Abstract
Nowadays, the use of the (four-wire) automatic resistance bridge is widespread in thermometry, up to the point that it is believed to be the only method to measure the resistance of thermometers with the required accuracy. However, before the introduction of this type of bridge, other methods were used in thermometry that, specifically with the comparison of thermometers, may still have their advantages. One of these is the so-called two-wire potentiometric method, described here shortly, where—unlike the four-wire method—all thermometers of the same type are placed in a series configuration, and only voltages are measured with a carefully characterized potentiometer. Additionally, a variant of the method is given which may successfully be applied with future thermometer comparisons.
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1. Introduction
The introduction, in the 1980s–1990s, of the automatic resistance bridge (ARB) in thermometry labs throughout the world coincided with the increasing use of the computer in the measurement process. Resistance bridges did already exist, such as the Guildline (or Kusters) Bridge [1, 2] model 9975, but these were completely manual, needing human presence for its operation. The computer allowed the user to automate measurements, in the absence of the operator, even during the night. Therefore, the introduction of both of them in the laboratory appeared to be a major step forward. However, this led to previous methods to be completely forgotten. One of these methods—especially the accompanying thermometer circuitry—was the two-wire potentiometric method, which was successfully applied specifically with thermometer comparisons. Although the potentiometric method may seem to be forgotten, it is actually implemented in the current ARBs in such a way that most users are not aware anymore of the method itself. Relevant information about the ARB and its development (starting with the A7 bridge by ASL) is given in [3–6]. During a recent international thermometry meeting, the author could ask some of the major participants what method they used for the comparison of thermometers. The answer was invariably: an ARB. Moreover, when asked about the potentiometric method, very few had even heard of it! Indeed, even the first key comparison CCT-K2 (capsule standard resistance thermometers, cSPRTs, below 273 K) [7] made use—not without difficulties—of an ARB, as did CCT-K1 (rhodium–iron thermometers below 27 K) [8]. The ARB performs invariably a four-wire resistance measurement for each thermometer, where all wires are detached on each change of thermometer with the subsequent interruption of heater power from the measurement current. A short description of the two-wire potentiometric method is followed by the description of an alternative, which with thermometer comparisons has some advantages over the ARB. The discussion relies heavily on experience in the cryogenic temperature range with cSPRTs, but the proposed method for thermometer comparison is easily adapted also to long-stem SPRTs.
1.1. The potentiometric method
This method essentially consists of supplying a known current to a resistor whose resistance is to be determined and counterbalancing the voltage over this resistor with a known voltage generated by a potentiometer. The remaining imbalance is then amplified and measured with a voltmeter, not unlike the procedure used inside ARBs. Before the advent of ARBs, voltmeters were not yet able to measure the voltage drop over the resistor directly with the accuracy required in thermometry, which only the potentiometric method could offer, see figure 1. A stable source such as a car battery was used in the past to generate the current. The current wires are attached to both ends of the circuit. The voltage wires led into the cryostat are attached directly at both ends of the thermometer, thereby eliminating the disturbing voltage drop over the connecting wires since they do not carry any current. Any thermal EMFs are eliminated by inverting the current several times. Since this method measures only voltages, thermometers of like design, e.g. standard platinum resistance thermometers (SPRTs), can be arranged in a series configuration, where the current for the circuit—common to all thermometers in the circuit—is measured with an associated calibrated standard resistor, included in the circuit. SPRTs are taken here as an example, but the method can be applied to any other type of thermometer, rhodium–iron, platinum–cobalt or germanium. The voltage over each thermometer is then measured one after the other. In case also thermometers of different types are present, such as germanium thermometers (which can arrive at several kΩ), these are arranged in their own (serial) circuit, each with its associated current source and calibrated standard resistor. The resistance of the thermometer is finally obtained from the ratio of the voltage drops over the thermometer and the associated standard resistor. Such a configuration has allowed the comparison of rhodium–iron thermometers in the range up to 27 K with residuals less than 0.2 mK, see figure 2, taken from [9].
Figure 1. Scheme of a thermometer circuit and of a potentiometric measurement.
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Figure 2. Points Δ are residuals of fit from the calibration of RhFe-thermometer Nr. 4 (R(0 °C) = 50 Ω) against a calibrated 100 Ω RhFe-thermometer; points depicted by O represent results from a different comparison between the same thermometers. Text adapted from [9].
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1.2. A modern variant for thermometer comparisons
High-quality voltmeters have now developed to the point where the voltage drop over a thermometer can be reliably measured (8.5-digit resolution) with a relative accuracy equivalent to the required μΩ level (for a 25 Ω SPRT). Thus, there is no need any more to resort to the potentiometer and the successive amplification of the residual voltage. However, maintaining the series configuration of thermometers in circuits of like design, such as the 25 Ω SPRT, has distinct advantages over the ARB with the comparison of thermometers:
- (a)Less wires are required in the cryostat, since—with n thermometers in a circuit—2*n current wires are substituted with only two, thereby reducing the heat load for the cryostat;
- (b)A voltage measurement requiring only two wires, almost twice the number of thermometers can be accommodated in a scanner with respect to a four-wire resistance measurement;
- (c)Once the thermometers are in thermal equilibrium with their environment, the measurements cause no thermal disturbance at all, not even with thermometers of different type (potentially of higher resistance), since all thermometers always carry their measurement current. With an ARB, the change in heat generation on such a change is one of the main difficulties with a thermometer comparison, since it disturbs thermal equilibrium. Although the scanners of modern ARBs provide 'keep-warm' currents, in many cases they only approximate the needed measuring currents, thus still giving rise to thermal disturbance;
- (d)With all thermometers being always supplied with the measurement current, there is no need for a scanner option to keep them warm;
- (e)Quadrature effects requiring careful wiring are absent (this a.c. effect can occur at temperatures below about 25 K);
- (f)A voltage measurement is faster than a resistance measurement, at this level, although partially offset by the necessity to change current direction several times;
- (g)Being a comparison, there is no requirement for high long-term stability for the voltmeter, only short-time stability;
- (h)Absolute voltage accuracy is not required.
The measurement instrumentation needed is: a high quality (8.5-digit resolution) voltmeter, a stable current source and a two-wire scanner; all with either a GPIB- or USB-port for computer control.
There is (only?) one drawback to the series configuration: it requires a purpose-built apparatus, wired specifically for use with thermometer comparisons.
2. Conclusion
It appears that, in the case of thermometer comparisons, modern instrumentation allows the adoption of voltage ratio measurements directly without resorting to the use of an ARB. When thermometers of different type are being compared, direct voltage measurements with the thermometers arranged in different circuits with a series configuration, with those of like design in the same circuit, may have its merits. Specifically, changing to a thermometer of different type does not affect the temperature of the block hosting the thermometers. This greatly favors temperature equilibrium, thereby increasing the accuracy of the comparison.
Ethical statement
This paper adheres to the ethical policy of metrologia.