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Journal of Applied Physics

Analog-to-digital conversion with a SQUID: Conditions for a countable pulse train

Robert L. Peterson

Published Jun 1, 1979• 16 citations
Publisher

Abstract

A superconducting loop containing a Josephson junction develops voltage pulses when it admits and expels magnetic flux quanta, and thus may be used as an A/D converter. We here develop and discuss several conditions which must be satisfied for the generation by the SQUID of an unambiguously countable pulse train, from which the analog signal can be faithfully reconstructed. These conditions can be satisfied over a broad range of realizable values of inductance and resistance. The capacitance, however, must be carefully controlled. The results of simulations are also presented, illustrating the various ways in which the pulse trains are affected.

DOI
10.1063/1.326455

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A superconducting loop containing a Josephson junction develops voltage pulses when it admits and expels magnetic flux quanta, and thus may be used as an A/D converter. We here develop and discuss several conditions which must be satisfied for the generation by the SQUID of an unambiguously countable pulse train, from which the analog signal can be faithfully reconstructed. These conditions can be satisfied over a broad range of realizable values of inductance and resistance. The capacitance, however, must be carefully controlled. The results of simulations are also presented, illustrating the various ways in which the pulse trains are affected.
Digital Josephson circuits that do not latch into the voltage state provide an opportunity for high-speed serial processing. These fast logic gates must ultimately generate and record small fast pulses generated by single fluxoid events. This is demonstrated in a concept for a high-speed analog-to-digital (A/D) converter. Low β-value unlatched SQUID's are used throughout for ultimate speed, sensitivity, and simplicity. The analog signal is quantized by a single-junction SQUID and converted into a pulse train resulting from fluxoid transitions. These are counted in a chain of bistable two-junction SQUID's which successively scale the pulse train by a factor 2. These SQUID's perform both logic and memory functions at the single fluxoid level. The bit count stored in the array is gated out each sampling interval to provide the digitized signal. The performance of this device has been simulated and criteria established for the unlatched SQUID design. These include dimensionality, impedance, damping, intra- and inter-SQUID delays and β factor. Large analog dynamic range is available with the high intrinsic linearity of the SQUID quantizer and a long chain of scalers.
Measurements of extremely weak magnetic fields in unshielded environments require sensors providing a high dynamic range and slew rate while maintaining a high resolution. At present, analog Superconducting Quantum Interference Devices (SQUIDs) are the most sensitive sensors for magnetic flux. Due to their room-temperature feedback electronics necessary to maintain a stable point of operation, slew rates of those sensors are limited. The dynamic range is usually restricted by the resolution of classical analog to digital converters. The digital SQUID follows a different approach: a change of the magnetic field penetrating the pickup loop is translated by the sensor into a stream of voltage pulses. Each pulse represents the change of the magnetic flux inside the pickup loop by one flux quantum Φ0. By fast counting of these flux quanta, it is possible to outperform the analog SQUID in terms of dynamic range and maximum slew rate. We present our latest results with respect to the internal mechanisms of the digital SQUID and present a method to compensate the main source for nonlinear behavior of the sensor. The analyzed circuit was fabricated by FLUXONICS Foundry (1) in a 1 kA/cm² niobium fabrication process.
High speed, single flux quantum (SFQ) binary scalers are important components in superconducting analog-to-digital converters (ADC). This paper reviews the concept for a SQUID ADC and the design of an SFQ binary ripple counter, and reports the simulation of key components, and fabrication and performance of non-latching SQUID scalers and SFQ binary ripple counters. The SQUIDs were fabricated with Nb/Nb2O5/PbIn junctions and interconnected by monolithic-superconducting transmission lines and isolation resistors. Each SQUID functioned as a bistable flip-flop with the input connected to the center of the device and the output across one junction. All junctions were critically damped to optimize the pulse response. Operation was verified by observing the do I-V curves of successive SQUIDs driven by a cw pulse train generated on the same chip. Each SQUID exhibited constant-voltage current steps at 1/2 the voltage of the preceding device as expected from the Josephson voltage-to-frequency relation. Steps were observed only for the same voltage polarity of successive devices and for proper phase bias of the SQUID. Binary frequency division was recorded up to 40GHz for devices designed to operate to 28GHz.
Amplification of SFQ pulses to higher signal levels has been achieved using the general technique of inductive isolation. A multiple-flux-quantum generator, which produces quantum-accurate waveforms suitable for ADC applications, and an output data link were demonstrated. Both circuits were implemented using critically damped, dc-powered SQUIDs stacked in series. In the past, the voltage output achievable with this approach has been severely limited by parasitic capacitance to ground and to the control lines. Parasitic capacitance inhibits SQUID operation both at turn-on and turn-off. Using inductive isolation between SQUIDs, parasitic capacitance was completely tuned out. A 100-flux-quantum waveform generator, based on a series stack of 100 SQUIDs, operated at 6 Gb/s, fabricated in a 4.5 kA-per-square-cm Josephson junction process. The output amplifier produced a 1 mV swing at 12 Gb/s non-return-to-zero. This circuit is based on a stack of only two SQUIDs, and uses both inductive isolation and asymmetric resistive shunting to enhance the out-of-phase oscillation mode.
Over the past few decades, superconducting circuits have been used to realize various novel electronic devices such as quantum bits, SQUIDs, parametric amplifiers, etc. One domain, however, where superconducting circuits fall short is information storage. Superconducting memories are based on the quantization of magnetic flux in superconducting loops. Standard implementations store information as magnetic flux quanta in a superconducting loop interrupted by two Josephson junctions (i.e., a SQUID). However, due to the large inductance required, the size of the SQUID loop cannot be scaled below several micrometers, resulting in low-density memory chips. Here, we propose a scalable memory consisting of a voltage-biased superconducting ring threaded by a half-quantum flux bias. By numerically solving the time-dependent Ginzburg-Landau equations, we show that applying a time-dependent bias voltage in the microwave range constitutes a writing mechanism to change the number of stored flux quanta within the ring. Since the proposed device does not require a large loop inductance, it can be scaled down, enabling a high-density memory technology.
Superconducting Josephson devices have been developed for various electronics fields such as highly sensitive magnetometers, voltage standards, and high-speed digital signal processing. In this paper, the author describes two kinds of superconducting digital-to-analog （D/A） converters that generate quantum voltages. One is a balanced-ternary D/A converter comprising asymmetric superconducting quantum interference devices, in which the generation of either a positive or a negative zero-crossing Shapiro step is controlled by an external magnetic flux. The other is a single-flux-quantum （SFQ） D/A converter, in which SFQ pulse-frequency modulation is employed. They generate quantum voltage defined by the reference microwave frequency and the AC Josephson effect.