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European Style Transformer Design Equations

Following are a few equations which are useful in transformer design:


Number of turns (N ) required to support a voltage (E ) at a frequency (f ) on a selected core cross section (A ) at a design flux density (B ) (for square wave change 4.0 to 4.44) is given by:




Inductance (L) of a coil of (N) turns on a core with a cross section (A), path length (lc) having a permeability (m) is given by:


Effective permeability (mg) of a core having a path length (lc ), with an air gap (lg) with a material having permeabilty (m) is given by:

(This only holds for low (<100 mT) magnetic fields)
* for high permeability materials



Magnetising force (H) for a core having a path length (lc ), with current (I) passing though a coil of (N)turns is given by:



Units:

A :
m2  
f :
Hz
L :
Henrys  
N :
Number of turns
B :
Tesla  
H :
A/m
lc :
m  
m :
Permeability
E :
Volts (rms)  
I :
Amperes (rms)
lg :
m  
m0 :
Permeability constant = 4p x 10-7 H/m