Analysis of the stability of adiabatic reversible logic using the theory of normal modes in coupled oscillators

Abstract

The stability of adiabatic stepwise charging reversible logic is discussed from the viewpoint of coupled oscillators. For adiabatic logic with asymmetric tank capacitors, we derive a matrix that connects the initial voltage with the voltage change after the charge-recycle process. This matrix is the same as the mechanical oscillator matrix of a string with equally spaced beads having different mass. From the theory of normal modes in coupled oscillators, it is proved that the eigenvalue of the matrix connecting the initial voltage with the final one is less than 1, which shows that a step waveform is spontaneously generated after many charge-recycle processes.