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IEEE Transactions on Applied Superconductivity

Single-Flux-Quantum Multiplier Circuits for Synthesizing Gigahertz Waveforms With Quantum-Based Accuracy

Manuel A. Castellanos-Beltran, David I. Olaya, Adam J. Sirois, Christine A. Donnelly, Paul D. Dresselhaus, Samuel P. Benz, P. F. Hopkins

Published Feb 3, 2021• 14 citations
Publisher

Abstract

We designed, simulated, and experimentally demonstrated components for a microwave-frequency digital-to-analog converter based on single flux quantum (SFQ) circuits and an amplifier based on superconducting-quantum-interference-device (SQUID) stacks. These are key components for a self-calibrated programmable waveform reference for communications metrology capable of synthesizing high-frequency signals with quantumbased output accuracy. The amplifier is an SFQ voltage multiplier circuit that consists of a network of SFQ-splitters and SQUID transformers that provides output signals consisting of quantized pulses. The circuits were fabricated using our Nb/NbxSi1-x/Nb Josephson-junction (JJ) fabrication process, which produces selfshunted JJs with Nb-doped silicon barriers. In order to demonstrate quantum-based reproducibility, stability and performance at 4 K, we synthesized single-tone and multitone waveforms at gigahertz frequencies and demonstrated their operation over a range of synthesizer output and experimental bias parameters. We also propose circuit designs for achieving higher synthesis frequencies and higher output power with improved power accuracy and spectral purity, and discuss the potential limitations of these circuits.

DOI
10.1109/tasc.2021.3057013

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We designed, simulated, and experimentally demonstrated components for a microwave-frequency digital-to-analog converter based on single flux quantum (SFQ) circuits and an amplifier based on superconducting-quantum-interference-device (SQUID) stacks. These are key components for a self-calibrated programmable waveform reference for communications metrology capable of synthesizing high-frequency signals with quantumbased output accuracy. The amplifier is an SFQ voltage multiplier circuit that consists of a network of SFQ-splitters and SQUID transformers that provides output signals consisting of quantized pulses. The circuits were fabricated using our Nb/NbxSi1-x/Nb Josephson-junction (JJ) fabrication process, which produces selfshunted JJs with Nb-doped silicon barriers. In order to demonstrate quantum-based reproducibility, stability and performance at 4 K, we synthesized single-tone and multitone waveforms at gigahertz frequencies and demonstrated their operation over a range of synthesizer output and experimental bias parameters. We also propose circuit designs for achieving higher synthesis frequencies and higher output power with improved power accuracy and spectral purity, and discuss the potential limitations of these circuits.
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.
We synthesize single- and multiple-tone waveforms at gigahertz frequencies from arrays of Josephson junctions and demonstrate their quantum-locked operation over a range of experimental input parameters. We first use a lumped-element circuit to synthesize 1 and 2 GHz single-tone waveforms with -71 dBm output power and in-band spurious-free dynamic range (SFDR) of -66 dBc. We then introduce a narrow-band diplexer circuit and synthesize a 1 GHz sinusoid with higher power (-49 dBm) and in-band SFDR of -79 dBc. To demonstrate the spectrally selective power- and phase-programmability of the diplexer circuit, we also synthesize multisine waveforms with total waveform power of -51 dBm. The spectral purity of the reported waveforms is limited by the room-temperature electronics rather than by the quantized pulse-based synthesis technique. This article provides direction for future circuit designs and uncovers the main factors that must be addressed to achieve higher power, higher spectral purity, and improved output power accuracy. The reported results represent significant progress towards a JAWS-based primary RF reference source that synthesizes programmable, quantum-referenced, low-distortion signals at gigahertz frequencies.
Precise voltage generation is a unique feature of single-flux-quantum (SFQ) circuits, in addition to their high-speed digital signal processing with low power consumption. We investigated SFQ pulse-frequency modulation D/A converters for metrological applications. In our SFQ-based D/A converters, the maximum output voltage is determined by the maximum SFQ pulse-frequency at the pulse number multiplier, and by the voltage multiplication factor at the voltage multiplier. In this study, we present our new design for a double-flux-quantum amplifier (DFQA) that works as a quantum voltage multiplier. In the new parameter set, we tuned the damping parameters of the Josephson junctions to realize proper propagation of SFQ pulses. A 1000-fold DFQA designed with the new parameter set was fabricated using a 25-μ A/μ m2Nb/AlOx/Nb integration technology. A 1000-fold voltage multiplication was confirmed for the input voltage up to 43 μV, with a corresponding SFQ repetition frequency of 21 GHz. That is, the output voltage reached 43 mV.
Digital to analog converters based on the Josephson effect are promising for voltage standards, because they produce voltage steps with ultimate precision and stability. In this paper, we describe a project to develop a Josephson D/A converter designed for synthesizing a sinusoidal waveform with metrological accuracy. The D/A converter is based on RSFQ (Rapid Single Flux Quantum) logic circuits, and consists of a frequency multiplier (FM), a pulse distributor (PD), and a number of voltage multipliers (VMs). Each VM circuit, corresponding to the n-th bit digital code, multiplies the number of SFQ pulses by a factor of 2/sup n/. By gating the input SFQ pulses from the FM to the VMs using the PD circuits, a programmable output voltage is obtained. Possible sources of uncertainties in the measurement of the rms value of the synthesized sine wave are discussed.
We have developed a Josephson digital-to-analog converter, otherwise know as a Josephson arbitrary waveform synthesizer, with 300 mV peak output voltage. This is the first system of its kind with demonstrated quantum accuracy. We show precision synthesized waveforms from dc to 100 kHz with measured distortion and harmonic content below 115 dBc (dB below the carrier or fundamental). The heart of the system is a superconducting microwave integrated circuit with two Josephson junction arrays biased in parallel for the microwave drive and connected in series to double the voltage for the audio frequency output waveforms. New superconducting integrated circuits with twice as many stacked junctions and improved microwave circuits have allowed us to more than double the output voltage of our recent system. We also demonstrate that quantum-based synthesized arbitrary waveforms (not just sine waves) can be used for precision measurements of a high-performance commercial analog-to-digital converter.
Precise voltage generation is a unique feature of superconducting single-flux-quantum (SFQ) circuits, and hence, several SFQ-based digital-to-analog converters (DACs) have been designed for metrological applications. In this letter, we propose a dual double-flux-quantum amplifier (dual-DFQA) that extends DAC output voltage from unipolar to bipolar. An SFQ-based DAC comprising a 4-bit variable pulse number multiplier and a ±20-fold dual-DFQA is fabricated using a niobium integration technology. A 1-kHz, ±0.29-mV sinusoidal voltage waveform is successfully synthesized.