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IEEE Transactions on Applied Superconductivity

VHF Josephson Arbitrary Waveform Synthesizer

Jeremy N. Thomas, Nathan E. Flowers-Jacobs, Anna E. Fox, Akim A. Babenko, Samuel P. Benz, Paul D. Dresselhaus

Published Jul 1, 2024• 8 citations
Publisher

Abstract

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 as${{h/2e}}$. 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 50$\Omega$load 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.

DOI
10.1109/tasc.2024.3418332

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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.
We present the design and characterization of a broadband RF Josephson arbitrary waveform synthesizer (RF-JAWS) with a series array of 4500 Josephson junctions (JJs) and integrated low-pass/high-pass five-pole superconducting diplexers. The integrated diplexers enable broadband filtering of the feedthrough signal components in the drive-current pulses with decade-wide instantaneous bandwidth. The diplexers have at least 30 GHz passband with less than 0.8 dB insertion loss. The JJ array is driven with a delta-sigma pulse sequence that encodes 10 kHz and 1.005 GHz tones, and generates an open-circuit voltage of 22 mV rms (−26.18 dBm available power assuming a 50Ω\mathrm{\Omega }ΩThevenin equivalent source) at 1.005 GHz—a 25% increase compared to the state of the art. The drive current pulses undergo a three-step equalization to compensate for the linear distortion of the room-temperature electronics, the on-chip diplexers, and the remaining on- and off-chip components. The measured parasitic feedthrough voltages at 1.005 GHz are around −33 dBc, and their effect on the quantum locking ranges (QLRs) is quantified by measurements. The results demonstrated in this article show a significant step toward a broadband, integrated, quantum-based microwave voltage source with useful power above −30 dBm.
We demonstrate the use of a Josephson Arbitrary Waveform Synthesizer (JAWS) for linearity measurements of two instruments: an RF power sensor and a fast ADC. The VHF-JAWS source consists of a chip with 12,810 Josephson junctions located in a cryocooler and driven to produce quantum-based ac waveforms at frequencies up to 50.05 MHz and power up to -19 dBm. We first confirm that the device is operating correctly by measuring the dc bias current quantum-locking range and then measure the system output power with an RF power sensor and a high-speed digitizer. After removing an overall scale factor, the ten-nanowatt scale differences between the programmed JAWS values and the measured values indicate better than ±0.5 % DUT linearity for frequencies in the VHF band.
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.
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.
The output voltage of Josephson arbitrary waveform synthesizers (JAWS) is limited by the number of Josephson junctions (JJs) that can be driven by a single pulse-generator channel. Here, we double the number of JJs driven by one generator channel to 51 200 JJs by distributing the pulse bias between four JJ arrays by use of two layers of Wilkinson dividers. We use this single bias to generate a voltage at 1 kHz with an rms magnitude of 1 V. This voltage is quantum-accurate over an operating current range of 1.4 mA. For comparison, the operating current range of a recent design that uses a single layer of Wilkinson dividers is twice as large, but requires two pulse-bias channels to generate 1 V. We also show that we can recover this performance by incorporating in the pulse generator a finite-impulse response (FIR) filter that acts as an equalizer. The FIR filter creates a custom transfer function that compensates for the bandwidth-limited transfer function of the Wilkinson dividers. Optimizing the FIR filter parameters increases the operating current range from 1.4 to 2.7 mA. This ability to drive additional JJ arrays with a single pulse-generator channel will enable future JAWS chips and systems to achieve significantly larger output voltages. This will increase the voltage range for JAWS calibrations of ac thermal converters and improve precision voltage measurements that require quantum-accurate, stable, and distortion-free waveforms with a large signal-to-noise ratio.