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Yesterday, 22:59 #21
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Re: High Freq XFMR winding optimization for DC resistance ?
Yes, I figured out FvM was referring to a single wire afterwards.
I was initially posting about "transformer windings" where it is assumed windings are wound in layers and hence only 1D H field is possible, hence Dowell expression is somehow accurate.
The strange thing is Easy Peasy's claim of 15% rise of their Rac with respect to Rdc with the claimed wire size. Obviously he is hiding some details.

Yesterday, 22:59

Yesterday, 23:37 #22
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Re: High Freq XFMR winding optimization for DC resistance ?
I get the same result:
   Updated   
He says " the sec wires are paralleled at the transformer terminations to give up to 50A in some apps."
He must be using wire larger than .7mm for the secondary, or a lot of strands of .7mm bundled. Look at my measurements showing the rise in Rac/Rdc just by winding the .7mm wire into a single close wound layer. I'll do some more measurements in a few days.
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Today, 04:56 #23
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Re: High Freq XFMR winding optimization for DC resistance ?
Also, just for completeness, if you have a resonant converter with basically sinusoidal current, then harmonics don't come into play, for square wave currents the harmonics add very little, as the first is I/3, 2nd is I/5 and so on, the I^2 R product of these and vector summation amounts to <5% extra losses ...
   Updated   
per the above, #22, what are the y axes for the 2 other plots? all the information was in my posts, just have to read more carefully ...
   Updated   
really only a good FEA look at the current distribution will tell you how a Tx is best wound for lowest skin depth losses...
   Updated   
The skin depth at 70kHz is about 0.25mm (skin depth being that depth where the current density falls to 1/e, ~36.8%), so in an interleaved Tx, we are using at least .25mm on each side of the wire, leaving a "band" of 0.70.5 = 0.2mm that looks like it may not carry much current...?
But, in a single layer winding, where does the proximity effect try to push the current density? if you can map out the magnitude of each effect and superpose them you will see why there is one ( and generally only one) optimal winding geometry that reduces AC frequency effect losses in Tx windings ( different for chokes ).
Also  now consider the square wave (current) converter, after the switching edge the current is near constant ( i.e. DC ) until the next switching edge. The current in the wire does not "know" when that next edge will be  so how are the losses due to AC effected? For a sine wave current the current is always changing at the cos(freq) rate  so the wire "knows" or "can see" the instantaneous rate of change of current and the losses due to self induced mag fields and current density displacement are right there, forcing the current to the outside and increasing wire resistance.
This is not the case for square wave current. Really what is transpiring is that the Rac is very high during the transient switching edge, when the di/dt is very high, and then this effect decays in the time afterwards, until and to when the current is static (no changing mag field, or very little), thus higher frequencies of square wave current give higher losses. To say that there is a fundamental sine wave + harmonics is not strictly correct, but it is the accepted engineering way of calculating losses (or trying to) in transformers (and other magnetics) to this day. As the results give answers that are close to real, it is accepted, and: it is very hard to measure these losses accurately  deepening the problem.
To illustrate; consider a Tx running at 100kHz, square wave current, with a large core (much larger than needed) at the end of a half cycle the fets are commanded to stay on for 50uS say, instead of switching after 5uS, as they normally would, how do you calculate the Rac in the 5uS after the last switch? do you calculate it at the 100kHz fundamental rate? or at the DC rate? or at a 10kHz rate (assuming we move to 10kHz switching, 50uS + 50uS)  you see my point?
Polite answers welcome ...
   Updated   
See also:
http://docplayer.net/47452601Qualit...spartii.html

Today, 04:56

Today, 09:47 #24
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Re: High Freq XFMR winding optimization for DC resistance ?
per the above, #22, what are the y axes for the 2 other plots?
I don't yet fully understand your point with square waves and harmonic currents. Presumed the current waveform is mainly determined by the external circuit, you calculate Rac for each harmonic component separately (due to orthogonality) and sum the losses.
Similarly, the possibly unequal current sharing in parallel windings can be calculated for each harmonic component separately.
Also, just for completeness, if you have a resonant converter with basically sinusoidal current, then harmonics don't come into play, for square wave currents the harmonics add very little, as the first is I/3, 2nd is I/5 and so on, the I^2 R product of these and vector summation amounts to <5% extra losses ...
Additionally, there will be a surcharge for the proximity effect in the top and bottom winding layers, pulling the current towards the adjacent winding. Also current asymmetry at the winding borders.
Finally current sharing between paralleled windings must be analyzed in detail. I don't see an obvious reasoning why it should be exactly equal.
   Updated   
Yes, I figured out FvM was referring to a single wire afterwards.
I was initially posting about "transformer windings" where it is assumed windings are wound in layers and hence only 1D H field is possible, hence Dowell expression is somehow accurate.

Today, 10:16 #25
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Re: High Freq XFMR winding optimization for DC resistance ?
Dear FvM, as you say, you presume. Is your calc for the harmonics based on the Rac you get in an interleaved Tx ... ? I think not.
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