Effects of Nonsinusoidal Current Phase Relationships on Single Flux Quantum Circuits

While the relationship between current and phase in a Josephson junction is canonically assumed to be sinusoidal, both the materials of the electrodes and the properties of the barrier will influence this relationship. This current-phase relationship (C<inline-formula><tex-math notation="LaTeX">$\Phi$</tex-math></inline-formula>R) is investigated here in terms of circuit operation for simple digital circuits based on single flux quantum (SFQ) logic. It is found that changing the C<inline-formula><tex-math notation="LaTeX">$\Phi$</tex-math></inline-formula>R changes the timing of SFQ pulses, thereby changing the timing and current margins of the Josephson transmission line and T flip-flop circuits. This article motivates the investigation of C<inline-formula><tex-math notation="LaTeX">$\Phi$</tex-math></inline-formula>Rs for various junction technologies in order to correctly simulate and optimize Josephson-junction-based circuits.