Hi, This is the schematic of a doorbell that is widely produced in my country. Please take a look at it and tell me your idea. As you see the supply is 220Vac and the piezo is directly connected to the mains. There is no trasnformer and the 220V is converting to a low voltage via just resistors and transistors. As far as the components get so hot, this would be so dangerous. But why the circuit is running well?