It works by using a high voltage capacitor to drop the mains ac current to the required lower level which may be suitable for the connected electronic circuit or load.
Simple 12v power supply circuit without transformer.
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.
Here is a series of power supply without a simple transfomer.
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.
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.
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.
To be safe when there is a short circuit series always use a fuse on the input voltage is 220v.
We can convert the high voltage ac into low voltage such as 5v 6v 9v 12v dc without using the transformer which is called transformerless power supply.
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.