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We have developed a dc-SQUID amplifier with intra-coil resistors based on second-order parallel gradiometers. The measured results show that intra-coil resistors can significantly increase the flux–voltage transfer coefficient VΦ as well as smooth out resonances and produce a smooth flux–voltage (V–Φ) characteristic curve. It has been observed through a comparison of various intra-coil damping resistors that the flux–voltage transfer coefficient VΦ as a function of the resistance of the intra-coil resistors rises as the corresponding electrical conductance increases. The measured results of the flux noise at 4.2 K demonstrate explicitly that the flux–voltage transfer coefficient can greatly increase detection sensitivity and successfully reduce the noise contribution from the electronics operating at room temperature. [ABSTRACT FROM AUTHOR]

The development of superconductor integrated circuits (SCIC) places increasing demands on electronic design automation (EDA) tools. Circuit simulation is a crucial step in the design process of superconducting quantum interference devices (SQUID) and single flux quantum (SFQ) circuits. Over the years, there have been many SC circuit simulators, like JSPICE, JSIM, WRspice, JoSIM, PSCAN2, JSICsim, PrimeSim HSPICE, Spectre, and more. The previous studies have compared the differences in results among some simulators for the same circuit cases. However, designers of SC circuits still face challenges when choosing simulators and setting simulation parameters. The performance of these simulators lacks comprehensive and quantitative evaluations to date. To evaluate the performance of the simulators, we focused on three aspects: the differences among the IV results, accuracy, and speed. For characterizing the accuracy of the simulators, we proposed a method that uses the relative error between the numerical and analytical solutions at the L - C resonance point on the IV curve of a dc SQUID. In this article, we have selected five representative simulators JoSIM, JSIM, WRspice, PSCAN2, and JSICsim for our study. By using multiple cases of the bare and coupled dc SQUID, multiple IV curves, and the analytical solution as a reference, we comprehensively compared the performance of these simulators. Additionally, we quantitatively examined the impact of two key simulation parameters, namely, the maximum allowed simulation timestep (max timestep) and relative tolerance (RelTol), on the performance of these simulators. Our results show that the normalized voltage differences in the IV curves of different simulators are relatively small (within 0.06) in regions far from the L - C resonance point, while they increase significantly near the L - C resonance point (maximum is 0.4). PSCAN2 exhibits a significant relative error of approximately 16% when the max timestep is 0.6ps and RelTol is 1 × 1 0 − 1 , which is close to its default RelTol value. Our work provides some insights and references for the designers of SC circuits on how to choose simulators and set simulation parameters. • Comprehensively studied the performance of the five simulators (JoSIM, JSIM, WRspice, PSCAN2, and JSICsim) from three aspects: the differences among the IV results, accuracy, and speed. • Proposed a reliable method to characterize the accuracy of simulators by using the relative error between the numerical and analytical solutions at the L - C resonance point of the dc SQUID's IV curve. • Evaluated and compared the performance of simulators, and quantitatively examined the impact of simulation parameters (max timestep and RelTol) on the simulators' performance. [ABSTRACT FROM AUTHOR]

There are two bias schemes, namely current-bias and voltage-bias, for the directly coupled readout circuit of direct current superconducting quantum interference device (dc SQUID). In order to find out the difference between two bias schemes, we present the theoretical analyses on their equivalent circuits, working point locations, and noise performances. The theoretical analysis and experimental validation prove that the voltage-bias scheme achieves a larger transfer coefficient and exhibits a better noise performance than the current-bias scheme in the reading of conventional dc SQUID. [ABSTRACT FROM AUTHOR]

It has been found that when superconducting quantum interference device magnetometers operate in a geomagnetic field environment, its output will occasionally show small momentary jumps with the change of the external magnetic field, which seriously affects the measurement accuracy of the geomagnetic field and needs to be eliminated. A magnetic flux jump model called the parasitic superconducting ring model was built to explain the causes of these small jumps, and Helmholtz coils were set up to study the jump and verify this model in the laboratory. The experimental results showed that the position and amplitude of the jumps were consistent with the model. It is believed that this model can guide the design of superconducting chips in geophysical applications. [ABSTRACT FROM AUTHOR]

Practical superconducting quantum interference devices (SQUIDs) have been developed into multiloop hybrid electric circuits with Josephson junctions and normal elements such as resistor, inductor and capacitor. To find a common circuit analysis and simulation method for different types of SQUID hybrid circuits consist of both superconducting and normal components, we introduce a mesh-current method, which can derive both the general system model and uniform circuit equations directly from the equivalent circuit. The mesh-current method is demonstrated in the simulation of a SQUID additional positive feedback circuit. The numerical simulation results are presented and verified with the measurements. Compared with the conventional nodal analysis method, the mesh-current method is excellent in dealing with the relations including external flux, self and mutual inductances in multiloop hybrid circuit analysis; its final circuit equations directly exhibit the physical theorems; its general system model reveals the quantum interference mechanism inside SQUID circuits, and is applicable for further dynamics studies. [ABSTRACT FROM AUTHOR]

Direct current superconducting quantum interference device (dc SQUID) can be regarded as a hybrid system with two nonlinear Josephson currents driving a linear network consists of conventional resistors (R), inductors (L), and capacitors (C). There must be LC resonances inside the SQUID loop with influences on its static current-voltage characteristics. To study the working principle of the LC resonance, we build an equivalent dynamic system model transformed directly from the circuit equations of dc SQUID. With dynamic system analyses in both dc and alternating current (ac) domains, we derive the analytical expressions of the resonance point with only the RLC circuit parameters. The analytical derivation proves that the LC resonance inside a symmetrical dc SQUID with resonance frequency ω = 1/√LC results in the flux modulation suppression with I–V curves concentrated on one resonance point. Based on those mathematical expressions, the resonance point is easily indentified from the measured I–V curves, and can be utilized for practical SQUID parameters characterization. [ABSTRACT FROM AUTHOR]

As part of the efforts to establish a reliable fabrication process of superconducting integrated circuits at Center for Excellence in Superconducting Electronics (CENSE) in China, we investigated the influences of various deposition conditions on the properties of molybdenum (Mo) thin films. Thin-film resistors were fabricated based on these films by using a lift-off process. It was found that Mo structures made from films peeled off easily from the substrate after lift-off. We have optimized the deposition conditions to grow Mo films with compressive or weakly tensile stress. Mo thin-film resistors with a sheet resistance of several ohm/square and surface roughness of less than 1 nm were successfully fabricated and were used in the fabrication of superconducting quantum interference devices and small-scale superconducting integrated circuits. [ABSTRACT FROM AUTHOR]

To implement a flux quanta counting (FQC) scheme in the wide range magnetic field measurement using a superconducting quantum interference device (SQUID), we present a SQUID proportional feedback amplifier (PFA) circuit. It is a simplified version of the direct readout flux-locked loop (FLL) electronics without an integrator. It achieved a periodically repeated (with a period of 1Φ0), quasi-linear flux-to-voltage characteristics with an input range extended to 2Φ0. Its working point is reset spontaneously with 1Φ0 of flux jump caused by the over range flux input. The resultant wide range measurement is achieved by the synthesis of the PFA voltage output and the flux jumps recorded using the FQC scheme. We simulated and experimentally verified the working principles of SQUID PFA. The FQC scheme using SQUID PFA was demonstrated with measurements in both shielded and unshielded environment. SQUID PFA is simple and easy-to-operate suited for applications in the Earth's magnetic field. [ABSTRACT FROM AUTHOR]

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 ×10−15 Wb. Our two-stage SQUID readout circuit is easy-to-operate and suited for high-performance practical SQUID systems. [ABSTRACT FROM AUTHOR]

A superconducting quantum interference device (SQUID) planar gradiometer is an extremely sensitive sensor for magnetic gradient measurements. It has been shown to have potential applications for aeromagnetic detection. The major challenge when operating an aeromagnetic SQUID system in actual environment is the motion noise, including the inherent response resulting from gradiometer imbalance and from magnetic interferences. Three orthogonal reference magnetometers are usually adopted to improve the gradiometer balance. However, magnetic interference coming from the system itself also needs to be compensated. In this article, a mathematical model of the motion noise picked up by the gradiometer is derived from the traditional magnetic total field compensation method. Based on the model, the signals from the triaxial magnetometer can also be used to compensate the eddy current contribution to the magnetic interference. To verify the compensation method, a SQUID planar gradiometer system was set up and used for flight trials. The gradient field noise and imbalance of our homemade gradiometer were measured to be 100 fT/m/rt(Hz) and 2E-4 in the lab. In flight, the motion-induced peak-to-peak output of the gradiometer was reduced from 170 to about 0.1 nT/m, so that a magnetic anomaly signal of about 2 nT/m from a cargo ship was clearly recognized. [ABSTRACT FROM AUTHOR]

Transient electromagnetic method (TEM) is an effective way for mineral resource prospecting if an induction coil is used as the traditional sensor. Superconducting quantum interference device (SQUID) obtains excellent sensitivity at low frequency as compared to coil. Thus, the exploration depth and the accuracy of TEM can be greatly improved. However, an ultrahigh slew rate (>10 mT/s) is needed for transient primary field recording, which is a great challenge for a single high-sensitivity SQUID receiver. In this paper, two SQUIDs with different sensitivities (1.5 nT/Φ0 and 99 nT/Φ0) are employed to record the whole TEM decaying signal. The high-sensitivity SQUID (1.5 nT/Φ0) is in reset status when transmitting and is locked after tens of microseconds after transmitting has been cut off. The low-sensitivity SQUID (99 nT/Φ0) remains locked during the whole procedure with high slew rate (∼198 mT/s) to record the fast-switching transmitting field. The two channel SQUID outputs are combined together to form a complete decaying curve. A field test was carried out. The decaying curve with a noise level of 100 fT@DC-25 kHz and a fast-switching field of ∼630 nT cutting off in tens of microseconds (slew rate up to ∼56 mT/s) was recorded after stacking. This dual-channel SQUID-based TEM system obtains high stability, which is useful for small transmitting loop (<50 m) configuration. [ABSTRACT FROM AUTHOR]

• A frequency-phase-locking (FPL) model is presented to intuitively interpret the dynamics inside dc SQUIDs. • A general analytical expression of dc SQUIDs is derived to quantitively describe how the current-voltage characteristics are decided by circuit parameters. • A practical method is found to evalue the performance of dc SQUIDs directly through network impedances. Direct-current superconducting quantum interference devices (dc SQUIDs) are ultra-sensitive flux-to-voltage convertors widely applied for biomagnetism and geophysics; they are a kind of magnetic-field-effect transistors (MFETs) with flux-modulated current-voltage characteristics. Compared to semiconductor FETs, dc SQUIDs still lack analytical expressions to interpret their inner formation mechanisms of the current-voltage characteristics. This article presents a frequency-phase-locking (FPL) model to derive the analytical expression of dc SQUIDs and reveal how the current-voltage characteristics are shaped by the circuit parameters between two Josephson junctions. The application of the analytical expression in the calculations of current-voltage characteristics is demonstrated; the results are compared with the numerical simulations. It is shown that a dc-SQUID is an FPL system inside and works as a current-modified nonlinear resistor in readout circuits; its current-voltage characteristics are the projections of three impedances of the network between Josephson currents. Those understandings enable electronic engineers to evaluate the design of dc-SQUID circuits directly through three network impedances extracted from the layout. [ABSTRACT FROM AUTHOR]

• The superconducting quantum interference working principle of DC SQUID is intuitively interpreted with an interferometric equivalent circuit and the concise dynamic system model. • The interference phenomena inside DC SQUID are simulated and visualized with distributions of the AC current and voltage inside the SQUID to improve the understanding of interferometer mechanism of DC SQUID for both SQUID design and application. Flux modulated static current-voltage characteristics are the basis of DC SQUID being the flux-to-voltage convertor utilized in high-performance magnetic field measurement systems. Those static behaviors are the results of the internal quantum interference between two Josephson junctions. However, the interferometric working principle and the interference phenomena are difficult to be intuitively visualized, either through simulation with conventional models, or through the in-situ measurement inside DC SQUID. Therefore, we redraw the equivalent circuit of DC SQUID in form of the microwave interferometer, and transform it into a concise dynamic system model to study the interferometric mechanism. The double-slit like interference phenomena inside the DC SQUID are visualized through simulations of the AC oscillation current and voltage along the SQUID washer. The concept that DC SQUID is a microwave integrated circuit working as the microwave interferometer rather than a static nonlinear transducer is demonstrated and emphasized. Those concepts help users and designers improve their understandings of quantum interference mechanism of DC SQUID for both circuit design and the practical application system development. [ABSTRACT FROM AUTHOR]

• We presented a complete circuit analysis of SQUID direct readout schemes based on the elementary SQUID small signal model. • A unified equivalent circuit is presented for analyses of all the internal feedback schemes with Trans-Impedance Amplifier (TIA) model. • The analyses are experimentally verified and the methods are easily understood with fundamental electric circuit theorems. To better understand working principles of Superconducting Quantum Interference Device (SQUID) direct readout schemes which are working in different bias and amplifier modes with different internal feedback schemes, we present the complete circuit analyses based on SQUID small signal model. SQUID bias and amplifier circuits are analyzed using SQUID Thevenin's equivalent circuit, and the general equivalent circuit of SQUID with different internal feedback schemes is derived and analyzed with trans-impedance amplifier model. Transfer characteristics and noise performances of different direct readout schemes are analyzed and experimentally characterized. It is shown that, amplifier noise suppression is only depended on SQUID flux-to-voltage transfer coefficient and irrelevant to the configuration of bias and amplifier; SQUID with internal feedback scheme improves the transfer coefficient with voltage feedback, and regulates the dynamic resistance with current feedback. [ABSTRACT FROM AUTHOR]

• We presented a simple two-terminal SQUID amplifier circuit for wide range magnetic field measurement. SQUID merits of wide bandwidth and wide range are fully exploited in this scheme. • This scheme uses only two terminals led out with coaxial cable to achieve both high speed and low heat dissipation. • This SQUID amplifier scheme can be easily fabricated on one chip as a novel SQUID integrated circuit specific for unshielded application systems in Earth's magnetic field. To implement wide range measurement using direct current Superconducting Quantum Interference Device (dc SQUID), we presented a simple two-terminal SQUID amplifier consists of a shunt resistor and a conventional SQUID in series with feedback coil. Only two terminals are led out with coaxial cable for high speed and low heat loss. Periodically repeated quasi linear flux-to-voltage transfer characteristics are achieved by internal flux feedback. Wide range flux input is modulated by the SQUID amplifier into voltage signal with rapid transient edges. The reconstructed output is the synthesis of measured voltage and counts of flux-quanta counting. Working principles of linearized SQUID amplifier were simulated and experimentally verified. Wide range measurement with error within ±0.1Φ 0 was demonstrated in the experiment. [ABSTRACT FROM AUTHOR]

• With Flux Feedback Amplifier (FFA) model, the SQUID readout circuit is simplified as a low noise differential amplifier with no more than two operational amplifiers. Two FFA schemes were conducted to build very simple FLLs. • The dynamic performances of two simple FFAs were characterized and compared in experimental results. The one-pole FFA scheme is suited for wideband FLL, the two-pole FFA scheme is suited for high slew rate FLL. • The SQUID in-loop characterization and working point reset in FFA is enabled with only one switch. Operations of FLL are simplified for practical applications. We introduced the Flux Feedback Amplifier (FFA) to design simple and easy-to-use Flux-Locked Loop (FLL) used to operate Superconducting Quantum Interference Device (SQUID) for practical applications. The SQUID FFA is a hybrid operational amplifier (op amp) with SQUID as flux input end and feedback coil as flux output end. The room temperature circuit is simplified as a low noise differential amplifier with no more than two op amps, and operated with only one switch. Two SQUID FFA schemes were demonstrated and the dynamic performances were characterized and compared in the experimental results. The scheme with a monolithic op amp achieves one-pole open loop gain with slope of 20 dB/decade and is suited for the wideband FLL. The scheme with two op amps achieves two-pole open loop gain with slope of 40 dB/decade and is suited for the FLL with high slew rate (up to 1Φ 0 /μs). [ABSTRACT FROM AUTHOR]

• We have developed a cross-line process to fabricate sub-micron Josephson tunnel junctions. • In the process, step sidewall was introduced to achieve the passivation of the junction utilizing the Al-Alox layer in situ and a self-aligned insulating layer. • A SQUID magnetometer with sub-micron junctions was made to verify the process. We have developed a cross-line process to fabricate sub-micron Josephson tunnel junctions using i-line stepper lithography and RIE etching. In the process, step sidewall was introduced to achieve the passivation of the junction utilizing the Al-AlOx layer in situ and a self-aligned insulating layer. The effect of junction area shrinkage in the process enables one to form smaller junction with dimension even at or below lithography limitation. Josephson junction with minimum area of 0.7 × 0.35 μm2 was obtained. The junction with gap current density of 1 kA/cm2 demonstrated high junction quality with a gap voltage of 2.8 mV and small sub-gap leakage current. The cross-line process for sub-micron junctions could be used in SQUID or other superconducting circuits where a low capacitance is desired. To verify the process, a SQUID magnetometer was also presented. [ABSTRACT FROM AUTHOR]

Abstract How to reduce of low frequency noise of low Tc DC superconducting quantum interference device (DC SQUID) has been an important problem and bias reversal readout scheme is an effective method to tackle it. However, the effect varies with the change of the parameter of sensors. Wang et al. found that DC SQUID with different ranges of β c matches different readout circuits to gain the lowest white noise. It is regrettable that this study did not involve the discussion of low frequency. In this work, we compare the noise of SQUID with a large range of β c measured by static bias and bias reversal. The preamplifier used is six parallel connected bipolar transistors (6 × SSM2220). Finally, we found that the bias reversal scheme is suitable to match SQUIDs with β c < 1. [ABSTRACT FROM AUTHOR]

We have developed low-noise direct current-superconducting quantum interference devices (DC-SQUIDs) based on Nb/Al-AlO x /Nb Josephson junctions on thermally oxidized silicon substrate. The SQUID fabrication was realized with a simple 5-mask-level process, in which one single insulting layer (SiO 2 ) was used not only to insulate different metal layers, but also to protect the junction shunt resistor from oxidation or corrosion. In our SQUID design, a washer-type loop with an inductance of 140 pH and a coupled flux transformer with a multi-turn spiral input coil connecting to a pickup coil of 8.5 × 8.5 mm 2 were used, thus leading to a SQUID magnetometer with magnetic field sensitivity of 0.7 nT/Φ 0 . We measured the voltage-flux characteristics and flux noise in superconducting niobium shielding at 4.2 K. The measured white flux noise in a flux-locked loop was 5 µΦ 0 /√Hz, corresponding to magnetic filed noise of 3.5 fT/√Hz. [ABSTRACT FROM AUTHOR]