DC magnetisation of transfromers and chokes.

The formula for woking out turns on an output transformer is

N = 22.5 x V x 10,000 / ( Afe x B x F )

where N is turns,
V is the voltage in Vrms across the winding,
10,000 is a constant for all equations,
Afe is the core area in sq. mm,
B is the flux density in Tesla,
F is the frequency.

I try to have the ac Bmax = 1.2 Tesla at 14Hz, so the bass response of
any amp is very good.

However, where you have an OPT for an SE amp there is DC in the core and
one has to limit ac Bmax to 0.6T
approximately to allow for 0.6T of dc magnetization of the core
in a transformer carrying DC through its primary.

The formulas I have give the DC flux in Tesla = 12.6 x µe x N x Idc / (
FeMl x 10,000 ),

where 12.6 is a constant, µe is the effective permeability when a gap is
installed, and is often a value
below 500, and calculated with another formula taking into account the u
max for interleaved material
and the air gap,
N is the primary turns,
Idc is in amps dc,
FeMl = iron core magnetic path length in millimetres,
10,000 is a constant for all equations.

For example, a 100mm stack of 50mm tongue E&I material with 600mA of
Idc, and 1,480 turns and µe = 184
and FeMl = 280mm has a dc field strength

= 12.6 x 184 x 1,480 x 0.6 / ( 280 x 10,000 ) = 0.73 Tesla,
so if total ac and dc flux cannot exceed 1.2T, then
I could have 0.46T max for ac Bmax.


However, if there was not a gap in the transformer, how does one
calculate the DC field strength?
Is µe just µ with ungapped material?
in my case µ is 17,000 maximum for the lams that I have when testing
with ac.

There is a case where I want to build a push-pull amp with two 1,480
turn windings
in series with balanced dc flows in each 1/2 of the transformer, in the
standard fashion.
The PP has the two windings in series, with a CT taken to the B+, and a
fully interleaved stack of
GOSS, 100 mm stack of 50 mm tongue material.

If there is a DC imbalance to the two tubes working in PP, say 6mA, then
I could have a net
dc flow from one end of 2,960 turns to the other of 6mA, so the using
the above formula,

dc Bmax = 12.6 x 17,000 x 2,960 x 0.006 / ( 280 x 10,000 ) = 1.36 Tesla



This seems a "silly result" because in many amps I have seen a dc
imbalance, or net dc flow in one direction
and seen no saturation problems.

Does anyone have a better idea how to **calculate** the dc flux density
in gapped or ungapped
laminated steel cores?

perhaps the µ for dc use varies non linearly with dc flow so that µ is
low at low dc and high with high dc,
similarly to what ac voltage produces.

Best regards,

Patrick Turner.










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