The output voltage excursions are double as we have the battery voltage and the EMF (electrotive force) induced at the coil added.
For example a 12V amplifier with an output transformer is similar in that respect to a 24V amplifier with anode, collector or drain resistor.
And impedance matching can be arranged by the turn ratio between the primary and secondary windings.
So we can have maximum power transfer or in other words no reflections of the electromagnetic wave. So no power coming back to the amplifier being reflected at the load.
Output transformers can be made by winding the primary and secondary on Magnetec ring cores which are Nanocrystalinne and have a tremendous inductance index. They are also excellent for microphone input transformers. Pleiades transformers use the Magnetec Nanoperm series.
Reference:
Applied Electronics - MIT Staff
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