A High-Throughput Multiply-Accumulate Unit With Long Feedback Loop Using Low-Voltage Rapid Single-Flux Quantum Circuits

Abstract

In this article, we demonstrated a high-throughput gate-level-pipelined 8-bit multiply-accumulate (MAC) unit with a long feedback loop using low-voltage rapid single-flux quantum (LV-RSFQ) logic. The long feedback loop in the MAC unit is an obstacle for high-throughput operation because the logic gates must wait for the delayed inputs from the feedback loop. The LV-RSFQ logic makes high-frequency operation even more difficult by larger and more variable feedback delay. We design the feedback loop by using counter-flow clocking and adding many D flip-flops to divide the long feedback loop into shorter paths. The target clock frequency of the MAC unit with a feedback loop was set to 30 GHz by the experimental results of the MAC unit without a feedback loop. We model the clock frequency and its circuit overhead in a feedback loop to design the feedback loop in the MAC unit achieving 30 GHz with a minimum overhead. The test chips are fabricated using the national institute of advanced industrial science and technology (AIST) 10-kA/cm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{^{2}}$</tex-math></inline-formula> Advanced Process 2. We have successfully obtained high-throughput 30-GHz operations in the LV-RSFQ MAC unit with a long feedback loop by using the model-based design. The maximum operating frequency of the MAC unit reaches 40 GHz.