Timing of multi-gigahertz rapid single flux quantum digital circuits

Rapid Single Flux Quantum (RSFQ) logic is a digital circuit technology based on superconductors that has emerged as a possible alternative to advanced semiconductor technologies for large scale ultra-high speed, very low power digital applications. Timing of RSFQ circuits at frequencies of tens to hundreds of gigahertz is a challenging and still unresolved problem. Despite the many fundamental differences between RSFQ and semiconductor logic at the device and at the circuit level, timing of large scale digital circuits in both technologies is principally governed by the same rules and constraints. Therefore, RSFQ offers a new perspective on the timing of ultra-high speed digital circuits. This paper is intended as a comprehensive review of RSFQ timing, from the viewpoint of the principles, concepts, and language developed for semiconductor VLSI. It includes RSFQ clocking schemes, both synchronous and asynchronous, which have been adapted from semiconductor design methodologies as well as those developed specifically for RSFQ logic. The primary features of these synchronization schemes, including timing equations, are presented and compared. In many circuit topologies of current medium to large scale RSFQ circuits, single-phase synchronous clocking outperforms asynchronous schemes in speed, device/area overhead, and simplicity of the design procedure. Synchronous clacking of RSFQ circuits at multigigahertz frequencies requires the application of non-standard design techniques such as pipelined clocking and intentional non-zero clock skew. Even with these techniques, there exist difficulties which arise from the deleterious effects of process variations on circuit yield and performance. As a result, alternative synchronization techniques, including but not limited to asynchronous timing, should be considered for certain circuit topologies. A synchronous two-phase clocking scheme for RSFQ circuits of arbitrary complexity is introduced, which for critical circuit topologies offers advantages over previous synchronous and asynchronous schemes.