English: An Oudin coil, a resonant transformer circuit invented by Paul Marie Oudin in 1892, which generates high voltage, low current, high frequency AC electricity, used in the obsolete medical field of electrotherapy around the turn of the 20th century. The high voltage terminal at the top of the coil (B) was connected through a wire to a handheld electrode which produced luminous streamer arcs, which were applied to the body to treat various medical conditions. It was very similar to a Tesla coil, the only difference being that in the Oudin the output voltage was taken across both the primary and secondary windings of the coil in series, like an autotransformer.

An induction coil (not shown) provided high voltage 2 - 15 kV current to repeatedly charge the Leyden jar capacitors (L), which discharged by a spark across a spark gap in the box (S). This caused oscillating currents to flow through the heavy bottom primary winding of the Oudin coil (O), which formed a tuned circuit with the capacitors. This induced oscillating currents in the upper secondary winding, which resonated with the parasitic capacitance of the coil. The number of turns of the primary in the circuit could be adjusted by the tap (G) which changed its resonant frequency. When the primary and secondary circuits were adjusted to resonate at the same frequency very high voltage oscillations were induced in the secondary. Oudin coils could produce voltages of 250,000 to 1,000,000 volts. Instead of a single capacitor, two are used, one in each leg of the primary circuit, to completely isolate the patient from the power transformer voltage, which could be lethal.