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IEEE Transactions on Applied Superconductivity

Implementation of phase-mode arithmetic elements for parallel signal processing

Takeshi Onomi, Y. Horima, M. Kobori, I. Shimizu, K. Nakajima

Published Jun 1, 2003• 3 citations
Publisher

Abstract

We report the preliminary designs and the experimental results of high-speed digital processing elements based on phase-mode logic circuits. The core cell of these elements is a bit-serial adder cell consisting of the ICF gate which is the basic gate of phase-mode logic. Our main target is the application of the logic circuits to Digital Signal Processing. The basic arithmetic operations of DSP are a multiplication and an addition. Basic concept of the phase-mode pipelined parallel multiplier has been proposed previously. We design a 2 /spl times/ 2 AND array block and a 2-bit ripple-carry adder for the primitive parallel pipelined multiplier and also a 2-bit subtractor with a pipelined structure. These processing elements have been fabricated using NEC standard 2.5 kA/cm/sup 2/ Nb/AlOx/Nb process. The low-speed test results of these elements show correct operations. Numerical simulations show that a carry save adder (a 2-bit ripple carry adder) can operate over 10 GHz. We also discuss the prospects of large-scale SFQ DSP based on Nb junction technology.

DOI
10.1109/tasc.2003.813952

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We report the preliminary designs and the experimental results of high-speed digital processing elements based on phase-mode logic circuits. The core cell of these elements is a bit-serial adder cell consisting of the ICF gate which is the basic gate of phase-mode logic. Our main target is the application of the logic circuits to Digital Signal Processing. The basic arithmetic operations of DSP are a multiplication and an addition. Basic concept of the phase-mode pipelined parallel multiplier has been proposed previously. We design a 2 /spl times/ 2 AND array block and a 2-bit ripple-carry adder for the primitive parallel pipelined multiplier and also a 2-bit subtractor with a pipelined structure. These processing elements have been fabricated using NEC standard 2.5 kA/cm/sup 2/ Nb/AlOx/Nb process. The low-speed test results of these elements show correct operations. Numerical simulations show that a carry save adder (a 2-bit ripple carry adder) can operate over 10 GHz. We also discuss the prospects of large-scale SFQ DSP based on Nb junction technology.
Abstract: We have developed and experimentally evaluated at high-speed, a complete set of arithmetic circuits (multiply, add, and accumulate) for high performance digital signal processing (DSP). These circuits take advantage of the unique features of the Rapid Single-Flux Quantum (RSFQ) logic/memory family, including fusion of logic and memory functions at the gate level, pulse representation of clock and data, and the ability to maintain inter cell propagation delays using Josephson transmission lines (JTLs). The circuits developed have been successfully used in the implementation of a serial radix 2 butterfly, a decimation digital filter, and of an arithmetic unit for digital beam forming. The 8×8-bit RSFQ multiplier uses a two- level parallel carry- save reduction tree that significantly reduces the multiplier latency. The 80-GHz carry-save reduction is implemented with asynchronous data-driven wave pipelined [4:2] compressors built with toggle flip-flop cells.
We have designed an SFQ pipeline multiplier using a cell-based design method. The cell-based design method enables us to expand the circuit-scale easily and is essential for the design of large-scale circuits. In the construction of the multiplier, a serial-parallel type was adopted. This type performs the partial products and the summation of the products in a bit-serial form. The multiplier designed here is a 3-bit serial-parallel structure with a seven-stage pipeline and is composed of destructive read-out (DRO) gates, nondestructive read-out (NDRO) gates and carry save serial adders (CSSA's). This circuit was fabricated by the NEC standard process. The number of Josephson Junctions is 1150. We have successfully tested the full operation with a bias margin of /spl plusmn/5.5%.
We have designed a Rapid Single-Flux-Quantum (RSFQ) bit-serial real-time pipeline multiplier for digital signal processing (DSP) applications. A single-bit module of this multiplier consists of 96 Josephson junctions and uses a B-flip-flop-based carry-save adder (CSA). For HYPRES' standard 1-kA/cm/sup 2/ Nb process with 3.5 /spl mu/m-diameter Josephson junctions the module occupies all area of 350/spl times/600 /spl mu/m/sup 2/. Simulations show that the circuit should dissipate 28 /spl mu/W of power at 2.6 mV dc supply voltage and operate at frequencies of up to 25 GHz. We have successfully tested all cells of the module and verified correct operation of a simplified version of the module at low frequencies. According to numerical simulations, the speed of the multiplier is limited by the CSA. In order to overcome this bottleneck we have developed a concept of a fast carry-save pipeline adder based on XOR gates which uses an RSFQ-specific algorithm for carry bit calculation.>
We present the design and the fabrication of an adder circuit in the extended phase-mode logic family. The phase-mode logic is a single flux quantum (SFQ) logic which utilizes an SFQ as an information bit carrier. The single-bit adder circuit is made up of an INHIBIT gate which is the basic device of the phase-mode logic. The circuit has been designed and fabricated using Nb/AlO/sub x//Nb Josephson junctions with Josephson critical current density of 1.0 kA/cm/sup 2/. In order to confirm the circuit operation, the fabricated adder circuit has been tested at low speed. For investigating the possibility of a high-frequency operation, dc voltages generated by fluxon pulse trains have been measured. From the Josephson voltage-frequency relation, the result shows that the circuit has potential to complete the carry operation within 20 psec.
The Fast Fourier Transform (FFT) is extensively used in image processing, wireless communication, and other applications. Some applications that involve very complicated, real-time FFT processing require specialized hardware for performing high-speed FFT processing. We have been developing high-speed FFT processors based on single flux quantum (SFQ) circuit technology. In this study, we developed a butterfly processing element for FFT processors that uses SFQ circuits. The butterfly processing element consists of complex number adders, subtractors, and multipliers. The circuit structure was modified compared to that of previous SFQ FFT processors to reduce latency. Several buffer circuits were inserted in the multipliers to compensate for timing jitter accumulation and discrepancies due to signal propagation delay. We designed and implemented a four-bit bit-serial butterfly processing element that contains 5763 Josephson junctions using the ISTEC Nb 2.5-kA/cm2standard 2 process and the CONNECT cell library. Correct operation of the butterfly processing unit was experimentally confirmed at a clock frequency of 25 GHz.
We present a design for parallel pipelined carry-lookahead Kogge-Stone 32and 64-bit integer adders with the traditional concurrent flow timing scheme, and the results of its gate-level logical simulation using a VHDL model, with parameters reduced from the physical-level simulation of RSFQ cells. The design uses only five different types of bit processing blocks and is easily scalable to any length of the operands. The multi-pulse logic representation together with interchanging logical polarity between pipeline stages is used to simplify the design of the blocks, which contain only two types of clocked RSFQ gates: an inverter and a D-flip-flop. Simulations show that in the absence of thermal fluctuations and random parameter spread the clock frequency of the adder implemented in the projected 0.8 /spl mu/m Nb-trilayer technology could be as high as 150 GHz. However, an approximate account of these factors shows that in order to achieve a 99% adder fabrication yield and a 10/sup -25/ adder error rate the maximal frequency should be reduced to 60 GHz for 1.5% Josephson junction spread and to 52 GHz for 3% spread. Adder latency is close to 260 ps for 32 bits and 320 ps for 64 bits. We plan to re-design the adders to increase their speed.