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]

when you buy real litz from a reputable manufacturer there is a spec for how far along the "wire" it takes for a conductor to travel from the outside to the middle to the outside again, e.g. 1.5"

You can check this under a u-scope

once on a volume prod line - the losses in a 3kW converter went up by 2.5 watts at full power - this was considered an anomaly and investigated - turns out a new litz wire had been purchased for the winding dept which did not have the same "weave" per inch - simple replacement with an older type AC choke proved the investigation - the new supplier was quietly dropped and things went back to normal.

 

[c_mitra]

I actually believe that they just intend to have 60 strands "Junked" together willy nilly.....which means, according to our discussion, that
most of the inner strands wouldnt even conduct?

No of strands cannot be arbitrary; they must pack nicely so that max contact between strands is ensured with little void space.

How to optimally pack circles inside a bigger circle?

Please see https://math.ucsd.edu/~ronspubs/98_01_circles.pdf

Common number of strands are: 1, 3, 7, 19, 31 (or 37), 61 and the list goes.

Once the number 31, the strands are more or less random.

IN this packing scheme, they are not woven and individual strands are not symmetrically placed.

If you have large number of strands, it is often more efficient to make a rope (strand of strands)- i.e., three strands of 7, 7 strands of 7 etc etc.

 

[The Electrician]

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?

Post #17 of the referenced thread has this: "Yes the bus cable is 7 strands of 1mm diam copper in a sheath." You don't say whether the individual strands are insulated; are they?

This seems like Type 1 litz. With Type 1 litz the strands don't transition from inside the bundle to outside the bundle along the length of the cable. By not doing this the decrease in AC resistance that would result is lost. Type 2 litz does transition the strands and should have lower AC resistance.

Earlier in this thread the question of whether bundled wire without insulation on each individual strand can be useful even though it's not as good as true litz was dealt with.

Do an experiment; try a cable with more strands (uninsulated) of smaller diameter wire.

The experiment could be as simple as taking a meter of the cable you're using now, and a meter of another cable with more strands but the same cross sectional area and measuring their respective AC resistances with an impedance analyzer.

 

[FvM]

according to our discussion, that
most of the inner strands wouldnt even conduct

I'd rather say, according to a simplistic concept of proximity effect. Typically there's more than one turn in a winding and you need to consider all field contributions. If you look at a full winding layer, mainly the end turns show an increase of inner wire AC resistance. Average effect on the winding is smaller.

Similarly, measuring the AC resistance of an isolated litz wire isn't necessarily representative for the winding behaviour.

 

[c_mitra]

I'd rather say, according to a simplistic concept of proximity effect. Typically there's more than one turn in a winding and you need to consider all field contributions. If you look at a full winding layer, mainly the end turns show an increase of inner wire AC resistance. Average effect on the winding is smaller.

Similarly, measuring the AC resistance of an isolated litz wire isn't necessarily representative for the winding behaviour.

Actually (#24) it is not my opinion; I just quoted from (#18).

The real problem can be more complex. There is intra-strand (current crowing within the coductor) and inter-strand (proximity effect due to external magnetic field) effect. All multi-strand cables are twisted and that too has some effect (with a tight twist, each strand acts like a solenoid). When wound in the bobbin, it introduces another layer of complexity. The magnetic core will also have some effect on the distribution of the magnetic field.

The simplest solution is to experiment.

It is not possible to give specific suggestions because of the general nature of the question. Depending on the working frequency and the power level, a selection need to be made and it is quite possible that a simple 3 or 5 strand solution may be acceptable.

 

[FvM]

In case of "type 1" concentric stranded wires like the bus cable presented in post #13, there's effectively no difference in AC resistance between isolated and non-isolated wires if we look a single straight conductor, and neither to a solid wire of same cross section as the below shown AC magnetic simulation shows. I'm simulating a 7x1.2 mm respectively 1x3.2 mm conductor at 50 kHz, AC resistance is per m.

As previously mentioned, the representative is not representative for the behaviour of litz wire in a winding with multiple turns and layers.

 

[c_mitra]

In case of "type 1" concentric stranded wires like the bus cable presented in post #13, there's effectively no difference in AC resistance between isolated and non-isolated wires if we look a single straight conductor, and neither to a solid wire of same cross section as the below shown AC magnetic simulation shows. I'm simulating a 7x1.2 mm respectively 1x3.2 mm conductor at 50 kHz, AC resistance is per m.

Excellent simulations but Litz wires shall be most effective when the diameter of the individual wires is of the order of the skin depth (for copper at 50 kHz the skin depth is 0.29mm) and the equivalent solid conductor has diameter many times the skin depth.

Your results are fine because individual wires (each strand) are already too thick. Meaningful results can be seen by running the same simulation at 1 kHz (when the skin depth is about 2mm) or 5 kHz (when the skin depth is 0.9mm)

 

[mtwieg]

Wow, lots of misconceptions to correct....
1. Stranded wire is not a poor-man's litz wire, not even close. Anything claiming otherwise is doing something wrong, or maybe is characterizing things at an inappropriate frequency.
2. Yes, the fields and currents absolutely do "see" the thin insulation, even at high frequencies. The resistivity of PU and copper is different by 18 orders of magnitude.
3. Perimeter/surface area is basically irrelevant. Litz wire is effective because of its twisting scheme, and the insulation between conductors.

--- Updated Jun 16, 2021 ---

In case of "type 1" concentric stranded wires like the bus cable presented in post #13, there's effectively no difference in AC resistance between isolated and non-isolated wires if we look a single straight conductor, and neither to a solid wire of same cross section as the below shown AC magnetic simulation shows. I'm simulating a 7x1.2 mm respectively 1x3.2 mm conductor at 50 kHz, AC resistance is per m.

Just clarifying: these simulations are only meant to compare solid wire vs stranded wire (not insulation), not actual litz wire of any type, right? Because even simple type I litz wire with that cross section would show a significant improvement over non-litz wire.

 

[FvM]

Just clarifying: these simulations are only meant to compare solid wire vs stranded wire (not insulation), not actual litz wire of any type, right? Because even simple type I litz wire with that cross section would show a significant improvement over non-litz wire.

Thanks for reviewing the post. In the simulation, I'm also comparing with 7-wire "type 1" litz wire. It's the second picture showing isolated wires.

The result is surprizing at first sight, at least it was for me. But, as mentioned, the setup is not representative for a practical wiring. The trick is the strictly rotational symmetric arrangement, which would be still maintained if you twist the outer wires around the center. But the symmetry is broken if you put the strand in a winding.

 

[mtwieg]

Thanks for reviewing the post. In the simulation, I'm also comparing with 7-wire "type 1" litz wire. It's the second picture showing isolated wires.

The result is surprizing at first sight, at least it was for me. But, as mentioned, the setup is not representative for a practical wiring. The trick is the strictly rotational symmetric arrangement, which would be still maintained if you twist the outer wires around the center. But the symmetry is broken if you put the strand in a winding.

The basic premise of litz wire is that each conductor carries equal current. But it's pretty clear in your sim that the center wire carries much less than the others. Try forcing each conductor to have equal current, and the resistance should decrease.

 

[Easy peasy]

paralleled strands, even if insulated, behave the same as solid, this has been shown many times, it is only the periodic edge to centre weave of litz that forces current to flow in all parallel strands ....

 

[The Electrician]

paralleled strands, even if insulated, behave the same as solid, this has been shown many times, it is only the periodic edge to centre weave of litz that forces current to flow in all parallel strands ....

This is only true when the strands are held close together so that proximity effect is large. If the situation allows the strands to be spaced apart, there is a reduction of AC resistance compared to a solid conductor, for example: https://studyelectrical.com/2019/01/bundled-conductors.html

Obviously this can't be done for the wire used to make the transformer in a switch mode power supply.

 

[Easy peasy]

.. and since we are talking, in the main, about transformers ....

[ p.s. that link is pretty far from convincing ]

 

[The Electrician]

.. and since we are talking, in the main, about transformers ....

[ p.s. that link is pretty far from convincing ]

What are you not convinced of? Do you not believe that if several strands are separated from one another sufficiently that the proximity effect will be reduced?

FvM, would you redo your magnetic simulation for the case of the seven strands, but where the strands are all separated by several wire diameters?

 

[Easy peasy]

That link is concerned with 50/60Hz - where the skin depth is 9cm, it is more about lowering L and increasing C for a transmission line - if you care to read it thoroughly.

 

[The Electrician]

That link is concerned with 50/60Hz - where the skin depth is 9cm, it is more about lowering L and increasing C for a transmission line - if you care to read it thoroughly.

Perhaps this article will be more to your liking. See: https://www.electrical4u.com/advantages-of-bundled-conductors

Under the heading "Advantages of Bundled Conductors", point no. 6: "The ampacity i.e. the current carrying capacity of bundled conductors is much increased in comparison to single large conductor owing to reduced skin effect."

--- Updated Jun 18, 2021 ---

Wow, lots of misconceptions to correct....
1. Stranded wire is not a poor-man's litz wire, not even close. Anything claiming otherwise is doing something wrong, or maybe is characterizing things at an inappropriate frequency.

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

I made some measurements comparing AC resistance of solid magnet wire and simple stranded wire (without individual strand insulation). The stranded wire is ordinary wire used for the safety ground in house wiring. It's new so the strands are shiny copper with essentially no corrosion. It consists of 41 strands of 30 AWG, which is equivalent to 14 AWG; it has a very show twist and was not constructed in such a way as to cause each strand to spend equal time in the inside of the bundle and in the outside. The solid wire was just ordinary 14 AWG magnet wire with heavy formvar film insulation.

Here's a picture of the two wires; it shows the stranded wire stripped enough to show the strands. I didn't twist the strands after stripping so the lack of much twist can be seen.

'

Next I used an impedance analyzer to measure and display the AC resistance of the 14 AWG solid magnet wire from 100 Hz to 1 MHz. The green curve shows the magnitude of the impedance and the yellow curve is the AC resistance (Rs):

Next is the AC resistance of the stranded wire:

Here are the two sweeps superimposed:

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.

 

[Easy peasy]

Actually the stranded wire has a slight twist introduced at manufacture to help it stay together during the coating process ( when one strips the ends one tends to undo any residual twist ) - the grouped individual strands also have more total periphery - i.e. skin - than solid, this accounts for the differences.

 

[c_mitra]

Next is the AC resistance of the stranded wire:

I have not heard about AC resistance before; do you mean the real part of the complex impedance?

It is however important to note that the complex impedance (magnitude) does not change whether the cable is solid or stranded. This agrees with expectations and shows that the experiment has been performed successfully.

at 1 MHz, the real part of the impedance (resp for dissip) is approx 3 times less; at that freq even 30 AWG is too thick!

Although the imag part of the imped does not contrib to dissip, it reduces the current and causes inefficiency.

 

[Easy peasy]

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 .....

 

[The Electrician]

I have not heard about AC resistance before; do you mean the real part of the complex impedance?

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"?

It is however important to note that the complex impedance (magnitude) does not change whether the cable is solid or stranded. This agrees with expectations and shows that the experiment has been performed successfully.

Of course it changes; although it doesn't change much if the geometry of the wire doesn't change. Since the real part (AC resistance) changes, the impedance magnitude must change unless the imaginary part (reactance) just happens to change in the opposite direction so as to perfectly compensate for the change in the real part. Look at the third image in post #36. The two curves for the impedance magnitude (green) are not perfectly superimposed at the high frequency end of the green curves because the impedance magnitudes are slightly different. At the left end of the image the start of the 4 curves are perfectly superimposed (within a pixel).

at 1 MHz, the real part of the impedance (resp for dissip) is approx 3 times less; at that freq even 30 AWG is too thick!

Although the imag part of the imped does not contrib to dissip, it reduces the current and causes inefficiency.

--- Updated Jun 18, 2021 ---

Actually the stranded wire has a slight twist introduced at manufacture to help it stay together during the coating process ( when one strips the ends one tends to undo any residual twist ) - the grouped individual strands also have more total periphery - i.e. skin - than solid, this accounts for the differences.

Of course it has a slight twist. In post #36 I said "it has a very show twist and was not constructed in such a way as to cause each strand to spend equal time in the inside of the bundle and in the outside." I heated the insulation as I stripped the wire to avoid the undoing of the twist so I could get an idea of the amount of twist. See this image; you can see the slight twist where the strands exit the insulation:

--- Updated Jun 18, 2021 ---

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 .....

What or who are responding to here?