Skin effect difference when wound in core and when unwound in core

[kanmaedexandzelbladex]

Hey guys, I am currently designing an inductor for a boost converter. It is to be run at 10A DC with small ripple, about 0.4A peak-to-peak. Switching frequency is at 100kHz and the chosen core is a High Flux toroid core. I have Litz wire (small cross-sectional area wires bundled together) in which the diameter of the strands that bundle up are equal to the skin depth at 100kHz. Well, the DC resistance of the wire is 20milliohms which is good but I have a problem with the AC resistance.

I am measuring my AC resistance with the use of the LCR meter using the ESR parameter along with the Ls parameter (measuring inductance with the ESR). When I have not wound my wire, in other words it's just the plain wire, the ESR is at 20 milli ohms at 100kHz but then when I have wound it to the core, the ESR measured is at 3 ohms! So, with a 0.4A peak-to-peak ripple, there will be a 1.2V AC voltage ripple added to the inductor just due to this skin effect and this might cause problems for me. I am concerned with what I can do, and if whether or not what I am measuring is accurate? I have repeated it a number of times and it seems to be the case. I thought that wire skin effect is solved by using Litz wire, the diamater chosen to match the skin depth and it did turned out good when the wire is not wound to the inductor. But when the wire was wound, it's 3 ohms so is this due to the core? Can you explain the phenomenon?

If this is not a wrong interpretation and this is really due to the core can you suggest some tips for me? I have lots of turns because I am preventing my inductor to saturate at the volt-seconds it will be experiencing and I already chose the number of turns such that when I input a pulse-wave to the inductor using a signal generator, the pulse-wave does not get distorted so I cannot reduce the number of turns. Also, the thickness of the wire itself is already chosen for the 10A. The winding has already occupied all space of my inductor, well it's a single layer winding so increasing parallel strands to reduce resistance isn't really gonna' work unless I wound the inductor in double layer.

 

[FvM]

A proper designed litz wire winding would show about no skin effect, AC resistance is almost equal to DC resistance.

I doubt that you are able to measure winding AC resistance with your inductor. ESR will be always a combination of core and winding losses.

 

[chuckey]

The 3 ohms is due to the inductance of the wire now wound around a core?. Put a second winding on and short circuit it. What you now have is the leakage inductance which is a true loss.
Frank

 

[kanmaedexandzelbladex]

Well I'm not sure if I'm doing the measurement right but this is how I did it.

I have the bundle of wire, then I attached the wire (both ends) to the LCR meter where it displays, Ls and ESR in the screen (it's labelled Ls and ESR, so it displays two measurement). Of course, the Ls would be not useful since the wire is not yet wound. The ESR reads 20 milli ohms when I switch the frequency from 50Hz to 100kHz so I'm assuming that there is no skin effect here? Then when I try to wind my core with the same wire then I measure it with the LCR meter again. The inductance Ls measures 475uH and the ESR measures 3 ohms at 100kHz but at low frequencies, 50Hz it measures to 20 milliohms.

Questions:

So I was just wondering if it is really skin effect I am witnessing here?
or some other effect that is due to the core?
or maybe I am doing the measurements in the wrong way? XD

and let's assume I try to use finer wires, larger AWG maybe and try to make my own Litz wire, does it have to have some special kind of bundling? Like twisting and all that reduces some unwanted effects? or any bundling scheme is ok?
Is using finer and finer wires better? Or are there tradeoffs that come with it? Let's say I use larger AWG for smaller diamater wires but I increase their quantity so that the ampacity of the bundle of wire is still good. I would also like to know how to choose the proper size per strand? let's say the skin depth is at 0.2mm. Should I choose a diameter that is significantly lower than that, by how much? Or is equal to that enough?

Thank you guys for your help. I am really lacking in knowledge when it comes to inductor design.

 

[FvM]

As already said, the assembled inductor shows core losses that can't be distinuished from skin effect losses. In so far an increased Rs must be expected.

The other question is, if the 3 ohm value represents real core losses or possibly a measurement error of the LCR meter. A small phase error can already cause a large Rs error when Xs is considerably higher (about 300 ohm in this case).

Single wires are usually considered fine enough if the wire radius is smaller than the skin depth but there will be still a small resistance increase. In wire strands and windings, you also observe proximity effect, at worst case the current is concentrated at one side of the wire. So it's a good idea to have the wire diameter smaller than the skin depth.

A wire "bundle" can only work as litz wire if it's sufficiently stranded, and of course the wires must be insulated against each other. Stranded magnet wire can work for this purpose.

 

[chuckey]

Xl = ~ 6 X 10^5 X .5 X 10 ^ -3 = 300, Q = Xl/R = 300/3 = 100 looks about right for ferrite losses. If you want lower loses, use a more suitable ferrite. Your skin effect on an air cored former should give you a Q of 200 - 500, depending on the number of conductors in the litz and if it was basket wound or solenoid or wave wound also on the impregnation.
Frank .

 

[FvM]

Loss factor of 0.01 doesn't sound like too much for a power inductor. I also don't understand why 3 ohm Rac causes problems with 0.4 Apeak-peak ripple current, respectively 0.14 Arms or 60 mW losses.

 

[The Electrician]

As FvM has already pointed out, you are measuring core loss as well as losses due to skin effect. It is a fact that as soon as you wind a length of wire into a coil, you get more losses due to proximity effect; that is what you should be concerned about. See:

https://en.wikipedia.org/wiki/Proximity_effect_(electromagnetism)

Professor Sullivan at Dartmouth has a lot of papers concerning the design of low loss inductors:

https://engineering.dartmouth.edu/inductor/bytopic.shtml#fringing

If you really want to know what only the wire losses in your inductor are, you could make yourself a wooden or plastic toroid the same dimensions as your High Flux core, wind it with the wire and measure the AC resistance. The wire losses on the plastic toroid will be slightly different due to the somewhat different magnetic field configuration in the absence of a magnetic core, but the difference is not great. But, it is not possible to measure the wire losses alone when the wire is wound on the High Flux core.

 

[kanmaedexandzelbladex]

Well, I am not yet sure if it will cause problems since I am a beginner and my boost converter design I assumed my Rac to be small. I'm not sure what happens if there is a ripple voltage across the inductor which is around 1Vpp due to Rac. It may still work but the waveforms might get ugly and all. Well I have lots of time anyway so I just wanted to optimize my inductor but thanks for pointing it out. It does sound like it isn't going to have big problems since my boost converter is at 90W. XD