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IEEE Transactions on Applied Superconductivity

1 GHz Waveform Synthesis With Josephson Junction Arrays

Christine A. Donnelly, Nathan E. Flowers-Jacobs, Justus A. Brevik, Anna E. Fox, Paul D. Dresselhaus, P. F. Hopkins, Samuel P. Benz

Published Jul 31, 2019• 21 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2019.2932342

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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.
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.
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We report on the design, fabrication, and measurement of a very high frequency band Josephson arbitrary waveform synthesizer (VHF-JAWS) at frequencies from 1 kHz to 50.05 MHz. The VHF-JAWS chip is composed of a series array of 12 810 Josephson junctions (JJs) embedded in a superconducting coplanar waveguide. Each JJ responds to a pattern of current pulses by creating a corresponding pattern of voltage pulses, each with a time-integrated area related to fundamental constants ash/2e{{h/2e}}h/2e. The pulse patterns are chosen to produce quantum-based single-tone voltage waveforms with an open-circuit voltage of 50 mV rms (–19.03 dBm output power into 50Ω\OmegaΩload impedances) at frequencies up to 50.05 MHz, which is more than twice the voltage that has been generated by previous RF-JAWS designs at 1 GHz. The VHF-JAWS is “quantum-locked,” that is, it generates one quantized output voltage pulse per input current pulse per JJ while varying the dc current through the JJ array by at least 0.4 mA and the amplitude of the bias pulses by at least 10 %. We use the large bias pulse quantum-locking range to investigate one source of error in detail: the direct feedthrough of the current bias pulses into the DUT at VHF frequencies, which adds an unwanted, in-band component to the measured voltage. We reduce this error by high-pass filtering the current bias pulses and measure the error as a function of input pulse amplitude using two techniques: 1) by measuring small changes over the quantum-locking range and 2) by passively attenuating the input pulse amplitude so that the nonlinear JJs no longer generate voltage pulses while the error is only linearly scaled.
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This article presents a superconducting voltage source that generates modulated microwave waveforms with quantum-based stability. The voltage source—an RF Josephson Arbitrary Waveform Synthesizer (RF-JAWS)—uses a superconducting IC with an array of 4500 series-connected Josephson junctions (JJs) that are embedded in a coplanar waveguide (CPW) transmission line. The JJs are driven with 100-ps wide current pulses that force each JJ to generate voltage pulses with a quantized integrated area. A pulse sequence is created using a delta-sigma ($\Delta –––\Sigma )algorithmtogeneratea101−tonewaveformwitha40−MHzinstantaneousbandwidtharound1005MHzwithaflatpowerdistributionof−53dBmandaSchroederphasedistribution.TheJJ’squantum−basednonlinearityproducesanamplitudestabilitywithrespecttovariousdriveandbiasparametersof±0.005dBandadetrendedphasestabilityof±0.05°.Thestabilityofthesourceisverifiedwithouttheneedforcalibratedmeasurements.Another) algorithm to generate a 101-tone waveform with a 40-MHz instantaneous bandwidth around 1005 MHz with a flat power distribution of −53 dBm and a Schroeder phase distribution. The JJ’s quantum-based nonlinearity produces an amplitude stability with respect to various drive and bias parameters of ±0.005 dB and a detrended phase stability of ±0.05°. The stability of the source is verified without the need for calibrated measurements. Another)algorithmtogeneratea101−tonewaveformwitha40−MHzinstantaneousbandwidtharound1005MHzwithaflatpowerdistributionof−53dBmandaSchroederphasedistribution.TheJJ’squantum−basednonlinearityproducesanamplitudestabilitywithrespecttovariousdriveandbiasparametersof±0.005dBandadetrendedphasestabilityof±0.05°.Thestabilityofthesourceisverifiedwithouttheneedforcalibratedmeasurements.Another\Delta –––\Sigma $pulse sequence generates a 10-MHz quadrature-phase shift-keying (QPSK) waveform on a 1005-MHz carrier that has the same stability and the mean error vector magnitude (EVM) of −48 dB. This work is a step toward creating a quantum-based reference source for power and cross-frequency phase calibrations, as well as a reference-modulated signal source for calibrating telecommunication links.