Impedance at high frequency in audio cables

[pwnell]

The OP focused on inductance due to 40 meters of 18 g wire while only looking at the upper limit of the audio frequency range. My main point (which I didn't say directly) was he ended up ignoring the forest for the trees.

I appreciate your response. However, it is quite frustrating to ask a specific question and have it shot down because of reasons not relevant to the question. I did not ask a general question and needed to be reminded that these effects are negligible and I should look elsewhere. I asked a specific question because I am interested in a 40m length of AWG18 wire at 22kHz. If you take a 40m length of cable at 18kHz (which most people CAN hear) you will STILL find the inductive reactance to be greater than the resistance.

Using https://www.eeweb.com/toolbox/parallel-wire-inductance/ for 22kHz:
R = 0.85 Ohms
XL = 2.25 Ohms

For 18kHz:
XL = 1.84 Ohms

I do not want to debate the merits of my question - I just want to understand:

1) Did I perform my inductance calculation correctly given these parameters?
2) If my calculations were correct and inductance is significantly larger than resistance for these parameters, why do people focus on wire thickness as inductance actually only gets worse the thicker the wire.

You also mention:

Straight speaker wire lacks an inductor coil, therefore the inductive reactance is insignificantly low, and the OP's original premise is wrong.

Which again is making assumptions about what I am trying to understand. You are very wrong if you believe two straight parallel conductors have no or insignificant inductive reactance. I just calculated it for you above - that is not a coil, it is just two parallel conductors. And it is greater than the resistance by a factor of more than 2. Whether it is relevant in an audio system is a separate question.

I never said capacitance is not an issue. In fact, I have previously calculated it using C = (pi * epsilon * l) / arcosh(d/(2a)), which gives 13.7pF thus it changes the impedance from 2.25 to 2.25012) and its effect is truly negligible (by a factor of approximately 10000 compared to inductance).

And lastly:

In my opinion, the OP is trolling and should be ignored. I'm sorry I didn't realize this sooner.

That is extremely rude. You have no basis for such a remark. You must be a millennial, with no manners.

The first link is probabally the most important link to show why the transmission line model does not work in audio frequencies. The bolded part should answer your question.

My understanding is that this article is mostly about wave propagation - something very important in transmission line design due to the extended lengths of the cables. In audio environments this is negligible because at 22kHz a quarter wavelength of light is 3.4km, which is way longer than typical cable runs - hence the reflection property of electromagnetic waves can be ignored.

There are much more aspects of transmission line analysis that are relevant to audio speaker cables. The fact that you have two conductors with opposing currents in parallel carrying low frequency currents are all the same. Therefore the inductance and capacitance analysis, including skin effect and proximity effect are all similar. That said, due to the shorter lengths these attributes are of course much more benign.

My intent with this post is to calculate just how benign it is, and not just take it on word of mouth.

 

[mtrycrafts]

....

My intent with this post is to calculate just how benign it is, and not just take it on word of mouth.

This article has some interesting calculations and graphs of 12 cables. He had a JAES paper on this afterwards. While the article uses or calculates on 10 ft cables. You can extend this to longer cables.

https://acmebass.com/archive_files/mag_articles/audio_magazine/testing_spkr_cables_for_audibility_07-1993.pdf

The paper also shows dB loss vs frequency.
Now, of course we need wire, so the comparison is between cables. Certainly the lowest inductance gives a flatter response but is the delta between two cables sufficient to be audible? The JND(just noticeable difference) also increases a lot with frequency, around 3 dB at 16 kHz.

Just curious why you picked 40 meters(131ft) to analyze?

ps.

from one of the links above about long wire, especially in his 2nd paragraph:

What about Wires Longer Than 50 Feet?

Besides losses due to cable resistance, longer cables begin to exhibit a significant reactive component of capacitance and inductance regardless of the wire size. Measurements I have made show that response in the 10 kHz to 20 kHz region is affected by a small amount. Then why are differences in extended wire lengths not heard? There are at least two reasons. Both are related to our hearing ability.

An article was published in Audio, July 1994 titled "Speaker cables: Measurements Vs Psycho-acoustic data" by Edgar Villchur. The psycho-acoustic data shows that for pure tones at 16kHz the smallest average detectable difference in level is 3.05 dB. He also indicates: "It can be predicted that at a given level the just noticeable difference will be increased by a significantly greater amount by the masking effect of musical sound below 10 kHz." (See note 1). The findings were based on individuals 20 to 24 years old that had normal hearing to 20 kHz (See note 2). This is what might be called the best of conditions for hearing differences.

However, as we age, our sensitivity to high frequencies decreases dramatically. The chart is from Modern Sound Reproduction by Harry F. Olson. It shows the average hearing loss Vs age for men and women at frequencies from 250 Hz to 8000 Hz. This means that for a man at age 35, sensitivity is down about 11 dB at 8000 Hz. For a woman at that age, sensitivity is down only about 5 dB. We can infer that sensitivity is down a whole lot more at 20kHz.

So for these two reasons this measurable high frequency wire loss in the 10 to 20kHz region is not audible for moderately long wires like 50 feet. Longer runs may still not be audible for some people, provided the wire resistance is kept low enough.

(Note 1) An article was published in the Journal of the Audio Engineering Society by Lipshitz and Vanderkooy titled "The Great Debate: Subjective Evaluation" Volume 29, No. 7/8 July/August. They estimated that when level differences occurred over a wide band, they were detectable down to 0.2 dB. However, in a phone conversation with Villchur, Lipshitz agreed this figure is not applicable to speaker cables where the level differences are all in the highest audio octave.

(Note 2) Villchur gives a reference of Florentine, Buns and Mason "Level Discrimination As a Function of Level for Tones from 0.25 to 16kHz" Journal of the Acoustical Society of America, Vol. 81, No. 5 (May 1987)

 

[pwnell]

Thanks for this - I will review it shortly.

As to your question for my reason for choosing 40m, that represents a 20m run of speaker cable (40m including the return path). 20m is in my calculation the longest run one would typically have in a home theatre system for surround speakers, considering wiring through walls / around obstacles. I wanted to choose a maximum length and highest frequency as that would cover all shorter lengths and lower frequencies implicitly.

 

[mtrycrafts]

Thanks for this - I will review it shortly.

As to your question for my reason for choosing 40m, that represents a 20m run of speaker cable (40m including the return path). 20m is in my calculation the longest run one would typically have in a home theatre system for surround speakers, considering wiring through walls / around obstacles. I wanted to choose a maximum length and highest frequency as that would cover all shorter lengths and lower frequencies implicitly.

Thanks. The other thing that is mentioned in Roger Russell paper is that the R should not be more than 5% of the speaker's nominal impedance, if you would.
So, your 18Ga is too resistive for an 8 Ohm speaker at 40m total length, hence the lower ga wire. 14 ga for that run.
A 4 Ohm speaker would need half that R, of course.

 

[3db]

Also
There are much more aspects of transmission line analysis that are relevant to audio speaker cables. The fact that you have two conductors with opposing currents in parallel carrying low frequency currents are all the same. Therefore the inductance and capacitance analysis, including skin effect and proximity effect are all similar. That said, due to the shorter lengths these attributes are of course much more benign.

My intent with this post is to calculate just how benign it is, and not just take it on word of mouth.

People like Swerd and myself (I have a degree in Electrical Engineering) have tried to help you. Your responses back such as "word of mouth" are quite frankly ignorant and very rude. If you want to discuss further the quantization of transmission line parameters, I suggest very strongly that you alter your tone and stop the troll like behaviour you are currently exhibiting.

 

[pwnell]

People like Swerd and myself (I have a degree in Electrical Engineering) have tried to help you. Your responses back such as "word of mouth" are quite frankly ignorant and very rude. If you want to discuss further the quantization of transmission line parameters, I suggest very strongly that you alter your tone and stop the troll like behaviour you are currently exhibiting.

I really wish you guys would be less hypersensitive and relax. My comment about "word of mouth" was not directed at any member of this forum. It was directed to anyone stating facts without being able to substantiate them. It was meant as a way of expressing that I am not interested in emotional and subjective responses, but rather just the facts and whatever can be proven scientifically. Too often people would respond with comments like "It is negligible, trust me". That is the kind of response I indicated, I do not want as I want to *calculate* these effects for myself.

And just for your reference, I have a degree in electrical engineer myself. I am a bit rusty on some subjects, but it does not mean I am trolling.

Stop reading things between the lines. I am not that kind of person.

 

[pwnell]

As a final comment, I'd like to thank @mtrycrafts - as he gave me a definitive answer to my original question without being insulting or arrogant or presumptuous. People like him and @Speedskater promote constructive discussions and are the real helpful people here.