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Flux transformers are the necessary component of all superconductor digital integrated circuits utilizing flux biasing and ac power excitation and clocking of logic cells, e.g., adiabatic quantum flux parametron (AQFP), reciprocal quantum logic (RQL), superconducting sensor arrays, qubits, etc. On average, one transformer is required per one Josephson junction. We consider limitations to the integration scale (device number density) imposed by the critical current of the ac power transmission lines (primary of the transformers) and cross-coupling between the adjacent transformers. The former sets the minimum linewidth and the mutual coupling length in the transformer, whereas the latter sets the minimum spacing between the transformers. Decreasing linewidth of superconducting (Nb) wires increases kinetic inductance of the transformer&#x0027;s secondary, decreasing its length and mutual coupling to the primary. This limits the minimum size. As a result, there is a minimum linewidth   ${{\boldsymbol{w}}}_{\mathbf{min}}\sim $  100 nm, which determines the maximum achievable scale of integration. Using AQFP circuits as an example, we calculate dependences of the AQFP number density on linewidth for various types of microstrip-based and stripline-based transformers and inductors available in the SFQ5ee fabrication process developed at MIT Lincoln Laboratory, and estimate the maximum circuit density as a few million AQFPs per cm 2 . We propose an advanced fabrication process for a 10&#x00D7; increase in the density of AQFP and other ac-powered circuits. In this process, inductors are formed from a patterned bilayer of a geometrical inductance material, Nb, deposited over a layer of high kinetic inductance material, e.g., NbN. Individual pattering of the bilayer layers allows to create stripline inductors in a wide range of inductances, from the low values typical to Nb striplines to the high values typical for NbN thin films, and preserve sufficient mutual coupling in stripline transformers with extremely low cross-talk. Energy efficiency of ac-powered circuits is limited by dielectric losses in the ac power transmissions lines. Problems of scaling associated with multiphase ac power distribution are discussed.

Scalability of Superconductor Electronics: Limitations Imposed by AC Clock and Flux Bias Transformers