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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]

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 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 SQUID Bootstrap Circuit (SBC) for direct-coupled readout of SQUID signals in voltage bias mode was recently demonstrated. In addition to the conventional dc SQUID, the SBC incorporates a shunt resistor Rs, and two coils coupled to the SQUID via mutual inductances M1 and M2. In this paper, basic equations of SBC are formulated based on its equivalent circuit model. The expression of equivalent flux noise from the preamplifier is also given. The effect of the three adjustable parameters (M1, M2 and Rs) on the characteristics of SBC and the preamplifier noise suppression are numerically simulated. The SBC combines current and voltage feedbacks in one circuit, allowing for an effective suppression of the preamplifier voltage noise through increased flux-current transfer coefficient and dynamic resistance. In contrast to other direct-coupled schemes, it offers not only a good noise performance, but also tolerance to a wide range of adjustable parameters. [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 introduced a SQUID system design for practical magnetocardiography working in unshielded environment by embedding the whole readout electronics in the cryostat to improve both the stability and the electromagnetic compatibility. • We presented a compact readout scheme using only few integrated circuits to implement the low-drift readout, the MCU-free internal control, the flexible multi-channel integration, and the fiber optic isolation of external accessing. To promote the adaptability of the practical Magnetocardiography (MCG) system working in unshielded environment, the SQUID readout electronics is required to improve its stability and the Electromagnetic Compatibility (EMC). It should be low-drift to the variation of cryogenic liquid level in long-time running, avoid Electromagnetic Interference (EMI) internally from the control circuit, be electrical isolated from host computer, and finally be compact to be embedded in the cryostat to implement external EMI shielding and filtering. Accordingly, we presented a low-drift and compact readout circuit design. It applies the differential amplifier in the Flux-Locked Loop (FLL) to reject the voltage drift, and avoids the internal EMI by using control circuit without Micro-Controller Unit (MCU). It simplifies the integration of multi-channel FLLs and the isolated accessing from host computer by using the Inter-Integrated Circuit (IIC) bus with fiber optic interface. In the experimental results, our MCU-free FLLs successfully suppressed the voltage drift, and exhibited the high consistency in reading of 9-channel gradiometers with noise level of about 6.5μΦ 0 /√Hz. Finally, we set up a 9-channel MCG system using our multi-channel SQUID readout electronics, and demonstrated the high quality 9-channel measurements of adult MCG signals in the unshielded environment. [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]

• 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]

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]

We recently presented a direct readout technique for the dc Superconducting QUantum Interference Device (SQUID) without flux modulation (FM), operated in voltage bias mode, and named it the SQUID Bootstrap Circuit (SBC). The SBC combines additional voltage and current feedbacks to minimize the room-temperature preamplifier noise. The main point of this paper is to compare the flux noise performance of the SBC readout with that of the FM scheme using a sine wave modulation signal. Several liquid-helium-cooled SQUID magnetometers with different layouts and loop inductances were characterized using these two readout schemes. Measured noise was comparable to or even lower than that measured by FM electronics. Furthermore, the SBC noise performance was evaluated as function of resistance which, when properly adjusted, permits us to nearly fulfill the critical noise suppression condition. We believe SBC to be a promising candidate for multi-channel SQUID systems. [ABSTRACT FROM AUTHOR]