CataM
Advanced Member level 4
- Joined
- Dec 23, 2015
- Messages
- 1,275
- Helped
- 314
- Reputation
- 628
- Reaction score
- 312
- Trophy points
- 83
- Location
- Madrid, Spain
- Activity points
- 8,409
Why would the length increase ? The length depends on the mean-length-per-turn (MLT) which is dependent on the bobbin geometry.The effective ratio is even worse due to increasing winding length on a given core.
Then your XFMR is high voltage-low currents, due to the small wire you have (to keep current density within limits) - current harmonics reduce really fast in your application. Your implementation again proves what I was saying.We have 70kHz, 2kW Tx's on ETD49 using 0.7mm solid wire in single layers with low Rac/Rdc ...
Proves what exactly?Your implementation again proves what I was saying.
It reduces proximity effect to a minimum by achieving an almost rotational symmetrical current distribution. Ordinary skin effect rules still.Keeping each layer to one layer of pri or sec and having a longer bobbin/core is well proven to give min losses for solid wire.
O.K. maybe "prove" is not the best word that describes what I was thinking.Proves what exactly?
well, yes and no, the sec wires are paralleled at the transformer terminations to give up to 50A in some apps.Then your XFMR is high voltage-low currents
Suggest reviewing the book again. It is not the "radius" you have to plug in, it is the diameter (assume h~diameter).I reviewed my theoretical electrical engineering text book about skin effect and found, that the estimation in my previous post is wrong. I took it from an apparently inappropriate estimation of the MDT calculation tool. The expectable skin effect induced Rac/Rdc for r/δ = 1.4 is about 1.1.
Of course they can not understand it unless they see the full picture. The full picture is when taking into account the current harmonics as well, like I have explained in post #1.we have had so many engineers look at our Tx running at full power and obviously low temp rise ( with solid wire ) and say - how is that possible without litz?
How is that possible with 0.7mm thickness at 70 kHz ?simple physics gives the answers - such that we can now design our Tx's with regard to Rdc only and know that the Rac will be ~ 15% higher worst case ...
As calculated in the previous post r=0.35mm, δ=0.25, cross section ratio 1.09How is that possible with 0.7mm thickness at 70 kHz ?
You can make a first order estimation assuming the current concentrated in a cylindrical layer at the surface of thickness δ. Gives an Rac/Rdc ratio of 0.35²/(0.35² - 0.1²) = 1.09
I agree with the first order estimation and hence agree with your result. But I am using the real part of Dowell expression, as explained in Optimizing the AC Resistance of Multilayer Transformer Windings with Arbitrary Current Waveforms.As calculated in the previous post r=0.35mm, δ=0.25, cross section ratio 1.09
Yes, that is the whole point. Minimize Rac via extremely minimizing Rdc so that the Rac@highest harmonic with RMS>1 is still low.Unfortunately I don't understand your "harmonics" consideration at all. The basic skin depth calculation, as e.g. above, is for fundamental wave only. If you have relevant harmonic content, things become even worse.
The downside is that as the harmonics frequency increase, the AC resistance increase because of the further reduction in skin depth.. but this is up to a certain point because the RMS current of the harmonics decrease as the frequency increase.
Can't agree. You can make a first order estimation assuming the current concentrated in a cylindrical layer at the surface of thickness δ. Gives an Rac/Rdc ratio of 0.35²/(0.35² - 0.1²) = 1.09 for the discussed case per cross section. An exact calculation needs to evaluate Bessel functions and gives a slightly different result.
I agree with the first order estimation and hence agree with your result. But I am using the real part of Dowell expression, as explained in Optimizing the AC Resistance of Multilayer Transformer Windings with Arbitrary Current Waveforms.
Equation (1) with p=1 leaves only skin effect.
"h" I was talking about in previous posts is called "d" (lowercase "d") in that article: h=d=sqrt(pi/4)*D (fig. 1) --> assume h~D.
η1 (fig 1) =1 for N=1 and w=D~h=d
Then, eq (1) reduces to this:
Rac/Rdc=h/δ*[(sinh(2*h/δ)+sin(2*h/δ)]/[(cosh(2*h/δ)-cos(2*h/δ)] <-- only skin effect accounted
Insert that expression into a calculator for D=0.75mm and δ=0.25mm and you get Rac/Rdc=2.803
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?