Here is a series of power supply without a simple transfomer.
Simple 12v power supply circuit without transformer.
To be safe when there is a short circuit series always use a fuse on the input voltage is 220v.
However for achieving a regulated dual power supply with the desired level of dual voltage at the output is something which normally requires a complex design using.
For example if the transformer secondary is rated at 12 volts then the acquired 12 volts from the transformer secondary will be a 12 volt ac across the relevant wires.
Designing a simple dual power supply actually involves a just a center tap power supply and a bridge rectifier along with a couple of high value filter capacitors as shown below.
Circuit is simple voltage dropping capacitor of 225j is connected in series with phase line of ac this is a non polarised capacitors so it can be connected.
And this series of works using capacitive reactance and resistance are not using this will reduce the heat on the circuit.
The transformer is one of the main components in a power supply circuit because we need to convert the higher voltage available in the power point into a lower voltage we needed.
Here is the circuit diagram and explanation for transformerless power supply.