Recent interest in monotriode amplifier has restarted designs of
transformers allowing a continuous current thru their
windings. Exmaination of the curve B=f(H) for usual ferromagnetic
materials shows that a continuous current in windings move the mean
biasing point to the highly non linear saturation region. This
behavoir is unacceptable for an audio transformer, either because of
the induced increase of distorsion and because of decrease in dynamic
permeability, yielding an increase in the number of turns (which have
a detrimental effect on bad pass: see section above). There is thwo
solutions to that problem : one can makes a continuous current flows
thru an auxillary winding in order to neutralize the first one or one
can open an air gap in the core for reluctance sharing between iron
(staurable) and air (unsaturable). That last solution is by far the
most common and will be described now. We make the approximation that
air gap length 
is small enough so that field lines will
stay approximately parallel. Under those hypothesis, for an induction
B and a normal section S, we will have for N turns in which
flows a current I :
with l mean length of the magnetic circuit in the iron. Let us now
find the air gap length for which inductance will be maximum. Let us
denote by 
the derivative of B= f(H= with respect to
H. The dynamic inductance is then :
for a fixed induction B and a continuous current I, one have :
This last function admits a maximum with respect to ,
which allows to find optimal gap length and then the number of turns
needed. For very high permeability cores, optimal length can be so
small that they will be impossible to realize : experimenting is then
needed ...