How to Build a 110 Volt to a Low Voltage Transformer

1.Determine your target voltage and current needs. This is important as it will dictate the later steps. for the sake of example, we will be assuming 110 volts in, 11 volts out at 1 ampere of current.
2.Calculate the mains current. A transformer is a device that multiplies and divides. Since we are dividing voltage, the current will be multiplied by an
equal ratio. In our example, we are dividing the current by a factor of 10 (110/11 = 10), which means that to arrive at 1 ampere, our mains current is 100 milli-amperes (Mains current x 10 = 1 ampere -> 1/10 amperes = 100 milli-amperes = mains current).
3.Determine wire gauge. You will need two gauges of wire, one for your primary, mains coil, and one for the lower voltage secondary coil. Since the secondary is at a higher current, it will be thicker than the other. Pick wire gauges that are appropriate for 1.5 to twice the rated current. We are going to go with 30 gauge for the mains wire, and 24 for the secondary coil. Note that you will also need more of the mains wire, by about the same ratio as the voltages, which in our case means we will need more than ten times the length of the 30 gauge.
4.Wind the coils. This is the meat of the project, and will require patience. You will need to wind the ferrite core with the wires twice, once for each coil. The number of loops for each coil will be following the same proportions. In our example, there will be ten times as many loops in the mains coil thanthe second ary coil. You will also want to start with a larger number of secondary turns. In our example, we will use ten turns for the secondary coil, which
implies 100 for the primary.
5.Choose more turns over fewer. Why not just do one turn for the primary, and 10 for the secondary? There are a few reasons, but the biggest are two fold: more wire is safer in the case of a short power surge, and it is easier to adjust the mains transformers. No wire is perfect, and at an exact 10 to 1 ratio, you may not get the exact voltage you need. If you went with 1 to 10 turns, then to adjust you could add or subtract a turn to the mains, with the effect of roughly 1/10 of the voltage. With a 10 to 100 ratio, a single turn can adjust by a much smaller increment, making it easier to fine tune.
6.Start with extra turns on the primary, and trim back. After winding the secondary coil, wind the primary with a few extra turns, in our case the aim should be for about 120 turns. Cut and strip the ends of the wires, and carefully attach the primary coil to mains, and using the multimeter, measure your output voltage. In our case, we measure about 9.5 volts. So we detach the voltages, take a turn or two off of the primary coil, and repeat the measurement. Once we
measure 11 volts from the secondary coil, then the transformer is made.
7.Seal the transformer and secure the coils. This step is to ensure that the coils do not become undone. Many would use cloth based or electrical based tape.
If intended for continuous and repeated usage, one could take the extra step of a resin dip, protecting the exposed ends of the coils, but using a casting
resin or rubber material to make the coils into a single, solid mass. This will not only ensure better heat distribution, but makes it extra unlikely that a
short can occur.

mains transformers

Let us discuss the fundamentals of transformers in a bit greater detail. 

Two coils are wound around a ferromagnetic core: one the primary coil and the remaining coil the secondary.  We apply alternating current to the primary coil, and it travels through the core to the secondary usually experiencing only hysteresis losses.  Then the secondary coil feels the magnetic field and if there is a load or other connection present current will flow from the primary to the secondary.

Depending on the ratio of turns in each coil the secondary voltage will be higher or lower than the primary.  When the field is applied to the other coil it becomes the primary and the other coil becomes the secondary.

If we apply a 60 HZ AC signal of 120 watts on the primary, we get 120 watts at 60 HZ AC on the secondary.  The difference is the voltage.

Using Ohm's Law: E=IR
Where:
E= EMF (measured in volts)
I= Inductance (curerent, measured in amperes)
R= Resistance (measured in Ohms)

For this discussion we will not discuss eddy currents and hysteresis.

We determine that to get 12 VAC 60 HZ from the secondary we will employ a 10:1 turns ratio.  We will form a primary coil of 100 turns of 22 gauge varnished transformer wire at the primary and 10 turns of 14 gauge varnished transformer wire at the secondary.

The thicker wire is necessary because of the higher current that will pass around it.