Single flux quantum (SFQ) circuits are known for their low power consumption and high-speed operation [1]. One strong point of SFQ circuits is the availability of a passive transmission line (PTL) for long-distance wiring, where an SFQ pulse propagates ballistically at nearly the speed of light. Power consumption is independent of the length, making it suitable for long-distance interconnection. However, it was reported that the operating margin of SFQ circuits with long PTL interconnection deteriorated, especially for the high-critical current density Josephson process [2]. The reason is thought to be the reduction of the SFQ pulse height due to the attenuation and dissipation in the PTL. There are two main causes of attenuation. One is surface resistance due to the skin effect, and the other is due to surface irregularities and impurities. Our research aims to characterize the attenuation and dispersion of the SFQ pulse on PTL for the high-critical current density Josephson process to design high-frequency SFQ circuits.

Our study focused on the skin effect and calculated the attenuation constant of transmission lines using the two-fluid model [3] and Mattis-Bardeen theory [4]. We investigated the propagation of the SFQ pulse by calculating its frequency spectrum and taking the frequency-dependent attenuation factor into account. Based on these calculations, the dependence of the SFQ pulse height on the PTL length was derived for the Josephson processes with different critical current densities. We also experimentally investigated the attenuation characteristics of the SFQ pulse by measuring the operating margins of the SFQ circuits with PTL of different wiring lengths using the AIST Josephson process with the critical current density of 10kA/cm² and 25kA/cm².

Reference
[1] K. K. Likharev and V. K. Semenov, “RSFQ logic/memory family: a new Josephson-junction technology for sub-terahertz-clock-frequency digital systems,” IEEE Trans. Appl. Supercond., 1991.
[2] K. Takagi et al., "SFQ Propagation Properties in Passive Transmission Lines Based on a 10-Nb-Layer Structure," IEEE Trans. Appl. Supercond., vol. 19, no. 3, pp. 617-620, June 2009.
[3] Theodore Van Duzer and Charles W. Turner, “Principles of  Superconductive Devices and Circuits Second Edition,” Prentice Hall, 1998, pp.123-144.
[4] D. C. Mattis and J. Bardeen, “Theory of the Anomalous Skin Effect in Normal and Superconducting Metals,” Phys. Rev. 111, 412 (1958).

Keywords: Single Flux Quantum, Passive Transmission Line, Attenuation