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Review of Scientific Instruments

Digital-to-analog converter using a superconducting quantum interference device

Masakazu Nakanishi

Published Nov 1, 2012• 3 citations
Publisher

Abstract

We developed a digital-to-analog converter (DAC) having a current output and incorporating a superconducting quantum interference device (SQUID). The linearity of the device is based on the periodic dependence of the SQUID response on the magnetic flux coupling to the SQUID ring. The period is a flux quantum (Φ(o) = h/2e, where h is Planck's constant and e is the elementary charge). Because of the device's quantum accuracy, the output is essentially linear. The SQUID DAC was constructed using a commercially available rf-SQUID, the periodicity of which has been experimentally verified below 3420 Φ(o). An adjustable number of current amplitudes are dependent on maximum output (I(max)). The output current is adjustable to ~100 000 different values when I(max) ~1 mA and ~1,000,000 when I(max) ~0.1 mA. The short-term fluctuation of ~0.15 ppm was attributable to flux resolution of the SQUID. As a demonstration, measurements showing the voltage linearity of a digital multimeter were performed.

DOI
10.1063/1.4765743

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We developed a digital-to-analog converter (DAC) having a current output and incorporating a superconducting quantum interference device (SQUID). The linearity of the device is based on the periodic dependence of the SQUID response on the magnetic flux coupling to the SQUID ring. The period is a flux quantum (Φ(o) = h/2e, where h is Planck's constant and e is the elementary charge). Because of the device's quantum accuracy, the output is essentially linear. The SQUID DAC was constructed using a commercially available rf-SQUID, the periodicity of which has been experimentally verified below 3420 Φ(o). An adjustable number of current amplitudes are dependent on maximum output (I(max)). The output current is adjustable to ~100 000 different values when I(max) ~1 mA and ~1,000,000 when I(max) ~0.1 mA. The short-term fluctuation of ~0.15 ppm was attributable to flux resolution of the SQUID. As a demonstration, measurements showing the voltage linearity of a digital multimeter were performed.
Responses of a superconducting quantum interference device (SQUID) are periodically dependent on magnetic flux coupling to its superconducting ring and the period is a flux quantum (Φo = h/2e, where h and e, respectively, express Planck's constant and elementary charge). Using this periodicity, we had proposed a digital to analog converter using a SQUID (SQUID DAC) of first generation with linear current output, interval of which corresponded to Φo. Modification for increasing dynamic range by interpolating within each interval is reported. Linearity of the interpolation was also based on the quantum periodicity. A SQUID DAC with dynamic range of about 1.4 × 10(7) was created as a demonstration.
It is theoretically explained that a response of a superconducting quantum interference device (SQUID) is periodically dependent on total magnetic flux coupling to the SQUID ring (Φ) and its period is a flux quantum (Φ(o)=h/2e, where h and e, respectively, express Planck's constant and elementary charge). For example, the voltage of an electromagnetically oscillated rf-SQUID or a current biased dc-SQUID is thought to be periodically dependent on Φ with a period of Φ(o). In this paper, we propose an accurate method to check the periodicity of a SQUID response by using a set of sensing coils covered with a superconducting sheath. As a demonstration, we measured periodicity of a commercially available thin-film type rf-SQUID response in magnetic flux ranging up to approximately 4300Φ(o). Its flux dependence was periodic below about 3400Φ(o).
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.
Recently we designed and successfully tested a prototype of a superconducting digital-to-analog converter (DAC) based on processing single flux quantum (SFQ) pulses. Two unique features make the device very attractive for metrology applications: (i) The generation of output voltage is based on the fundamentally accurate Josephson frequency-to-voltage relationship. (ii) The device does not require any external signals with frequencies higher than 100 MHz. It is expected that the DAC will be used as a key component of novel standards and calibrators of ac voltage with frequency up to 1 MHz. The implemented prototype has low magnitude of output voltage (about 10 mV) which is far lower than the 1 to 10 V target magnitude.
Abstract A superconducting quantum interference device with differential output or ‘DSQUID’ was previously proposed for operation in the presence of large common-mode signals. The DSQUID is the differential connection of two identical SQUIDs. Here we show that besides suppression of electromagnetic interference this device provides effective linearization of the DC SQUID voltage response. In the frame of the resistive shunted junction model with zero capacitance, we demonstrate that spur-free dynamic range of the DSQUID magnetic flux-to-voltage transfer function is higher than 100 dB while the total harmonic distortion of a signal is less than 10 −3 % with a peak-to-peak amplitude of a signal being a quarter of half flux quantum, 2Φ a = Φ 0 /8. Analysis of the DSQUID voltage response stability to a variation of circuit parameters shows that DSQUID implementation allows for highly linear magnetic flux-to-voltage transformation at the cost of a high identity of Josephson junctions and high-precision current supply.