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Superconductor Science and Technology

SQIF-based dc SQUID amplifier with intrinsic negative feedback

Thomas Schönau, Matthias Schmelz, Viatcheslav Zakosarenko, Ronny Stolz, Solveig Anders, Ludwig Fritzsch, H.‐G. Meyer

Published Dec 5, 2011• 6 citations
Publisher

Abstract

We report on a two-stage system consisting of a dc SQUID magnetometer inductively coupled to an amplifying second stage realized by a SQIF. The SQIF is a series or parallel connection of dc SQUIDs with various inductances, which facilitates a unique global minimum in the voltage?flux characteristic and ensures a stable operating point, a high voltage swing and a large transfer function of the system. The noise of the amplified signal is dominated by the input stage and its voltage swing exceeds 1?mV, which reduces the demands on the readout electronics. A part of the current of the SQIF can optionally be fed back to the feedback coil of the first-stage SQUID, so that an on-chip linearization of the voltage?flux characteristic is realized. The short feedback path enables a substantially higher bandwidth compared to a flux-locked loop using a room temperature amplifier. From experimental results it can be expected that this set-up is capable of measuring magnetic fields with a high slew rate and dynamic range.

DOI
10.1088/0953-2048/25/1/015005

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We report on a two-stage system consisting of a dc SQUID magnetometer inductively coupled to an amplifying second stage realized by a SQIF. The SQIF is a series or parallel connection of dc SQUIDs with various inductances, which facilitates a unique global minimum in the voltage?flux characteristic and ensures a stable operating point, a high voltage swing and a large transfer function of the system. The noise of the amplified signal is dominated by the input stage and its voltage swing exceeds 1?mV, which reduces the demands on the readout electronics. A part of the current of the SQIF can optionally be fed back to the feedback coil of the first-stage SQUID, so that an on-chip linearization of the voltage?flux characteristic is realized. The short feedback path enables a substantially higher bandwidth compared to a flux-locked loop using a room temperature amplifier. From experimental results it can be expected that this set-up is capable of measuring magnetic fields with a high slew rate and dynamic range.
User-friendly ultra-high-speed readout electronics for dc superconducting quantum interference devices (SQUIDs) are presented. To maximize the system bandwidth, the SQUID is directly read out without flux modulation. A composite preamplifier is used consisting of a slow dc amplifier in parallel with a fast ac amplifier. In this way, excellent dc precision and a high amplifier bandwidth of 50 MHz are achieved, simultaneously. A virtual 50 Ω amplifier input resistance with negligible excess noise is realized by active shunting, i.e., by applying feedback from preamplifier output to input via a high resistance. The white voltage and current noise levels are 0.33 nV Hz −1 and 2.6 pA Hz −1/2 , respectively. The electronics is fully computer controlled via a microcontroller integrated into the flux-locked loop (FLL) board. Easy-to-use software makes the various electronic settings accessible. A wide bias voltage range of 1.3 mV enables the readout of series SQUID arrays. Furthermore, additional current sources allow the operation of two-stage SQUIDs or transition edge sensors. The electronics was tested using various SQUIDs with input inductances between 30 nH and 1.5 µH. Typically, the maximum FLL bandwidth was 20 MHz, which is close to the theoretical limit given by transmission line delay within the FLL. Slew rates of up to 4.6 Φ 0 µs −1 were achieved with series SQUID arrays. Current noise levels as low as 0.47 pA Hz −1/2 and coupled energy sensitivities between 90 h and 500 h were measured at 4.2 K, where h is the Planck constant. The noise did not degrade when the system bandwidth was increased to the maximum value of about 20 MHz. With a two-stage set-up, intrinsic white energy sensitivities of 30 h and 2.3 h were measured at 4.2 and 0.3 K, respectively.
We describe a low-noise, two-stage dc Superconducting QUantum Interference Device (SQUID) amplifier that is designed for applications requiring high bandwidth and dynamic range. The output signal of a low-noise SQUID in the input stage coherently modulates a series array of identical SQUIDs in the output stage via a common modulation line. The input stage is designed so its output signal does not produce multiple modulation periods in the output stage. The output stage is designed to have sufficient gain so the output noise is dominated by the amplified noise of the input SQUID and exceeds the noise of a preamplifier in the room temperature readout electronics. The SQUID amplifier may therefore be operated without flux modulation or any impedance matching network, resulting in a large dynamic range and high bandwidth.
We present a novel dc-SQUID readout scheme that provides linearization of the relation between the input and output signal without using a conventional flux-locked loop circuit. It relies on applying a periodic, sawtooth-shaped magnetic flux signal to the modulation coil of the SQUID to continuously measure the flux-to-voltage SQUID characteristic within each period of the flux ramp. In case that the amplitude and repetition rate of the ramp are chosen such that multiple flux quanta are induced in the SQUID and that the input signal is quasistatic within one period of the flux ramp, the input signal adds a constant magnetic flux offset to the SQUID that leads to a phase shift of the SQUID characteristic being proportional to the input signal. We show that this scheme allows for significantly increasing the dynamic range and that it intrinsically allows for MHz frequency-division SQUID multiplexing.
We have fabricated and tested thin film, niobium edge junction, double transformer, dc superconducting quantum interference devices (SQUID’s) that were stable under room-temperature storage and thermal cycling and that had very good noise performance. The input inductance, approximately 1.7 μH, was large enough to facilitate good matching to many experiments. When the SQUID was operated as a small-signal amplifier, the minimum detectable energy per unit bandwidth (Se) was 5×10−33 J/Hz at 100 kHz, referred to the SQUID loop (uncoupled). The minimum detectable energy per unit bandwidth was 1.8×10−31 J/Hz at 100 kHz, referred to the input coil. The SQUID’s had good characteristics for flux-locked operation since the small signal Se was low over a substantial range of bias current and magnetic flux. For operation in a flux-locked feedback circuit, Se was 6×10−32 J/Hz at 1 kHz.
Nonlinearity with multiple working points limits the practical applications of a two-stage superconducting quantum interference device (SQUID) readout circuit, which is promising for low-noise performance. To solve this problem, we proposed a simple two-stage SQUID readout circuit with two conventional dc SQUIDs improved with proportional feedback schemes, where transfer coefficient of the first-stage SQUID circuit is enhanced by additional positive feedback circuit; transfer characteristics of the second-stage SQUID circuit are linearized by an additional negative feedback circuit. Two proportional feedback schemes are cooperated together based on matching conditions to achieve both noise suppression and working point matching. Working principles were verified in experiment results. The overall transfer characteristics achieved have only one working point and are simply adjusted according to the voltage swing of an amplifier. Transfer coefficient of the first-stage SQUID circuit was raised up to 10 (20 dB), and the total flux noise of two-stage SQUID readout circuit was reduced below 1 μΦ0/√Hz, where Φ0= 2.07×10-15Wb. Our two-stage SQUID readout circuit is easy-to-operate and suited for high-performance practical SQUID systems.
We report on the continuous feedback operation of a two-stage dc Superconducting Quantum Interference Device (SQUID) system in which one SQUID works as a low-noise preamplifier to read out a second low-noise sensor SQUID. We first flux-locked the readout SQUID and measured the characteristics of the sensor SQUID, including its current-voltage characteristics, current-flux characteristics, and noise spectrum. We then investigated how the two SQUIDs could work together by simultaneously flux-locking both the sensor and the readout SQUIDs. With this two-SQUID flux-locking scheme, we recovered the noise spectrum of the sensor SQUID to within 4%. We discuss how to understand and optimize the two-stage SQUID feedback system.