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Direct measurements of propagation delay of single-flux-quantum circuits by time-to-digital converters

Kazunori Nakamiya, Nobuyuki Yoshikawa, Akira Fujimaki, Hirotaka Terai, Yoshihito Hashimoto

Published Jan 1, 2008• 5 citations
Publisher

Abstract

Direct measurements of propagation delay of single-flux-quantum (SFQ) circuits were performed using SFQ double-oscillator time-to-digital converters. The propagation delay of several SFQ logic gates in our cell library named CONNECT were measured in picosecond resolution. Small discrepancy in the propagation delay of picosecond level was observed between measurement and circuit simulation results. The discrepancy is well explained assuming the parasitic inductance around shunt resistors of Josephson junctions.

DOI
10.1587/elex.5.332

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•Jan 1, 1993•0 citations
Direct measurements of propagation delay of single-flux-quantum (SFQ) circuits were performed using SFQ double-oscillator time-to-digital converters. The propagation delay of several SFQ logic gates in our cell library named CONNECT were measured in picosecond resolution. Small discrepancy in the propagation delay of picosecond level was observed between measurement and circuit simulation results. The discrepancy is well explained assuming the parasitic inductance around shunt resistors of Josephson junctions.
We have been developing a time-to-digital converter (TDC) using single-flux-quantum (SFQ) circuits in order to realize an imaging system based on a superconducting strip single-photon detector (SSPD). In this system, the absorption position of a single photon in a meander-shaped SSPD is determined by measuring the delay time of the detected signal propagating through an SSPD delay line. Increasing the time resolution of the TDC is the primary concern for improving the spatial resolution of the system. Here we focused on the double-oscillator SFQ TDC, where the difference of oscillation periods between two SFQ ring oscillators determines the time resolution. In the previous study, a time resolution of about 4 ps was demonstrated by using the Nb standard Josephson integrated circuit (IC) process with a critical current density of 2.5 kA/cm2. In this study, we improved the time resolution by adopting the Nb advanced Josephson IC process with a critical current density of 10 kA/cm2and by optimizing the circuit parameters of the coincidence detector. The histogram and the linearity of the delay measurements show that the time resolution is improved to up to 2 ps.
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.< >
We study a single-shot single-flux-quantum (SFQ) readout circuit based on current-to-time conversion for superconducting flux qubits. Circulating currents representing states of a qubit were converted to propagation delay time of SFQ pulses, and then detected by a time discriminator. The key parameter which determines the availability of single-shot readout is current resolution. We evaluated the current resolution by measuring the gray zone which was defined as the transition width in the output probability of the current-to-time converter with 1000 trials for each value of an input current. For reducing unwanted effects on the qubit, shunt resistors are required to be removed for Josephson junctions in the readout circuit. We designed two readout circuits for comparison, the circuit composed of shunted junctions and that of unshunted junctions. Gray zones were measured to be 4.8μA\mu{\rm A}μAfor unshunted junctions and 2.2μA\mu{\rm A}μAfor the shunted ones at 4.2 K. These gray zones may originate from Johnson noise. Operation at a reduced temperature and employment of a likelihood decision circuit will lead to reduced gray zone, i.e., improved current resolution sufficient for single-shot readout.
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.>
Delay analysis for superconductive Single Flux Quantum (SFQ) logic is performed for Self-Timing-Aligned Clock Synchronization Technique (STAC). With its pipelined-structure, the SFQ generates and propagates pulses that are to be processed sequentially through serial-connected functional logic blocks, and thus it is critical to acquire a ultra-high-speed and exactly synchronized clock/control signals with a few pico-second resolution. Both passive and Josephson-Junction circuits are investigated for the delay control. These delays, being connected in parallel with input line, and to the clocked-power/control node, produce a self-timing-aligned synchronization. Ways to achieve precision delays are seek by using Mo resistors along with junction inherent capacitors. Both current margins for the bias and critical timing information for the maximum throughput are also investigated. Layouts for the test SFQ circuits, such as D- and RS-flip-flops are done with XIC, and verifications are done through WRSpice with Hypres process parameters.
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-