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IEEE Transactions on Applied Superconductivity

Simulation and optimization of binary full-adder cells in rapid single flux quantum logic

S.S. Martinet, Mark F. Bocko

Published Mar 1, 1993• 6 citations
Publisher

Abstract

The authors consider the design of a binary carry full-adder cell using the logic gates and buffers belonging to the rapid single-flux-quantum (RSFQ) logic family. They have taken advantage of the unique properties of RSFQ pulse logic to realize two designs: one using two logic gates and a toggle flip-flop in two stages of logic, the other using two logic gates in one stage of logic. They have determined the parameter margins of the two full-adder cells and optimized them to obtain critical margins approaching +or-30%. Simulations of the full-adder cells have revealed critical delays and maximum clock frequencies of 58 ps and 17 GHz and 33 ps and 30 GHz, respectively.>

DOI
10.1109/77.233989

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We are introducing a new subfamily of rapid single-flux-quantum (RSFQ) digital cells, based on a single B flip-flop template. The template can be considered as an SFQ flip-flop with up to 4 inputs and 6 outputs. Each input SFQ pulse can change the flip-flop's internal state. Each output presents (in the form of SFQ pulses a specific logic function of the initial state of the cell and input signals. Simple connection of various inputs and/or outputs, combined with shortening or opening of certain branches of the template allows one to implement a variety of RSFQ cells with wide margins. Of these various RSFQ cells, we have designed and successfully tested the T1 cell (asynchronous toggle flip-flop with synchronous destructive readout), single-bit full adder, and single-bit stage of an up-down counter. Experimentally measured margins for dc power supply voltage for these circuits were /spl plusmn/24%, /spl plusmn/24%, and /spl plusmn/17%, respectively.>

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Simulations are used to optimize the design of simple rapid single flux quantum (RSFQ) logic gates and to determine their margins. Optimizations based on maximizing the smallest (critical) margin result in critical margins in the range of 19-50%. A Monte Carlo approach is used to illustrate the relationship between margins and process yield. Based on single gate simulations, the results show that 1 sigma parameter spreads of less than about +or-5% will be required to make medium- or large-scale integrated RSFQ logic circuits. A single-bit full adder using five RSFQ gates and a local self-timing network are simulated with discrete components. The full adder used 2000-A/cm/sup 2/ junctions with a specific capacitance of 0.04 pF/ mu /sup 2/ and had a logic delay of 87 ps and a worst-case margin of +or-19%. A small margin reduction which is not present in the individual gate simulations results from loading.>

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IEEE Transactions on Applied Superconductivity•Jun 1, 1999•40 citations
The authors consider the design of a binary carry full-adder cell using the logic gates and buffers belonging to the rapid single-flux-quantum (RSFQ) logic family. They have taken advantage of the unique properties of RSFQ pulse logic to realize two designs: one using two logic gates and a toggle flip-flop in two stages of logic, the other using two logic gates in one stage of logic. They have determined the parameter margins of the two full-adder cells and optimized them to obtain critical margins approaching +or-30%. Simulations of the full-adder cells have revealed critical delays and maximum clock frequencies of 58 ps and 17 GHz and 33 ps and 30 GHz, respectively.>
We are introducing a new subfamily of rapid single-flux-quantum (RSFQ) digital cells, based on a single B flip-flop template. The template can be considered as an SFQ flip-flop with up to 4 inputs and 6 outputs. Each input SFQ pulse can change the flip-flop's internal state. Each output presents (in the form of SFQ pulses a specific logic function of the initial state of the cell and input signals. Simple connection of various inputs and/or outputs, combined with shortening or opening of certain branches of the template allows one to implement a variety of RSFQ cells with wide margins. Of these various RSFQ cells, we have designed and successfully tested the T1 cell (asynchronous toggle flip-flop with synchronous destructive readout), single-bit full adder, and single-bit stage of an up-down counter. Experimentally measured margins for dc power supply voltage for these circuits were /spl plusmn/24%, /spl plusmn/24%, and /spl plusmn/17%, respectively.>
Simulations are used to optimize the design of simple rapid single flux quantum (RSFQ) logic gates and to determine their margins. Optimizations based on maximizing the smallest (critical) margin result in critical margins in the range of 19-50%. A Monte Carlo approach is used to illustrate the relationship between margins and process yield. Based on single gate simulations, the results show that 1 sigma parameter spreads of less than about +or-5% will be required to make medium- or large-scale integrated RSFQ logic circuits. A single-bit full adder using five RSFQ gates and a local self-timing network are simulated with discrete components. The full adder used 2000-A/cm/sup 2/ junctions with a specific capacitance of 0.04 pF/ mu /sup 2/ and had a logic delay of 87 ps and a worst-case margin of +or-19%. A small margin reduction which is not present in the individual gate simulations results from loading.>
Some basic cells in the rapid single-flux quantum (RSFQ) family of superconductive logic circuits were studied. An input stage, a buffer, and an OR gate were simulated and laid out for a standard niobium-based fabrication process. The resulting circuits perform properly for clock speeds up to 1 GHz. For the simpler circuits tested, the measured margins are wide, consistent with simulations, and not very dependent on clock speed. However, margin decreases with increased circuit complexity. The input stage converts a rising edge into an SFQ pulse, which has a small amplitude and narrow width in time. On the present circuits, these pulses are about 200 mu V in amplitude and 10 ps in width. To facilitate measurement, the authors have chosen as the output an asymmetrical superconducting quantum interference device (SQUID) consisting of two Josephson junctions. It converts SFQ pulses into 2.5 mV latching output levels on chip. By inductively coupling SFQ pulses into the SQUID loop, DC current isolation between the RSFQ circuit-under-test and the output stage is provided. The SQUID was optimized for 2 GHz operations.>
We have developed a novel, so-called "push-forward" design approach in Rapid Single-Flux-Quantum (RSFQ) logic. This approach leads to a more efficient circuit design at the gate level using fewer Josephson junctions combined with reasonable circuit parameter margins. Other advantages include higher operational speed and smaller power dissipation. This novel method is based on a specific type of interaction (pushing forward) between single flux quanta already stored by RSFQ gates and newly arriving data SFQ pulses. It implies a reuse of an internal gate memory as well as realization of multi-quantum storage. Using this push-forward design approach, we have designed, optimized, fabricated, and successfully tested two versions of Carry-Save Serial Adders for digital signal processing applications.>
An architecture of rapid single-flux-quantum logic circuits using clockless gates is proposed. Compared with a circuit composed of only clocked gates, a circuit using clockless gates includes fewer clocked gates, and therefore, a smaller clock distribution network. A circuit in the proposed architecture is constructed from pipeline stages. Each pipeline stage consists of a column of clocked gates and a succeeding block of clockless gates. The function of a pipeline register of a stage is implemented by the latching function of the clocked gates in the column. The combinational logic of a stage is implemented by the logic function of the clocked gates in the column and that of the clockless gates in the block. We designed a two-stage-pipelined 4-bit carry-lookahead-adder using clockless gates as a design example of the proposed architecture. It had reductions of the count of clocked gates and the area by 33 and 13%, respectively, compared with that composed of only clocked gates. The 4-bit adder in the proposed architecture was fabricated and demonstrated with the maximum clock frequency of 21.4 GHz and the bias margin of ±16%.
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.