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The double-tuned overcoupled air transformer, commonly used in radio-frequency high-voltage supplies, is represented by an equivalent primary circuit. This circuit can be used very advantageously to develop the theory of operation of the oscillator, including the two possible operating frequencies, the necessary conditions for oscillation and maximum efficiency, and the variation of operating frequency and load resistance with primary tuning. It is shown that, at the operating frequency, the load impedance is purely resistive. The various resistances in the circuit representing the power losses and the load resistance are included in the equivalent circuit resistance, which appears as the plate load of the class-C oscillator tube. This greatly facilitates the design of a circuit to give any required power and voltage output. There are several ways in which this design problem can be approached, and the paper outlines the method which was used and found successful by the author.