IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011 681 Multitone Waveform Synthesis With a Quantum Voltage Noise Source Samuel P. Benz, Fellow, IEEE, Paul D. Dresselhaus, and Charles J. Burroughs Abstract—We have developed a quantum voltage noise source tance , and measurement bandwidth (QVNS) based on pulse-driven Josephson arrays and optimized [7], and it is accurate to 1 part in for frequencies below its waveform synthesis for use with Johnson noise thermom- 1 MHz and temperatures above 25 K. Because the relation is etry (JNT). The QVNS synthesizes multitone waveforms with equal amplitude harmonic tones and random relative phases in fundamental, JNT is one of the few techniques that can de- order to characterize the amplitude–frequency response of the termine absolute (thermodynamic) temperatures. NIST devel- analog and digital electronics of the JNT system. We describe the oped the QVNS-JNT system to investigate deviations of the QVNS circuit design and operation, including the lumped-array International Temperature Scale of 1990 (ITS-90) from ther- Josephson-junction circuit and the unipolar bias technique. In modynamic temperature at temperatures in the range of 505 particular, we describe the primary design considerations that determine the voltage accuracy of the harmonic tones. K–933 K, which overlaps the ranges of both acoustic gas-based and radiation-based thermometry [8]. Another application of the Index Terms—Correlation, digital–analog conversion, QVNS-JNT system is as an “Electronic Kelvin” that links the SI Josephson arrays, Johnson noise, noise measurement, quanti- zation, thermometry. kelvin to quantum-based electrical measurements [9]. Research is underway [10]–[16] to produce an electronic determination of Boltzmann’s constant with a combined uncertainty of 6 . I. INTRODUCTION The main challenge of JNT is that it requires accurate, low- HE FIRST ac and dc voltages synthesized by a Josephson noise, cross-correlation techniques to measure the extremely T arbitrary waveform synthesizer (JAWS) were produced small noise voltage of a 100 resistor at the with unipolar pulses of a single polarity and small output triple point of water (273.16 K) [7]. Cross correlation is neces- voltages of less than 10 mV [1], [2]. Since then, there have sary for these measurements because the small noise voltage is been many improvements in bias technique and circuit design comparable to that of low-noise amplifiers. The small voltage that increased the output rms voltage to 250 mV, which en- also determines the design voltage of the QVNS synthesized abled quantum-accurate characterization of the ac–dc voltage waveforms. Our QVNS-JNT system uses the switched digital response of thermal converters [3]. In order to emphasize dif- cross-correlator [4], [7], which was first implemented by Brixy ferent applications, the quantum-based pulse-driven Josephson et al. [17]. In cross-correlation, a signal is simultaneously mea- synthesizer has used different names, including the pulse-driven sured with two separate amplifier chains. Continued integration Josephson digital-to-analog converter (JDAC), the ac Josephson of the cross-correlated signals gradually reduces the uncorre- voltage standard (ACJVS), and JAWS [1], [2]. The primary lated white noise of the independent amplifier chains to reveal focus and development challenge for JAWS has been to produce the source signal [7], [11], [17]. The switched correlator in- dc and sine-wave waveforms with the largest possible voltages, cludes a switching network at the input leads of the electronics which require a large number of Josephson junctions. to alternately measure the source or the reference. In a digital This paper describes a low-voltage realization of JAWS correlator, analog-to-digital converters (ADCs) digitize the sig- called the quantum voltage noise source (QVNS), which was nals from each channel and allow Fourier analysis of all signals. developed specifically for the application of Johnson noise For typical JNT, the reference is usually a resistor at the triple thermometry [4]–[6]. In contrast to the typical JAWS system, point of water, and the sense resistor is at the unknown tem- the QVNS produces multi-tone pseudo-noise waveforms with perature to be measured. For the NIST system, the QVNS pro- small ( peak) voltage amplitudes that require only a few vides an intrinsically accurate voltage reference, which charac- Josephson junctions. terizes the amplitude–frequency response of the cross-correla- Johnson noise thermometry (JNT) is a primary thermometry tion electronics. The sense resistor can be measured at various technique based on the Johnson–Nyquist noise of a resistor, temperatures for temperature scale characterization, or it can be which is a fundamental result of the fluctuation–dissipation the- measured at the triple point of water to measure Boltzmann’s orem. The Nyquist equation states that the mean-square voltage constant. The QVNS-JNT system is particularly useful for mea- is proportional to Boltzmann’s constant , temperature , resis- suring arbitrary temperatures, not just those at fixed points; be- cause the QVNS waveform voltage is intrinsically accurate and fully programmable with respect to spectral content and ampli- Manuscript received August 03, 2010; accepted September 27, 2010. Date of publication November 09, 2010; date of current version May 27, 2011. This tude, it makes an accurate reference that allows the JNT system work was supported by the National Institute of Standards and Technology. It to measure a wide range of temperatures. is a contribution of the U.S. government that is not subject to U.S. copyright. A QVNS pseudo-noise waveform is a “comb” of harmonic The authors are with the National Institute of Standards and Technology, Boulder, CO 80305 USA. tones that are equally spaced in frequency (typically odd con- Digital Object Identifier 10.1109/TASC.2010.2083616 secutive tones) and have identical amplitudes and random rel- U.S. Government work not protected by U.S. copyright. 682 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011 Fig. 1. (a) Resistor and (b) QVNS output wiring circuits for two-channel JNT cross-correlation measurements. Fig. 2. Microscope photo of the QVNS chip @I mA with lumped Josephson arrays and low-inductance common ground (center). DCG biases are applied at ative phases [4], [10]. The accuracy of the QVNS waveform is the coplanar waveguide (CPW) launches (top and bottom). The three-terminal provided by digital synthesis that is based on the perfectly quan- output leads for each channel are on each side. tized voltage pulses of Josephson junctions [1], [2]. The time-in- tegrated area of every Josephson pulse is precisely equal to the flux quantum, , the ratio of Planck’s constant to twice the grounded lumped array (as shown in Fig. 1). We have made electron charge. Knowledge of the number of pulses and their QVNS circuits both with and without the termination resistor. position in time is sufficient to precisely determine the voltage Both circuits produce waveforms with satisfactory “operating of any synthesized waveform. The remainder of this paper will margins”, which are the current ranges over which various describe the features and characteristics of the QVNS and its arrays maintain quantum accuracy. For recent measurements, synthesized waveforms, including some of the issues and con- we typically use the circuits without the termination resistor, siderations relevant to their optimization for JNT. because larger pulse current amplitudes can be provided by the DCG. Room-temperature 6 dB attenuators are used in the DCG coaxial connections to damp reflections. II. CIRCUIT DESIGN Fig. 2 shows a micrograph of the QVNS circuit layout. The The QVNS circuit design is primarily determined by the DCG signals are applied at the top and bottom of the chip to each three-wire input configuration of the low-noise preamplifiers set of three bright-colored Au–Pd pads, which define the begin- [7], [12], which are inherently differential. Fig. 1 shows the ning of the coplanar waveguide (CPW) structures, which extend electrical schematic of both the sense resistor and the QVNS vertically from both center pads. All the wiring on the chip is circuits. Three wires are used in each channel (A and B) for the Nb (gray color). The Nb extending from the chip center is the differential pair and ground. Both the sense resistor (typically low-inductance superconducting common ground. The ground ) and the QVNS junctions (typically ,20 extends to the center pad of each channel’s output leads (at the or 512 junctions) are equally divided with respect to ground. left and right chip edges) and to the outer two pads of the CPW. Complementary pulse bias signals provided by the digital code The CPW conductors are tapered to preserve the 50 generator (DCG) drive each array of junctions to produce impedance such that the center conductor width reduces to the opposite polarity waveforms. 16 . The termination resistor, if present, forms the center The common microwave ground for each array (triangle) conductor between the tapered CPW and the output lead is also the common ground for the QVNS output leads. This connection. The Nb center conductor remains continuous for common ground is essential for removing common mode circuits not using the termination. Six slots in the Nb ground are signals in the QVNS circuit, either from termination resistors on either side of the array CPW to reduce magnetic fields in the or from inductance in any connecting leads between the two junctions. Rectangular junctions, which are arrays. This common ground significantly reduces the common in area, are distributed at 10 μm intervals along mode signals as compared to the JAWS circuit that was used the CPW center conductor. A 256 junction array fits between in our earliest measurements, which used two long distributed the output lead connection and the ground at the bottom edge arrays and a long superconducting wire that connected them as of the farthest slots.