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IEEE International Superconductive Electronics Conference (ISEC)

Dc-SQUID Readout with High Dynamic Range and Intrinsic MHz Frequency-Division Multiplexing Capability

Daniel Richter, A. Fleischmann, C. Enss, Sebastian Kempf

Published Jul 1, 2019• 1 citation
Publisher

Abstract

We present a novel dc-SQUID readout scheme that provides linearization of the relation between the input and output signal without using a conventional flux-locked loop circuit. It relies on applying a periodic, sawtooth-shaped magnetic flux signal to the modulation coil of the SQUID to continuously measure the flux-to-voltage SQUID characteristic within each period of the flux ramp. In case that the amplitude and repetition rate of the ramp are chosen such that multiple flux quanta are induced in the SQUID and that the input signal is quasistatic within one period of the flux ramp, the input signal adds a constant magnetic flux offset to the SQUID that leads to a phase shift of the SQUID characteristic being proportional to the input signal. We show that this scheme allows for significantly increasing the dynamic range and that it intrinsically allows for MHz frequency-division SQUID multiplexing.

DOI
10.1109/isec46533.2019.8990966

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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.
User-friendly ultra-high-speed readout electronics for dc superconducting quantum interference devices (SQUIDs) are presented. To maximize the system bandwidth, the SQUID is directly read out without flux modulation. A composite preamplifier is used consisting of a slow dc amplifier in parallel with a fast ac amplifier. In this way, excellent dc precision and a high amplifier bandwidth of 50 MHz are achieved, simultaneously. A virtual 50 Ω amplifier input resistance with negligible excess noise is realized by active shunting, i.e., by applying feedback from preamplifier output to input via a high resistance. The white voltage and current noise levels are 0.33 nV Hz −1 and 2.6 pA Hz −1/2 , respectively. The electronics is fully computer controlled via a microcontroller integrated into the flux-locked loop (FLL) board. Easy-to-use software makes the various electronic settings accessible. A wide bias voltage range of 1.3 mV enables the readout of series SQUID arrays. Furthermore, additional current sources allow the operation of two-stage SQUIDs or transition edge sensors. The electronics was tested using various SQUIDs with input inductances between 30 nH and 1.5 µH. Typically, the maximum FLL bandwidth was 20 MHz, which is close to the theoretical limit given by transmission line delay within the FLL. Slew rates of up to 4.6 Φ 0 µs −1 were achieved with series SQUID arrays. Current noise levels as low as 0.47 pA Hz −1/2 and coupled energy sensitivities between 90 h and 500 h were measured at 4.2 K, where h is the Planck constant. The noise did not degrade when the system bandwidth was increased to the maximum value of about 20 MHz. With a two-stage set-up, intrinsic white energy sensitivities of 30 h and 2.3 h were measured at 4.2 and 0.3 K, respectively.
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