Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Models of superconducting coplanar transmission lines

Sasan Razmkhah, Pascal Febvre, Kyle Jackman, C. Fourie

Published Jul 28, 2019• 0 citations
OpenAlex

Abstract

The objective of this work is to develop compact models of PTLs to perform fast simulations of SFQ pulse propagation along PTLs. We focus here on coplanar PTLs.The first step was to find accurate analytical models that match results obtained by 2.5D and 3D numerical solvers.These models are adapted to take into account the behaviour up to THz frequencies, above the superconductor gap.

Related papers

Propagation of picosecond pulses on superconducting transmission line interconnects *

Vladimir V. Talanov, Derek Knee, David C. Harms +5 more

Abstract Interconnects are a major discriminator for superconducting digital technology, enabling energy-efficient data transfer and high-bandwidth heterogeneous integration. We report a method to simulate propagation of picosecond pulses in superconducting passive transmission lines (PTLs). A frequency-domain propagator model obtained from the Ansys high-frequency structure simulator (HFSS) field solver is incorporated in a Cadence Spectre circuit model, so that the particular PTL geometry can be simulated in the time-domain. The Mattis Bardeen complex conductivity of the superconductor is encoded in the HFSS field solver as a complex-conductivity insulator. Experimental and simulation results show that Nb 20 Ω microstrip PTLs with 200 nm interlayer dielectric thickness can support propagation of a single-flux-quantum pulse up to 7 mm and a double-flux-quantum pulse up to 28 mm.

arXiv:2104.07371•Superconductor Science and Technology•Feb 22, 2022•8 citations

Accurate Small Signal Simulation of Superconductor Interconnects in SPICE

Paul le Roux, Coenrad Johann Fourie, Sasan Razmkhah +1 more

Superconductor electronics is gaining traction as the increasing density of integration of recent and future digital circuits pushes the limits of available simulation models. Designers often make assumptions in the behavioral models of circuit elements when simulating circuits. For instance high-frequency effects have been neglected so far in the design of superconductor digital circuits, while much has been done in the past to model them. Indeed these effects had little influence on the accuracy of digital circuits simulations until recently. The increase in clock frequency, combined with longer paths between cells and higher yield requirements for large scale circuits fabrication, has led to the need of more accurate models, including in particular high frequency effects such as quasi-particle losses. To do so, this work uses a state-space model that describes the circuit under study with internal state variables and a set of first-order differential equations. We extract the state-space model while analytically enforcing the DC requirements of superconductors that are required to account for flux-trapping. The model accurately traps flux at DC, and given the model is fitted with enough poles, the high-frequency effects are also accurate relative to the reference model. The high-frequency effects have been investigated on a practical circuit: a long-distance Passive Transmission Line (PTL) designed for the high-density MIT Lincoln Labs SFQ5ee process. Results obtained in the time domain allow to observe the effects of dispersion of pulses traveling on long paths of PTLs. Indeed the energy of voltage pulses is sufficient to break Cooper pairs for the highest clock frequencies.

IEEE Transactions on Applied Superconductivity•Apr 7, 2021•2 citations

Fabrication and Characterisation of Superconducting Coplanar Waveguide Resonators for Circuit QED Applications

Martin G oppl, R. J. Schoelkopf, Andreas J. Wallraff

Bulletin of the American Physical Society•Mar 11, 2008•0 citations

Modeling of Superconducting Passive Transmission Lines

Paul le Roux, Kyle Jackman, Johannes A. Delport +1 more

Superconducting technologies are moving toward very large-scale integration (VLSI) of circuits. Passive transmission lines (PTLs) are used to quickly and efficiently propagate single flux quantum pulses between separated logic elements of these VLSI circuits. PTLs are often insufficiently modeled to correspond to reality. Therefore, the PTL needs to be thoroughly studied to determine realistic propagation characteristics. A quasi-transverse magnetic (TM) formulation is used to study superconducting passive transmission lines. The ambient temperature and changes in penetration depth with frequency are taken into account when solving the electromagnetic fields of a PTL. Per-frequency transmission line parameters are extracted from the quasi-TM field solutions. The results show a very close correlation to TetraHenry, an existing 3D solver, at significantly reduced computational cost. The results also clearly show that PTL propagation characteristics are sensitive to frequency and temperature.

IEEE Transactions on Applied Superconductivity•Mar 18, 2019•13 citations

Modeling dielectric loss in superconducting coplanar-waveguide resonators

Veikka Taka

•Dec 18, 2020•0 citations

Repeater Insertion in SFQ Interconnect

Tahereh Jabbari, Gleb Krylov, Stephen R. Whiteley +2 more

Superconductive passive transmission lines (PTL) are widely used for signal routing in large-scale rapid single flux quantum (RSFQ) circuits. Due to the imperfect matching of the transmission lines between the driver and receiver, single flux quantum (SFQ) pulses are partially reflected. The round trip propagation time of these reflections can coincide with the following SFQ pulse, resulting in a decrease in bias margins or incorrect circuit behavior. This resonant effect depends upon the length of the PTL and the clock frequency of the signal. A methodology to reduce and manage this effect is the focus of this article. A closed-form expression describing the dependence of the resonance frequency on the length of the PTL is presented. This expression describes a set of forbidden lengths for PTL interconnect segments in RSFQ circuits. The proposed methodology and algorithm insert active PTL-based repeaters into long superconductive interconnect while ensuring the length of the line segment is outside the forbidden region and increasing bias margins.

IEEE Transactions on Applied Superconductivity•Jun 9, 2020•58 citations
The objective of this work is to develop compact models of PTLs to perform fast simulations of SFQ pulse propagation along PTLs. We focus here on coplanar PTLs.The first step was to find accurate analytical models that match results obtained by 2.5D and 3D numerical solvers.These models are adapted to take into account the behaviour up to THz frequencies, above the superconductor gap.
Abstract Interconnects are a major discriminator for superconducting digital technology, enabling energy-efficient data transfer and high-bandwidth heterogeneous integration. We report a method to simulate propagation of picosecond pulses in superconducting passive transmission lines (PTLs). A frequency-domain propagator model obtained from the Ansys high-frequency structure simulator (HFSS) field solver is incorporated in a Cadence Spectre circuit model, so that the particular PTL geometry can be simulated in the time-domain. The Mattis Bardeen complex conductivity of the superconductor is encoded in the HFSS field solver as a complex-conductivity insulator. Experimental and simulation results show that Nb 20 Ω microstrip PTLs with 200 nm interlayer dielectric thickness can support propagation of a single-flux-quantum pulse up to 7 mm and a double-flux-quantum pulse up to 28 mm.
Superconductor electronics is gaining traction as the increasing density of integration of recent and future digital circuits pushes the limits of available simulation models. Designers often make assumptions in the behavioral models of circuit elements when simulating circuits. For instance high-frequency effects have been neglected so far in the design of superconductor digital circuits, while much has been done in the past to model them. Indeed these effects had little influence on the accuracy of digital circuits simulations until recently. The increase in clock frequency, combined with longer paths between cells and higher yield requirements for large scale circuits fabrication, has led to the need of more accurate models, including in particular high frequency effects such as quasi-particle losses. To do so, this work uses a state-space model that describes the circuit under study with internal state variables and a set of first-order differential equations. We extract the state-space model while analytically enforcing the DC requirements of superconductors that are required to account for flux-trapping. The model accurately traps flux at DC, and given the model is fitted with enough poles, the high-frequency effects are also accurate relative to the reference model. The high-frequency effects have been investigated on a practical circuit: a long-distance Passive Transmission Line (PTL) designed for the high-density MIT Lincoln Labs SFQ5ee process. Results obtained in the time domain allow to observe the effects of dispersion of pulses traveling on long paths of PTLs. Indeed the energy of voltage pulses is sufficient to break Cooper pairs for the highest clock frequencies.
Superconducting technologies are moving toward very large-scale integration (VLSI) of circuits. Passive transmission lines (PTLs) are used to quickly and efficiently propagate single flux quantum pulses between separated logic elements of these VLSI circuits. PTLs are often insufficiently modeled to correspond to reality. Therefore, the PTL needs to be thoroughly studied to determine realistic propagation characteristics. A quasi-transverse magnetic (TM) formulation is used to study superconducting passive transmission lines. The ambient temperature and changes in penetration depth with frequency are taken into account when solving the electromagnetic fields of a PTL. Per-frequency transmission line parameters are extracted from the quasi-TM field solutions. The results show a very close correlation to TetraHenry, an existing 3D solver, at significantly reduced computational cost. The results also clearly show that PTL propagation characteristics are sensitive to frequency and temperature.
Superconductive passive transmission lines (PTL) are widely used for signal routing in large-scale rapid single flux quantum (RSFQ) circuits. Due to the imperfect matching of the transmission lines between the driver and receiver, single flux quantum (SFQ) pulses are partially reflected. The round trip propagation time of these reflections can coincide with the following SFQ pulse, resulting in a decrease in bias margins or incorrect circuit behavior. This resonant effect depends upon the length of the PTL and the clock frequency of the signal. A methodology to reduce and manage this effect is the focus of this article. A closed-form expression describing the dependence of the resonance frequency on the length of the PTL is presented. This expression describes a set of forbidden lengths for PTL interconnect segments in RSFQ circuits. The proposed methodology and algorithm insert active PTL-based repeaters into long superconductive interconnect while ensuring the length of the line segment is outside the forbidden region and increasing bias margins.