The isolation transformer's theory is the as the general transformer, which is based on the electromagnetic induction theory. Isolation transformer usually refers to the 1:1 transformer. The isolation is safe for using for its secondary winding not being connected to the ground.
An isolation transformer is a transformer used to transfer electric power from a source of alternating current(AC) power to some equipment or device while isolating the powered device from the power source, usually for safety. Isolation transformers provide galvanic isolation and are used to protect against electric shock, to suppress electrical noise in sensitive devices, or to transfer power between two circuits which must not be connected together.
Suitably designed isolation transformers block interference caused by ground loops. Isolation transformers with electrostatic shields are used for power supplies for sensitive equipment such as computers or laboratory instruments.
Strictly speaking any true transformer, whether used to transfer signals or power, is isolating, as the primary and secondary are not connected by conductors but only by induction.
For isolation transformers, there is one very obvious feature. By isolating the primary from secondary circuits, ground loop and other noise problems may be reduced or eliminated from high-performance audio circuits.
In its basic form, a isolation transformer is a primary winding (inductor) wrapped around a core with a secondary winding wrapped around the same core.
When an AC signal is applied to the primary winding, the changing magnetic flux around the primary will cut through the secondary windings, inducing current in the secondary. This action allows the transfer of AC signals from the primary to the secondary circuit without a direct-current connection.
Mastering the isolation transformer theory do a lot to make correct use of it.