How You Build A Transformerby kpp 
The core material selected dictates parameters such as core loss and magnetic saturation. For this project, we will select microsil material (aka 33XX, M6, and grain oriented silicon steel). This is a commonly selected material for power transformers since it provides relatively low losses at an affordable price. The lamination size must be determined based on the desired VA (aka VoltAmp) capacity of the design. The number of primary turns must be calculated such that the core can support the desired voltage without saturating. The secondary turns will be calculated such that the proper voltage will appear on the secondary winding of the transformer.
SPECIFY DESIGN REQUIREMENTS 
Ep=120VAC 
Es=12VAC 
Is=1A 
f=60Hz 
S=1700 (current density) 
Bmax=17000 Gauss, max flux density for microsil 
PERFORM CALCULATIONS 
Calculate VA requirement 
VA=Ep*Ip=Es*Is=(12VAC)*(1A)=12VA 
Calculate min WindowArea*CoreArea product 
min WAxCA=(VA*10^8)/(4.55*S*Bmax*freq)=(12*10^8)/(4.55*1700*17000*60)=0.152 in^4 
Select lamination 
The author happens to have 68EI3314 laminations available from previous projects and therefore will use those for this project. The manufacturer page for this lamination is here. Note that the WAxCA product of 0.167in^4 for a square stack of this lamination exceeds our minimum requirement. 
Calculate Primary Turns 
Npri=(Ep*10^8)/(4.44*freq*Bmax*Asqcm)=(120*10^8)/(4.44*60*17000*3.05*0.9)=965 turns 
Calculate Primary Wire Size (using industry accepted value of 500 cir mils/amp 
cir mils= I[Amp]*(cir mils/amp)=(VA/Ep)*(cir mils/amp)=(12/120)*500=50 cir mils 
From a wire table, like this one, one can see that 33AWG is the proper size for our primary winding. 
Calculate Secondary Turns  ignoring core loss 
Npri=(Np*Es)/Ep=(965*12)/120)=97 turns 
Calculate Secondary Wire Size (using industry accepted value of 500 cir mils/amp 
cir mils= I[Amp]*(cir mils/amp)=(Is)*(cir mils/amp)=(1)*500=500 cir mils 
From a wire table, like this one, one can see that 23AWG is the proper size for our secondary winding. 
Summary 
We will build a transformer using a square stack (0.687" stack height) of 68EI3314 with Np=965 turns 33AWG and Ns=97 turns of 23AWG. 
To create cardboard bobbin, follow these directions.
