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IEICE Transactions on Electronics

Asynchronous Single Flux Quantum OR Gate with Input-Pattern-Insensitive Output Delay

Taisei YAHATA, Nobuyuki Yoshikawa, Yuki Yamanashi

Published Apr 22, 2026• 0 citations
Publisher

Abstract

We propose an asynchronous OR gate based on the self-clocking method in single flux quantum (SFQ) circuits, which achieves output delay characteristics insensitive to input patterns. In a conventional self-clocking asynchronous OR gate, an imbalance in the number of SFQ pulses used for internal clock generation when generating an output pulse causes a significant input-pattern dependence in output delay. The proposed OR gate removes this imbalance by combining a self-clocking exclusive-OR gate and a self-clocking AND gate. We designed and evaluated the proposed OR gate assuming the use of the 10 kA/cm2 Nb fabrication process. At the standard bias voltage of 2.5 mV, the proposed OR gate exhibited no output delay difference among input patterns. The proposed OR gate has a more complex structure, leading to increased power consumption and gate area. In addition, 2N-input asynchronous OR circuits constructed using the proposed OR gate maintained stable operation as the number of logic stages increased, which could not be achieved using the conventional OR gate. By suppressing the output delay difference, the proposed OR gate enables stable operation of cascaded asynchronous OR structures with many logic stages.

DOI
10.1587/transele.2025sep0001

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We propose an asynchronous OR gate based on the self-clocking method in single flux quantum (SFQ) circuits, which achieves output delay characteristics insensitive to input patterns. In a conventional self-clocking asynchronous OR gate, an imbalance in the number of SFQ pulses used for internal clock generation when generating an output pulse causes a significant input-pattern dependence in output delay. The proposed OR gate removes this imbalance by combining a self-clocking exclusive-OR gate and a self-clocking AND gate. We designed and evaluated the proposed OR gate assuming the use of the 10 kA/cm2 Nb fabrication process. At the standard bias voltage of 2.5 mV, the proposed OR gate exhibited no output delay difference among input patterns. The proposed OR gate has a more complex structure, leading to increased power consumption and gate area. In addition, 2N-input asynchronous OR circuits constructed using the proposed OR gate maintained stable operation as the number of logic stages increased, which could not be achieved using the conventional OR gate. By suppressing the output delay difference, the proposed OR gate enables stable operation of cascaded asynchronous OR structures with many logic stages.
We propose an asynchronous single flux quantum (SFQ) logic gate composed of a conventional clocked logic gate and an input signal merger that generates a self-clock for the clocked logic gate. By using this self-clocking, we can design any 0-preserving logic gate, including exclusive OR (XOR). The proposed asynchronous SFQ logic gates have adjustable allowable input skew by varying the delay between the merger and internal clock input for the clocked logic gate. We design and evaluate the asynchronous AND, OR, and XOR gates that have an allowable input skew of approximately 8 ps assuming the use of the 10 kA/cm2Nb fabrication process using the proposed design method. We experimentally confirm the correct operation of the asynchronous SFQ XOR gate. We design a completely asynchronous 4-bit-input carry-lookahead adder (CLA) using the designed asynchronous gates. We found that the circuit area and number of Josephson junctions required to design a 4-bit-input CLA can be reduced by > 50% compared to that of the synchronous concurrent-flow 4-bit-input CLA without deterioration of the throughput.
Superconductive single flux quantum (SFQ) digital circuits can operate at a clock frequency of several tens of gigahertz. The operating margin of an SFQ logic circuit generally decreases with an increase in the operating frequency because of the timing error in the low-bias region caused by the difference in bias dependence of the signal-propagation delay between the data and clock lines. We proposed an improvement in the operating margin by controlling the dependence of the signal-propagation time on the bias voltage. In the present study, we investigated a new optimization method for an SFQ logic gate. We developed a new circuit parameter optimizer, which takes into account not only the bias margin but also the dependence of the signal-propagation delay on the bias voltage. We defined an appropriate evaluation function for the optimization. From the result of the optimization using the defined evaluation function, we designed and demonstrated an SFQ AND gate optimized using the new optimizer.
In this study, we designed and tested dynamically reconfigurable AND/OR and NAND/NOR single flux quantum (SFQ) logic gates. The measured dc bias margins at low frequency were 99%-126% and 121%-144% for AND/OR and NAND/NOR gates, respectively. The experimentally confirmed maximum operating frequencies of the AND/OR and NAND/NOR gates were 36 and 24 GHz, respectively. We investigated a circuit design method that enables the efficient design of SFQ logic circuits by using dynamically reconfigurable SFQ logic gates. The logic circuits were designed with a small number of gates using the input data pattern dependence of the Boolean function and reconfiguring the dynamically reconfigurable SFQ logic gates. As a case study, we designed and tested a bit-serial SFQ full adder using the investigated circuit design method. Compared with the conventional bit-serial SFQ full adder, the delay of the proposed full adder was reduced by 27%, assuming a clock frequency of 20 GHz. We confirmed correct operation of the adder with a low-speed test.
In this study, we designed and tested dynamically reconfigurable AND/OR and NAND/NOR single flux quantum (SFQ) logic gates. The measured dc bias margins at low frequency were 99%-126% and 121%-144% for AND/OR and NAND/NOR gates, respectively. The experimentally confirmed maximum operating frequencies of the AND/OR and NAND/NOR gates were 36 and 24 GHz, respectively. We investigated a circuit design method that enables the efficient design of SFQ logic circuits by using dynamically reconfigurable SFQ logic gates. The logic circuits were designed with a small number of gates using the input data pattern dependence of the Boolean function and reconfiguring the dynamically reconfigurable SFQ logic gates. As a case study, we designed and tested a bit-serial SFQ full adder using the investigated circuit design method. Compared with the conventional bit-serial SFQ full adder, the delay of the proposed full adder was reduced by 27%, assuming a clock frequency of 20 GHz. We confirmed correct operation of the adder with a low-speed test.
Among the major issues in modern large-scale rapid single-flux quantum (RSFQ) circuits are the complexity of the clock network, tight timing tolerances, poor applicability of existing CMOS-based design algorithms, and extremely deep pipelines, which reduce the effective clock frequency. In this article, asynchronous dynamic single-flux quantum majority gates are proposed to solve some of these problems. The proposed logic gates exhibit high bias margins and do not require significant area or a large number of Josephson junctions as compared to existing RSFQ logic gates. These gates exhibit a tradeoff among the input skew tolerance, clock frequency, and bias margins. Asynchronous logic gates greatly reduce the complexity of the clock network in large-scale RSFQ circuits, thereby alleviating certain timing issues and reducing the required bias currents. Furthermore, asynchronous logic allows existing design algorithms to utilize CMOS approaches for synthesis, verification, and testability. The adoption of majority logic in complex RSFQ circuits also reduces the pipeline depth, enabling higher clock speeds in very large scale integration RSFQ circuits.
This paper presents a basic circuit concept for pulse-driven asynchronous circuits using superconducting rapid single-flux-quantum (RSFQ) logic gates. Today's computer systems perform using a synchronous clock distributed over the whole system. The distribution of the clock signal becomes more difficult as the clock frequency increases because the wavelength of the clock signal becomes shorter than the system size. One way to solve this problem is to use asynchronous circuits in which all circuits perform their functions only under the law of cause and effect. We propose an implementation of the basic asynchronous circuit performing OR/AND logic operations between SFQ pulses. The operations are confirmed by SPICE simulation. We will show a design method for combinational circuits using the proposed basic circuits.