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IEEE Transactions on Applied Superconductivity

Flux-Coupled Direct Feedback in a SQUID Amplifier

B. A. Hines, K. M. Sundqvist, D. N. Seitz, M. E. Huber

Published Dec 22, 2010• 7 citations
Publisher

Abstract

The Cryogenic Dark Matter Search (CDMS) employs DC Superconducting Quantum Interference Device (SQUID) Series Array Amplifiers (SSAAs) in its phonon readout system. These amplifiers are in a transresistance topology utilizing feedback from room-temperature electronics. The input coil of each SSAA is in series with a phonon sensor composed of many parallel transition edge sensors (TES's). The SSAA consists of 100 individual SQUIDs, each surrounded by planar input and feedback coils with an electrically isolated flux-focusing washer, which increases the inductive coupling between the SQUID and each coil. A room-temperature gain stage completes the feedback loop between the SSAA output voltage and the feedback coil current. We report on a significant mutual inductance that exists directly between the feedback and input coils, on its impact on the feedback network of the amplifier, and on the resulting transfer function. The consequent effects include a partial nulling of the input coil's self-inductance, as well as resonant peaking in the closed-loop response that depends on the impedance of the input coil circuit.

DOI
10.1109/tasc.2010.2091617

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The Cryogenic Dark Matter Search (CDMS) employs DC Superconducting Quantum Interference Device (SQUID) Series Array Amplifiers (SSAAs) in its phonon readout system. These amplifiers are in a transresistance topology utilizing feedback from room-temperature electronics. The input coil of each SSAA is in series with a phonon sensor composed of many parallel transition edge sensors (TES's). The SSAA consists of 100 individual SQUIDs, each surrounded by planar input and feedback coils with an electrically isolated flux-focusing washer, which increases the inductive coupling between the SQUID and each coil. A room-temperature gain stage completes the feedback loop between the SSAA output voltage and the feedback coil current. We report on a significant mutual inductance that exists directly between the feedback and input coils, on its impact on the feedback network of the amplifier, and on the resulting transfer function. The consequent effects include a partial nulling of the input coil's self-inductance, as well as resonant peaking in the closed-loop response that depends on the impedance of the input coil circuit.
Superconducting quantum interference devices (SQUIDs) are low-noise amplifiers that are essential for the readouts of translation edge sensors (TESs). The linear flux range is an important parameter for SQUID amplifiers, especially those controlled by high-bandwidth digital flux-locked-loop circuits. A large linear flux range conduces to accurately measuring the input signal and also increasing the multiplexing factor in the time-division multiplexed (TDM) readout scheme of the TES array. In this work, we report that the linear flux range of an SQUID can be improved by using self-feedback effect. When the SQUID loop is designed to be asymmetric, a voltage-biased SQUID shows an asymmetric current–flux (I–Φ) response curve. The linear flux range is improved along the I–Φ curve with a shallow slope. The experimental results accord well with the numerical simulations. The asymmetric SQUID will be able to serve as a building block in the development of the TDM readout systems for large TES arrays.
Arrays of dc-superconducting quantum interference devices (dc-SQUIDs) were investigated, in which each dc-SQUID element has a multiturn input coil. The dependence of flux noise on the number of turns of the input coil was studied for current amplifiers. SQUID arrays were fabricated by a Nb/AlO x /Nb Josephson tunnel junction fabrication process. Results show that the flux noise of the SQUID array amplifier does not depend on the turn number of the input coil. A SQUID array amplifier consisting of 128 dc-SQUID elements was fabricated, in which each element had a 7-turn input coil and a mutual inductance between the input coil and the SQUID loop of 460 pH. This amplifier showed an ultrahigh current resolution of 1 pA/Hz0.5 and a maximum input current of 11 µA for signals of 50 kHz, which is sufficient bandwidth for X-ray detection applications. These values correspond to a large dynamic range of 87 dB. The flux-voltage characteristics of this SQUID array, however, showed asymmetric behavior, which originated from electronic resonance in stray capacitance and the mutual inductance between the SQUID loop and the multiturn input coil.
We have designed and demonstrated a superconducting quantum interference device (SQUID) array linearized with cryogenic feedback. To achieve the necessary loop gain, a 300-element series array SQUID is constructed from three monolithic 100-element series arrays. A feedback resistor completes the loop from the SQUID output to the input coil. The short feedback path of this linearized SQUID array (LISA) allows for a substantially larger flux-locked loop bandwidth as compared to a SQUID flux-locked loop that includes a room temperature amplifier. The bandwidth, linearity, noise performance, and 3 Phi(0) dynamic range of the LISA are sufficient for its use in our target application: the multiplexed readout of transition-edge sensor bolometers.
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.
The dc Superconducting Quantum Interference Device (dc-SQUID) is one of the most sensitive magnetic field sensors available. In this thesis we concentrate on its application as an amplifier. In this configuration, an input circuit of interest can be connected by means of a coupling coil. The intended application of our developed low-Tc SQUID amplifiers is the readout of the first spherical gravitational wave antenna MiniGRAIL. Using small-signal analysis as well as numerical simulations, we study the achievable signal-to-noise ratio of such sensors in practical measurements. Published theories and studies could be extended. Some interesting points treated are the influence of the often used negative feedback (flux-locked loop), an altered input impedance of the SQUID amplifier and the influence of back-action noise, which directly affects the object of interest. The altered operation of the SQUID due to the presence of the input circuit is studied in numerical experiments. Another important issue, the influence of integrated input coils on the dynamics of SQUIDs, is investigated theoretically and experimentally. The performance of our developed sensors is compared to numerical simulations on detailed models. The results give insights into the behavior, design and usage of dc-SQUIDs with integrated coils. For a SQUID with input inductances of 1.5 μH we reached a good coupled energy sensitivity of about 170 ¯h in a dilution refrigerator. Furthermore, we investigated the hot-electron effect. This effect typically limits the sensitivity of superconducting electronics at sub-Kelvin bath temperatures due to a weakened electron-phonon coupling. We performed heating experiments on thin-film resistors which are similar to the shunt resistors of the Josephson junctions used in our sensors. The suppression of the hot-electron effect via electronic thermal transport to attached cooling fins is investigated both experimentally, theoretically and numerically. The numerical technique turns out to be a useful tool for the thermal design of superconducting electronics.
The measured input impedance of an amplifier involving a coil tightly coupled to a dc superconducting quantum interference device (SQUID) is found to depend on the current and flux biases of the SQUID. Variations in the input inductance arise from the reflected dynamic inductance of the SQUID, and are in reasonable agreement with the predictions of an analog simulator. Variations in the input resistance, on the other hand, arise from feedback between the output of the SQUID and the input circuit, and are in approximate agreement with the predictions of a simple model.