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IEEE Transactions on Applied Superconductivity

50 GHz RSFQ pseudo-random number generator design

Xingxiang Zhou, S. Xu, Pavel Rott, C.A. Mancini, M. J. Feldman

Published Mar 1, 2001• 12 citations
Publisher

Abstract

Simple RSFQ gates can be very robust, and operate up to high clock speeds in simulation. Larger RSFQ circuits are generally much more limited in clock speed. We believe that this is partly due to less than optimal choice of the timing inter-connections between gates. Timing design is especially problematic for circuits including data loops (feedback). We have developed a new technique for timing design of RSFQ data loops which may be called "balanced skew clock scheduling." It involves equalizing the minimum clock period between every pair of gates. Mathematical analysis proves the optimality of this scheme and reveals the global timing constraints unique to RSFQ data loops. We used this technique for the design of a simple useful clocked RSFQ circuit, a four-bit pseudo-random number generator (PRNG). Constructed from our standard library cells for a 3.5 /spl mu/m 1000 A/cm/sup 2/ Nb-trilayer process, the PRNG worked up to 50 GHz in Jspice simulation.

DOI
10.1109/77.919420

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IEEE Transactions on Applied Superconductivity•Jun 1, 2005•12 citations
Simple RSFQ gates can be very robust, and operate up to high clock speeds in simulation. Larger RSFQ circuits are generally much more limited in clock speed. We believe that this is partly due to less than optimal choice of the timing inter-connections between gates. Timing design is especially problematic for circuits including data loops (feedback). We have developed a new technique for timing design of RSFQ data loops which may be called "balanced skew clock scheduling." It involves equalizing the minimum clock period between every pair of gates. Mathematical analysis proves the optimality of this scheme and reveals the global timing constraints unique to RSFQ data loops. We used this technique for the design of a simple useful clocked RSFQ circuit, a four-bit pseudo-random number generator (PRNG). Constructed from our standard library cells for a 3.5 /spl mu/m 1000 A/cm/sup 2/ Nb-trilayer process, the PRNG worked up to 50 GHz in Jspice simulation.
A low-skew frequency divider and clock controller have been designed for high-frequency timing of superconductor rapid single-flux-quantum (RSFQ) digital systems. The circuits have only about 10-ps skew between input and output signals and are applicable for multirate digital systems (e,g., oversampling analog-to-digital converter and bit-serial digital systems). Several circuits have been fabricated in conventional Nb-trilayer technology with a critical current density of 1 kA/cm/sup 2/. The most complex clock controller generates trains of 2/sup 24/ single-flux-quantum pulses with a period of less than 70 ps. The long-term relative stability of these intervals has been measured to be better than 6/spl times/10/sup -5/. The basic component of the controller, a frequency divider, operates at input frequencies above 85 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.
This paper describes the design, analysis and test results for a 4-bit pseudo-random bit-sequence generator (PRBSG) implemented with complementary output switching logic (COSL) gates. The PRBSG was optimized using a Monte Carlo simulation method for 10-GHz operation. The circuit has been fabricated using niobium technology with critical current density of 1 kA/cm/sup 2/ and sheet resistance of 1 /spl Omega//sq. The 4-bit PRBSG consists of 12 gates and its area is 1530/spl times/950 /spl mu/m/sup 2/. It has been fully tested with a three-phase power supply, and its power consumption is 0.15 mW. The correct operations have been verified experimentally at clock frequencies of up to 2 GHz.
We have experimentally demonstrated high-speed operation of RSFQ circuits using on-chip testing system and confirmed normal operation up to 30 GHz. The system includes high-frequency pulse generators and shift registers (SRs) serving as an interface circuit between high-speed internal signals and low-speed external signals. We adopted two ladder-type pulse generators. One generates clock pulses of 10 GHz and the other generates 25 GHz. By increasing bias currents of JTLs, clock pulses can be generated at higher frequency. By using the system, an SR and a T flip-flop (TFF) gate are examined. The circuits were fabricated by NEC's standard process based on Nb/AlO x /Nb junction technology with J c = 2.5 kA cm -2 . We optimized circuit parameters by using Monte Carlo simulation. In addition, the effect of parasitic inductances can be reduced by decreasing I c . As a result, the systems for SR and TFF worked correctly up to 30 GHz and 27.5 GHz, respectively. The SR and TFF have wide bias margins of ±39% and ±20%, respectively. We confirmed that the bias margins of the SR are independent of operation frequency. The limits of operation frequency are thought to be much higher than 30 GHz.
We have carried out measurements of bit error rate (BER) of Rapid Single-Flux-Quantum (RSFQ) XOR gates with various nominal dc power supply voltages (from 0.1 V to 1.0 mV), operating at speeds up to 25 GHz. (For these gates, implemented using HYPRES' standard, 3.5-/spl mu/m, 10 /spl mu/A//spl mu/m/sup 2/ Nb-trilayer process, this speed is close to maximum.) A special on-chip RSFQ test circuit allowed high-speed measurements of BER in the range from 10/sup -9/ to 10/sup -13/ to be carried out. As a result of these experiments, a new type of thermal-fluctuation-induced digital errors in RSFQ circuits has been identified. These "timing" errors arise at high speed due to time jitter of data and clock pulses. We have developed a simple theory of these errors which allows a fair description of the experimental data. The theory shows that in some cases the timing errors may be an important factor limiting speed performance of RSFQ circuitry. Nevertheless, our XOR gates could operate at 25 GHz with BER below 10/sup -13/ at the standard temperature (4.2 K) at any dc power supply voltage in our range. For the lowest voltage (0.1 Volt) the calculated static power dissipation in the gate was as low as 23 nanowatts, lower than the unavoidable dynamic dissipation (43 nanowatts).
At the typical operating temperature of 4.2 K, the theoretical upper limit of the clock frequency of the Low-Temperature Superconductive (LTS) Nb based Rapid Single Flux Quantum (RSFQ) digital circuits is several hundred GHz. Nevertheless, the few middle-scale RSFQ circuits reported on up to now operate at only some tens of GHz. An important performance-limiting factor is in this case the clock signal distribution, so nowadays asynchronous RSFQ designs are often considered. Our previous studies have shown that it is an important advantage of a given asynchronous RSFQ cell library to contain gates with tunable delays. We have already shown by simulations that the RSFQ gate delays are best adjusted by changing the Stewart-McCumber parameter /spl beta//sub c/ of the Josephson junctions-this method tunes the delay within a large interval of values while scarcely affecting the margins and the fabrication yield of the RSFQ gates. In order to prove this statement experimentally, we have designed, fabricated, and tested several ring-shaped oscillators with identical topologies but different Stewart-McCumber parameters of the Josephson junctions. Their operating speeds and margins are measured and compared.