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IEEE Transactions on Applied Superconductivity

The Relationship Between Bit-Error Rate, Operating Speed and Circuit Scale of SFQ Circuits

Hirotaka Terai, Y. Hashimoto, Shinichi Yorozu, Akira Fujimaki, Nobuyuki Yoshikawa, Ziji Wang

Published Jun 1, 2005• 12 citations
Publisher

Abstract

Timing jitter is an important constraint for the performance of SFQ circuits. We focus on the timing jitter in a Josephson transmission line (JTL) that induces timing errors at logic gates. A proper data analysis of 2-bit shift registers gave a jitter value of about 0.08 ps for a single Josephson junction in a JTL powered at a designed bias current. The variations in timing parameters of logic cells also give rise to timing errors. We experimentally determined the timing parameters in several logic cells and found that the deviations between actual and nominal values are within 2 ps. The relationship between the gray zone and circuit scale was estimated by extrapolating the transition curves observed in 2-bit shift registers. The estimated circuit scale was 20,000-100,000 JJs and 1,000 JJs at an operating clock frequency of 20 GHz and 40 GHz, respectively.

DOI
10.1109/tasc.2005.849851

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IEEE Transactions on Applied Superconductivity•Dec 13, 2012•5 citations
Timing jitter is an important constraint for the performance of SFQ circuits. We focus on the timing jitter in a Josephson transmission line (JTL) that induces timing errors at logic gates. A proper data analysis of 2-bit shift registers gave a jitter value of about 0.08 ps for a single Josephson junction in a JTL powered at a designed bias current. The variations in timing parameters of logic cells also give rise to timing errors. We experimentally determined the timing parameters in several logic cells and found that the deviations between actual and nominal values are within 2 ps. The relationship between the gray zone and circuit scale was estimated by extrapolating the transition curves observed in 2-bit shift registers. The estimated circuit scale was 20,000-100,000 JJs and 1,000 JJs at an operating clock frequency of 20 GHz and 40 GHz, respectively.
Timing jitter is an important factor in determining the limit of speed and scale of single-flux-quantum circuits. We estimated the timing jitter by a simple method using 2-bit shift registers. It was estimated by observing the transition between 1- and 2-mode operations while changing the bias current to the clock line. A sharp transition was observed in the shift register with a smaller number of Josephson junctions in the clock and data lines, suggesting the existence of a finite timing jitter. The timing jitter per Josephson junction was estimated to be 0.09 ps at a designed bias current. The temperature dependence supported that the timing jitter comes from thermal fluctuation.
In single-flux-quantum (SFQ) circuits, the delay produced by the Josephson transmission line (JTL) is comparable with or larger than the one produced by the logic cells. Therefore, it is difficult to find the routes that satisfy the timing constraints in a large circuit manually. To overcome this obstacle, we propose a two-step automatic JTL routing technology that performs coarse and fine timing adjustments. First, an automatic router draws dummy wires within coarse timing constraints, and then the dummy wires are replaced with JTL cells. Fine timing adjustments are done in the latter step. Some JTL cells in clock and data paths are replaced with faster JTL cells so that clock signals always arrive earlier than data signals at clocked-gates. Two example circuits were designed using the automatic JTL routing technology. One is composed of nearly 600 Josephson junctions. It was experimentally tested up to 35 GHz with on-chip test components. The other is composed of about 4000 Josephson junctions. After the fine timing adjustment, logic simulation showed that it can operate at 20 GHz. We also experimentally confirmed its correct operations at low speed.
Rapid Single Flux Quantum (RSFQ) logic is well-known for its ultra-high switching speed and extremely low power consumption. In this paper, we present two original experiments to demonstrate that it's also a reliable technology and its reliability is sufficient even for such a large-scale system as a proposed petaflops-scale HTMT computer. We have measured the bit error rate (BER) for a circular register of inverters representing a critical path of a 64-bit integer adder, and timing jitter in a 200 Josephson junction (JJ) long transmission line, imitating a branch of a clock distribution tree, both being important and representative building blocks of the HTMT computer. For the adder critical path we have demonstrated the highest clock frequency of 17 GHz, latency of 860 ps and BER of 10/sup -19/ for 3.5 /spl mu/m technology of HYPRES, Inc. The value of timing jitter was 200 fs per JJ for 1.5 /spl mu/m technology of TRW, Inc. These figures are in good agreement with our simulations.
We report on the timing jitter characterization of the superconducting single flux quantum (SFQ) coincidence circuit, which is an essential component of the superconducting coincidence photon counter. Two superconducting nanowire single photon detectors (SSPDs), each of which is irradiated with optically time-controlled photons, are connected to the SFQ coincidence circuit, and the timing jitter of the SFQ circuit is evaluated by changing the relative time delay between two input ports for the SFQ comparator unit. We successfully observe the transition curve of the probability of obtaining the signal from the SFQ coincidence circuit by sweeping photon arrival time to each SSPD and confirm that this curve shifts temporally upon changing the bias current to the Josephson transmission line (JTL) in the SFQ circuit. A systematic investigation reveals that the relation between time delay and the bias current to JTL can be estimated. The full width half maximum timing jitter of the SFQ circuit is 1.1 ps, which is sufficiently low so that it does not influence the entire timing jitter of the coincidence photon counter.
Superconductive single flux quantum (SFQ) digital circuits can operate at a clock frequency of several tens of gigahertz. However, the operating margin of these circuits decreases with an increase in the operating frequency because a timing error occurs in the low bias region. In this study, a novel design method that enables a wide operating margin at a high operating frequency has been investigated. The proposed circuits incorporate an additional bias feeding line in addition to the conventional bias feeding lines of the conventional Josephson transmission lines (JTLs) and can control the dependence of signal propagation time on the bias voltage. We have shown experimentally that in our proposed JTLs, the signal propagation time becomes more sensitive to the bias voltage. Timing errors can be avoided by inserting proposed JTL cells in the critical data path of the SFQ digital circuits. Circuit simulation results indicate that the operating margin of a bit-serial SFQ full adder, designed assuming the 2.5 kA/cm2Nb process, can be improved by 15% compared with the conventional design at a frequency of 20 GHz by employing our novel design method.