Hi there,
There are formulas to simplify the construction of a transformer somewhat,
as long as you know your core material characteristics.
For the kind of transformer you are talking about, it sounds like a power
transformer that will be plugged into the line. For this we can use this
well known formula to get the flux density:
B=V*10^8/(K1*4.44*N*A*f)
where
B is the flux density in gausses
V is the rms ac voltage
N is the number of turns
A is the core cross sectional area in square cm
f is the frequency in Hertz
K1 is the stacking factor (taken as 0.9 for 1x1 interleaved)
From this you can calculate the number of turns required for the primary,
knowing the Bmax for your core material type and the other things.
A square cross section is an efficient design, so make your core
cross section square by stacking as many laminations as required.
It's also a good idea to leave some margin on B, such as 90 percent.
For a really good design, go with 75 percent. Thus, for a core material
that can go up to 20000 gauss design for 15000 instead. That leaves
room for high line too.
Next you have to figure out the wire gauge for both the primary and
secondary. You can do this by looking at some wire tables and
using a guide of 500 circular mils per amp, or look up some data on
some magnetics manufacturers sites for more direct tables for this.
Once you have the primary, you can calculate the secondary turns
according to the turns ratio required, and then the gauge of the
secondary.
Once you have all this, you can then calculate the area that both primary
and secondary (plus some mylar tape between windings) will take up
in the core window area, and decide if your core is large enough. If not,
you'll have to go to a bigger core. If there is too much room left over,
you might go to a smaller core.
There is also an isolation safey issue. You have to make sure that the
windings of the secondary can never come into contact with the windings
of the primary, even in the event of a melt down. One way of doing
this is to wind the primary on 1/2 of the length of the center post of the
core, and the secondary on the other 1/2, with insulation between.
After this you would want to varnish it by dipping it into an enclosed
pool of varnish and then pumping all the air out. This gets the varnish
into all the cracks. The varnish helps to reduce noise as well as
protects the construction, and also helps with heat conduction.
After you do all this you can plug it in and try it out, or you could
purchase one that already has the output you need and use that