|   An anatomy of a Zip cord.....revisited Pt1. | Mr Mono
May 7, 2002 11:38 AM | | I think the best way to find out about zip cord performance and its effect on audio would not be to just keep arguing about it. But rather we need to get into the heart of problem and evaluate a zip cord scientifically (with calculation) and see how it does effect audio signal from electrical point of view.
But before we go any further, we need to have a reference hearing point where ear can distinguish between volume changes. If we don't have this reference value (where everything else can be measured against), then our calculation become meaningless. I did some extensive research on this (and thanks to Mtry) and most audio engineers (I hope TT and Doc can back me up on this) do agree that ear can distinguish the change in volume if change is greater than 0.25 dB and only in midrange audio frequency. For lower and higher frequency, the volume change have be greater than 0.25 dB (1 dB is a good estimate...and that is what I kept telling Jon) to be noticeable.
So why do yessayars always trying to shoot down zip cords? Two sticky point here that they always base their argument on and we are going to confront these issue head on. Two sticky point being wire inductance and skin effect which we will break down one by one.
Inductance: Inductance (every wire have inductance) act like a Resistor(pure resistance..frequency independent), except that is frequency dependant (higher the frequency the higher the inductance). At 0Hz, there is no inductance, but as frequency increase, the value of inductance increase also. The reason effect of inductance is worse than pure resistance is that it tend to effect higher frequency more since it is frequency dependant. It will effect higher frequency than lower one thus if one send a signal that have equal amplitude cross audio frequency range thru an inductor, what you will get out is slope going down-ward (amplitude wise) as frequency increase. So you will have less amplitude at higher frequency (15-20khz) than lower frequency (0-100hz).
This effect is extremely undesirable because it alter the way music is reproduced. Yessyars claim that inductance of zip cord is too much so it will effect higher frequency thus making the sound too dull, thus more expensive cables tend to be twisted together or use a coax type cables to decrease inductance value.
But what is exactly inductance of zip cord and how does it effect signal. I found this old formula from 1949 text book Harnwell (Principles of
Electricity and Magnetism, McGraw, 1949) and Terman (Radio
Engineering, 3rd Ed, McGraw 1947) that give inductance value of zip cord.
Inductance of equal-diameter parallel wires, spaced by B (measure from center of conductor to center), with radius A is given by:
L = 0.281 * log (B /A) microhenries/foot
Here is measurement for inductance of 20 feet of 14 gauge zip cord.
conductor radius= A = 0.0285 inches
conductor spacing = b = 0.130 inches (measured center to center)
So b/a for my 14-2 zip cord is .130/.0285 = 4.56
Based on the formula I get:
L = 0.281 * log (b / a) microhenries/foot
L = 0.281 * log (4.56) microhenries/foot
L = 0.281 * .655 microhenries/foot
L = 0.184 microhenries/foot
So, for a 20 foot length of 14-2 zip cord L = 3.68 microhenries
At 20 kHz the impedance of this inductance is given by: Z = 2 * pi * f * L
Z = 2 * 3.14 * 20000Khz * .00000368
Z = 2 * 3.14 * .073
Z = 0.462 Ohms (at 20k Hz)
So to calculate 0.462 ohms inductance effect on volume output, we have to compare it to speaker inductance which is in series with it. Assuming we have an 8 Ohm speaker which probably have 10 Ohm impedance at 20k Hz. The drop in signal level at 20 kHz due to the inductance of the cable would be:
attenuation = 20 * log ( 10 / 10.462 )
attenuation = -0.39 dB
So you might say that change in volume due to cable inductance is greater than 0.25 dB, so we will hear the difference. That is good observation, but there |
| An anatomy of a Zip cord.....revisited Pt2. | Mr Mono
May 7, 2002 11:40 AM | | So you might say that change in volume due to cable inductance is greater than 0.25 dB, so we will hear the difference. That is good observation, but there is a problem. This dB change is for higher frequency which ear is less sensitive to (unless attenuation fall above 1 db, then the ear will not recognize it).
So in order to find out how this inductance effect midrange frequency where ear is most sensitive. We have to go back and recalculate since reference frequency has changed.
So inductance of zip cord at 2 khz (mid range) is:
Z = 2 * 3.14 * 2000Khz * .00000368
Z = 2 * 3.14 * .073
Z = 0.0462 Ohms (at 20k Hz)
And attenuation due to this inductance (since frequency has decrease we have to lower the value of speaker impedance also). 4 ohm seem like a conservative value for speaker impedance for midrange frequency:
attenuation = 20 * log ( 4 / 4.0462 )
attenuation = -0.104 dB
So inductance of this wire will cause the volume change of 0.104 dB which is well below the threshold value of 0.25 dB for midrange frequency. So from above formula (scientifically) the inductance of zip cord in negligible in audio frequency and something we don't have to worry about. More expensive cable might and do have less inductance, but why bother. The bridge is already over troubled water and any improvement will not register with the ear.
Now, assuming these more realistic numbers, let's ask how far we could run a "14-2 lamp cord" before it had enough level loss at 20kHz to have even the
slightest chance of being audible by someone with excellent hearing at this
frequency extreme.
Breaking the problem into parts, let's first see what series impedance is
required to give 1 dB attenuation at 20 Khz. For a 10 Ohm load I calculate that 1.22 Ohms of series impedance is required.
Now, what inductance results in 1.22 Ohms at 20kHz.
L = Z / (2 * pi * f ) = 1.22 / ( 2 * 3.14 * 20000 ) Henries
L = 1.22 / 125600 Henries
L = 0.00000971 Henries
L = 9.71 micro Henries
Now, what length of 14-2 cable has 9.71 micro Henries of inductance?
Since one foot of cable has 0.185 micro Henries,
Length = 9.71 / 0.185 = 52.5 feet
In other words, a speaker cable made of 14-2 zip cord would have to be about 52 feet long before someone with excellent hearing at 20kHz would have a chance of hearing any signal loss. And this is a cautious analysis!
Most of us certainly do not hear to 20kHz and my choice of 1 dB as a just
noticeable difference at this frequency is probably paranoid. I bet most of
us would not even hear the loss due to even longer runs of this cable!
Given that even 52 feet of 16-2 zip cord is very unlikely to have any audible effect due to cable inductance, I remain of the opinion that simple cable RESISTANCE is the only cable parameter that needs to be considered when specifying a speaker cable. Even then, only the longest runs of the lightest cable are likely to ever to break the threshold of audibility.
I was going to discussed skin effect issue in audio frequecy (it is already written), but seeing how long (and technical) the inductor issue got, I will stop here as to not making it too over welming. lets see if we can get thru this inductance issue in one piece (I know Jon is on his way), and I will post the skin effct of zip cord probably next week :) |
| Oh no no again i can see it now can you jon lol n-t | pinetop
May 7, 2002 12:41 PM | | |
| Oh yes. Get ready for another "wire" war :) | Mr Mono
May 7, 2002 1:43 PM | | I just hope it don't get messy like last time :) |
| No zip cord for this war maybe a zip gun lol n-t | pinetop
May 7, 2002 3:20 PM | | |
| You have the right idea | Norm Strong
May 7, 2002 9:00 PM | | But your calculations are off. Remember that inductive reactance is a quadrature component, and makes for a much lower effect at small phase angles.
Also, note that inductance is not frequency dependent. What you are terming inductance in the first part of your paper is actually inductive reactance.
But you've got the right idea. Figure it out; don't guess. |
| Thanks for correction Norm. | Mr Mono
May 8, 2002 12:11 PM | | You are right. Inductance reactance is what I meant, denoted by "Z".
By the way, what is quadrature component?? I have never heard of it :) |
| Consider this.. | Spott
May 8, 2002 6:18 AM | | If a tree falls in the woods, and no one hears it because of a 53 foot run of zip cord, does it still make a sound?
Sorry, couldn't help myself:) |
| Mr Mono it still looks like a set up for jon | pinetop
May 8, 2002 2:45 AM | | do you think he will take the bait? If he does harpoon the bastard good luck. bob d |
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