Applied Physics Letters

Minimization of timing errors in reproduction of single flux quantum pulses

Anna V. Gordeeva, A. L. Pankratov

Published Jan 9, 2006• 27 citations

Abstract

We present the analysis of the mean switching time and its standard deviation of an overdamped Josephson junction, driven by a direct current and a single flux quantum (SFQ) pulse. The performed analysis allows us to find the optimal value of the bias current of the clock generator, responsible for the shape of SFQ pulse, which minimizes noise-induced switching errors.

DOI: 10.1063/1.2164389

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Noise suppression in transmission of single flux quantum signals

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We present the analysis of the mean switching time and its standard deviation of an overdamped Josephson junction, driven by a direct current and a single flux quantum (SFQ) pulse. The performed analysis allows to find the optimal value of the bias current of the clock generator, responsible for the shape of SFQ pulse, which minimizes noise-induced switching errors.

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Minimization of thermal jitter in a balanced comparator single flux quantum cell

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Applied Physics Letters

Minimization of timing errors in reproduction of single flux quantum pulses

Anna V. Gordeeva, A. L. Pankratov

Published Jan 9, 2006• 27 citations

Publisher

Abstract

DOI: 10.1063/1.2164389

Related papers

Noise suppression in transmission of single flux quantum signals

Anna V. Gordeeva, A. L. Pankratov

We present the analysis of the mean switching time and its standard deviation of an overdamped Josephson junction, driven by a direct current and a single flux quantum (SFQ) pulse. The performed analysis allows to find the optimal value of the bias current of the clock generator, responsible for the shape of SFQ pulse, which minimizes noise-induced switching errors.

arXiv:cond-mat/0509207Sep 8, 20050 citations

Minimization of thermal jitter in a balanced comparator single flux quantum cell

Anna V. Gordeeva, A. L. Pankratov

The process of reproduction of single flux quantum pulses in a Josephson junction chain composed of a pulse generator, a balanced comparator, and a single Josephson junction is investigated. It is shown that the reproduction of single flux quantum pulses in such a chain is more stable and the mean and the standard deviation of switching time are minimal for the McCumber-Stewart parameter value from 0.5 to 1 and for a normalized clock generator current around 1.5. The influence of input and output inductances on the characteristics of a balanced comparator is investigated. The recommended value of the output inductance leading to smooth pulses and relatively small jitter is around unity.The process of reproduction of single flux quantum pulses in a Josephson junction chain composed of a pulse generator, a balanced comparator, and a single Josephson junction is investigated. It is shown that the reproduction of single flux quantum pulses in such a chain is more stable and the mean and the standard deviation of switching time are minimal for the McCumber-Stewart parameter value from 0.5 to 1 and for a normalized clock generator current around 1.5. The influence of input and output inductances on the characteristics of a balanced comparator is investigated. The recommended value of the output inductance leading to smooth pulses and relatively small jitter is around unity.

Journal of Applied PhysicsMay 15, 200810 citations

Investigation of Timing Parameters in Single-Flux-Quantum Circuits Using Low Critical-Current Junctions and Low Bias Voltages

Manami Kuniyoshi, Ken Murase, Ikki Nagaoka +4 more

In this study, the trade-off among power consumptions, operating frequencies, and error rates in low-power single-flux-quantum (SFQ) circuit is investigated. The power consumption of SFQ circuits can be reduced by the lowering critical currents ( $I_{\mathrm{c}}$ values) of the Josephson junctions (JJs), or the bias voltage ( $V_{\mathrm{b}}$ ). The shifts and spreads of timing parameter fluctuations when $I_{\mathrm{c}}$ and $V_{\mathrm{b}}$ were lowered were numerically analyzed, with consideration of thermal noise at 4.2 K. The timing behaviors after $I_{\mathrm{c}}$ was lowered were relatively simple, being based on the signal-to-noise ratio, whereas those for lowered $V_{\mathrm{b}}$ values were complicated because of the dynamic behaviors of JJs driven at reduced voltage. The simulation results imply that the operating frequencies decreased because the timing windows narrowed, but the highest energy efficiency was obtained when we lowered $I_{\mathrm{c}}$ or $V_{\mathrm{b}}$ to 6.25% of their conventional values, and the energy reduction after lowering of $V_{\mathrm{b}}$ was 26% better than that after lowering of $I_{\mathrm{c}}$ . Moreover, if a small error rate (for example $10^{-6}$ ) is acceptable, further improvement in energy efficiency would be expected at significantly higher clock frequencies than would be the case if the SFQ circuit must exhibit error-free operation.In this study, the trade-off among power consumptions, operating frequencies, and error rates in low-power single-flux-quantum (SFQ) circuit is investigated. The power consumption of SFQ circuits can be reduced by the lowering critical currents ($I_{\mathrm{c}}$values) of the Josephson junctions (JJs), or the bias voltage ($V_{\mathrm{b}}$). The shifts and spreads of timing parameter fluctuations when$I_{\mathrm{c}}$and$V_{\mathrm{b}}$were lowered were numerically analyzed, with consideration of thermal noise at 4.2 K. The timing behaviors after$I_{\mathrm{c}}$was lowered were relatively simple, being based on the signal-to-noise ratio, whereas those for lowered$V_{\mathrm{b}}$values were complicated because of the dynamic behaviors of JJs driven at reduced voltage. The simulation results imply that the operating frequencies decreased because the timing windows narrowed, but the highest energy efficiency was obtained when we lowered$I_{\mathrm{c}}$or$V_{\mathrm{b}}$to 6.25% of their conventional values, and the energy reduction after lowering of$V_{\mathrm{b}}$was 26% better than that after lowering of$I_{\mathrm{c}}$. Moreover, if a small error rate (for example$10^{-6}$) is acceptable, further improvement in energy efficiency would be expected at significantly higher clock frequencies than would be the case if the SFQ circuit must exhibit error-free operation.

IEEE Transactions on Applied SuperconductivityMar 22, 20219 citations

Delayed pulses from high-transparency Josephson junctions

Songtao Xu, C.A. Mancini, M. J. Feldman

Calculations of the shape and the timing of single-magnetic-flux quanta (SFQs) generated by high-current-density “self-shunted” Josephson junctions are presented. The junction current is assumed to be due in part to multiple Andreev reflections within the high-transparency barrier. The SFQ pulses from these junctions show several differences when compared to those from lower-current-density resistively shunted Josephson junctions, the most important being that the pulses are significantly delayed in the self-shunted junctions, by as much as many times the pulse width.Calculations of the shape and the timing of single-magnetic-flux quanta (SFQs) generated by high-current-density “self-shunted” Josephson junctions are presented. The junction current is assumed to be due in part to multiple Andreev reflections within the high-transparency barrier. The SFQ pulses from these junctions show several differences when compared to those from lower-current-density resistively shunted Josephson junctions, the most important being that the pulses are significantly delayed in the self-shunted junctions, by as much as many times the pulse width.

Applied Physics LettersMay 14, 20014 citations

Noise Induced Timing Jitter: A General Restriction for High Speed RSFQ Devices

Thomas Ortlepp, Friedrich Uhlmann

All complex devices in rapid single flux quantum (RSFQ) technique work at much lower clock rates than possible for simple cells. New data driven self timed or asynchronous concepts can reduce this gap, but even in this case still a discrepancy between simulation and experiment is shown. It has been pointed out in previous studies, that the influence of thermal fluctuations in RSFQ circuits is divided into static and dynamic switching bit errors as well as timing jitter induced failures. The bit error rate depends exponentially on the temperature and is not the main issue in the low temperature technique. Our last results show for the first time, that the variance of the switching time is much slower decreased by reducing the temperature and is still important at 4.2 K. We describe a general method for calculating the switching time distribution for RSFQ cells. Furthermore, we present detailed results for a timing analysis of a dc/SFQ-converter. The delay between output signal and the input current ramp shows a variation over 1 ps which is more than 10% of the switching time itself. This new understanding of the background of timing jitter enables a goal-oriented improvement in the design process of RSFQ circuits.All complex devices in rapid single flux quantum (RSFQ) technique work at much lower clock rates than possible for simple cells. New data driven self timed or asynchronous concepts can reduce this gap, but even in this case still a discrepancy between simulation and experiment is shown. It has been pointed out in previous studies, that the influence of thermal fluctuations in RSFQ circuits is divided into static and dynamic switching bit errors as well as timing jitter induced failures. The bit error rate depends exponentially on the temperature and is not the main issue in the low temperature technique. Our last results show for the first time, that the variance of the switching time is much slower decreased by reducing the temperature and is still important at 4.2 K. We describe a general method for calculating the switching time distribution for RSFQ cells. Furthermore, we present detailed results for a timing analysis of a dc/SFQ-converter. The delay between output signal and the input current ramp shows a variation over 1 ps which is more than 10% of the switching time itself. This new understanding of the background of timing jitter enables a goal-oriented improvement in the design process of RSFQ circuits.

IEEE Transactions on Applied SuperconductivityJun 1, 200521 citations

Sub-picosecond measurement of time intervals using single flux quantum electronics

Peter A. Rosenthal

A single-flux-quantum (SFQ) pulse coincidence detector based on resistively shunted nonhysteretic Josephson junctions was designed and simulated. The coincidence detector generates an SFQ pulse when the delay between the arrival of SFQ pulses at its two inputs is less than the coincidence threshold. Simulations indicate that the minimum coincidence threshold time can be as short as 400+or-200 fs, assuming Josephson junction characteristic voltages of 1 mV, overdamped dynamics, and 4.2 K operating temperatures. Circuit architectures exploiting this gate are suggested. Estimates of the effects of thermal noise on resolution are presented, indicating the potential for various time-domain measurements with subpicosecond resolution.< >A single-flux-quantum (SFQ) pulse coincidence detector based on resistively shunted nonhysteretic Josephson junctions was designed and simulated. The coincidence detector generates an SFQ pulse when the delay between the arrival of SFQ pulses at its two inputs is less than the coincidence threshold. Simulations indicate that the minimum coincidence threshold time can be as short as 400+or-200 fs, assuming Josephson junction characteristic voltages of 1 mV, overdamped dynamics, and 4.2 K operating temperatures. Circuit architectures exploiting this gate are suggested. Estimates of the effects of thermal noise on resolution are presented, indicating the potential for various time-domain measurements with subpicosecond resolution.< >

IEEE Transactions on Applied SuperconductivityMar 1, 19934 citations

I_{\mathrm{c}}

values) of the Josephson junctions (JJs), or the bias voltage (

V_{\mathrm{b}}

). The shifts and spreads of timing parameter fluctuations when

I_{\mathrm{c}}

and

V_{\mathrm{b}}

were lowered were numerically analyzed, with consideration of thermal noise at 4.2 K. The timing behaviors after

I_{\mathrm{c}}

was lowered were relatively simple, being based on the signal-to-noise ratio, whereas those for lowered

V_{\mathrm{b}}

values were complicated because of the dynamic behaviors of JJs driven at reduced voltage. The simulation results imply that the operating frequencies decreased because the timing windows narrowed, but the highest energy efficiency was obtained when we lowered

I_{\mathrm{c}}

V_{\mathrm{b}}

to 6.25% of their conventional values, and the energy reduction after lowering of

V_{\mathrm{b}}

was 26% better than that after lowering of

I_{\mathrm{c}}

. Moreover, if a small error rate (for example

10^{-6}

) is acceptable, further improvement in energy efficiency would be expected at significantly higher clock frequencies than would be the case if the SFQ circuit must exhibit error-free operation.