Stable adiabatic circuit using advanced series capacitors and time variation of energy dissipation

We discuss the stability of an adiabatic stepwise-charging circuit with advanced series capacitors, which is effective for the reduction of the applied voltage to each capacitor. SPICE simulation shows that this circuit is stable even if the initial voltages are lower than zero. For the analytical discussion, we derive a matrix that connects charge and voltage in the circuit and show that the matrix is a positive-definite symmetric one. Therefore, the step voltage is generated spontaneously. We also derive energy dissipation analytically using tank capacitor voltage. Using this formula and SPICE simulation, we clarify that energy dissipation decreases monotonically as a function of time and finally reaches the minimum value.