Stability of adiabatic circuit using asymmetric 1D-capacitor array between the power supply and ground

The stability of a new adiabatic stepwise charging circuit with an asymmetric 1D capacitor array is discussed. SPICE simulation shows that this circuit, like the one with a symmetric array, is stable. For the analytical discussion, we derive a matrix that connects charge and voltage in the circuit with the asymmetric 1D-capacitor array and show that the matrix is the positive-definite symmetric one. Using matrix theory, it is proved that the eigen value of the matrix connecting the initial voltage deviation from the step value with that after the charge-recycling process is smaller than 1. Therefore, the voltage deviation becomes zero after many charge-recycling processes.