Resonant transformer for downhole electrocrushing drilling

A method, comprising:

• placing a drill bit downhole in a wellbore;
• providing electrical power from a power source at a frequency to a pulse-generating circuit electrically coupled to the drill bit, the pulse-generating circuit including:
• an input stage tank circuit electrically coupled to the power source, the input stage tank circuit configured to have a resonant frequency approximately equal to the frequency;
• a series tank circuit electromagnetically coupled to the input stage tank circuit, the series tank circuit configured to have a resonant frequency approximately equal to the frequency;
• and
• an output stage tank circuit electromagnetically coupled to the series tank circuit, the output stage tank configured to have a resonant frequency approximately equal to the frequency;
• generating an electric pulse with the pulse-generating circuit, the electric pulse stored in an output capacitor and generated by electrical resonance at the frequency;
• forming an electrical arc between a first electrode and a second electrode of the drill bit, the first electrode and the second electrode electrically coupled to the output capacitor;
• discharging the output capacitor by the electrical arc;
• fracturing a rock formation at an end of the wellbore with the electrical arc;
• and
• removing fractured rock from the end of the wellbore.