Elsevier

Measurement

Volume 171, February 2021, 108647
Measurement

Common model to approximate the time-variant behaviour of air humidity-change influence on some fundamental standards of precision electromagnetic measurement

https://doi.org/10.1016/j.measurement.2020.108647Get rights and content

Highlights

  • A model developed for describing the dependence of Zener voltage on air humidity.

  • The model could be suitable to more other areas of electromagnetic measurements.

  • Universality has been verified via new experiments on impedance & resistance areas.

  • The physical mechanisms is a macro-relaxation process in an air interaction space.

  • Model together with humidity data tracking the humidity effect can be compensated.

Abstract

In this work, a mathematical model originally developed for describing the dependence of Zener voltage output on air humidity is intended to be generalized by applying it to inductance and resistance measurements. It is shown that the influence of varying humidity behaviors, through the exponential decay diffusion of water vapor followed by corresponding variations of electromagnetic features, as a macro-relaxation process inside the air interaction space of measured object. The relaxation time constant of this process, ranging from minutes to weeks, is determined by the sealing conditions. Results of experimental studies on air humidity-change influence on ac self-inductance, dc mutual inductance and dc resistance measurements at NIM agree well with the theoretical analyses using this model. So far, the experiments make this model more suitable for main areas of electromagnetic measurement: using the model and tracking humidity data, the time-variant effect can be approximately compensated.

Introduction

Dating back over a century, observations and investigations were undertaken to check whether part of the observed fluctuations in some electrical measurement results were due to variations in atmospheric humidity [1], [2]. Since the 1990s, this subject has appeared more frequently and in broader areas of precision electrical measurement [3], [4], [5], [6], [7], [8], [9], [10], [11], also in other fields [12], [13], [14].

It is necessary to mention [7]: From 1996 to 1997, the National Metrology Centre of Singapore (NMC) coordinated the 3rd Asia Pacific Metrology Program (APMP) comparison of dc voltage using a Zener traveling standard. The comparison results at 1.018 V showed a zigzag curve among those laboratories that used their Josephson Array Voltage Standards (JAVSs) for this comparison. The amplitude of the zigzag was more than 1 part in 107, much larger than the typical uncertainty of such standards. These results motivated NMC to search for an explanation, which finally led to the development of an approximate mathematical model to describe this phenomenon [7]. In 2000, the results of another APMP comparison of ac-dc difference had to be declared invalid due to unexpected poor agreement among participating laboratories and the higher the measurement frequency the disparity even more. The culprit of this turned out to be again the humidity effect, as suggested by NMC and experimentally confirmed by the pilot laboratory. Soon afterwards, [10] revealed similar humidity influence behavior in the ac application.

To understand the physics behind these observations and to find out whether the model and conclusions derived from [7], [10] are appropriate for describing air humidity-change influence on other types of electromagnetic measurement, three experiments under varying humidity were designed and conducted at the National Institute of Metrology of China (NIM). The three experimental results on measuring ac self-inductance, dc mutual inductance and dc resistance by means of ordinary instrumentation and existing methodology are reported in this paper. The mechanisms behind the experimental observations are analyzed using usually adopted equivalent circuits, when needed. The layout is aiming at the influence behavior of humidity changes, rather than precisely measuring the electromagnetic quantity amount itself and therefore the Type-B uncertainties of the measurements seem relatively larger.

This paper is organized as follows: Section 2 gives a brief review of the mathematical model drawn from [7]. 3 Air humidity-change influence on measurement of ac self-inductance, 4 Air humidity-change influence on measurement of dc mutual inductance, 5 Air humidity-change influence on measurement of dc resistance describe the measurement setups and results of the experiments on ac self-inductance, dc mutual inductance and dc resistance under controlled varying ambient humidity conditions respectively. The mechanisms behind the experimental observations are analyzed as well. Section 6 defines the “air interaction space” of a measured object, in which a macro-relaxation process occurs. This is believed to be responsible for the common physical phenomenon governing the humidity effect of some important fundamental standards of electromagnetic measurement. In Section 7, we demonstrate that results of an international comparison can be improved by applying compensations using the model. Conclusions of this work are given in Section 8.

Section snippets

Dependence of Zener voltage output on humidity – A mathematical model

Reference [7] proposed a first order time-dependent differential equation to model the dependence of Zener voltage output function Ψ on humidity step-like change ΔH:dΨ/dt=τ-1[khΔH-Ψ]where kh is the humidity coefficient and τ is a time constant associated with moisture infiltration into the device. The general solution of equation (1) isΨt=Ψ0+khΔH[1-exp(-t/τ)]where Ψ(0) is an initial value at the starting point (t = 0) of the measurement. Equation (2) shows that the voltage output is expected to

General description

We select two measurands: one is a self-made hollow multi-layer inductive coil with Henry-order of inductance value (the measured results under different measurement frequencies show significant fluctuation); another is a NIM designed and by manufacturer made standard inductor with a rated inductance value of 0.1 H. Each measured inductor is measured by a set of GR1689M RLC bridge on an ac test source voltage of 1.0 V rms.

Inductor equivalent circuit with residual parameters

Fig. 1 shows the equivalent circuit of an inductor with residual

Methods of measurement

Determinations of the dc mutual inductance of a hollow mutual inductor were made in intervals by placing device under test in an air-tight container with atmosphere of a constant temperature of 16.9 °C and a relative humidity of 52%. The solution in the container was then changed: by putting Silica Gel to get 20%, and then putting saturated salt solution of NaCl to get 61%. After triggering each humidity change, the dc mutual inductance was measured by using a setup following the standard

Introducing this topic

Air humidity influence on measurement of dc resistance had been reported one century ago [1]. It seems to be the first study on the time-variant effect of changing ambient air humidity on precision electromagnetic measurements. That may be why some standards are gradually constructed to be immersed in oil or inert gas. This section attempts to assess the relationship between this humidity influence process and the applicability of formula (3) by means of experiments.

Measurement procedure

There are two measured

Common mathematical model on water molecules transport mechanism governing the humidity effect

As shown in sections of 3, 4 and 5, measured variations of ac self and dc mutual inductances as well as dc resistances in response to changes in air relative humidity are modeled as exponential decays like those used to characterize voltage output of a voltage standard referenced to Zener diode. The estimated humidity coefficient kh and the time constants τ+ and τ- in each test of this paper (for ac inductance measurement including those at each test frequency [10]) with estimated standard

Applying humidity model to reduce comparison uncertainty

In this section, an example of reduction of uncertainty introduced by humidity change achieved through applying compensations based on equation (3). Fig. 1 of [7] has depicted the humidity data and accordingly calculated dc voltage output in response to changes in humidity by the third APMP international comparison of dc voltage at 1.018 V level. In following Fig. 7, NMC as the pilot laboratory of this comparison is denoted Lab A. The comparison was so arranged, like “spoke article”, after

Conclusions

In this work, we have shown:

  • The experimental results agree well with data predicted by using the mathematical model, which is originally developed for describing the dependence of Zener voltage output on humidity. The commonality among different kinds of precision electromagnetic measurement regarding humidity-change influence can be interpreted as a macro-relaxation process: diffusion of water vapour in air, permeation of water molecules in materials and/or adsorption and desorption of water

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

Authors like to thank the following colleagues for support and help provided during the course of this work: Yu-Ning DUAN, for his great support for the experiments at NIM, China; Zhong-Tai QIAN for helpful discussion about the significance of residual capacitance contribution by ac inductance measurements; Gang WANG for dedication to perform the AC inductance and DC mutual inductance measurements; Yan YANG for providing 0.1 H inductor for measurement as well as Gan XU and Jinni LEE for

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