Application note from Coilcraft discussing the wideband transformer and the autotransformer. Link here (PDF)
In the simplest sense, a transformer is two or more windings coupled by a common magnetic field. This magnetic field provides the means to pass voltages and currents from one winding (primary) to the other winding (secondary). Magnetic flux is created when an alternating current flows through a winding.
Transformer have many uses, such as isolation of DC currents, voltage and current transformations, and impedance matching. The type of signals to be transferred from the primary to secondary windings dictate the type of transformer that should be used in an application. For instance, a transformer needed to provide DC isolation between two windings carrying large amounts of currents would be designed differently from a transformer that needs to provide an impedance match to a small signal communications network. In this article, the emphasis will be on two types of signal transformers that are designed specifically for the transmission of data at low power levels with DC isolation (the wideband transformer) and those designed to be non-isolating (the auto transformer). These types of transformers are not limited to low power capabilities, but the emphasis here is for use in communication and small signal applications.