i want to try this formula by rebotexx but im wondering where does 5.775 came from..
for me this is a simplified example...
Hello there,
That constant comes from deriving a turns/volt constant from the well
known transformer equation for max volts:
V=4.44*B*N*A*f*10^-8
where
V is the max rms voltage in volts
B is the max flux density in gauss
A is the area of the core in square centimeters
f is the frequency in Hertz
4.44 and 10^-8 are both constants.
Typical transformer material has a max flux density of 20kG, which
can change a bit with temperature, and taking into account high
line a safe design goal is to stay away from this by 25 percent, which
means 15kG is the target max flux density for a decent design, but
sometimes even a kG lower than that is used.
This is for typical transformer material that is often used for 50 and
60Hz transformer work, but the actual max kG could be lower depending
on material.
Anyway, taking that stuff into account we can come up with an
approximation by lumping several variables into one constant:
First converting square cm to square inches:
V=4.44*B*N*A*6.4516*f*10^-8
and after lumping we get:
TAPV=1/(4.44*B*6.4516*f*10^-8)
which is in units of turns*square_inches per volt.
Substituting B=15kG and f=50Hz, we get:
TAPV=4.655
which is a little less than the 5.775 quoted in your formula, so
that approximation was probably derived using a wider safety
margin with Bmax=12.2kG instead of 15kG:
TAPV=1/(4.44*B*6.4516*f*10^-8)
with B=12.2kG and f=50Hz we get:
TAPV=5.72
which is close to the quoted value.
It's not too hard to apply the original formula directly though,
so perhaps it's better to do that instead:
V=4.44*B*N*A*6.4516*f*10^-8 (with A in square inches again)
Solving for N, we get:
N=V*10^8/(4.44*B*A*6.4516*f)
which after inserting
V=220
B=12200
A=1.25*0.75
f=50
we get:
N=1343 turns.
Of course we could simplify the formula a little to this:
N=V*3.5e6/(B*A*f) (A again in square inches)
and we would get
N=1346 turns.