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Conference on Precision Electromagnetic Measurements

Design of delta-sigma feedback loop for quantum voltage digitizer

Jane Ireland, A. Cryer, Jonathan M. J. Williams, Ernest Houtzager, Ralph Hornecker, Helko E. van den Brom

Published Jul 1, 2016• 5 citations
Publisher

Abstract

A system utilizing a delta-sigma (DS) feedback loop to digitize an arbitrary voltage waveform in terms of the quantum-accurate output of a Josephson junction array (JJA) has been designed. Using commercially available components, a first order DS loop has been constructed and tested with direct feedback. At a sample rate of 20 MHz a signal to noise ratio of4was demonstrated.

DOI
10.1109/cpem.2016.7540457

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A system utilizing a delta-sigma (DS) feedback loop to digitize an arbitrary voltage waveform in terms of the quantum-accurate output of a Josephson junction array (JJA) has been designed. Using commercially available components, a first order DS loop has been constructed and tested with direct feedback. At a sample rate of 20 MHz a signal to noise ratio of4was demonstrated.
Quantum-accurate arbitrary voltage waveforms have been generated using electrical pulse driven Josephson junction arrays (JJAs) by several groups [1, 2]. An alternative method is to use optoelectronic components to convert the electrical pulse drive into an optical signal which is subsequently converted by a photodiode into an electrical drive signal connected directly to the JJA. This optoelectronic pulse drive system has several advantages. Due to the electrical isolation between electrical pulse drive and JJA, it is possible to connect several arrays in series without the requirement for complex electrical compensation circuits. This allows larger output voltages to be realized. An optoelectronic drive also offers the ability to easily tune pulse height, via continuous optical attenuation, allowing the drive signal to be tuned to the middle of the JJA constant voltage step giving optimum operation margins. We here present an optoelectronic pulse drive which forms part of a system incorporating a JJA and delta sigma feedback loop [3] for quantum-accurate digitization of arbitrary voltage waveforms. Results showing the generation of quantum-accurate voltages synchronized to the feedback loop master clock are presented.
The sigma-delta architecture is the method of choice for analog-to-digital converters (ADCs) for high dynamic range applications. This architecture uses oversampling and precise feedback to generate a shaped spectral distribution of the quantization noise. Subsequent digital filtering suppresses out-of-band quantization noise, yielding a large signal to in-band noise ratio. A unique advantage of superconducting electronics is the availability of the flux quantum to provide quantum mechanically accurate feedback at GHz rates. Josephson digital technology extends sigma-delta ADCs from MHz sampling rates to GHz sampling rates, from kHz signal bandwidths to MHz signal bandwidths, with comparable or better dynamic range when compared to semiconductor implementations. This paper presents circuits for Josephson sigma-delta ADCs, including single-loop and double-loop modulators operating at sampling rates up to 2 GHz, and circuits for quantized feedback. The first demonstration of double-loop noise shaping is also presented.
A pulse drive system capable of converting an arbitrary input signal into a delta sigma encoded pulse code stream in real time has been demonstrated. This system is based on the use of analog and digital hardware controlled by a Field Programmable Gate Array (FPGA) rather than using software to produce the delta sigma code and then loading it into the memory of a commercial Pulse Pattern Generator (PPG). The results of using the system to drive a Josephson junction array to synthesize quantum-accurate voltage waveforms are presented. The advantage of such a system includes the significant reduction in time required to change waveform parameters. This provides an easily tunable source of high-fidelity stable voltage waveforms at low temperature for future applications including validation of components for use in quantum technologies.
High performance oversampling delta-sigma data converters require high clock rates and accurate feedback of the digital output to the analog regime. Superconductor modulators offer the unique advantages of clock rates in the tens-of-gigahertz, comparator switching energy below attoJoules, and quantum-accurate digital-to-analog feedback. We have designed a two-loop baseband modulator whose noise transfer function was calculated using a simple, linear circuit model. The circuit was fabricated in a commercial superconductor IC process with 4.5 kA-per-square cm Josephson junctions and 1.5 micron minimum feature size. The circuit was tested at a derated sample rate of 5 GHz. Measured signal-to-noise dynamic range was 81 dB over a 10 MHz band. Third-order intercept was measured to be +24 dBsat in two-tone test. The measured noise transfer function was in excellent agreement with our linear model. The linear model indicates that with appropriate parameter values, this family of modulators extrapolates to significantly higher performance.
In order to establish double-loop feedback design, we have fabricated a prototype superconducting double-loop lowpass sigma-delta modulator. For digital feedback gain, multiple flux quanta are produced by a ladder circuit and carried through Josephson Transmission Lines (JTLs) to the feedback driver. The feedback driver consists of a single Josephson junction or two serially-connected junctions. Direct injection of the pulse current from the JTLs through a low-value resistor drives the feedback driver. The sigma-delta modulator was operated at the sampling frequency of 1.1 GHz and the measured power spectrum showed the noise shaping roughly of 12 dB/octave, which is characteristic of the second-order sigma-delta modulator.
An optoelectronic pulse drive system based on commercially available telecoms optoelectronic components and a field-programmable gate array has been developed. In order to allow the use of ac-coupled optoelectronic components, a method of adding and subtracting complementary pulses was developed. The system was used to drive a Josephson junction array to synthesize quantum-accurate voltage waveforms. These waveforms will be used in voltage waveform metrology applications. Results from the synthesis of sinusoidal unipolar voltage waveforms from 3 to 300 kHz are presented. The margin of operation was measured and shown to require an optical pulse height stability better than 0.15 mW. The use of delta-sigma code with repeated sections, suitable for a quantum voltage digitizer was also examined. A test code corresponding to a delta-sigma feedback loop rate of 250 MHz was used to synthesize a 3.125 kHz sinusoidal waveform.