An analytical expression for the time-dependent output voltage of the triple resonance Tesla transformer is presented. Presently there does not exist any closed-form solution for the output voltage, and the investigators must use circuit simulators to examine the transformer's performance. Such simulators are satisfactory in many regards, but they cannot furnish physical insight into the triple resonance device. A governing equation provides this needed insight and opens the way for obtaining optimal high-performance transformers. The present analysis treats the transformer as three oscillatory LC tank circuits feeding a load capacitance. The circuit is assumed to have a very high Q, which is a fundamental design practice for these pulsed power supplies. The formula is exercised using a known triple resonance circuit, and the results closely agree with the analysis of an industry standard circuit simulator.
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