Martin Götz

In this paper, we present novel impedance standards at a nominal value of 12.9 kΩ based on a series connection of four commercial, metallically encapsulated metal-foil resistors. Single metal-foil resistors have advantages that make them suitable for many applications, including as an impedance standard at kHz frequencies. Nevertheless, metrologists are seeking to achieve even better standards. Selecting single resistors whose deviation from the nominal dc resistance value and whose temperature dependence have opposite signs allows a reduction of these properties at the series-connected resistor. In addition, connecting four resistors in series reduces the dissipative parallel capacitance by a factor of four. To avoid limitation due to the capacitances between each metal foil and its metal encapsulation, voltage is supplied to the encapsulations in such a way that their capacitance contribution is not only greatly reduced but also that their residual capacitance cancels the residual parallel capacitance (at least partially). This reduces the total capacitance to a few tens of femtofarads and the corresponding frequency dependence to the range of (20 to 37) Ù 10^-9 kHz^-1. These properties are not accurately calculable but can be modeled with a remarkably low uncertainty by electrical quantities measured at each single resistor. As such, the series-connected metal-foil resistors represent excellent standards of impedance and time constant.

The Planck-Balance is a compact Kibble balance, designed for the realization of the unit of mass at values much smaller than 1 kg across multiple orders of magnitude. Recent advancements enable the Planck-Balance at PTB to measure mass with uncertainties equivalent to calibration accuracy classes E1 (up to 5 g), E2 (up to 50 g), and F1 (up to 100 g), while operating in air. Type B uncertainties limit the relative combined standard uncertainty for a mass of 100 g to the minimum achievable value of 4.5 · 1E−7. A measurement campaign was conducted using six mass standards (1 mg, 10 mg, 100 mg, 1 g, 10 g, and 100 g), yielding results consistent with the values specified in their E1 calibration certificates. The presented results demonstrate the feasibility of metrologically traceable small mass measurements without reliance on mass standards. Unique design features of the Planck-Balance will be discussed, including a rigidly mounted coil that minimizes geometrical alignment requirements, and an oscillatory velocity mode that achieves a high signal-to-noise ratio, even with a movement range of less than 0.2 mm. This approach could offer an alternative to calibration and dissemination using mass comparators.

Thanks to achievable uncertainties down to parts in 109, cryogenic current comparator-based measurement brid- ges are well-established in resistance metrology. Thanks to achievable uncertainties down to parts in 109, cryogenic current comparator-based measurement brid- ges are well-established in resistance metrology.

For more than three decades, GaAs/AlGaAs quantum Hall (QH) devices are being used as standards for the realization of the dc resistance unit ohm. Recently, the outstanding performance of graphene-based quantum Hall resistance (QHR) devices signifies an immense potential for a transition from GaAs to graphene-based devices in the field of resistance and also impedance metrology, with equally good accuracy. The recent developments in epitaxial graphene (EG) quality and fabrication of EG-based doped QHR devices and their improved performance tested in several national metrology institutes (NMIs) all over the world have demonstrated a more user-friendly dissemination of the unit ohm since they can be operated at relatively low magnetic fields and higher temperatures in comparison to existing GaAs-based devices. In this work, we have extensively tested the temporal stability of the magneto-transport properties of our graphene QH devices fabricated in the PTB and the resistance quantization performance by means of repeated high-accuracy cryogenic current comparator (CCC) measurements with several devices. Together with interlaboratory comparisons between NMI’s, the performance and stability assessment demonstrate the readiness of the technology for calibration purposes in resistance metrology.

This article compares two instruments for the traceable measurement of dc low currents, a custom capacitance–voltage ( $C\text{-} V$ ) source and the ultrastable low-current amplifier (ULCA), a commercial precision transresistance amplifier. The instruments are calibrated through independent traceability routes. The comparison base relative accuracy is in the $10^{-6}\!-\!10^{-5}$ range. Differences between the two instrument readings, in the $10^{-5}$ range, are interpreted as an effect of the frequency dependence of the capacitor employed in the $C\text{-} V$ source. Such frequency dependence can also affect primary metrology experiments in other fields.

The established calibration of the transresistance of the ultrastable low-noise current amplifier (ULCA) directly involves a cryogenic current comparator (CCC). Here, we present an alternative approach based on a calibrated set of three resistors and three digital voltmeters. This approach was experimentally verified for a two-channel ULCA with nominally 1 GΩ transresistance using PTB’s travelling 12 bit CCC setup in an on-site comparison at METAS. Series of interleaved experiments included calibrations of the input and output stages of two different ULCA channels. The consistency found between the conventional calibration with PTB’s CCC and calibration with METAS’ set of three resistors—each traced to the quantum Hall resistance with METAS’ CCC—confirms that the alternative traceability chain provides valuable results. If the standard resistors are calibrated without using a CCC, the new method even opens the possibility to calibrate the ULCA without any CCC in the traceability chain involved, however, typically at the expense of increased uncertainty.

Input and output stages of the second generation of ultrastable low-noise current amplifiers can be conveniently calibrated by means of a cryogenic current comparator. The uncertainty achievable for measurement durations of less than 2 h makes our calibration setup a helpful tool for the selection of hardware in the development of instrumentation tailored to meet the requirements of special applications.

The settling of the bridge voltage in resistance comparisons based on cryogenic current comparators is investigated starting 0.2 s after current reversal and sampling at a rate of 16 Hz. For certain configurations, the result obtained for a current reversal frequency of 0.1 Hz deviates from the result when waiting tens of seconds for the decay of transients by two parts in 10 9 , only.

Resistance calibration at PTB, Germany's national metrological institute (NMI), has been based on Cryogenic Current Comparators (CCC's) for almost two decades. So far, comparisons in the ensemble of normal resistors with nominal values from 1 Omega up to 1 MOmega and with the quantum Hall resistance RK-90 are performed by means of two complementary setups for high- or low-ohmic resistors, respectively. To replace both setups, we designed a new LHe probe equipped with an optimized PTB dc SQUID sensor as well as a digital state-of-the-art double-current source. In this paper, we describe basic features and highlight the advantages of the new system.