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arXiv:1712.01577 · Instruments

Transformer Coupling and Its Modelling for the Flux-Ramp Modulation of rf-SQUIDs

P. Carniti, L. Cassina, M. Faverzani, E. Ferri, Andrea Giachero, C. Gotti, Matteo Maino, Angelo Nucciotti, G. Pessina, Andrei Puiu

Published Dec 29, 2018• 1 citation
arXivHTMLPDF

Abstract

Microwave SQUID (Superconducting QUantum Interference Device) multiplexing is a suitable technique for reading a large number of detector channels, using only a few connecting lines. In the HOLMESexperiment, this is based on inductively coupled rf-SQUIDs fed by TES (Transition Edge Sensors). Operation of the whole rf-SQUID chain is achieved with a single transmission line, by means of the recently introduced flux-ramp modulation technique—a sawtooth signal which allows signal reconstruction while operating the rf-SQUIDs in an open loop condition. Due to the crucial role of the sawtooth signal, it is very important that it does not suffer from ground-loop disturbances and electromagnetic interference (EMI). Introducing a transformer between the sawtooth source and the SQUID is very effective in suppressing disturbances. The sawtooth signal has both slow and fast components, and the frequency can vary between a few kHz up to a MHz, depending on the TES signal and SQUID characteristics. A transformer able to handle such a broad range of conditions must have very stringent characteristics and needs to be custom designed. Our solution exploits standard commercial and inexpensive transformers for LAN networks, stacked in a user-selectable number, to better fit the bandwidth requirements. A model that allows handling of the low- and high-frequency operating range has been developed.

DOI
10.3390/instruments3010003

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Microwave SQUID (Superconducting QUantum Interference Device) multiplexing is a suitable technique for reading a large number of detector channels, using only a few connecting lines. In the HOLMESexperiment, this is based on inductively coupled rf-SQUIDs fed by TES (Transition Edge Sensors). Operation of the whole rf-SQUID chain is achieved with a single transmission line, by means of the recently introduced flux-ramp modulation technique—a sawtooth signal which allows signal reconstruction while operating the rf-SQUIDs in an open loop condition. Due to the crucial role of the sawtooth signal, it is very important that it does not suffer from ground-loop disturbances and electromagnetic interference (EMI). Introducing a transformer between the sawtooth source and the SQUID is very effective in suppressing disturbances. The sawtooth signal has both slow and fast components, and the frequency can vary between a few kHz up to a MHz, depending on the TES signal and SQUID characteristics. A transformer able to handle such a broad range of conditions must have very stringent characteristics and needs to be custom designed. Our solution exploits standard commercial and inexpensive transformers for LAN networks, stacked in a user-selectable number, to better fit the bandwidth requirements. A model that allows handling of the low- and high-frequency operating range has been developed.
We present a hybrid microwave superconducting quantum interference device (SQUID) multiplexer that combines two frequency-division multiplexing techniques to allow multiplexing a given number of cryogenic detectors with only a fraction of frequency encoding resonators. Similar to conventional microwave SQUID multiplexing, our multiplexer relies on inductively coupling non-hysteretic, unshunted rf-SQUIDs to superconducting microwave resonators as well as applying flux ramp modulation for output signal linearization. However, instead of utilizing one resonator per SQUID, we couple multiple SQUIDs to a common readout resonator and encode the SQUID input signals in sidebands of the microwave carrier by varying the flux ramp modulation frequency for each SQUID. We prove the suitability of our approach using a prototype device and argue by means of fundamental information theory that our approach is particularly suited for reading out large cryogenic bolometer arrays.
We present a MHz frequency-division direct-current superconducting quantum interference device (dc-SQUID) multiplexer that is based on flux ramp modulation and a series array of N identical current-sensing dc-SQUIDs with tightly coupled input coil. By running a periodic, sawtooth-shaped current signal through additional modulation coils being tightly but non-uniformly coupled to the individual SQUIDs, the voltage drop across the array changes according to the sum of the flux-to-voltage characteristics of the individual SQUIDs within each cycle of the modulation signal. In this mode of operation, an input signal injected in the input coil of one of the SQUIDs and being quasi-static within a time frame adds a constant flux offset and leads to a phase shift of the associated SQUID characteristics. The latter is proportional to the input signal and can be inferred by channelizing and down-converting the sampled array output voltage. Using a prototype multiplexer as well as custom readout electronics, we demonstrate the simultaneous readout of four signal sources with MHz bandwidth per channel.
We present a MHz frequency-division direct-current superconducting quantum interference device (dc-SQUID) multiplexer that is based on flux ramp modulation and a series array of N identical current-sensing dc-SQUIDs with tightly coupled input coil. By running a periodic, sawtooth-shaped current signal through additional modulation coils being tightly but non-uniformly coupled to the individual SQUIDs, the voltage drop across the array changes according to the sum of the flux-to-voltage characteristics of the individual SQUIDs within each cycle of the modulation signal. In this mode of operation, an input signal injected in the input coil of one of the SQUIDs and being quasi-static within a time frame adds a constant flux offset and leads to a phase shift of the associated SQUID characteristics. The latter is proportional to the input signal and can be inferred by channelizing and down-converting the sampled array output voltage. Using a prototype multiplexer as well as custom readout electronics, we demonstrate the simultaneous readout of four signal sources with MHz bandwidth per channel.
In order to read out current signals from large-scale arrays of transition edge sensors (TES), microwave SQUID multiplexers (MW-MUX) have been developed by several groups. Reduction of crosstalk induced in the multiplexer is important in order to maintain the energy resolution or the noise equivalent power of detector arrays. In the present study, crosstalk between channels in MW-MUX with five different designs is experimentally evaluated. The resonance frequency separation is ten times as large as the resonator bandwidth. Without flux-ramp modulation, crosstalk between two adjacent channels neighboring in position decreases to ≈1 × 10-3with increasing resonance frequency separation to ≈100 MHz. Crosstalk between SQUID channels neighboring in resonance frequency also decreases to 4 × 10-3with increasing the distance to 2.5 mm. We show that nonlinear error can occur due to the crosstalk with flux-ramp modulation. Flux readings from a well-designed multiplexer exhibit crosstalk of less than 1 mΦ0peak-to-peak and nonlinear errors of less than 2 mΦ0peak-to-peak, which is sufficient for the readout of the gamma-ray TES arrays being developed. These results can provide guidelines for suppressing both the crosstalk and the nonlinear error to less than the criterion of TES spectrometers with typical energy-resolving ability.
Abstract A microwave SQUID multiplexer ( μ MUX) with a high multiplexing factor is a promising readout approach for large-scale superconducting transition-edge sensor (TES) bolometer arrays. This paper reports on the characteristics of 16-channel μ MUX prototype chips and a 60-channel readout module developed to read out TES bolometers for the Ali cosmic microwave background polarization telescope (AliCPT). We designed two different coupling structures between the resonator and the radio-frequency superconducting interference device: design A with a mutual inductance ( M T ) of 2.3 pH and design B with an M T of 6.5 pH. For design A, the mean resonator bandwidth ( Δ f BW ) and peak-to-peak frequency shift ( Δ f pp ) are approximately 610 kHz and 290 kHz, respectively. The measured mean open-loop current noise is less than 40 pA / Hz . Preliminary results indicate that crosstalk between adjacent channels is below 1% in our design A μ MUX chip. A measured channel with design B shows a Δ f BW of 586 kHz and a current noise of 33 pA / Hz , similar to the design A channels. In comparison, the Δ f pp of 803 kHz is much larger than the design A channels due to a larger M T . The readout module, consisting of two design A chips and two design B chips, shows 60 resonances, corresponding to a yield of 94%. In the future, we will place 32 design A channels within the same chip dimension to increase the channel density and build a larger readout module suitable for AliCPT TES arrays.
Resonant frequencies and SQUID inductancesLSin a microwave SQUID multiplexer are studied for the purpose of reliable design applicable for a future large-format array of transition edge sensors (TESs). The key element of the multiplexer chip is a quarter-wave-length resonator terminated by a dissipationless rf SQUID connected to TES. For the resonator, we found that a small correction to the effective length of the resonators made the designed resonant frequencies fit the experimental one over the whole readout band of 4-8 GHz covered by our cryogenic amplifier. We also found that microstrip-type SQUIDs with vertical loops are suitable for accurate design of small inductanceLS<; 10<; pH to operate the rf SQUID in dissipationless regime. Based on these well-designed resonators and SQUIDs, we have successfully demonstrated the multiplexing of three pulsed signals with 1-ms width and spacing given at the input ports of three SQUIDs. The equivalent noise current refer to the SQUID input is not dominated by SQUIDs and estimated to be 200-270 pA/ √Hz, whose improvement approach is quantitatively discussed.