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Re: [Amps] Big transformers?

To: amps@contesting.com
Subject: Re: [Amps] Big transformers?
From: Manfred Mornhinweg <mmornhin@gmx.net>
Date: Wed, 13 Jun 2007 18:48:47 -0400
List-post: <mailto:amps@contesting.com>
Hi David!

> It would appear that HyperSil is no more than a standard grain-oriented 3% 
> Si-Fe material which is available under a variety of different names such as 
> Magnesil, Orthosil, Microsil, Supersil, etc., from a wide range of 
> suppliers.

Yes, that's right. The problem is that the guys in the store that can 
sell me transformer laminations have no idea what they are selling. From 
looking at it, it looks like a decent but not brilliant non-aligned 
silicon steel. Still, these come with losses varying from less than 
1W/kg at 1T, to more than 4W/kg! So I don't know on what to base my design.

Just in case, if any group member might be interested, here is what I 
came up with, regarding the scaling of transformers:

-------------------------------------------------------------------
An exercise on transformer scaling, by Manfred Mornhinweg
==================================

Assuming a well designed transformers, and a second transformer of the 
same materials, with linear dimensions twice the first:


Geometrical facts:
------------------

Turn length, thermal path length, increase 2-fold.
Core area, window area, dissipation surface area, increase 4-fold.
Volume, weight, cost, increase 8-fold.

Heat dissipation capability at same surface temperature increases less 
than 4-fold (typically 3.6. Radiative dissipation increases 4-fold, 
convective dissipation less than that, non-linear. Ratio between 
convective and radiative depend on temperature, color, surroundings.)


Assuming SAME flux density and SAME current density:
----------------------------------------------------

Turns per Volt decreases 4-fold.
Wire length per Volt decreases 2-fold.
Area per wire increases 16-fold.
Power increases 16-fold.
Absolute loss increases 8-fold.
Percentual loss, voltage drop, decrease 2-fold.
Dissipation per surface area increases 2-fold!
Temperature rise on surface increases nearly 2-fold.
Temperature rise inside winding increases more than 2-fold!
TRANSFORMER BURNS OUT!!!!   (unless cooling is dramatically improved)

Adjusting for safe temperature rise:
------------------------------------

To allow same temperature inside winding, power loss is limited to about 
3-fold increase. Exact value depends on thermal resistance of winding, 
radiative component of dissipation, etc.

Volumetric loss in iron and copper must decrease to 3/8! That requires 
designing for about 70% the flux density (depends on exact material and 
point on the curve), and for 9/16 (61%) the current density.

So:

Turns per Volt decreases 2.8-fold.
Wire length per Volt decreases 1.4-fold.
Area per wire increases 11.2-fold.
Power increases 6.8-fold.
Absolute loss increases 3-fold.
Percentual loss, voltage drop, decrease 2.3-fold.
Dissipation per surface area decreases slightly.
Temperature rise on surface decreases very slightly.
Temperature rise inside winding stays the same.
Bottom line: Slightly worse power per cost, but better efficiency.
-----------------------------------------------------------------

That's it. We can't linearly scale a transformer! Which means that those 
cookbook rules of always using 1 Tesla and 2 amperes per square 
millimeter are nonsense!

Manfred.

----------------------------
Visit my hobby website!
http://ludens.cl
----------------------------
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