Cp, Ls, R, How about D, Q, and ESR

[Mudcat]

Gene, John, and all other knowledable members of the plastic pocket protector brigade,

Aside form the obvious cable parameters such as capacitance, inductance, reactance, and resistance. How important are quality (Q), dissipation (D), and Equivelent Serial Resistance (ESR) when it comes capacitance and inductance, and how important is phase angle when it comes to AC resistance?

I am of course referring to speaker cables, and I plan on having some time this weekend to measure a bunch of "industrial", and speaker cables in my persuit of making garden hose size (for looks only, but seeking the best performance) cables cheap.

 

[gene]

Mud;

Phase Angle:
You can't measure phase angle of a speaker cable per se. In order to make a meaningful measurement here, you would need a non inductive resistive load to terminate the cable as a reference. Alternatively you can measure this paramater of just the resistor and normalize the response accordingly.

ESR:
ESR doesn't really apply to a cable. Measuring DCR and AC resistance is just fine.

Dissipation Factor:
Dissipation Factor/ Dielectric Absorption is again a non issue to consider for speaker cables. Check out an article I did on this at:

http://www.audioholics.com/techtips/audioprinciples/interconnects/CableDielectricAbsorption.html

In order to measure Dielectric Absorption, it involves some external circuitry , see:

http://www.national.com/rap/Application/0,1570,28,00.html

Again this is an issue with capacitors of some dielectrics in some applications, not speaker cables.

 

[Mudcat]

So, I take that as a no!

 

[gene]

If you are dealing with speaker cables in particular than yes its a "No". RLC are the primary factors to measure and concern yourself with here. Sheilding in very rare instances may also come into play for speaker cables.

Note that C is dependent on the conductor spacing and dielectric material so by simply measuring Cp, you confirm a good/bad conductor spacing and dielectric used. Rs will show you when skin effect really does start becoming an issue. It is always measurable but usually not audible, especially in the bandwidth in question and the humans ears that are listening.

I am sure Jneutron will come here and discuss the moons gravitational flux density affecting the tachyon emissions of the wire, and he will probably even model it for you, but I suspect he wont provide a measurement or a way to auditorally confirm it Sorry John, I had to draw first blood here

 

[Mudcat]

I'm not going to worry about tachyon emmissions since they are in the terahertz range and kill all they encounter (which would make my listening experience less enjoyable). However, the moon's gravtitational flux could be a problem here in Northern Virginia, since the moon reaches apopgee usually between 9 and 10:30 pm (depending on the time of year). Since we know the moon's mass (7.354 x 10^22 kg), and it's distance to the mean radius of the earth (384664 km), we can determine the effect on a strand of loosely twisted copper wire in my speaker cable as:


F=Gx(Mxm)/r^2

Where * is the gravitational constant 6.672 x 10^-11 Nm^2 kg^2
and F is the force exerted in newtons
M is the moon's mass
m is the mass of one meter of 38 awg copper strand (7.22 x 10^-5 kg )

We can see that the moon will pull on my strands with a force of 2.4 x 10^-9 newtons (or 5.38 x 10^-8 lbs). This is significant in that it can pull the strands out to the shielding and create a hollow tube which will attenuate the bass frequencies.

I don't even want to get into how this will change Planck's "constant" and the elementary charge of the electron.

 

[jneutron]

Note that C is dependent on the conductor spacing and dielectric material so by simply measuring Cp, you confirm a good/bad conductor spacing and dielectric used. Rs will show you when skin effect really does start becoming an issue. It is always measurable but usually not audible, especially in the bandwidth in question and the humans ears that are listening.

C_p measurement will only provide the actual capacitance, it will not tell you if the conductor spacing is good or bad, nor will it tell you if the dielectric is any good. It is only a metric.

Determination of whether it is good or not is dependent on what criteria is set. If,for example, you feel that minimum wire energy storage is wanted, then the characteristic impedance of the cable has to be the same as that of the load..this can be derived by inspection of the equations:

E_L = ¹/₂L I²
E_C = ¹/₂C V²

By simply inserting the numbers based on an 8 ohm load line, and plotting characteristic impedance vs. stored energy, it is easily seen that the storage minima coincides with the load impedance used.. Although impedance matching is typically a reflection coefficient transmission line thing, it turns out that the energy storage in the wire is indeed following the same mechanism responsible for wave propogation along a transmission line.

If I could have posted the graph I wished, that would be obvious to all..Also of note, is that for a typical 200 nH per foot parallel run, the characteristic impedance is 119.87 ohms, C_p is 13.918 pf per foot, and energy storage is 25 uJoules per foot (using a 100 watt reference at 8 ohms).

As to audibility of that level of storage, keep in mind that 100 W_RMS at 10Khz, is 200w/20,000cps, or .01 Joules per pulse, 10 millijoules, or 10,000 uJoules..a ten foot zip run stores 250 uJoules peak at this power level, or 2.5%. A half cycle 10Khz is 50 uSec, so in theory, a zip cord feeding an 8 ohm load can store the equivalent inductive energy of 1.25 uSec worth of 10Khz sine wave. (Some simplifications were used, but if you wish a rigorous determination, no problem).

Should the system impedance dip, the energy storage will be proportional to the square of the current..if it reaches 4 ohms, the current doubles, the power by a factor of 4, the time energy equiv of 5 uSec..well within human lateralization perception..again, a graph would help..

I am sure Jneutron will come here and discuss the moons gravitational flux density affecting the tachyon emissions of the wire, and he will probably even model it for you, but I suspect he wont provide a measurement or a way to auditorally confirm it Sorry John, I had to draw first blood here

Be careful what you start..unless you really want me to get technical on ya..

Cheers, John

PS..mudcat: I didn't miss the "pocket protector" statement...you will get yours, you mechanical engineer you..

 

[Mudcat]

John,

You haven't confused me yet. But just throwing out 25 ujoules per 100 watt load doesn't mean too much yet, what is the current and voltage? I mean, I can have 0.00001 amp load at 10^6 volts (100 watts) and a capacitive energy of 696 joules/foot.

You also appear to be saying that dissipation does matter. But you choose a single frequency. This release of energy could be a basis of a snake oil vendors claim to cause a cable to be bright or muddy at a lower frequency. What happens on a typical audio spectrum of pink, white, guitar cord noise?

 

[gene]

John;

Cp measurement will only provide the actual capacitance, it will not tell you if the conductor spacing is good or bad, nor will it tell you if the dielectric is any good. It is only a metric.

My point here was if you know what the conductor spacing is, you can determine the effective dielectric constant by measuring Cp and using the formulas in my chart provided by Henry Ott. The same is true if you know what the effective dielectric constant is, you can measure Cp to determine the conductor spacing.

You can further this by studying the correlation between Cp and Ls to determine conductor spacing and geometry of the cable.

As far as energy storage of a cable, I don't see it being relevent for speaker cables. Take a look at my article on Dielectric Absorption/Dissipation Factor. If you want me to plug away some stuff for you in Mathcad or PSPICE, let me know.

 

[jneutron]

You haven't confused me yet. ?

Aha...the gauntlet has struck...ohhhhhkaaaayy...I was being gentle, seeing as you were a <i>mechanical</i> engineer...but I see now you will not be so easily buried...to the next level then....hmmm..._{(the force is strong in this one)}

But just throwing out 25 ujoules per 100 watt load doesn't mean too much yet, what is the current and voltage? I mean, I can have 0.00001 amp load at 10^6 volts (100 watts) and a capacitive energy of 696 joules/foot.?

The energy is assumed to be released to the load eventually, which is 8 ohms...it's all normalized. So, the peak current is 5 amps, peak voltage is 40. And the instantaneous energy storage in the wire is 2.5% of that delivered to the load. Shifted 90 degrees, of course. Note that the inductive and capacitive storages will be 180 degrees apart..if the cable matches the load, then they are equal and opposite...hence the resistive "nature" of a transmission line..

The real unknown is how would that energy be dissipated in the load..I make the assumption that it is just simple phase shift, you know, the standard R-L thing. And if the cable impedance is below the load's, then it would be a C-R thing.

Audibility? who knows..I'll let someone else model the numbers, and run them to see if there's a time shift that falls within human capabilities..I'm content putting together another cable to test the amp to speaker differential error.

You also appear to be saying that dissipation does matter. But you choose a single frequency. This release of energy could be a basis of a snake oil vendors claim to cause a cable to be bright or muddy at a lower frequency. What happens on a typical audio spectrum of pink, white, guitar cord noise?

The frequency was chosen as an example..Audibility of 1.5 uSec L-R shifts has been demonstrated from about 1.5 Khz to 12Khz, and per pulse energies at 10Khz, in joules, is small, even though it represents 100 wrms..
I haven't seen a single wire vendor discussing this energy storage release mechanism..honestly, most of them don't have the expertise to consider it, but will find it on some guru site, then embellish the crap outta it...and all without ever trying to test for it..or even doing the simple math.

Given a 200 nH wire pair, the capacitive storage is 111 picojoules.. If one considers a capacitor model not unlike the one presented by Pease, then one is faced with a dissipative storage model, where less than roughly a picojoule is actually lost due to resistive elements...I certainly won't lose sleep over that loss..

As for music and the storage mechanism? I'm developing the test method and equipment to be able to look at that for myself..

Cheers, John

 

[Mudcat]

uuhhhhhhh
pico is 10^-12

and nano is 10^-9

and kilo is 10^3


right?

 

[jneutron]

My point here was if you know what the conductor spacing is, you can determine the effective dielectric constant .

I knew what your point was, Gene...but, don't forget....<i>you drew first blood...</i> (geeks have fun too, you know)

You can further this by studying the correlation between Cp and Ls to determine conductor spacing and geometry of the cable..

Yep.. did that already with my double braid..

As far as energy storage of a cable, I don't see it being relevent for speaker cables. Take a look at my article on Dielectric Absorption/Dissipation Factor. If you want me to plug away some stuff for you in Mathcad or PSPICE, let me know.

You do not address capacitive or inductive energy storage in your article in any way which is relevant to human lateralization capabilities, you have addressed only human hearing bandwidth. The article also includes dielectric conductance, a simple but for the most part, accurate portrayal of actual dielectrics, for the dissipation..which I concur is rather insignificant. The numbers I have been speaking of are only of interest w/r to low microsecond timing issues, not about frequency response..

Modelling...

OK....model a 4 ohm resistive load, with 2 uH inductance in series..use a square wave excitation, and compare it to the same load same waveform, but use 100 nH inductance..

Q: what is the delay between the load waveforms? Don't forget, humans can discern 1.5 uSec..L-R delay issues.

Cheers, John

 

[Dan Banquer]

Speaker Cable Energy Storage

"The real unknown is how would that energy be dissipated in the load..I make the assumption that it is just simple phase shift, you know, the standard R-L thing. And if the cable impedance is below the load's, then it would be a C-R thing."
Now that's what I call a real variable, given that loudspeakers are complex reactive loads, and not exactly uniform from speaker to speaker.
This appears to be one heckuva variable John.
d.b.

 

[jneutron]

uuhhhhhhh
pico is 10^-12

and nano is 10^-9

and kilo is 10^3

right?

kilo is 10³

milli is 10^-3

And micro is 10^-6

And I erred in the 111 picojoules..it was 111 nanojoules.

Cheers, John

PS...when you gonna use sub and sup?

 

[Unregistered]

"The real unknown is how would that energy be dissipated in the load..I make the assumption that it is just simple phase shift, you know, the standard R-L thing. And if the cable impedance is below the load's, then it would be a C-R thing."
Now that's what I call a real variable, given that loudspeakers are complex reactive loads, and not exactly uniform from speaker to speaker.
This appears to be one heckuva variable John.d.b.

Dan, your a master of understatement.

That's why I'll be testing with a load capable of a coupla Mhz bandwidth..

Cheers, John

 

[Mudcat]

PS...when you gonna use sub and sup?

Where are they?

I still use a slide rule and abacus. I get someone to turn my computer on in the morning. BTW, what are those B I and U and all those little lines and dots mean in this reply field?

 

[Unregistered]

Where are they?

I still use a slide rule and abacus. I get someone to turn my computer on in the morning. BTW, what are those B I and U and all those little lines and dots mean in this reply field?

What reply field???

e^t is actually e{sup}t{/sup}, replace "{" with "<"

E_L is E{sub}L{/sub}.

Makes equations easier to read, but it's murder to write them.

And I have my 9 year old do my computer stuff..But when she tries to explain it to me, I get lost..

Cheers, John

 

[Dan Banquer]

Speaker Cable Energy Storage

Hi John; You lost me when you remarked that you were testing out to 2 Mhz.
The master of undersatement:
d.b.

 

[jneutron]

Hi John; You lost me when you remarked that you were testing out to 2 Mhz.
The master of undersatement:
d.b.

I'm not interested in looking at 20Khz stuff, <i>that's just what they'd expect me to do...</i>

I'm interested in looking for transient information differences in the 1 uSec range..to do that requires a bandwidth far in excess of 20Khz, more on the 2 to 10 Mhz range, for test accuracy.

My resistive load rev "B" had inductance below .01 uH, but I couldn't measure it any lower than that. My rev "C" load, by the time I complete it, I will be able to take it out to 60Mhz, looking for any B dot error components. Once I have a phase linear load out to those high freq's, I'll be able to use it with my next wire set, to look for sub microsecond error between the amp terminals and the load terminals..if the time errors are under a microsecond, then there is nothing audible there..if errors are in the 10 plus range, further study is warranted.


Cheers, John

 

[Mudcat]

Like this

e^t

E_L

 

[Mudcat]

I think I've got it