Resonant clocking technologies provide clock networks with improved frequency, jitter and power dissipation characteristics, however, often require novel automation routines. Resonant rotary clocking technology, for instance, entails multi-phase and nonzero clock skew operation and supports latch-based design. This paper studies the effects of multi-phase synchronization schemes on the minimum clock period for rotary-clock-synchronized circuits, which necessitate the application of clock skew scheduling and employ level-sensitive registers. In experimentation, single, dual, three- and four-phase clocking schemes generated by rotary clock synchronization are applied to a suite of level-sensitive-transformed ISCAS'89 benchmarks. Average clock period improvements of 30.3%, 24.8%, 17.7% and 12.0%, respectively, are observed on average compared to the flip-flop based, zero clock skew circuits. As the number of clock phases increases, smaller improvements are observed due to lesser overall effectiveness of the complementary effects of clock skew scheduling and time borrowing. It is shown, however, that for some circuits (23% of the benchmarks), multi-phase synchronization leads to significant performance benefits in operating frequency.
Multi-Amplitude and Multi-Phase Synchronization Phenomena in Nonlinear Large-Scaled Oscillating Cellular Neural Networks