We experimentally studied two important parameters of helium-cooled superconducting quantum interference devices (SQUIDs) in the voltage bias mode: the dynamic resistance Rd and the flux-to-current transfer coefficient ∂i/∂Φ, with different junction shunt resistors RJ. We investigated a voltage-biased SQUID using the direct readout current-to-voltage converter scheme involving an operational amplifier. At higher RJ, the flux-to-voltage conversion coefficient ∂V/∂Φ becomes sufficiently large to effectively suppress the room-temperature amplifier's noise without any need for additional feedback circuits. The McCumber parameter limits the rise of ∂V/∂Φ. We discuss the performance of voltage-biased SQUIDs at different effective McCumber parameters.
We experimentally studied two important parameters of helium-cooled superconducting quantum interference devices (SQUIDs) in the voltage bias mode: the dynamic resistance Rd and the flux-to-current transfer coefficient ∂i/∂Φ, with different junction shunt resistors RJ. We investigated a voltage-biased SQUID using the direct readout current-to-voltage converter scheme involving an operational amplifier. At higher RJ, the flux-to-voltage conversion coefficient ∂V/∂Φ becomes sufficiently large to effectively suppress the room-temperature amplifier's noise without any need for additional feedback circuits. The McCumber parameter limits the rise of ∂V/∂Φ. We discuss the performance of voltage-biased SQUIDs at different effective McCumber parameters.
We experimentally studied weakly damped superconducting quantum interference devices (SQUIDs) shunted by an external resistor Rs and operated in either current- or voltage-bias mode. The SQUID parameters, such as the flux-to-voltage transfer coefficient ∂V/∂Φ and the dynamic resistance Rd, are reduced due to Rs, while the SQUID intrinsic noise remains unchanged. The reduced parameters can be enhanced again by using voltage feedback circuitry. Furthermore, Rs can be used to damp the SQUID in order to avoid the appearance of hysteresis or oscillation in SQUID characteristics. SQUID shunted by small Rs is always operated in mixed-bias mode.
We investigate niobium thin film superconducting quantum interference devices (SQUIDs) with different Steward—McCumber parameters βc operated in both current- and voltage-bias modes. We experimentally prove that there is no difference between the two bias modes with respect to the SQUID intrinsic noise and the noise contribution from the preamplifier. Furthermore, the relationships of the SQUID dynamic parameters, (Rd)current bias ≈ (Rd)voltage bias and (∂V/∂Φ)current bias ≈ [(∂i/∂Φ)Rd]voltage bias, are always satisfied. For a strongly damped SQUID with βc ≈ 0.25, additional positive feedback (APF) and noise cancellation (NC) were employed to enhance ∂V/∂Φ, the former showing a degradation in the linear flux range but otherwise the same with NC. For a weakly damped SQUID with βc ≈ 3, it is directly connected to the preamplifier without APF or NC, and a low SQUID system noise of about 4 μΦ0/√Hz is measured, which is close to its intrinsic noise.
Recently, we demonstrated and analysed the superconducting quantum interference device (SQUID) bootstrap circuit (SBC). It is a direct readout scheme for dc SQUID in the voltage bias mode, permitting one to suppress the preamplifier noise. The SBC enables us to control the two key parameters of a voltage-biased SQUID: the flux-to-current transfer coefficient and the dynamic resistance. The flux-to-current, I??, 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 point W2 on the steeper I?? slope) or negative (W1 on the less steep slope). The dynamic resistance is controlled by the additional voltage feedback. In our publications to date we presented only the SBC operation at W2, while in this paper we demonstrate operation at W1 and show that also in this regime the preamplifier noise suppression is possible. We used a liquid-helium-cooled Nb SQUID with a loop inductance of 350 pH and attained white flux noise of 2.5? ??0?Hz ? 1/2 both at W2 and at W1. In the latter case, the linear flux range exceeded one half-flux quantum ?0. This large linear range should lead to a significantly improved stability and slew rate of the system and also make the tolerable spread in circuit parameters much wider than in all SQUID direct readout schemes known to date. Consequently, operation in this regime opens a new path to possible SBC optimization.
A simple approach to understanding and analyzing direct readout schemes for superconducting quantum interference devices (SQUIDs) is presented. It is shown that the existing methods for suppression of room temperature amplifier noise are based on voltage feedback and current feedback in the SQUID, that were introduced in the original schemes of additional positive feedback and bias current feedback. It is also shown that the way the SQUID is biased (at constant current or voltage) does not affect the noise suppression.
Dependence of SQUID Intrinsic Flux Noise on Stewart–McCumber Parameter βc of Josephson Junction
It is known that three superconducting quantum interference device (SQUID) parameters, namely, the intrinsic flux noise δΦs, the flux-to-voltage transfer coefficient ∂V/∂Φ, and the dynamic resistance Rd, increase with increasing the Stewart- McCumber parameter βcof Josephson junction. It is very difficult to obtain the low values of δΦsfor a strongly damped SQUID due to its small ∂V/∂Φ. In this paper, we employ a two-stage scheme (TSS) to measure δΦsdirectly. Here, we use single chip readout electronics and a weakly damped SQUID with a βcof flux noise of the readout-SQUID system is about 4.8 μΦ0/√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 Mi. In our experiment, the flux gain for a readout SQUID, i.e., GΦ= Mi× (∂I/∂Φ)front-endis adjusted to be 20. Using the TSS, we measured δΦswith different βcchanging from 0.3 to 13.5 and found δΦsincreasing from 1.0 to 5.0 μΦ0/√Hz. We also discussed the relations between Ls, βc, and δΦsquantitatively. Finally, we proposed designing a suitable βcto match the preamplifier in a direct readout scheme to simplify a SQUID measurement system.
The dynamics and noise of a dc superconducting quantum interference device (SQUID) with the McCumber parameter βc=2πR2IcC/Φ0 close to the unity (where Ic, R, C are the critical current, the shunt resistance, and the capacitance of the Josephson junctions comprising the SQUID, respectively, and Φ0=2.07×10−15 Wb is the magnetic flux quantum) integrated with a planar spiral input coil have been experimentally studied. The length of the spiral input coil was chosen to match its λ/4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance enhances the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, increases the dynamic resistance Rd and the gradient of the flux-to-voltage characteristics ∂V/∂Φ without hysteresis. This relaxes the tolerance for the βc parameter, simplifies the technological process, and improves the yield of devices. A dc SQUID with loop inductance L=31.4 pH, βc=0.72, and a six turn input coil has demonstrated a nondistorted quasisinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of approximately 140 μV peak-to-peak. A spectral density of the intrinsic magnetic flux noise as low as 3.5×10−7 Φ0/Hz1/2 has been measured in the double stage configuration at a temperature of 4.2 K using direct read-out electronics. This corresponds to the intrinsic energy resolution of ε=12.5h. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz1/2 with an input coil inductance of 58 nH. The coupled energy resolution is εc=45h in the white noise region.