Multi stranded non-enamelled wire...skin effect?

[treez]

Post #15 of this...

https://www.edaboard.com/threads/waterproof-led-lighting-system-with-no-contacts.377465/

..suggests that Litz wire is best done with multiple enamelled strands, and isn't so good with just multi-stranded , non-insulated copper wire.
What are your thoughts?

 

[Easy peasy]

it is possible to get too carried away on this or any topic.

 

[The Electrician]

What you are saying is - " a strand of wire has inductance "

All copper wire has "skin effect" the tendency for the current to flow in the skin as the freq goes up - thus less area is used to carry current - thus the AC resistance is higher - all due to the way the mag fields act on the current at higher freqs, for 50Hz, it is 9cm ( approx ) - thus for a wire 30cm in dia the current density will drop to 37% at a depth of 9cm ( approx ) and proportionally smaller for higher freqs .....

I guess you got carried away when you posted this. The skin depth in copper wire at 50 Hz is 9 mm, not 9 cm.

A post describing skin effect is somewhat redundant; I think everybody on this thread knows what skin effect is.

 

[c_mitra]

In post #15 you said: "Just like a thin sheet; for the same cross section, the foil conductor has lower AC resistance." What did you mean by the term "AC resistance"?

I should have posted that within double quotes. I meant the dissipative part of the complex impedance, the real part. Some may consider that (AC resistance) I meant V/I where V and I are alternating voltages and currents (that shall give you the magnitude of the impedance). Sorry for not being clear enough. The reactive part is out of phase and is hence lossless.

The approx exponential change of the impedance (magnitude) with frequency should not be geometry dependent (as long as the wavelength is comparable or smaller than the transverse section of the conductor). Unfortunately I do not have the ready reference but I can search.

In other words, the capacitance and inductance have now become a function of frequency. But I do not know whether the effect has been calculated exactly for any other geometry (except circular).

Interesting point to note is the impedance (magnitude) starts increasing much earlier compared to the "AC resistance" in the last graph. At 10kHz the increase in the resistive component is about 10% or so but the impedance has become quite appreciable at that frequency.

 

[mtwieg]

Do you dispute the results reported by Sullivan: https://engineering.dartmouth.edu/inductor/papers/stranded.pdf
He shows an improvement in AC resistance (Figure 6 in his paper) of 3 times at 100 kHz

The paper is interesting and I don't dispute their data, but they only compare stranded vs solid wire, and don't make any comparison to actual litz wire. Which is an extremely bizarre omission, given their title suggesting that stranded wire is an alternative to litz wire. Makes it really hard to take the whole thing seriously.

Without even selecting a stranded wire having rapid twist we see that stranded wire (without individual strand insulation) gives AC resistance that is better than solid wire by a larger margin than "not even close". A stranded wire consisting of "bundles of bundles" (like Litz type 2) would be much better. In Sullivan's paper, his figure 6 shows stranded wire having AC resistance 3 times lower than equivalent solid wire at 100 kHz.

Thanks for taking the time to do this experiment! I'm betting the difference is due to the strands being loosely packed. I'm betting if you were to gradually twist the ends more and more (while keeping the wire under tension in order to get the twisting distributed along the length) during the measurement, the AC resistance would rise until it's the same as solid wire. Though strands breaking might also confound the experiment...

Not that I think having tighter twisting will affect AC resistance directly. But in practice, tighter twisting will cause the bundle to be more compact, and increase conductivity between adjacent strands, and thus behave more like solid wire.

--- Updated Jun 18, 2021 ---

I should have posted that within double quotes. I meant the dissipative part of the complex impedance, the real part. Some may consider that (AC resistance) I meant V/I where V and I are alternating voltages and currents (that shall give you the magnitude of the impedance). Sorry for not being clear enough. The reactive part is out of phase and is hence lossless.

AC resistance is a common term. Like you said, it's the real part of complex impedance at a given frequency, effectively the same as ESR. For analyzing the losses in inductors and transformers, this is usually considered separately from the imaginary impedance (which usually has a much simpler relationship to frequency).

 

[Easy peasy]

For the benefit of the electrician, oops, .9cm, not 9cm

and - brief precis of skin effect was in reponse to

I have not heard about AC resistance before

on post #38

 

[The Electrician]

I should have posted that within double quotes. I meant the dissipative part of the complex impedance, the real part. Some may consider that (AC resistance) I meant V/I where V and I are alternating voltages and currents (that shall give you the magnitude of the impedance). Sorry for not being clear enough. The reactive part is out of phase and is hence lossless.

To me the very word "resistance" implies dissipation. However, students at an elementary level of study about AC circuits are sometimes told that the opposition to the flow of current exhibited by capacitors and inductors is a "resistance" even though it's not a dissipative property. The instructor (or elementary text) does this because the student is not ready for phasors and the accompanying complex arithmetic, but they want to call it something the student already knows about that is an opposition to current flow.

People whose learning has progressed to a knowledge of complex impedance (that would be the participants of this thread) know to distinguish between "resistance" (real part of the impedance, the dissipative part) and "reactance" (imaginary part of the impedance, reactive part). Among such people the term "AC impedance" seems to be generally understood to be the real part of the impedance, which is what I mean by it, and apparently you do also.

The approx exponential change of the impedance (magnitude) with frequency should not be geometry dependent (as long as the wavelength is comparable or smaller than the transverse section of the conductor). Unfortunately I do not have the ready reference but I can search.

But the highest frequency I show in my images is 1 MHz, with a wavelength of about 300 meters, which is not at all comparable to the transverse section of the conductor, so we shouldn't expect the impedance to remain constant, should we?

In other words, the capacitance and inductance have now become a function of frequency. But I do not know whether the effect has been calculated exactly for any other geometry (except circular).

Interesting point to note is the impedance (magnitude) starts increasing much earlier compared to the "AC resistance" in the last graph. At 10kHz the increase in the resistive component is about 10% or so but the impedance has become quite appreciable at that frequency.

Also note that the dependence of AC resistance due to skin effect is proportional to SQRT(f), as the slope of the yellow curve shows.

 

[Easy peasy]

In fact a short hand way of remembering skin depth is that it = 0.066 / SQRT ( MHz ) in mm, thus for 50kHz, 0.066 / (0.05 )^0.5 = 0.295 mm.

 

[The Electrician]

The paper is interesting and I don't dispute their data, but they only compare stranded vs solid wire, and don't make any comparison to actual litz wire. Which is an extremely bizarre omission, given their title suggesting that stranded wire is an alternative to litz wire. Makes it really hard to take the whole thing seriously.

I suspect that his paper is aimed at people who have already noticed that true litz is expensive, and knew what the price was. He wanted to demonstrate an alternative; his readers could make their own comparison of prices of true litz compared to ordinary stranded wire.

Thanks for taking the time to do this experiment! I'm betting the difference is due to the strands being loosely packed. I'm betting if you were to gradually twist the ends more and more (while keeping the wire under tension in order to get the twisting distributed along the length) during the measurement, the AC resistance would rise until it's the same as solid wire. Though strands breaking might also confound the experiment...

Not that I think having tighter twisting will affect AC resistance directly. But in practice, tighter twisting will cause the bundle to be more compact, and increase conductivity between adjacent strands, and thus behave more like solid wire.

--- Updated Jun 18, 2021 ---

The strands are in the shape of what the mathematicians would call a "right circular cylinder" (very long ones, to be sure). No matter how hard you squeeze them together, the contact patch between any pair of them is of very small area. This is the point of Sullivan's squeezing the bundle in a specially built anvil. The contact resistance between strands is rather high even when you squeeze hard. I suppose if you squeezed hard enough to cause the copper to flow one could achieve a very low contact resistance. Or, if the strands had a square cross section rather than circular, squeezing the flat sides of two strands together could achieve a very low contact resistance. Failing one of those two options, squeezing very hard won't cause the bundle resistance to rise until it's the same as solid wire; that is Sullivan's finding. The final conclusion is that stranded wire without individual strand insulation is, in fact, a poor man's litz.

AC resistance is a common term. Like you said, it's the real part of complex impedance at a given frequency, effectively the same as ESR. For analyzing the losses in inductors and transformers, this is usually considered separately from the imaginary impedance (which usually has a much simpler relationship to frequency).

 

[c_mitra]

To me the very word "resistance" implies dissipation. However, students at an elementary level of study about AC circuits are sometimes told that the opposition to the flow of current exhibited by capacitors and inductors is a "resistance" even though it's not a dissipative property. The instructor (or elementary text) does this because the student is not ready for phasors and the accompanying complex arithmetic, but they want to call it something the student already knows about that is an opposition to current flow.

People whose learning has progressed to a knowledge of complex impedance (that would be the participants of this thread) know to distinguish between "resistance" (real part of the impedance, the dissipative part) and "reactance" (imaginary part of the impedance, reactive part). Among such people the term "AC impedance" seems to be generally understood to be the real part of the impedance, which is what I mean by it, and apparently you do also.

But the highest frequency I show in my images is 1 MHz, with a wavelength of about 300 meters, which is not at all comparable to the transverse section of the conductor, so we shouldn't expect the impedance to remain constant, should we?

Also note that the dependence of AC resistance due to skin effect is proportional to SQRT(f), as the slope of the yellow curve shows.

people whose learning has not progressed to a complex level often confuse:

Is AC resistance (R) same as impedance (no)
Real part of Impedance is resistance

Is AC conductance (G) reciprocal of AC resistance (no)
Real part of admittance is conductance

Impedance is defined as Z=V/I; just like Ohm's law: R=V/I; why Z is not called AC resistance? (just a matter of nomenclature)

Your graph for impedance plot terminates at 20kHz (not 1 MHz); impedance should be geometry independent of the cross section (stranded or solid)

I am not sure that the sqrt(f) dependence has been established for any other cross section except circular. If you have a source, please post. The impedance (magnitude) does not depend on the geometry of the cross section; it will be same for a circle, square or an ellipse, as long as the area is same.

 

[The Electrician]

I have taken four 30 inch long strands of 14 AWG solid magnet wire. I soldered the ends of the strands together so that I have a cable consisting of 4 strands of magnet wire in parallel. I then wrapped the whole length of the bundle with strong thread to hold the strands in close contact along their length. Here's a picture of the setup:

Next I swept this cable with the impedance analyzer:

Next I removed the thread clamping the bundle and spread out the strands so that each strand is many strand diameters away from every other, like this:

Now another sweep with the impedance analyzer:

Now superimposing the two sweeps. I had to redo the sweep with the strands held together with tape rather than wrapped with thread, so it's slightly different than the first image above, but this sweep shows the difference between the two cases--strands clamped together, strands spread apart:

See how different the impedance curves (green) and Rs curves (yellow) are due to spreading the strands. The inductance and AC resistance (Rs) are both reduced by spreading the strands.

Clearly the cross sectional area of the cable is not changed by spreading the strands, so this shows that the inductance of a cable depends on the cross sectional geometry of the cable.

 

[c_mitra]

tes

I have taken four 30 inch long strands of 14 AWG solid magnet wire. I soldered the ends of the strands together so that I have a cable consisting of 4 strands of magnet wire in parallel. I then wrapped the whole length of the bundle with strong thread to hold the strands in close contact along their length. Here's a picture of the setup:

View attachment 170269

Next I swept this cable with the impedance analyzer:

View attachment 170270

Next I removed the thread clamping the bundle and spread out the strands so that each strand is many strand diameters away from every other, like this:

View attachment 170271

Now another sweep with the impedance analyzer:

View attachment 170272

Now superimposing the two sweeps. I had to redo the sweep with the strands held together with tape rather than wrapped with thread, so it's slightly different than the first image above, but this sweep shows the difference between the two cases--strands clamped together, strands spread apart:

View attachment 170273

See how different the impedance curves (green) and Rs curves (yellow) are due to spreading the strands. The inductance and AC resistance (Rs) are both reduced by spreading the strands.

Clearly the cross sectional area of the cable is not changed by spreading the strands, so this shows that the inductance of a cable depends on the cross sectional geometry of the cable.

I am unable to figure out how the experiment was carried out. The details you have provided appear to be correct.

I would suggest that you tape the two ends of the cables, stretched straight, on a table with some adhesive tape.
The four strands in the middle part of one of the cables can be stretched out sideways and taped. The separation at the centre may be 1-2 cms but there should not be any curling (coiling to be avoided). The separation near the end may be 0.5-1.0 cm approx.

The distance between the two ends should not be different by more than 10 cm (one case it is 30cm and in the other case it may be 20-25cm)

I do not have any evidence but I suspect that the strange behavior is due to the cables not lying straight on a surface.

If you repeat the experiment, do you get the same (reproducible) values for the two cables? Is the excitation voltage less than 1V (or is that software controlled)

 

[The Electrician]

tes

I am unable to figure out how the experiment was carried out. The details you have provided appear to be correct.

I would suggest that you tape the two ends of the cables, stretched straight, on a table with some adhesive tape.
The four strands in the middle part of one of the cables can be stretched out sideways and taped. The separation at the centre may be 1-2 cms but there should not be any curling (coiling to be avoided). The separation near the end may be 0.5-1.0 cm approx.

The distance between the two ends should not be different by more than 10 cm (one case it is 30cm and in the other case it may be 20-25cm)

I do not have any evidence but I suspect that the strange behavior is due to the cables not lying straight on a surface.

If you repeat the experiment, do you get the same (reproducible) values for the two cables? Is the excitation voltage less than 1V (or is that software controlled)

What behavior do you mean by "strange behavior"?

 

[The Electrician]

What behavior do you mean by "strange behavior"?

The measurements reported in post #50 are intended to verify the statements made in points 1 and 6 here:

https://www.electrical4u.com/advantages-of-bundled-conductors

Under the heading "Advantages of Bundled Conductors" point 1 is reduction of inductance due to replacing a single solid conductor with a bundle of smaller strands, and spreading the strands apart.

Point 6 is reduction of AC resistance. Even if the solid conductor is replace with several strands, the AC resistance is not reduced when the strands are closely packed together as Easy peasy mentioned in post #31. But is the strands are spread apart the AC resistance of the overall bundle is reduced as described in point 6 of the web page, and as shown in the measurements I reported in post #50.