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IEEE Transactions on Applied Superconductivity

100-GHz Single-Flux-Quantum Bit-Serial Adder Based on 10-${\rm kA/cm}^{2}$ Niobium Process

Masamitsu Tanaka, Hiroyuki Akaike, Akira Fujimaki, Yuki Yamanashi, Nobuyuki Yoshikawa, Shuichi Nagasawa, Kazuyoshi Takagi, Naofumi Takagi

Published Jan 7, 2011• 29 citations
Publisher

Abstract

This paper reports the design and test results of a single-flux-quantum (SFQ) bit-serial adder, which we designed with a target-clock frequency of 100 GHz, to investigate several techniques for producing ultra-high-speed computations using SFQ circuits. The bit-serial adder was designed based on a new cell library developed for the ISTEC Advanced Process, where the critical current density and McCumber-Stewart parameters of Josephson junctions were increased to 10 kA/cm2and 2.0, respectively, to obtain higher operating frequencies. In addition, we adopted a circuit-design technique based on state transitions excluding a feedback loop in a typical bit-serial adder, and redesigned the NOR gate with the McCumber-Stewart parameter increased to 4.0 to improve performance. As a result, we experimentally obtained a sufficient dc bias margin of ±18% from low frequencies to 60 GHz, and verified the correctness of operations up to 93 GHz. We also demonstrated that the introduction of a higher bias voltage or large inductors in series with bias resistors is effective for achieving faster operation.

DOI
10.1109/tasc.2010.2101034

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100-GHz Single-Flux-Quantum Bit-Serial Adder Based on 10-kA/cm2{\rm kA/cm}^{2}kA/cm2 Niobium Process
This paper reports the design and test results of a single-flux-quantum (SFQ) bit-serial adder, which we designed with a target-clock frequency of 100 GHz, to investigate several techniques for producing ultra-high-speed computations using SFQ circuits. The bit-serial adder was designed based on a new cell library developed for the ISTEC Advanced Process, where the critical current density and McCumber-Stewart parameters of Josephson junctions were increased to 10 kA/cm2and 2.0, respectively, to obtain higher operating frequencies. In addition, we adopted a circuit-design technique based on state transitions excluding a feedback loop in a typical bit-serial adder, and redesigned the NOR gate with the McCumber-Stewart parameter increased to 4.0 to improve performance. As a result, we experimentally obtained a sufficient dc bias margin of ±18% from low frequencies to 60 GHz, and verified the correctness of operations up to 93 GHz. We also demonstrated that the introduction of a higher bias voltage or large inductors in series with bias resistors is effective for achieving faster operation.
A single flux quantum (SFQ) logic cell library has been developed for the 10kA/cm2 Nb multi-layer fabrication process to efficiently design large-scale SFQ digital circuits. In the new cell library, the critical current density of Josephson junctions is increased from 2.5kA/cm2 to 10kA/cm2 compared to our conventional cell library, and the McCumber-Stwart parameter of each Josephson junction is increased to 2 in order to increase the circuit operation speed. More than 300 cells have been designed, including fundamental logic cells and wiring cells for passive interconnects. We have measured all cells and confirmed they stably operate with wide operating margins. On-chip high-speed test of the toggle flip-flop (TFF) cell has been performed by measuring the input and output voltages. The TFF cell at the input frequency of up to 400GHz was confirmed to operate correctly. Also, several fundamental digital circuits, a 4-bit concurrent-flow shift register and a bit-serial adder have been designed using the new cell library, and the correct operations of the circuits have been demonstrated at high clock frequencies of more than 100GHz.
We are developing a large-scale reconfigurable data-path (LSRDP) based on single-flux-quantum (SFQ) circuits to establish a fundamental technology for future high-performance computing systems. In the LSRDP, an SFQ floating-point adder (FPA) is one of the main and most complicated circuit blocks. In our previous study, we implemented an SFQ half-precision (16-bit) bit-serial FPA using the ISTEC 2.5 kA/cm2standard process, and demonstrated the correct operations at 24 GHz by on-chip high-speed tests. In this study, we designed and implemented an SFQ half-precision bit-serial FPA using a cell library for the AIST 10 kA/cm2Nb nine-metal-layer process (ADP2), and carried out on-chip high speed tests. The designed FPA contains 9661 Josephson junctions and occupies a circuit area of 12.95 mm2. Its target operation frequency is 50 GHz. We have demonstrated the correct operation of the FPA at the maximum frequency of 62 GHz although there is a functional error in the design. The measured DC bias margin ranges from 102% to 108% at 50 GHz operation. The total power consumption is measured to be 2.9 mW.
Design and Implementation of Component Circuits of an SFQ Half-Precision Floating-Point Adder Using 10-kA/cm2^{2}2 Nb Process
We have been developing a large-scale reconfigurable data-path (LSRDP) based on single-flux-quantum (SFQ) circuits to establish a fundamental technology for future high-performance computing systems. The SFQ floating-point adder (FPA) is one of the principal and most complicated circuit blocks in an LSRDP. In this study, we designed and implemented component circuits of an SFQ bit-serial half-precision FPA using the cell library for a 10-kA/cm2Nb process and performed on-chip high-speed tests. We demonstrated correct operation of the four-bit shifter for the significand at the clock frequencies of up to 76 GHz. The dependence of the measured DC bias margin on the operating frequency agrees reasonably well with the margin calculated using a digital simulation. The operation of the normalizer for the significand has been also confirmed at low speeds.
We propose an algorithm of digit-serial adders using single-flux-quantum (SFQ) circuits. The proposed digit-serial adder adapts the carry look-ahead (CLA) adder architecture to generate carry signals, which are generated from the digit-serial data and fed back internally to the following digit-serial data to increase the throughput of the calculation. We have designed and implemented a 4-bit digit-serial adder using the SRL 2.5kA/cm2 niobium standard process to demonstrate its high-speed operation. The total number of Josephson junctions is 2316. We have successfully tested full operations of the 4-bit digit-serial adder with a bias margin of ± 15% at 25GHz. Its maximum operation frequency was 30GHz.
We have designed a high-speed SFQ bit-serial carry-save adder based on the binary decision diagram (BDD). A simple bit-serial carry-save adder based on the BDD we first designed has a carry-feedback loop. Its input data frequency is limited by the propagation delay in the feedback loop. In our second adder design, we have replaced one BDD gate with a nondestructive binary switch, by which we can eliminate the carry-feedback loop. We have designed the high-speed BDD SFQ bit-serial adder using the NEC 2.5 kA cm −2 Nb standard process and the CONNECT cell library. The circuit simulation indicates that the maximum operating frequency is 38 GHz and the dc bias margin at 10 GHz is ±23%. We have confirmed its correct operation in the on-chip high-speed test. The maximum operating frequency was found to be 23.8 GHz.
Designs and test results for a single-flux-quantum (SFQ) eight-bit shift register circuit operating at frequencies above 100 GHz are described. The high-speed performance was realized by introducing a planarized 10 kA cm −2 Nb fabrication process as an advanced process and by adopting middle-damped junctions with McCumber parameters β c of 1.8–2.9 in the circuit. The middle-damped junctions were used to reduce the repulsion between SFQ pulses and to adjust the timing. The circuit was designed using a cell-based design method and was tested by constructing an on-chip test system with a ladder-type four-bit high-frequency clock generator. We confirmed its correct operations up to 120 GHz.