Fixed-point Realization Research Articles

Characterization of a New Zinc Fixed-Point Cell for ITS-90 Realization

A new zinc fixed-point cell for the dissemination of International Temperature Scale (ITS-90) was realized at the Italian National Metrological Institute (Istituto Nazionale di Ricerca Metrologica, INRiM). This paper presents the results of its characterization, including fabrication details. In particular, immersion effects and influences of impurities on the freezing point of zinc were studied. The new open-type cell was prepared using a high purity sample, chemically analyzed, and the depression of the fixed-point temperature was calculated using the method of Sum of Individual Estimates (SIE). The new cell presents a smaller freezing point depression compared with the national reference for which the Overall Maximum Estimate (OME) method was applied. This behavior was confirmed also by the direct comparison of the two cells. These results provide confidence on the agreement between the experimental comparison and the SIE/OME evaluation. Finally, the improvement of the new zinc cell is reflected also in a lower uncertainty budget for the fixed-point realization.

A Flexible FPGA-Based Channel Emulator for Non-Stationary MIMO Fading Channels

In this paper, a discrete non-stationary multiple-input multiple-output (MIMO) channel model suitable for the fixed-point realization on the field-programmable gate array (FPGA) hardware platform is proposed. On this basis, we develop a flexible hardware architecture with configurable channel parameters and implement it on a non-stationary MIMO channel emulator in a single FPGA chip. In addition, an improved non-stationary channel emulation method is employed to guarantee accurate channel fading and phase, and the schemes of other key modules are also illustrated and implemented in a single FPGA chip. Hardware tests demonstrate that the output statistical properties of proposed channel emulator, i.e., the probability density function (PDF), cross-correlation function (CCF), Doppler power spectrum density (DPSD), and the power delay profile (PDP) agree well with the corresponding theoretical ones.

Realizations of the ITS-90 from 273.16 K to 933.473 K (COOMET.T-K3.3)

The COOMET.T-K3-3 comparison is the regional comparison of ITS-90 fixed point realizations in the range from the triple point of water to the freezing point of aluminum. Six national metrology institutes: VNIIM (Russian Federation), BelGIM (Belarus), NSC IM (Ukraina), KazInMetr (Kazakhstan), NIM (Republic of Moldova), GEOSTM (Georgia) participated in this regional COOMET comparison. VNIIM was appointed as the pilot laboratory and the coordinator of the comparison. The link between the regional and key comparisons was provided by VNIIM.Two standard platinum resistance thermometers (25 ohm), manufactured at VNIIM, was used as a transfer standards.The degree of equivalence of measurement standards of the national metrology institutes participating in the COOMET comparison is determinated relative to the reference values of the CCT-K3 through the measurement results received by VNIIM, which took part in comparison. The report presents the results of this comparison and gives detailed information about the method of estimation of the degree of equivalence of NMI standards and its uncertainties.The comparison results have confirmed the uncertainty values, claimed by NMIsMain textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCT, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Comparison of xenon triple point realizations

It is widely recognized that the Mercury triple point (MTP) being situated very close to the Water triple point (WTP) constitutes a weakness in the International Temperature Scale of 1990 (ITS-90), in addition to safety concerns related to the use and transportation of Mercury. As such, a substitution for a safer, high-quality fixed point about half way between the Argon and Water triple points would be highly desirable. Now, a direct comparison is described of a Xenon cell filled in 2005 by the National Research Council Canada (NRC) and a more recently produced cell of the Istituto Nazionale di Ricerca Metrologica (INRIM). The present paper discusses the INRiM 2017 measurements on both the INRiM and NRC cells, with a follow-up measurement at NRC, and presents the difference between the two cells, (0.17 ± 0.08) mK with the uncertainties of each cell’s realization of the Xenon triple point (XeTP), 0.11 mK for the INRiM cell and 0.07 mK for the NRC cell (k = 1). In addition, the effect of substituting Mercury with Xenon on Type 1 non-uniqueness (‘SRI’, subrange inconsistency), Type 3 non-uniqueness (‘NU3’, cSPRT variability) and propagation of fixed point realization uncertainty is shown and discussed.

Optimizing FDTD Memory Bandwidth by Using Block Float-Point Arithmetic

Finite-difference time-domain is a numerical method used for modelling of computational electrodynamics. The method is resource intensive, especially regarding memory usage. Multiple memory accesses are required per single computation so memory bandwidth acts as a bottleneck limiting the overall performance. Existing solutions use either fixed-point or floating-point arithmetic, depending on the complexity of the target platform, to model the data. Floating-point requires less memory access but the computation is more intensive due to the normalisation. Fixed-point is the opposite – simple computation but with more memory access for the same precision. The novelty of this paper is in the block floating-point realization which is the middle ground between the two. The approach is less compute intensive than the floating-point solutions while using less memory than the fixed-point realization. This makes the solution an alternative for bit-exact platforms, such as field-programmable gate arrays. The results are compared to both floating-point and fixed-point implementations and the memory bandwidth and other resources needed for targeted platform are calculated. DOI: http://dx.doi.org/10.5755/j01.eie.24.4.21475

Effect of Impurities on the Freezing Point of Zinc

The knowledge of the liquidus slope of impurities in fixed-point metal defined by the International Temperature Scale of 1990 is important for the estimation of uncertainties and correction of fixed point with the sum of individual estimates method. Great attentions are paid to the effect of ultra-trace impurities on the freezing point of zinc in the National Institute of Metrology. In the present work, the liquidus slopes of Ga–Zn, Ge–Zn were measured with the slim fixed-point cell developed through the doping experiments, and the temperature characteristics of the phase diagram of Fe–Zn were furthermore investigated. A quasi-adiabatic Zn fixed-point cell was developed with the thermometer well surrounded by the crucible with the pure metal, and the temperature uniformity of less than 20 mK in the region where the metal is located was obtained. The previous doping experiment of Pb–Zn with slim fixed-point cell was checked with quasi-adiabatic Zn fixed-point cell, and the result supports the previous liquidus slope measured with the traditional fixed-point realization.

FPGA system-level based design of multi-axis ADRC controller

The real-time control of high precision multi-axis system with modeling uncertainties and strong nonlinear coupling dynamics is a demanding task for conventional multivariable control applications. To this end, this research addresses the design of Active Disturbance Rejection Control (ADRC) for multi-axis system and its implementation in the Field Programmable Gate Array (FPGA) platform. For the ADRC algorithm, the minimum plant model information is necessary, and that enables a strong system robustness and adaptability under modeling uncertainty, coupling effects and external disturbances. Distinct from the traditional Very high speed integrated circuit Hardware Description Language (VHDL) design, the proposed FPGA implementation of ADRC is based on the system level design and it considerably reduces the design cycle. Moreover, the optimal fixed-point realization and controller architecture are selected as a tradeoff between control performances and FPGA resource occupancy. The ADRC tracking performances, robustness and stability are confirmed through the frequency domain analysis and experimentally validated on three-axis didactic radar antenna control system in different working conditions.

New Experimental Technique for the Study of Phase Transition Evolution in Fixed-Point Cells

A new advanced technique was developed at the Hungarian Metrological Institute (MKEH), devoted to optimizing the realization of the International Temperature Scale ITS-90. The work was performed within the framework of the European project “Novel techniques for traceable temperature dissemination.” The paper is devoted to describing this new measurement technique and its setup. The time evolution of the solid fraction and melt fraction along the phase transformation has been followed, using a technique based on the difference of the electrical conductivity between the solid and liquid phases of the metal. The measurement technique provides electrical signals, which are suitable for improving the quality of the freezing plateaus realized in the case of different fixed-point realizations, covering the temperature range from \(-39\,^{\circ }\mathrm{C}\) to \(962\,^{\circ }\mathrm{C}\). The ideal section of the freezing plateau can be maintained by ensuring a continuous flow of mass and energy of the fixed-point substance in the axial direction. The intervention is achieved by modifying the temperatures of the different zones of the furnace controller with more degrees, with the aid of developed intervening devices. Recent developments permit the selection of the ideal section of a freezing plateau and, what is more, the increase of this plateau section to practically unlimited for all metal fixed points.

Final report on COOMET.T-S1. Comparison of type S thermocouples at the freezing points of zinc, aluminium and copper 2014—2015

Regional comparison of type S thermocouples at the freezing points of zinc, aluminium and copper was initiated by COOMET TC1.1-10 (the technical committee of COOMET `Thermometry and thermal physics'). Three NMI take part in COOMET regional comparison: D I Mendeleev Institute for Metrology (VNIIM) (Russian Federation), National Scientific Centre (Institute of Metrology) (NSC IM, Ukraine), Republic State Enterprise (Kazakhstan Institute of Metrology) (KazInMetr, Republic of Kazakhstan). VNIIM (Russia) was chosen as the coordinator-pilot of the regional comparison.A star type comparison was used. The participants: KazInMetr and NSC IM constructed the type S thermocouples and calibrated them in three fixed points: zinc, aluminum and copper points, using methods of ITS-90 fixed point realizations. The thermocouples have been sent to VNIIM together with the results of the calibration at three fixed points, with the values of the inhomogeneity at temperature 200 °C and the uncertainty evaluations of the results. For calibration of thermocouples the same VNIIM fixed points cells were used. Participating laboratories repeated the calibration of thermocouples after its returning in zinc, aluminum and copper points to determine the stability of its results. In result of the comparison was to evaluate the equivalence of the type S thermocouples calibration in fixed points by NMIs to confirm corresponding lines of international website for NMI's Calibration and Measurement Capabilities (CMC). This paper is the final report of the comparison including analysis of the uncertainty of measurement results. Main text.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCT WG-KC, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Fixed point realization of partial updating adaptive algorithm for active noise control

An efficient low cost realization of the partial updating FXLMS algorithm is proposed in this paper. Unlike the conventional partial updating adaptive filters, the modified sign-LMS algorithm is used to make it easier to be implemented in a fixed point DSP. Moreover, the calculation of the filtered reference signal is divided into several steps, which further reduces the whole computational burden. An active noise controller using TMS320C5502 DSP chip is designed based on the proposed algorithm. The experiment results demonstrate that at a reasonable updating rate, the proposed algorithm has exactly the same performance with the normal float-point FXLMS algorithm while the computational burden is much lower.

On the Inter-Conversion Between Hermite and Laguerre Local Image Expansions

The nice relationship existing among the Hermite-Gauss and the Laguerre-Gauss image expansions, whose basis functions span the same signal space, is investigated. As a result, a novel efficient method for Cartesian to polar coordinate inter-conversion, especially suited for dedicated hardware realization, is proposed. Applications to local image rotation, based on the simple steerability of the Laguerre-Gauss expansion, and to local image analysis, based on Gaussian derivatives, are considered in detail. A possible fixed-point realization of the proposed inter-conversion scheme is discussed.

Improved Thermal Model for the Realization of the Triple Points of Cryogenic Gases as Temperature Fixed Points

The realization of the triple points of the cryogenic gases hydrogen, neon, oxygen, and argon as temperature fixed points at the highest level of accuracy requires consideration of the special properties of these fixed-point substances, as done in a general measurement protocol published elsewhere. The protocol is applied to the apparatus and methodology used for an international star intercomparison of sealed fixed-point cells. A generalized thermal model is developed to include the coexistence of different solid–liquid interfaces and various thermal resistances. This results in further components in the detailed uncertainty budget for the correction of the measuring power of the thermometer and for the extrapolation to the liquidus point. As a basis for an optimum fixed-point realization, especially an explanation is given why extremely long time periods may be necessary for the thermal recovery after pulses of the intermittent heating used for the calorimetric method.

Experimental and Numerical Investigation of the Temperature Field of a Fixed-Point Cavity

The temperature field non-uniformity of a blackbody cavity is one of the components of uncertainty of fixed-point realization. Here a study of the design and opportunities of the temperature furnace used in VNIIM is described. The dependence of the uniformity of a temperature field on various factors is shown by results of numerical calculations of a temperature field of VNIIM’s copper and gold fixed-point cells, realized with the software packages Elcut 5.3 and Ansys 11.0. A thermophysical model of the phase transition considered as steady state with convection and radiation heat exchange to an environment is applied. The basic focus is made on calculation of the radiation heat exchange between crucible elements and the environment and a furnace cavity, as a dominating component of the heat transfer. Results using analytically and numerically calculated angular factors of radiation of heat exchange are discussed. The data obtained in measurements of a temperature field of a cavity fixed point during phase transitions of copper and gold by a spectrocomparator with high sensitivity, are also shown here. Both theoretical calculation and experiment were realized at various distributions of temperature along an external surface of a crucible. Good agreement of results between steady-state calculation of a temperature field and the measured data with the best entry conditions is observed. The average value of non-uniformity of a temperature field along a cavity for points of phase transition of copper and gold for an 88 mm long graphite crucible with a 54 mm deep, 8 mm diameter cavity was 40 mK, and the temperature drop across the graphite wall was 20 mK. In this paper the reasons for occurrence of large gradients inside a fixed-point cavity during the phase transition, received during some experimental research, are also discussed.

Measurement of Al Freezing-Point Temperature: Effect of Initiation Process

In CCT documents it is stated that “...for the freezing curves of the metallic fixed points, the maximum observed temperature on the plateau should be taken as the best approximation of the liquidus temperature. The fixed points should be realized with the inner and outer liquid-solid interfaces and extend past the maximum by 10 % to 20 % of the fraction frozen, to clearly establish the value of the maximum and the resolution of its determination.” Also, it is accepted that “...the inner interface is essentially static. It is the temperature of the inner liquid/solid interface that is measured by the thermometer.” The analysis of freezing curves obtained by the standard method of fixed-point realization shows that the parameters of the initial part of the freezing curve, the mean temperature value of which is usually taken as the liquidus temperature, depend on how the inner interface is initiated. Variations in the duration and intensity of initiation cause changes in the initial part of the freezing curve and in the resulting SPRT measurement. Moreover, the relation between the duration of the initial section of the plateau with a minor temperature change and the duration of its final section with a significant slope also depend on the initiation method used and on the furnace temperature. The effect of freezing initiation conditions on the measurement result is individual for each fixed point because of the differences in thermophysical properties of metals and in conditions of the heat transfer from the liquid–solid interface to the thermometer. Aluminum has a maximum value of the melting specific heat in comparison with other metals used in ITS-90 fixed points; in the present study, the effect of the intensity and duration of the inner liquid–solid interface initiation was investigated both experimentally and through calculation.

Validation of the fixed-point realization of the thermocouple scale using a radiation thermometer in the temperature range between the freezing points of Ag and Pd

We have developed a blackbody comparison system to validate the fixed-point realization of the thermocouple temperature scale using the radiation thermometry scale. Platinum/palladium, type S and type B thermocouples were calibrated at the fixed points of Ag, Cu, Fe–C, Co–C and Pd (only for type B). The radiation thermometer used was an LP4 linear pyrometer operating at a central wavelength of 650 nm. To assign the Fe–C eutectic melting temperature in our laboratory, a radiometric Fe–C cell was fabricated, and its melting temperature was determined as (1154.0 ± 0.1) °C with k = 2. Two scales were compared from 962 °C to 1555 °C in the blackbody comparison system. The two scales were consistent within 0.5 °C up to 1400 °C, but the discrepancy for the type B thermocouple increased to 2.3 °C at 1554.8 °C. The thermocouple and radiometric scales realized at our laboratory were in agreement up to the freezing temperature of Pd within the measurement uncertainty.

On the Transfer Function Error of State-Space Filters in Fixed-Point Context

This brief presents a new measure used for the implementation of filters/controllers in state-space form. It investigates the transfer function deviation generated by the coefficient quantization. The classical L 2-sensitivity measure is extended with precise consideration on their fixed-point representation in order to make a more valid measure. By solving the related optimal realization problem, fixed-point accurate realizations in state-space form can be found.

ITS-90 Scale Realization on the New Radiation Thermometer Calibration Facility at NMi VSL

In the first half of 2005, Nederlands Meetinstituut Van Swinden Laboratorium B.V. (NMi VSL) redesigned their facilities for radiation thermometry in a new laboratory building and an opportunity arose to implement new measurement methods. The new facility is used for ITS-90 realization and dissemination in the temperature range from − 50 °C to 3,000 °C. A study was performed to compare a silver-point realization with a fixed-point blackbody radiator (FP-BBR) to a sodium heat-pipe blackbody radiator (HP-BBR) traceable via a HTSPRT to a contact thermometry silver point. It was found that the fixed-point realization transfer to the sodium heat pipe results in an uncertainty from 0.2 K to 2.4 K for the ITS-90 over the temperature range from 961.78 °C to 3,000 °C.

High-Temperature Fixed-Point Facilities for Improved Thermocouple Calibration—Euromet Project 857

LNE, NPL, and PTB decided in 2005 to join their research efforts in the framework of Euromet Project 857 with the aim of reducing the calibration uncertainty of noble metal and other high-temperature thermocouples by at least a factor of two. This ambitious target will be met through the development and implementation of robust high-temperature fixed points based on metal–carbon eutectic technology. The Euromet project is structured around five work packages and ensures good and efficient cooperation between the partners to meet the objectives within the project timeframe of four years. Furthermore, a formal cooperative research agreement has been established with the National Metrology Institute of Japan (NMIJ) to demonstrate, on a worldwide basis, that this new method is a significant improvement over current calibration methods. In summary, the project consists of (a) the development of sets of cells at the cobalt–carbon eutectic point (1324◦C) and palladium–carbon eutectic point (1492◦C) and (b) the construction of platinum/palladium (Pt/Pd) thermocouples carefully stabilized for use to these temperatures. Supplementary research to be undertaken as part of this project is the improvement of fixed-point construction and realization capabilities through high-temperature furnaces with low thermal gradients. This paper describes the European project and gives an overview of current progress.

High-Purity Fixed Points of the ITS-90 with Traceable Analysis of Impurity Contents

The International Temperature Scale of 1990 (ITS-90) is based on thermodynamic equilibrium states of ideally pure substances. The largest contribution to the uncertainty budgets of most metallic fixed points is the influence of impurities on the fixed-point temperature. Therefore, a traceable chemical analysis of the remaining impurities with small uncertainty is the basis of further progress. Further requirements are better knowledge of the phase diagrams at very low impurity contents, impurity segregation, and the quantification and correction of thermal effects during a fixed-point realization. In this article, current and future activities at PTB and BAM in order to develop improved metallic fixed-point cells of the ITS-90 are reviewed.

A New Method for the Quantification and Correction of Thermal Effects on the Realization of Fixed Points

The temperature and flatness (shape) of a fixed-point plateau depend on both the amount and nature of specific impurities and on thermal effects that are influenced by the fixed-point cell design and furnace properties. A better understanding and experimental proof of the influence of specific impurities on fixed-point realizations require the separation of impurity influences from thermal effects. In this paper the influence of heat exchange between the thermometer and furnace is quantified via a method based on changing the furnace temperature during the fixed-point measurement. It will be shown that the corresponding correction of this thermal effect has a dominant influence on the plateau shape compared to the influence of impurities. This leads to an explanation for why the maximum of an induced freeze is the most reproducible temperature. A secondary outcome is an explanation of why natural freezes have less flat plateaux compared to induced freezes, resulting in fixed-point temperatures that are too low. Furthermore, the suggested procedure is the basis of the direct and quantitative comparison of fixed-point cells and the detection of weak points within a specific design. It allows optimization of fixed-point cells and furnaces, and helps to deepen the common understanding of the phase transition in fixed-point cells.