the worst case, lead to a change (voltage drop) of max 0.1 dB. (I don't know if this translates directly into SPL, but if it does it's inaudible.)
Keep in mind that many headphones have a much 'flatter' impedance curve, thus showing even much better results.

Results:
AWG 24
copper low: 8.6 meters / 28.2 feet
copper high: 86 meters / 282 feet

silver low: 9.6 meters / 31.5 feet
silver high: 96 meters / 315 feet

The difference between copper and silver is minimal (about 0.01 dB).
At those lengths the wire resistivity is about 2.3% of the speaker nominal impedance (Wikipedia recommends less than 5%, which would be about 0.2 dB).

Theoretically:
Using a 1 meter cable (copper), wires up to AWG 32 (0.2 mm diameter) could be used for the low ohm model and up to AWG 42 (0.06 mm diameter) for the high ohm model (based on their resistivity only!).

For 15 meters, low impedance AWG 22 should about do it, AWG 30 for high impedance.
For 30 meters: AWG 19 and 28 respectively.

----

Hope there are no severe mistakes. Hope it's useful for someone.
post #2 of 15
How do they sound? Do they have synergy with your rig? Do they help or hinder your gear?
post #3 of 15
Thread Starter 
Big Poppa, this is more or less theoretical. I didn't try this out because I don't have so much different cables around, but I might try to do some comparisons between a normal and lets say 8.6m (0.1dB), 25m (~0.3dB) and 50m (~0.5dB) cable.

I did however mess around with resistors, and the change was clearly audible .. of course, because I used 75, 120, etc. ohms. (And I didn't like the bloated bass at all.)
post #4 of 15
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post #5 of 15
Quote:
Originally Posted by xnor View Post
Big Poppa, this is more or less theoretical. I didn't try this out because I don't have so much different cables around, but I might try to do some comparisons between a normal and lets say 8.6m (0.1dB), 25m (~0.3dB) and 50m (~0.5dB) cable.
50m cable will have rather high capacitance (quite easily as high as 5nF) and hence the result will depend a lot on the specifics of the cable and how well the amplifier can actually drive capacitive loads. Even if it is low capacitance cable, 0.5nF loads can still cause problems.

Quote:
Originally Posted by xnor View Post
I did however mess around with resistors, and the change was clearly audible .. of course, because I used 75, 120, etc. ohms. (And I didn't like the bloated bass at all.)

Measuring this stuff using my multimeter would be a waste of time, because it has much higher measurement errors.
120 ohms is obviously audible, and also the iec standard headphone output impedance. Its not really the impedance that is at fault but rather your amplifier.

And its rather oscilloscope you want for such measurements, not multimeter
post #6 of 15
Thread Starter 
Yeah you're right, of course capacitance would increase a lot with such long cables. I totally forgot about it when I wrote that comment, but the main thread mentions that these calculated lengths are based on the resistivity only.

About the output impedance, it's not that the amp couldn't handle it but the headphones I tried this out with (PX 100) because they have too much bass even without the added resistors imho.
post #7 of 15
the cable capacitance can be critical since many feedback amplifiers can be pushed into instability by excess Cload - even (the incorrectly called "no feedback") descrete emitter follower buffers
post #8 of 15
Quote:
Originally Posted by jcx View Post
even (the incorrectly called "no feedback") descrete emitter follower buffers
No no, emitter followers don't have "feedback." It's called "emitter degeneration."

Do you remember when Charles and I locked horns on that one over at diyAudio?

k
post #9 of 15
you mean where he argued degeneration is not feedback in the 1st paragraph then used Blackman's formula in the next to compute the input impedance?

I guess if you sell "no feedback" amplifiers then its critical to make the (nonexistant) distinction
post #10 of 15
Quote:
Originally Posted by jcx View Post
you mean where he argued degeneration is not feedback in the 1st paragraph then used Blackman's formula in the next to compute the input impedance?
Yeah, that one.

Quote:
I guess if you sell "no feedback" amplifiers then its critical to make the (nonexistant) distinction
Sadly.

k
post #11 of 15
Thread Starter 
Hmpf I found a cable loss calculator and I get a 3 dB treble attenuation at 331573 Hz with a 50 m cable (300pF/m).

So does this even matter, provided that the amp isn't crap?

edit: a picofarad is 0.000 000 000 001, that's nothing!
post #12 of 15
Quote:
Originally Posted by xnor View Post
Hmpf I found a cable loss calculator and I get a 3 dB treble attenuation at 331573 Hz with a 50 m cable (300pF/m).

So does this even matter, provided that the amp isn't crap?

edit: a picofarad is 0.000 000 000 001, that's nothing!
Attenuation is essentially insignificant until you get to cables in the kilometer range. The effect of capacitance is not so much on attenuation but in amplifiers (in)ability to drive large capcitive loads (where large starts at 500pF or even lower). Unless the amplifier has an output stage built with capacitive loads in mind, it is liable to reacting poorly and having sever overshoot and ringing problems.

Is it really a problem? Depends. Its something you have to sometimes think about. Like getting think low capacitance cable for long runs. Or putting a line driver / receiver between the preamp and power amp.
post #13 of 15
Quote:
Originally Posted by sanderx View Post
Attenuation is essentially insignificant until you get to cables in the kilometer range. The effect of capacitance is not so much on attenuation but in amplifiers (in)ability to drive large capcitive loads (where large starts at 500pF or even lower). Unless the amplifier has an output stage built with capacitive loads in mind, it is liable to reacting poorly and having sever overshoot and ringing problems.
And in such instances these can be helpful.

Jensen JT-OLI-3

k
post #14 of 15
Thread Starter 
How would e.g. a Mini3 'react' / how much could it handle?
post #15 of 15
The capacitive load it is able to drive is based on the opamp itself and the resistor tacked on the output of the opamp. The ferrite beads on the output also provides an improvement to this (as noted on AMB's website...). I'm going to say you shouldn't have any reasonable problems with any headphone loads (unless we're talking meters upon meters of cable...). You can do the actual calculations (in SPICE), but it's pretty much safe to say you'll be okay.

~Thomas
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