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IEEE Transactions on Applied Superconductivity

SFQ balanced comparators at a finite sampling rate

Vasili K. Semenov, Timur V. Filippov, Yu. A. Polyakov, K. K. Likharev

Published Jun 1, 1997• 52 citations
Publisher

Abstract

We have extended our previous study of SFQ balanced comparators which use two overdamped Josephson junctions to (a) finite sampling rate and (b) junctions with higher critical current density. The effective width /spl Delta/I/sub x/ of the gray zone of the comparators fabricated using the niobium-trilayer technology of HYPRES, Inc. (j/sub c//spl ap/1 kA/cm/sup 2/) and Stony Brook's domestic planarized process (j/sub c//spl ap/5 kA/cm/sup 2/) has been measured as a function of the SFQ pulse rate (from 2.5 to 55 GHz) and temperature (from 1.6 to 4.2 K), for various drivers which determine the SFQ pulse shape and external impedance. The data have been compared with available theories of Josephson junction dynamics in the presence of thermal and quantum fluctuations. We have found that /spl Delta/I/sub x/ can be substantially reduced by using relatively broad ("soft") SFQ pulses. For high-j/sub c/ comparators fed by short (/spl sim/2-ps) SFQ pulses the temperature dependence is practically negligible, indicating the dominance of quantum fluctuations.

DOI
10.1109/77.622189

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We have extended our previous study of SFQ balanced comparators which use two overdamped Josephson junctions to (a) finite sampling rate and (b) junctions with higher critical current density. The effective width /spl Delta/I/sub x/ of the gray zone of the comparators fabricated using the niobium-trilayer technology of HYPRES, Inc. (j/sub c//spl ap/1 kA/cm/sup 2/) and Stony Brook's domestic planarized process (j/sub c//spl ap/5 kA/cm/sup 2/) has been measured as a function of the SFQ pulse rate (from 2.5 to 55 GHz) and temperature (from 1.6 to 4.2 K), for various drivers which determine the SFQ pulse shape and external impedance. The data have been compared with available theories of Josephson junction dynamics in the presence of thermal and quantum fluctuations. We have found that /spl Delta/I/sub x/ can be substantially reduced by using relatively broad ("soft") SFQ pulses. For high-j/sub c/ comparators fed by short (/spl sim/2-ps) SFQ pulses the temperature dependence is practically negligible, indicating the dominance of quantum fluctuations.
The Josephson balanced comparator, a decision-making circuit comprising two Josephson junctions (JJs) connected in series from a clocking perspective and in parallel for the current to be measured, is ubiquitous in single flux quantum (SFQ) logic. Its noise properties are crucial for the performance of logic devices. The characteristics of the balanced comparator can also be used to monitor fab process and design implementation as an indicator for excess noise, overheating, linearity, dynamic effects, etc. We designed several test structures to measure gray zone of various comparators fabricated in different nodes of process at MIT-LL. We used digital circuitry to measure comparator characteristics at low frequencies and an analog testbed to perform high frequency characterization. Experimental results for gray zone of comparators designed for fabrication nodes with different current densities, sheet resistances, critical damping are presented and studied as a function of clock frequency.
We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width Delta Ix of Josephson-junction balanced comparators. The calculated temperature dependence of Delta Ix in the range 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5 kA/cm2, without any fitting parameters.
The use of high-T/sub c/ Josephson junctions for digital applications requires a careful study of the influence of thermal noise on circuit performance. We investigated a balanced current comparator, which contains a basic component of all RSFQ circuits: two overdamped Josephson junctions connected in series. The dependence of the dc-voltage across the Josephson junctions on signal current was measured to determine the threshold uncertainty of switching of the comparator. The experimental data obtained at different sampling pulse frequencies, in a temperature range from 10 to 50 K, were compared with a theoretical model, taking into account the influence of thermal noise as well as of sampling pulse frequency.
The sensitivity of a balanced comparator composed of two overdamped Josephson junctions fed by single flux pulses is calculated, taking into account both thermal and quantum fluctuations. The results of the analysis are compared with those of recent experiments. Ultimate resolution of the balanced comparator with feasible junction parameters is estimated to be as high as approximately 50 pA/Hz/sup 1/2/ at 4 K and approximately 10 pA/Hz/sup 1/2/ at T to 0 K. Performance limits of the device are compared with those of its single-junction counterpart.
The Josephson comparator is one of the fundamental building blocks of rapid single flux quantum (RSFQ) electronics. Within this circuit family it is the exclusive device which provides logical data processing. The Josephson comparator is also the basic decision element for very fast analog-to-digital converters and sampler circuits for low input power and high-bandwidth signals based on the RSFQ technique. The performance of those devices is fundamentally determined by the characteristics of the Josephson comparator. In this study the gray zone dependency on the clock frequency of a Josephson comparator is investigated by simulations concerning the influence of thermal noise. This investigation is performed for a series of operating points defined by the bias current and different noise levels defined by the operating temperature. In contrast to former investigations, we analyzed the comparator embedded in a realistic environment for output data processing. We identified a characteristic clock frequency f c for a comparator topology designed for a 1 kA cm − 2 niobium fabrication technology. The gray zone of 8 µA remains constant for clock frequencies below f c = 15 GHz and starts to increase for larger frequencies. We also found out that this characteristic frequency is independent of the intensity of thermal noise and therefore independent of temperature.
We have designed and tested a Rapid Single-Flux-Quantum (RSFQ) circuit for experimental measurement of the fluctuation-induced threshold uncertainty of switching of SFQ comparators, which are essential components of RSFQ logic devices, analog-to-digital converters, and digital SQUIDs. Statistical density of the switching events in comparators using externally-overdamped Nb-trilayer Josephson junctions has been found to be in agreement with the distribution which follows from a simple theory based on a time-dependent harmonic-oscillator model of the device. Width of the distribution (i.e, the single-shot current resolution of the comparator) measured as a function of temperature in the range 1.7-4.2 K corresponds to fundamental (thermal/quantum) fluctuations, with no evidence of excess noise sources.>