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IEEE Transactions on Applied Superconductivity

Instabilities in SQUID Series Arrays due to the Internal and External Parasitics

Daniil Vili, M. Kiviranta

Published May 20, 2026• 0 citations
Publisher

Abstract

SQUID Series Arrays (SSAs) are widely used amplification devices for cryogenic readout chains such as Transition Edge Sensor (TES) matrices for space observation (Barrett et al., 2023) or quantum science (Hummatov et al., 2023). Either wiring-related external or on-chip internal parasitics often cause SSAs to show instabilities, which may limit the obtainable gain from a SSA design or may constrain the cryogenic setup that can be made stable for measurements. We shall show a rough model of typical parasitics in a setup and estimate the associated stability criteria. Modelling is backed up with experimental data from SSAs fabricated at VTT (M. Kiviranta et al., 2021) and operated at T = 4.2 K. In experiments the SSA has been augmented with a set of controlled external parasitic elements and the instability threshold observed. Results show correlation between simulations and experimental data, suggesting the SSAs to be prone to instabilities caused by internal and external parasitics.

DOI
10.1109/tasc.2026.3695300

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SQUID Series Arrays (SSAs) are widely used amplification devices for cryogenic readout chains such as Transition Edge Sensor (TES) matrices for space observation (Barrett et al., 2023) or quantum science (Hummatov et al., 2023). Either wiring-related external or on-chip internal parasitics often cause SSAs to show instabilities, which may limit the obtainable gain from a SSA design or may constrain the cryogenic setup that can be made stable for measurements. We shall show a rough model of typical parasitics in a setup and estimate the associated stability criteria. Modelling is backed up with experimental data from SSAs fabricated at VTT (M. Kiviranta et al., 2021) and operated at T = 4.2 K. In experiments the SSA has been augmented with a set of controlled external parasitic elements and the instability threshold observed. Results show correlation between simulations and experimental data, suggesting the SSAs to be prone to instabilities caused by internal and external parasitics.
Biasing arrangements in multi-channel multi-stage SQUID amplifier systems, such as Transition Edge Sensor matrices for astronomical observation (Barrett et al., 2023) or quantum science (Hummatov et al., 2023), typically require a large number of wires. This is due to the need for two or more cascaded SQUID stages to obtain sufficiently large power gain over a sufficient bandwidth, and due to moderate obtainable multiplexing factors, which forces implementation of many parallel readout chains to serve all the sensor pixels. We suggest an arrangement where one bias line and one flux setpoint line are shared by two cascaded SQUID stages on a single chip, halving the number of lines two cascaded stages would ordinarily require. The stages are connected in series, sharing a single supplycurrent, dual to ordinary integrated transistor circuits in which many transistor stages are connected in parallel and share a single supplyvoltage. We show experimental results atT= 4.2 K for a proof-of-concept amplifier chip, fabricated in the VTT Micronova foundry, using SWAPS Josephson junctions (Grönberg et al., 2017) atJC= 20 μA/(μm)2critical current density. The device shows larger than 3 kΩ transresistance, when operating fromLIN= 29 nH input inductance toRD< 150 Ω output dynamic resistance.
A cold preamplifier based on superconducting quantum interference devices (SQUIDs) is currently the preferred readout technology for the low-noise transition edge sensor (TES). In this work, we have designed and fabricated a series SQUID array (SSA) amplifier for the TES detector readout circuit. In this SSA amplifier, each SQUID cell is composed of a first-order gradiometer formed using two equally large square washers, and an on-chip low pass filter (LPF) as a radio-frequency (RF) choke has been developed to reduce the Josephson oscillation interference between individual SQUID cells. In addition, a highly symmetric layout has been designed carefully to provide a fully consistent embedded electromagnetic environment and achieve coherent flux operation. The measured results show smooth V–Φ characteristics and a swing voltage that increases linearly with increasing SQUID cell number N. A white flux noise level as low as 0.28 μ Φ 0/Hz1/2 is achieved at 0.1 K, corresponding to a low current noise level of 7 pA/Hz1/2. We analyze the measured noise contribution at mK-scale temperatures and find that the dominant noise derives from a combination of the SSA intrinsic noise and the equivalent current noise of the room temperature electronics.
Multiplexing technologies based on superconducting quantum interference devices (SQUIDs) are crucial to cryogenic readout of superconducting transition-edge sensor (TES) arrays. Demands for large-scale TES arrays promote the development of multiplexing technologies towards large multiplexing factors and low readout noise. The development of multiplexing technologies also facilitates new applications of TES arrays in a wide range of frequencies. Here we summarize different types of SQUID-based multiplexing technologies including time-division multiplexing, code-division multiplexing, frequency-division multiplexing and microwave SQUID multiplexing. The advances and parameter constraints of each multiplexing technology are also discussed.
We have investigated the transient response of superconducting quantum interference devices (SQUIDs) used in time-division multiplexing schemes for the readout from arrays of superconducting transition-edge sensors (TES). In time-division multiplexing the per channel settling time is an important parameter since it limits the multiplexing frequency as well as the signal-to-noise ratio. Although SQUIDs in general are fast cryoelectronic devices operating at a nanosecond scale, experimental evidence shows that the settling time in bias-switched SQUID multiplexers can, in the case of a low impedance input circuit, reach several microseconds. We have confirmed this behavior through numerical transient analysis using a Josephson circuit simulator. Within the simulation we have found that the transient response can be reduced using an extra inductor in series with the input coil of the dc SQUID. This result in turn has been confirmed experimentally. We furthermore discuss the conflicting constraints that a desired high signal bandwidth places on the parameters of the multiplexer, the readout SQUIDs, and the TES.
The development of large superconducting bolometer (Transition Edge Sensor: TES) arrays requires ultra low noise amplification and multiplexing electronics. The use of a first transducer stage such as a SQUID (Superconducting QUantum Interference Device) allows ultimate performance in terms of noise. However, the linearization of the SQUID characteristic requires low noise amplification. Furthermore, to realize a time domain multiplexer with SQUIDs, switched biasing is also needed. We have designed an Integrated Circuit (IC) in standard BiCMOS SiGe technology for the readout and the control of a SQUID multiplexer. It includes a low noise amplifier with multiplexed inputs, switched current sources for SQUIDs, and digital circuit for the addressing with only one room temperature clock signal. We have successfully tested this integrated circuit down to 2 K. To validate the operation of a SQUID multiplexer controlled by this SiGe cryogenic IC, we have developed a 2×2 SQUID hybrid demonstrator. It consists of four commercial SQUIDs connected to a SiGe IC.
Resonant frequencies and SQUID inductancesLSin a microwave SQUID multiplexer are studied for the purpose of reliable design applicable for a future large-format array of transition edge sensors (TESs). The key element of the multiplexer chip is a quarter-wave-length resonator terminated by a dissipationless rf SQUID connected to TES. For the resonator, we found that a small correction to the effective length of the resonators made the designed resonant frequencies fit the experimental one over the whole readout band of 4-8 GHz covered by our cryogenic amplifier. We also found that microstrip-type SQUIDs with vertical loops are suitable for accurate design of small inductanceLS<; 10<; pH to operate the rf SQUID in dissipationless regime. Based on these well-designed resonators and SQUIDs, we have successfully demonstrated the multiplexing of three pulsed signals with 1-ms width and spacing given at the input ports of three SQUIDs. The equivalent noise current refer to the SQUID input is not dominated by SQUIDs and estimated to be 200-270 pA/ √Hz, whose improvement approach is quantitatively discussed.