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IEEE Transactions on Magnetics

DC SQUID small signal analysis

Kenneth R. Carroll

Published Mar 1, 1991• 2 citations
Publisher

Abstract

A small signal analysis for the DC SQUID (superconducting quantum interference device) is presented. This analysis involves the linearization of the SQUID equations for a given flux and current bias. Considering the SQUID to be a two-port device, an impedance matrix can be determined for a SQUID coupled to a general input circuit. The two intrinsic noise sources referred to the input are computed. One advantage of this analysis over other models of the DC SQUID is that an analytic expression can be determined for the cross-correlation power spectral density of the noise sources. These results should be useful in determining the signal-to-noise ratio of low-noise SQUIDs for a given application. Other differences and similarities of the small signal analysis to other DC SQUID models are discussed.

DOI
10.1109/20.133845

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A small signal analysis for the DC SQUID (superconducting quantum interference device) is presented. This analysis involves the linearization of the SQUID equations for a given flux and current bias. Considering the SQUID to be a two-port device, an impedance matrix can be determined for a SQUID coupled to a general input circuit. The two intrinsic noise sources referred to the input are computed. One advantage of this analysis over other models of the DC SQUID is that an analytic expression can be determined for the cross-correlation power spectral density of the noise sources. These results should be useful in determining the signal-to-noise ratio of low-noise SQUIDs for a given application. Other differences and similarities of the small signal analysis to other DC SQUID models are discussed.
A low-noise coupled DC superconducting quantum interference device (SQUID) especially optimized for low frequency is discussed. Using large Josephson junctions and a low loop inductance the contribution of the critical current fluctuation to 1/f noise can be minimized. To minimize the inductance the Josephson junctions are placed in the center of the washer close to the SQUID loop. A scaled-up copper model of the SQUID and the signal coil is used to analyze the impedance of the SQUID loop affected by the signal coil. An equivalent circuit model describing the effective inductance of the SQUID loop as a function of the frequency is used to design appropriate damping of the resonances. The DC SQUID characteristics are smooth and the noise performance of the SQUID does not markedly suffer from resonances. The contribution of the 1/f noise at 1 Hz is found to be about 5*10/sup -7/ Phi /sub 0// square root Hz.>
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.
An analysis expression for the stationary probability distribution of the symmetric superconducting quantum interference device with two Josephson junctions (dc SQUID) driven by thermal noise is derived from two-dimensional Fokker–Planck equations where the potential condition is satisfied. The analytical formulae for SQUID characteristics, e.g. the circulating current, the current–voltage relationship and the transfer function, are obtained by using the probability distribution. The ‘ripple’ phenomenon of the circulating current versus the applied flux, the effects of thermal fluctuations on current–voltage relationship and the optimum operating condition of dc SQUID system are represented.
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 have designed, fabricated, and tested a Double Transformer (DT) coupled dc SQUID (Superconducting Quantum Interference Device) with low noise, an input inductance of 1μH and a smooth input-output characteristic. A transmission line model is presented to explain a resonance in the input-output characteristic of early versions of this device. Guided by the results of numerical simulations a new version of this device has been built and tested. Experimental results are presented that show that the resonance can be moved to a higher voltage by reducing the area of the SQUID loop. The voltage-external flux characteristic of some of these new devices agrees to within 10% with computer simulations. The minimum detectable energy per unit bandwidth (MDE) referred to the SQUID loop, is 10h, where h is Planck's constant. Computer simulations indicate an MDE of 6h.
Superconducting quantum interference devices (SQUIDs) are promising for detection of extremely weak power regimes for the Internet of Things and long-distance satellite networks. In low-frequency magnetic signal measurements, it has demonstrated superior performance over the traditional systems. We review the resistively and capacitively shunted junction model of dc SQUIDs and investigate its transfer function to magnetic flux signals while taking thermal fluctuation into account. We numerically evaluate the influence of bias current and bias flux signal to determine the operating parameters of the device. The performances related to SQUID ring inductance operating at 4.2 K and 77 K are demonstrated. Combined with common radio frequency front-end modules, including low-noise amplifier and low-pass filter, we evaluate the bit-error-rate performance of the system under different inductance values and inferred that the sensitivity of the system can reach −99 dBm at 100 MHz bandwidth.