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IEEE Transactions on Applied Superconductivity

Timing Jitter Measurement in Single-Flux-Quantum Circuits Based on Time-to-Digital Converters With High Time-Resolution

Terabe Masayoshi, Sekiya Akito, Takahiro Yamada, Akira Fujimaki

Published Jun 1, 2007• 26 citations
Publisher

Abstract

We evaluated timing jitter based on a time-to-digital converter (TDC) having sub-pico seconds time resolution. The measured jitter at liquid helium temperature was 65 fs for an optimally damped simple junction composing a conventional Josephson transmission line fabricated with the NEC standard process. The temperature dependence and shunt resistance dependence of jitter indicate that the jitter originates from thermal noise generated at the shunt resistor of the junction. We also found that the timing jitter of a balanced comparator is much larger than that of a JTL. The jitter of a balanced comparator is independent of temperature. This means that the jitter of a balanced comparator does not arise from thermal noise.

DOI
10.1109/tasc.2007.898560

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Journal of Applied Physics•May 15, 2008•10 citations
We evaluated timing jitter based on a time-to-digital converter (TDC) having sub-pico seconds time resolution. The measured jitter at liquid helium temperature was 65 fs for an optimally damped simple junction composing a conventional Josephson transmission line fabricated with the NEC standard process. The temperature dependence and shunt resistance dependence of jitter indicate that the jitter originates from thermal noise generated at the shunt resistor of the junction. We also found that the timing jitter of a balanced comparator is much larger than that of a JTL. The jitter of a balanced comparator is independent of temperature. This means that the jitter of a balanced comparator does not arise from thermal noise.
A single-flux-quantum (SFQ) pulse coincidence detector based on resistively shunted nonhysteretic Josephson junctions was designed and simulated. The coincidence detector generates an SFQ pulse when the delay between the arrival of SFQ pulses at its two inputs is less than the coincidence threshold. Simulations indicate that the minimum coincidence threshold time can be as short as 400+or-200 fs, assuming Josephson junction characteristic voltages of 1 mV, overdamped dynamics, and 4.2 K operating temperatures. Circuit architectures exploiting this gate are suggested. Estimates of the effects of thermal noise on resolution are presented, indicating the potential for various time-domain measurements with subpicosecond resolution.< >
Digital superconducting systems based on Josephson junctions make generally use of the synchronous timing strategy. Today, one of its most promising applications is the high speed and high dynamic range signal sensing. A digital signal acquisition system should have a high resolution as well as a short sampling interval with a well known and constant time period. Short term clock fluctuations (clock jitter) induced by thermal noise can significantly disturb the system operation due to hazards of timing constraint violations. This uncertainty in the time period is currently a strong limitation for further improvements of fast signal sensing systems based on superconductive electronics. Recently, several theoretical and experimental studies describe the timing jitter in simple circuits, like Josephson transmission lines. In the presented work, we analyse different fabrication technologies for rapid single flux quantum (RSFQ) electronics and predict their timing jitter by the numerical solution of stochastic differential equations. We obtained a very good agreement between our simulation data and recent experimental results.
Timing jitter is an important factor in determining the limit of speed and scale of single-flux-quantum circuits. We estimated the timing jitter by a simple method using 2-bit shift registers. It was estimated by observing the transition between 1- and 2-mode operations while changing the bias current to the clock line. A sharp transition was observed in the shift register with a smaller number of Josephson junctions in the clock and data lines, suggesting the existence of a finite timing jitter. The timing jitter per Josephson junction was estimated to be 0.09 ps at a designed bias current. The temperature dependence supported that the timing jitter comes from thermal fluctuation.
A single flux quantum (SFQ) pulse coincidence detector based on resistively shunted nonhysteretic Josephson junctions was designed and simulated. The coincidence detector generates an SFQ pulse when the delay between the arrival of SFQ pulses at its two inputs is less than the coincidence threshold. Simulations indicate that the minimum coincidence threshold time can be as short as 400 f 200 fs assuming Josephson junction characteristic voltages of 1 mV, overdamped dynamics and 4.2 K operating temperatures. Circuit architectures exploiting this gate are suggested. Estimates of the effects of thermal noise on resolution are presented indicating the potential for various time domain measurements with sub-picosecond resolution. I. INTRODUCTION The high speed properties of Josephson electronics offer unique possibilities for high time resolution metrology1 such as fast sampling, A-to-D conversion?^^ race arbiting? and time domain reflectometry5 In this paper I propose an ap- proach to time interval measurement that is based on a simple circuit consisting of several overdamped Josephson junctions. This circuit uses the picosecond pulses of Josephson junctions in a simple way that can be integrated naturally into a fre- quency vernier measurement apparatus? A junction with a nonhysteretic resistively shunted current-voltage characteristic can be induced to generate voltage pulses whose time integral is equal to the elementary flux quantum @pg = 2.07 mV-p~.~ In particular, the pulse width from an overdamped Josephson junction with a characteristic voltage VC = IcR~ is given by At = Q)/ VC and can be as short as 2 ps for a junction with a typical VC = 1 mV. The short widths of SFQ pulses combined with the high plasma frequencies possible with overdamped junctions can be exploited in a simple circuit that detects pulse coincidence from two inputs and has a coincidence threshold that can be as short as several hundred femtoseconds for junction IcR~ products around 1 mV. In the next section of this paper I describe the coincidence detection circuit operation, including the results of simulations estimating the potential- performance characteristics. The ef- fects of thermal fluctuations on resolution will be discussed. In Section I11 a time interval measurement system is de- scribed, based on the frequency vernier interpolation method. Using conventional electronics, the vernier method has at- tained time interval resolution limits of about 20 ps.* Our simulations show in principle that a carefully designed fre-
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 process of reproduction of single flux quantum pulses in a Josephson junction chain composed of a pulse generator, a balanced comparator, and a single Josephson junction is investigated. It is shown that the reproduction of single flux quantum pulses in such a chain is more stable and the mean and the standard deviation of switching time are minimal for the McCumber-Stewart parameter value from 0.5 to 1 and for a normalized clock generator current around 1.5. The influence of input and output inductances on the characteristics of a balanced comparator is investigated. The recommended value of the output inductance leading to smooth pulses and relatively small jitter is around unity.