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IEEE Transactions on Applied Superconductivity

Josephson Arbitrary Waveform Synthesizer for Flux-Ramp Modulation in Microwave SQUID Multiplexers

Matías Rolf Hampel, L.P. Ferreyro, Oliver Kieler, Ricardo Iuzzolino, Mariano Real, Stephan Bauer, Nahuel Agustín Müller, J. Bonilla-Neira, Manuel Elías García Redondo, J. Bonaparte, Enrico Petriella, Lucía Sucunza, Timo Muscheid, R. Gartmann, Luis Eduardo Ardila-Perez, Mathias Wegner, Alan Fuster, M. Platino, Sebastian Kempf, Marc Weber

Published Feb 25, 2026• 0 citations
Publisher

Abstract

Microwave SQUID multiplexers (μMUX) have become a key technology for the readout of large arrays of low-temperature detectors, particularly in cosmic microwave background experiments. A critical element of this technique is the flux-ramp modulation signal, whose noise, especially at low frequencies, directly limits the readout performance. This work proposes and experimentally demonstrates the use of a Josephson Arbitrary Waveform Synthesizer (JAWS) as a low-noise, high precision source for generating the sawtooth-shaped flux-ramp signal required in μMUX readout systems. The JAWS, based on the AC Josephson effect, provides intrinsically quantized and spectrally pure waveforms with excellent signal-to-noise ratio. The operation of a 9000-junction JAWS array is characterized and integrated with a cryogenic μMUX device and a custom SDR-based readout system. With this setup, the noise floor level around the harmonic typically used for phase demodulation of the SQUID signal to recover the detector signal was −104dBc/Hz, and the signal-to-noise ratio of this harmonic was 73dB. These results demonstrate the feasibility of using JAWS-based waveform synthesis for μMUX flux-ramp generation.

DOI
10.1109/tasc.2026.3668113

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Microwave SQUID multiplexers (μMUX) have become a key technology for the readout of large arrays of low-temperature detectors, particularly in cosmic microwave background experiments. A critical element of this technique is the flux-ramp modulation signal, whose noise, especially at low frequencies, directly limits the readout performance. This work proposes and experimentally demonstrates the use of a Josephson Arbitrary Waveform Synthesizer (JAWS) as a low-noise, high precision source for generating the sawtooth-shaped flux-ramp signal required in μMUX readout systems. The JAWS, based on the AC Josephson effect, provides intrinsically quantized and spectrally pure waveforms with excellent signal-to-noise ratio. The operation of a 9000-junction JAWS array is characterized and integrated with a cryogenic μMUX device and a custom SDR-based readout system. With this setup, the noise floor level around the harmonic typically used for phase demodulation of the SQUID signal to recover the detector signal was −104dBc/Hz, and the signal-to-noise ratio of this harmonic was 73dB. These results demonstrate the feasibility of using JAWS-based waveform synthesis for μMUX flux-ramp generation.
This paper presents the basic principle of the pulse-driven ac Josephson voltage standard, also called “Josephson arbitrary waveform synthesizer” (JAWS). We will mainly focus on activities and developments at the Physikalisch-Technische Bundesanstalt (PTB). The JAWS is suitable to generate high precision quantized waveforms, which can be arbitrarily programmed in the frequency and time domain with extremely high spectral purity (typical signal-to-noise ratios SNR of 120–140 dBc). A brief overview of the fabrication technology for highly integrated JAWS circuits with more than 50 000 junctions per chip will be described. This includes the stacked junction technology with up to 5-stacked junctions. The experimental setup and the key-features of JAWS will be shown too. New approaches designed to further increase the output voltage, to simplify the experimental setup, and to extend the range of applications are the on-chip power dividers, the optical pulse drive, and the RF-JAWS. A selected application of the JAWS is described to demonstrate the usability of sophisticated JAWS waveforms for the complex characterization of electrical devices. The PTB JAWS circuits already have a significant impact on the quantum ac voltage metrology community. JAWS chips made at PTB have been distributed to more than 10 national metrology and other research institutes within the framework of international research projects.
Sub-μm\mu{\rm m}μm SNS Josephson Junction Arrays for the Josephson Arbitrary Waveform Synthesizer
The experimental set-up of a Josephson arbitrary waveform synthesizer (JAWS) has been further optimized to generate AC voltages with fundamental accuracy. Josephson junction series arrays for the JAWS, consisting of sub-mum SNS type junctions (superconductor-normal conductor-superdonductor), are fabricated using a technology which combines electron-beam lithography and chemical-mechanical polishing. Bipolar pulses are realized by the superposition of unipolar pulses from a pulse pattern generator and a continuous sinusoidal microwave provided by a signal generator. A second-order delta-sigma modulator is optimized to generate a high-quality pulse code.
We review our development of Josephson-junction-based programmable reference sources to synthesize spectrally pure waveforms with quantum-based voltage accuracy for characterizing and improving future communication devices and systems. The goal is to provide sources that together span the entire radio frequency band, equivalent to seven orders of magnitude in frequency (20 kHz to 300 GHz). To synthesize waveforms in the microwave frequency band, we are extending the existing Josephson arbitrary waveform synthesizer (JAWS) technology used for ac voltage metrology at audio frequencies (<;20 kHz). Using new microwave circuits and experimental techniques, we demonstrate JAWS-based synthesis of single-tone waveforms at 1 GHz, with -49 dBm output power and 79 dBc spur-free dynamic range (SFDR). To synthesize waveforms in the millimeter-wave frequency band, we are exploiting single flux quantum (SFQ) superconducting digital technology to design circuits that amplify SFQ pulses using a network of pulse splitters. With our initial SFQ-based circuit, we demonstrate synthesis of a 4-GHz sine wave with -74 dBm output power and 70 dBc SFDR.
The Microwave SQUID Multiplexer (μMUX) is the device of choice for the readout of a large number of low-temperature detectors in a wide variety of experiments within the fields of astronomy and particle physics. While it offers large multiplexing factors, the system noise performance is highly dependent on the cold- and warm-readout electronic systems used to read it out, as well as the demodulation domain and parameters chosen. In order to understand the impact of the readout systems in the overall detection system noise performance, first, we extended the available μMUX simulation frameworks, including additive and multiplicative noise sources in the probing tones (i.e., phase and amplitude noise), along with the capability of demodulating the scientific data, either in the resonator’s phase or the scattering amplitude. Then, considering the additive noise as a dominant noise source, the optimum readout parameters to achieve minimum system noise were found for both open-loop and flux-ramp demodulation schemes in the aforementioned domains. Later, we evaluated the system noise sensitivity to multiplicative noise sources under the optimum readout parameters. Finally, as a case study, we evaluated the optimal demodulation domain and the expected system noise level for a typical software-defined radio readout system. This work leads to an improved system performance prediction and noise engineering based on the available readout electronics and the selected demodulation domain.
Suitable techniques for reading out large arrays of metallic magnetic calorimeters are very challenging and demand optimal performance in each system stage to preserve intrinsic fast signal rise time, excellent energy resolution, large energy dynamic range, and highly linear detector response. A multiplexer based on superconducting quantum interference device is the key component in achieving this goal. Linearity of the response requires a technique called flux-ramp modulation, which generates a phase-modulated complex waveform according to the sensor signal. At the end-cap of the signal processing chain it is currently recovered by a demodulation process referred to as Fourier measurement. In this letter, we prove that the mentioned method is equivalent to a maximum likelihood estimation, build an analogy to the sensor array-based direction of arrival estimation, propose an alternative approach based on the eigenvalue decomposition of a correlation matrix, present the mathematical formulation, discuss the results, and compare both methods. Our method is robust against transients due to flux ramp returning point and allows proper estimation in large phase ranges.
The Josephson arbitrary waveform synthesizer (JAWS) is a series array of thousands of superconducting Josephson junctions that are biased by current pulses such that the array produces voltage waveforms with quantum accuracy. Intrinsically accurate voltage waveforms synthesized with the quantized pulses from Josephson junctions were first demonstrated in 1996. Ten years later, a commercial ac standard was calibrated at an output root-mean-square (RMS) amplitude of 100 mV with the first practical superconducting digital-to-analog converter. Since then, many different bias techniques, pulse-drive electronics, and device technology have been developed and improved in order to achieve a maximum of 138 mV output RMS voltage per Josephson array. In this paper, we report new bias electronics and demonstrate two new pulse-bias techniques. The first technique has demonstrated 250 mV output RMS voltage per 6400-junction array and may enable a practical 1 V system with only four arrays. The second bias technique reduces inductance-related error signals at the signal frequency and should reduce systematic errors for waveforms with frequencies greater than 1 MHz.