Fully-digital impedance bridges are emerging as measuring instruments for primary electrical impedance metrology and the realization of impedance units and scales. This paper presents a comprehensive analysis of electronic fully-digital impedance bridges, for both generating (based on digital-toanalog converters) and digitizing (based on analog-to-digital converters) bridges. The sources of measurement error are analyzed in detail and expressed by explicit mathematical formulæ ready to be applied to the specific bridge and measurement case of interest. The same can be employed also as a basis to optimize the design and the operating parameters of digital bridges, and to evaluate the measurement uncertainty. A practical application of the analysis to the digital bridges developed and measurements performed in the framework of an international research project is presented.

This paper characterizes the metrological properties of a dual-channel high-resolution digitizer designed for use in a system to calibrate standard resistors with values between 1 $\hbox{m} \Omega$ and 10 $\Omega$ at frequencies from 40 Hz to 10 kHz. The possibility of using a digitizer to measure the complex voltage ratio is analyzed for both digitizer operating modes: the dual-channel mode with a simultaneous sampling and the single-channel mode with a sequential sampling in which an additional external multiplexer is used. The method of acquiring samples presented in this paper was used to investigate and compare the short-time stability and temperature influences on the metrological properties of the digitizer. This makes it possible to reduce the influence of the instability of the generator, being the signal source for the tested digitizer, on the research results. Moreover, presented in this paper are the frequency characteristics of the magnitude and phase of the complex voltage ratio, as well as the research results of the digitizer linearity and the phase measurement accuracy. All measurements discussed here were performed for both digitizer operating modes.

This paper presents a digital automatic unbalanced bridge designed for comparing the impedances of R-R, R-C, and C-C. The measurement principle uses initial balancing of the bridge using two digital sine wave sources, then measuring the ratio of voltage drops on the compared impedances as well as the finite bridge unbalance voltage. The present method is novel because it is not necessary to obtain a complete voltage nulling and also because it is readily implemented with a commercial data acquisition (DAQ) card. An NI USB6281 DAQ card was used to obtain the results; this card combines the two 16-bit digital-to-analog converters with one multiplexed 18-bit analog-to-digital converter. Such a measurement system, which is relatively simple and inexpensive, can compare impedances with an error below 10 ppm. Some considerations concerning the relationship between the measurement accuracy of unbalanced voltage and the level of the bridge unbalance are given.

In Poland, the national time and frequency standard (NTFS) is realized by means of three caesium atomic clocks, a system for the generation of the Polish time scale UTC(PL), and measuring systems for comparing directly and indirectly the atomic clocks and time scale. In order to ensure the best realization of NTFS, the Institute of Electrical Metrology at the University of Zielona Góra (IME UZ), in cooperation with the Central Office of Measures (GUM), has developed and built an integrated monitoring and control system. This system significantly increases the functional capabilities of autonomous measuring systems used previously at GUM and adds new features that increase the reliability and safety of the NTFS. Examples of such features are: automatic detection of invalid operating conditions (including breakdowns) of the atomic clocks and remote notification of alarms, as well as a new approach to predicting corrections for UTC(PL) using neural networks (NNs). In this paper, the presentation of hardware and software of the NTFS is limited to their general features. However, the application of NNs for predicting corrections for UTC(PL) and automation in determining the standard radio frequency deviation from its nominal value are presented in more detail.

This paper presents a sampling measurement system designed to compare ac standard resistors within a range from 1 mΩ to 10 Ω at frequencies ranging from 40 Hz to 10 kHz and for measurement currents up to 10 A. The system allows simultaneous measurement of both components of impedance of the calibrated resistor relative to the reference resistor. Built on the basis of commercial PXI modules, complemented by modules developed by the authors, the system stands out relatively simple structure and fully automatic operation. In order to reduce the impact of parasitic impedances on the comparison accuracy, a completely automated interchange method and the original way of connecting a digitizer to the compared impedances were applied. The consistency of the measured ac resistance ratios from 1:1 to 1:10 is better than 1 μΩ/Ω and phase difference better than 6 μrad, over the entire frequency range. The results of several comparisons and the analysis of their uncertainty show that for the comparisons of resistors with a resistance ratio close to one, the relative uncertainty of the resistance ratio measurement is 2.3 μΩ/Ω (k=2) over the entire frequency range. The uncertainty of the difference between the time constants of the compared resistors is at the level of 0.2 ns (k=2) at 1 kHz.

This paper presents the concept and some aspects of the physical implementation of a virtual training laboratory in the field of primary impedance metrology. The creation of a virtual training laboratory provides a novel method of disseminating metrological knowledge and expertise in a practical way and at a low cost. It will expose new users to the live experience of operating a digital impedance bridge thus helping to encourage the uptake of this novel and useful impedance measurement technology. The virtual training laboratory was developed as part of the EMPIR projects VersICal 17RPT04, A versatile electrical impedance calibration laboratory based on digital impedance bridges , and GIQS 18SIB07, Graphene impedance quantum standard .