Direct Readout Scheme Research Articles

Small signal analysis of SQUID direct readout schemes

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.

Study on Noise Matching Between SQUID Sensor and Its Readout Electronics

Noise matching between superconducting quantum interference device (SQUID) sensor and readout electronics has always been an important problem. Conventionally, in order to avoid the hysteresis, SQUIDs should be operated in the range of $\beta _{{{c}}}\, , where $\beta _{{{c}}}$ is the Stewart–McCumber parameter. Recently, Liu et al. extended the SQUID operating area to $\beta _{{{c}}}\,> \,1$ due to a large noise parameter Γ*. When $\beta _{{{c}}}\,> \,1$ , SQUID exhibits a large ∂ V /∂Φ, which is beneficial in reducing the noise contribution of the readout electronics, $\delta \Phi _{{{e}}}$ . In this work, we compare the SQUID system noise $\delta \Phi _{{{s}}}$ measured with four different readout electronics. Here, the four readout electronics employed are as follows: 1) the flux modulation scheme (FMS); 2) the direct readout scheme (DRS), which uses six parallel connected bipolar transistor as its preamplifier (DRS-PCBT); 3) the DRS, which uses a single preamplifier AD797 (DRS-AD797); and 4) the two-stage scheme. The preamplifier voltage noise of DRS-PCBT and DRS-AD797 are about 0.4 nV/√Hz and 0.9 nV/√Hz, respectively. For a two-stage scheme, the equivalent flux noise reaches about 0.25 μΦ0/√Hz, the measured SQUID intrinsic noise, δΦ $ _{{{i}}}$ , will dominate $\delta \Phi _{{{s}}}$ . In other readout schemes, however, $\delta \Phi _{{{s}}}$ depends on the value of $\beta _{{{c}}}$ . Finally, we found that FMS is suitable to match SQUIDs with $\beta _{{{c}}}\, . DRS-PCBT is a good choice for SQUIDs with $1\, whereas DRS-AD797 suffices for SQUIDs with $\beta _{{{c}}}\,> \,3$ .

Dependence of SQUID Intrinsic Flux Noise on Stewart–McCumber Parameter <inline-formula> <tex-math notation="LaTeX">$\beta_{c}$</tex-math> </inline-formula> of Josephson Junction

It is known that three superconducting quantum interference device (SQUID) parameters, namely, the intrinsic flux noise δΦ s , the flux-to-voltage transfer coefficient ∂V/∂Φ, and the dynamic resistance R d , increase with increasing the Stewart- McCumber parameter β c of Josephson junction. It is very difficult to obtain the low values of δΦ s for a strongly damped SQUID due to its small ∂V/∂Φ. In this paper, we employ a two-stage scheme (TSS) to measure δΦ s directly. Here, we use single chip readout electronics and a weakly damped SQUID with a β c of flux noise of the readout-SQUID system is about 4.8 μΦ 0 /√Hz 1.2, both acting as a readout-SQUID system (a preamplifier). The with a corner frequency of about 10 Hz. The front-end SQUID is coupled to the readout SQUID via the input coil with a mutual inductance of M i . In our experiment, the flux gain for a readout SQUID, i.e., G Φ = M i × (∂I/∂Φ) front-end is adjusted to be 20. Using the TSS, we measured δΦ s with different β c changing from 0.3 to 13.5 and found δΦ s increasing from 1.0 to 5.0 μΦ 0 /√Hz. We also discussed the relations between L s , β c , and δΦ s quantitatively. Finally, we proposed designing a suitable β c to match the preamplifier in a direct readout scheme to simplify a SQUID measurement system.

Flux modulation scheme for direct current SQUID readout revisited

The flux modulation scheme (FMS) is the standard readout technique of dc SQUIDs, where a step-up transformer links the SQUID to the preamplifier. The transformer's primary winding shunts the SQUID via a large capacitor while the secondary winding connects it to the preamplifier. A modulation flux having a frequency of typically 100 kHz generates an ac voltage across the SQUID, stepped up by the transformer. The SQUID with FMS is customarily operated in the current bias mode, because a constant dc bias current flows only through the SQUID due to the capacitor isolation. With FMS, however, the transformer ac shunts the SQUID so that in reality the operating mode is neither purely current-biased nor voltage-biased but rather nominal current-biased or “mixed biased.” Our objective is to experimentally investigate the consequences of ac shunting of the dc SQUID in FMS and the transformer's transfer characteristics. For different shunt values we measure the change in the SQUID bias current due to the ac shunt using another SQUID in the two-stage readout scheme, and simultaneously monitor the SQUID output voltage signal. We then explain our measurements by a simplified graphic analysis of SQUID intrinsic current-voltage (I–V) characteristics. Since the total current flowing through the SQUID is not constant due to the shunting effect of the transformer, the amplitude of SQUID flux-to-voltage characteristics V(Φ) is less as compared to the direct readout scheme (DRS). Furthermore, we analyze and compare V(Φ) obtained by DRS and FMS. We show that in FMS, the transfer characteristics of the SQUID circuit also depend on the isolation capacitance and the dynamic resistance of the SQUID.

Practical dc SQUID system: Devices and electronics

In order to set up a liquid helium-cooled practical dc SQUID system with acceptable noise figure, we employ a weakly damped dc SQUID with a large flux-to-voltage transfer coefficient ∂V/∂Ф in a direct readout scheme (DRS) without flux modulation. Two preamplifiers are utilized: (1) AD 797 for a so-called “single chip readout electronics” (SCRE); (2) 6 parallel-connected bipolar transistors (PCBT). The latter reduces the preamplifier voltage noise Vn but increases its current noise In, which plays a leading role in the system low-frequency noise. We introduce a current feedback circuit (CFC) consisting of an inductor Li coupled to the SQUID with mutual inductance Mi to improve the noise performance. In this work, the preamplifier In contribution and CFC are analyzed. To evaluate the In suppression with CFC, two criteria are presented. Furthermore, we establish a dimensionless parameter ξ to describe CFC quantitatively. The system noise is compared with and without CFC using the two preamplifiers. For a dc SQUID with a loop inductance of 350pH, an intrinsic noise of about 5μФ0/√Hz and a corner frequency at 2Hz are measured using PCBT with CFC.

A SQUID gradiometer module with large junction shunt resistors

A dual-washer superconducting quantum interference device (SQUID) with a loop inductance of 350 pH and two on-washer integrated input coils is designed according to conventional niobium technology. In order to obtain a large SQUID flux-to-voltage transfer coefficient, the junction shunt resistance is selected to be 33 Ω. A vertical SQUID gradiometer module with a baseline of 100 mm is constructed by utilizing such a SQUID and a first-order niobium wire-wound antenna. The sensitivity of this module reaches about 0.2 fT/(cm·Hz1/2) in the white noise range using a direct readout scheme, i.e., the SQUID is directly connected to an operational amplifier, in a magnetically shielded room. Some magnetocardiography (MCG) measurements with a sufficiently high signal-to-noise ratio (SNR) are demonstrated.

Investigation of Helium-Cooled Planar Transformer-Coupled SQUID Magnetometer

We investigated helium-cooled planar transformer-coupled SQUID magnetometers with regard to their field resolution δB by varying the SQUID loop inductance Ls, input coils and the pick-up loop Lp. It was found that the pick-up-loop area Ap is the most important parameter for δB of transformer-coupled magnetometers. δB with Ap = 10 × 10 mm2 reached about 3 fTA/□Hz, even using direct readout scheme without any feedback circuitries.

Multichannel fetal magnetocardiography using SQUID bootstrap circuit

Fetal magnetocardiography (MCG) is a sophisticated non-invasive technique for the fetal heart diagnosis. We constructed a multichannel fetal MCG system based on a novel superconducting quantum interference device (SQUID) direct readout scheme called SQUID bootstrap circuit (SBC). The system incorporates four SBC gradiometers for the signal detection and three SBC magnetometers as the references. The fetal MCG signal at a 28-weeks' gestation was measured. By the fetal MCG signal separation and average, the P-wave and QRS complex can be clearly identified. These results indicate that the SBC is one of the most promising techniques for the fetal MCG recordings.

Statistical characterization of voltage-biased SQUIDs with weakly damped junctions

Recently, it has been shown that voltage-biased readout of SQUIDs with weakly damped junctions (large Stewart–McCumber parameter βc, due to high shunt resistance) is useful for suppression of preamplifier noise. We experimentally studied the characteristics of 53 planar niobium–SQUID magnetometers with junction shunt resistors RJ nominally of 30 Ω fabricated on 5 × 5 mm2 chips. The field-to-flux transfer coefficient ∂B/∂Φ of the magnetometers was 1.5 nT/Φ0, with a SQUID loop inductance Ls of about 350 pH. The distributions of important SQUID parameters, such as the current swing Iswing, the dynamic resistance Rd, and the flux-to-voltage transfer coefficient ∂V/∂Φ, are given. Nearly all the SQUIDs could be stably operated in the voltage bias mode and their ∂V/∂Φ reached a large mean value of 380 μV/Φ0. In this case, the SQUIDs can be read out directly by a commercial operational amplifier without any additional means to suppress preamplifier noise. The mean flux noise of the SQUIDs was found to be 4.5 μΦ0 Hz−1/2, corresponding to a field resolution of 7 fT Hz−1/2. To demonstrate the applicability of these SQUIDs in the direct readout scheme, a simple four-channel SQUID gradiometer system was set up to perform magnetocardiography and magnetoencephalography measurements in a magnetically shielded room.

A SQUID gradiometer module with wire-wound pickup antenna and integrated voltage feedback circuit

The performance of the direct readout schemes for dc SQUID, Additional Positive Feedback (APF), noise cancellation (NC) and SQUID bootstrap circuit (SBC), have been studied in conjunction with planar SQUID magnetometers. In this paper, we examine the NC technique applied to a niobium SQUID gradiometer module with an Nb wire-wound antenna connecting to a dual-loop SQUID chip with an integrated voltage feedback circuit for suppression of the preamplifier noise contribution. The sensitivity of the SQUID gradiometer module is measured to be about 1fT/(cm√Hz) in the white noise range in a magnetically shielded room. Using such gradiometer, both MCG and MEG signals are recorded.

Bias Reversal Technique in SQUID Bootstrap Circuit (SBC) Scheme

Abstract Recently, a SQUID direct readout scheme called voltage-biased SQUID Bootstrap Circuit (SBC) is introduced to reduce preamplifier noise contribution. In this paper, we describe a concept of SBC with bias reversal technique which can suppress SQUID intrinsic 1/f noise. When applying a symmetrically rectangular voltage across SBC, two I-Φ characteristics appear at the amplifier output. In order to return to one I - Φ curve, a demodulation technique is required. Because of the asymmetry of typical SBC I-Φ curve, the demodulation method is realized by using a flux compensation of one half Φ0 flux shift. The output signal is then filtered and returned to one I-Φ curve for ordinary FLL readout. It was found, the reversal frequency f R can be dramatically enhanced when using a preamplifier consisting of two operational amplifiers. A planar Nb SQUID magnetometer with a loop-inductance of 350 pH, f R =50 kHz and a second order low pass filter with 10 kHz cut off frequency was employed in our experiment. Results prove the feasibility of SBC bias reversal method. Comparative experiment on noise performance will be carried out in further studies.

An approach to optimization of the superconducting quantum interference device bootstrapcircuit

Recently, we demonstrated and analysed the superconducting quantum interference device(SQUID) bootstrap circuit (SBC). It is a direct readout scheme for dc SQUID in thevoltage bias mode, permitting one to suppress the preamplifier noise. The SBCenables us to control the two key parameters of a voltage-biased SQUID: theflux-to-current transfer coefficient and the dynamic resistance. The flux-to-current,I–Φ, characteristics of SBC are made asymmetric by introducing the additional current feedback.Depending upon the choice of the working point, this feedback can be positive (working pointW2 on thesteeper I–Φ slope) ornegative (W1 on the less steep slope). The dynamic resistance is controlled by the additional voltagefeedback. In our publications to date we presented only the SBC operation atW2, while in this paper we demonstrate operation atW1 and show that also in this regime the preamplifier noise suppression is possible. We used aliquid-helium-cooled Nb SQUID with a loop inductance of 350 pH and attained white flux noise of 2.5 µΦ0 Hz − 1/2 both atW2 andat W1. In the latter case, the linear flux range exceeded one half-flux quantumΦ0. This large linear range should lead to a significantly improved stability and slew rate ofthe system and also make the tolerable spread in circuit parameters much wider than in allSQUID direct readout schemes known to date. Consequently, operation in this regimeopens a new path to possible SBC optimization.

Simplified analysis of direct SQUID readout schemes

A simple approach to understanding and analyzing direct readout schemes forsuperconducting quantum interference devices (SQUIDs) is presented. It is shown that theexisting methods for suppression of room temperature amplifier noise are based on voltagefeedback and current feedback in the SQUID, that were introduced in the original schemesof additional positive feedback and bias current feedback. It is also shown that the waythe SQUID is biased (at constant current or voltage) does not affect the noisesuppression.

Superconducting tunable flux qubit with direct readout scheme

We describe a simple and efficient scheme for the readout of a tunable flux qubit, andpresent preliminary experimental tests for the preparation, manipulation and final readoutof the qubit state, performed in the incoherent regime at liquid helium temperature. Thetunable flux qubit is realized by a double SQUID with an extra Josephson junction insertedin the large superconducting loop, and the readout is performed by applying a currentramp to the junction and recording the value for which there is a voltage response,depending on the qubit state. This preliminary work indicates the feasibility and efficiencyof the scheme.

Development of a SQUID Readout System for the MiniGRAIL

The MiniGRAIL is one of the three similar spherical gravitational wave detectors that are currently being developed. The detector has a resonant frequency of about 3 kHz and will be operated at 20 mK. The ultimate goal is to use a readout system consisting of six transducers coupled to nearly quantum limited two-stage SQUIDs. The two-stage SQUIDs are based on double relaxation oscillation SQUIDs, which enables a direct voltage readout scheme. We have developed nonintegrated two-stage SQUIDs and experimentally verified the proper operation of the system coupled to a capacitive transducer. Based on the results that were achieved, integrated two-stage SQUIDs were designed. Special attention has been paid to the sensor SQUID, the back action of the SQUID and the feedback scheme that is used for linearizing the SQUID output.

A spherical gravitational wave detector readout by nearly quantum limited SQUIDs

We are developing nearly quantum limited two-stage SQUID systems for the readout of the MiniGRAIL, the first spherical gravitational wave detector with a diameter of 65 cm and a mass of 1150 kg. The two-stage SQUID systems are based on a conventional dc SQUID as the sensor and a double relaxation oscillation SQUID (DROS) as the second stage. The SQUID systems will be coupled to the detector via a multi-mode inductive transducer. The large flux-to-voltage transfer of the two-stage SQUID system allows a direct voltage readout scheme, i.e. without (ac flux) modulation. At T = 4.2 K, the energy resolution in flux-locked loop was measured to be ε = 27 h, and at a temperature around 20 mK, the energy resolution is expected to reach the quantum limit.

A low noise HTS SQUID magnetometer with an on-chip pickup loop coupled via an intermediate flux transformer

For many SQUID applications robust, compact magnetometers are required with low flux noise and high effective area at 77 K. Low flux noise is achieved by using a low inductance SQUID. A low inductance SQUID will also have a high transfer function, allowing simplified direct readout schemes to be used. For maximum field sensitivity the SQUID needs to be coupled to a pickup loop of large area and therefore large inductance. We have modelled, designed and fabricated a novel HTS magnetometer consisting of a low inductance (<16 pH) dc SQUID coupled to a 28 nH pickup loop flux transformer fabricated on the same 1 cm2 substrate. Efficient coupling was achieved by using a flip-chipped intermediate flux transformer. This configuration produces a magnetometer with a high sensitivity per unit area. The magnetometers incorporate PrBa2Cu3O7 isolation layers and two 2 μm diameter CAM variant junctions. Thick YBa2Cu3O7 layers were used to improve coupling and decrease the demagnetisation factor wherever possible. Our device had a transfer function of 913 μV/Φ0 which allows direct readout without any matching or additional positive feedback arrangements. The measured effective area at 77 K was 0.58 mm2 (3.6 nT/Φ0). The magnetometer white noise was 18 fT/ and at 1 Hz was 380 fT/. This was reduced at 1 Hz to 120 fT/ using bias reversal. The measured white noise was higher than the design value and is largely due to Johnson noise from the PrBa2Cu3O7 isolation layer used in our devices.

Universal active dc biasing system for a high-T/sub c/ SQUID based on a liquid-nitrogen-cooled preamplifier

A system for the SQUID active dc biasing was developed and tested. This system provides an opportunity to change the output resistance of the biasing source over a wide range. The white flux-noise of a bicrystal SQUID-gradiometer has been measured in direct readout scheme with three different values of the biasing source output resistance. A maximum level of white noise of 11 /spl mu//spl Phi//sub 0//Hz/sup 1/2/@100 kHz was found in case of maximum output resistance (current-biasing). A white noise of 7,9 /spl mu//spl Phi//sub 0/Hz/sup 1/2/ was measured for the minimum of the biasing source resistance (voltage-biasing). The best level of the flux noise of 6 /spl mu//spl Phi//sub 0//Hz/sup 1/2/ was found at a biasing source resistance close to SQUID normal resistance R/sub n/ (power-biasing). Significant reduction of the cut-off frequency (near 10 kHz instead of 100 kHz) was found for the tested bicrystal SQUID-gradiometers due to the active dc voltage-and power-biasing systems in comparison with the standard current-biasing circuit.

HTS SQUID magnetometers with intermediate flux transformers

We have modeled and fabricated a novel HTS magnetometer with a d.c. SQUID which couples to an on-chip flux transformer via an intermediate flux transformer. This configuration allows high efficiency coupling between a 65 mm/sup 2/, 28 nH pickup loop and a low inductance (<15 pH) SQUID. The small SQUID inductance is required for low noise and high /spl part/V//spl part//spl Phi/ so that direct readout schemes may be used. The intermediate flux transformer was flip-chipped with a sub-micron separation to the main substrate. The magnetometer makes use of CAM junction technology, double thickness (/spl ap/0.7 /spl mu/m) YBa/sub 2/Cu/sub 3/O/sub 7/ layers, and a groundplaned SQUID slot. The measured responsivity at 77 K was 0.57 mm/sup 2/ (3.6 nT//spl Phi//sub 0/) with /spl part/V//spl part//spl Phi/=98 /spl mu/V//spl Phi//sub 0/ which is close to that predicted by our model. No resonances, which degrade the performance of similarly configured LTS devices, were observed. We attribute this to the use of PrBa/sub 2/Cu/sub 3/O/sub 7/ as the isolation barrier. Excess white noise, probably due to Johnson noise from the PrBa/sub 2/Cu/sub 3/O/sub 7/, limited the sensitivity in our first device to 33 fT//spl radic/Hz at 77 K.

Low noise DC SQUIDs fabricated in Nb-Al/sub 2/O/sub 3/-Nb trilayer technology

The authors have designed, fabricated and tested all-refractory DC SQUIDs in Nb-Al/sub 2/O/sub 3/-Nb trilayer technology that have noise performance comparable to the best previously reported for any technology. A variety of SQUID designs were incorporated as part of a trilayer process development test vehicle. SQUID inductance, junction area, and resistive shunt geometry were varied in matrix fashion to give SQUIDs with near-optimum parameter values for a factor of five range in Josephson current density and shunt sheet resistance. The devices were fabricated using a selective niobium anodization with a minimum feature size of 2 mu m. The base electrode and Nb wiring were patterned with dry etching, and the junction areas were defined by anodization: the Ti resistors were patterned with a lift-off process. Current density on different wafers was varied from 400 to 1000 A/cm/sup 2/ with typical junction V/sub m/'s of 60 mV. The shunt sheet resistance was varied in the 1-5- Omega / Square Operator range. The noise was measured with an RF SQUID direct small-signal readout scheme. A 50-pH SQUID with 3- mu m/sup 2/, 16- mu A junctions and 14- Omega shunt resistors was shown to have an ideally low white noise of 1*10/sup -13/ Phi /sub 0//sup 2//Hz, a white to 1/f crossover frequency at 7 Hz, and a noise level less than 6*10/sup -12/ Phi /sub 0//sup 2//Hz at 0.1 Hz.