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IEEE Transactions on Applied Superconductivity

Error rate of RSFQ circuits: theory

Quentin Herr, M. J. Feldman

Published Jun 1, 1997• 27 citations
Publisher

Abstract

For the first time, the bit-error rate of an active SFQ experiment is compared to theoretical prediction. The theory of thermally induced errors is developed using the Fokker-Planck equation. The equivalent noise temperature of the experiment is found to be 11.0 K. The error rate vs. bias current follows an error function dependence and extrapolates to vanishingly small error rate at optimal bias.

DOI
10.1109/77.621786

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For the first time, the bit-error rate of an active SFQ experiment is compared to theoretical prediction. The theory of thermally induced errors is developed using the Fokker-Planck equation. The equivalent noise temperature of the experiment is found to be 11.0 K. The error rate vs. bias current follows an error function dependence and extrapolates to vanishingly small error rate at optimal bias.
A major restriction in the development of a working Rapid Single Flux Quantum (RSFQ) logic circuit with high-Tc superconductors is given by the influence of thermal noise. This gives reason to ask for a general determination of the digital bit error rate. As other approaches, our method of calculating the switching probability is based on the Fokker-Planck equation. In the past few years the bit error rates for a single Josephson junction, SQUIDs and the comparator were calculated by using this theory. We demonstrate numerical solution of the multidimensional Fokker-Planck equation to calculate bit error rates due to thermal noise for a Toggle Flip Flop circuit. In the present work, we combine thermal noise analysis with the effects of process variations in order to derive rules for designing high-Tc RSFQ logic circuits.
The influence of thermal noise gives a major restriction in the development of Rapid Single Flux Quantum (RSFQ) logic circuits with high-T/sub c/ superconductors. In the past, we have demonstrated a general way for determining the digital bit error rate and for predicting operation ranges with good noise immunity. The method is based on a single Fokker-Planck equation which includes the full system dynamics. However, the complexity of this equation increases dramatically with the number of Josephson junctions. Our new approach describes a method to divide an RSFQ logic cell into several basic primitives. They can be characterized quickly in terms of switching probability for a lot of different parameters. From these analyses, look-up tables are built-up. We describe how to combine these data in order to achieve the bit-error rate for the whole cell. While saving more than 90% of computation time, the comparison with our previous results for full system analyses shows less than 4% difference. This approach provides for a powerful tool to include the influence of thermal noise into the optimization process of RSFQ logic circuits as well.
We measured the bit-error rate (BER) of an RS latch, a clocked SFQ circuit. A digital error-detection circuit was used to detect BER in the range unity to 10/sup -13/; below 10/sup -7/, the circuit was operated with a 12 GHz on-chip clock. BER was measured as a function of control current; both positive and negative control current was applied, leading to two distinct modes of error incidence. The error function curves extrapolate to 10/sup -80/ for optimal control current at a temperature of 5.5 K. Measurements were repeated over the range 3-7 K. Comparison to theoretical error-function estimates of BER indicate that the noise is strictly thermal.
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.
The problem of fluctuation-induced digital errors in a rapid single flux quantum (RSFQ) circuit has been very important issue. So in this experiment, we calculated error rate of RSFQ switch in superconductiyity ALU, The RSFQ switch should have a very low error rate in the optimal bias. We prepared two circuits Placed in parallel. One was a 10 Josephson transmission lines (JTLs) connected in series, and the other was the same circuit but with an RSFQ switch placed in the middle of the 10 JTLs. We used a splitter to feed the same input signal to the both circuits. The outputs of the two circuits were compared with an RSFQ XOR to measure the error rate of the RSFQ switch. By using a computerized bit error rate test setup, we measured the bit error rate of 2.18 when the bias to the RSFQ switch was 0.398mh that was quite off from the optimum bias of 0.6mA.