In contrast to transistor-based semiconductor circuits, there is currently no widely accepted formalised circuit theory or design methodology for superconductor RSFQ logic circuits. Experienced designers intuitively consider flux loops, nodal phase and branch currents when making design choices, but the lack of a formalised design process makes it difficult for inexperienced RSFQ circuit designers to construct a functioning logic cell without a reference. This results in new circuit designers mostly recycling templates from published circuit designs without fully understanding why the circuits function as they do. Inexperienced RSFQ circuit designers often follow an iterative process where cell parameter values are adjusted, and the cell is run through electronic simulation engines until the desired functionality is reached. We propose the development of a formalised circuit design theory for RSFQ logic from first principles using phase-based circuit analysis. The circuit is designed using DC analysis to establish the DC operating point of the circuit. Phase-based analysis and simulation are then used to verify the dynamic circuit functionality. To demonstrate this method, we discuss examples for well-known RSFQ cells. We analyse the initial operating margins of these designs and discuss design accuracy and efficiency. We also discuss how this design methodology can be used to design new circuits such as an RSFQ XNOR cell. We investigate how an inverting (NOT) cell can be combined with other logic cells to minimize cell latency.

Keywords: Circuit design, RSFQ, Superconducting integrated circuits