A proof-of-principle Tesla transformer circuit is introduced. The new transformer exhibits the high voltage-high power output signal of shock-excited transformers. The circuit, with specification of proper circuit element values, is capable of obtaining extreme oscillatory voltages. The primary and secondary portions of the circuit communicate solely by conduction. The destructive arcing between the primary and secondary inductors in electromagnetically coupled transformers is ubiquitous. Flashover is eliminated in the new transformer as the high-voltage inductors do not interpenetrate and so do not possess an annular volume of electric field. The inductors are remote from one another. The high voltage secondary inductor is isolated in space, except for a base feed conductor, and obtains earth by its self-capacitance to the surroundings. Governing equations, for the ideal case of no damping, are developed from first principles. Experimental, theoretical, and circuit simulator data are presented for the new transformer. Commercial high-temperature superconductors are discussed as a means to eliminate the counter-intuitive damping due to small primary inductances in both the electromagnetic-coupled and new conduction-coupled transformers.