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Calculable capacitor

    The calculable capacitor allows the realization of the SI unit of capacitance, the farad, and by use of a quadrature bridge, the SI unit of resistance, the ohm.

    The calculable capacitor is based on a theorem in electrostatics (described by A. Thompson and D. Lampard of CSIRO-NML in 1956) which allows the calculation of the capacitance of a special type of capacitor directly from a single dimensional measurement which can be made traceable to the SI unit of length.

    The Australian National Measurement Institute (NMIA) and the BIPM are constructing two new and improved calculable capacitors based on a previous design by the CSIRO of Australia which was developed and built about 40 years ago. At the conclusion of the project, each institute will have, and maintain, one instrument. Although the basic mechanical design will be similar, the measurement systems associated with them will differ, so helping to provide independent realizations. The design goal is an uncertainty of the order of 1 part in 108.

    Since the start of the project the National Research Council Canada (NRC) and the National Institute of Metrology (NIM), China, have joined. Each will build their own instrument using the same precision electrodes although some elements of the overall design will be different.

    The following pages give an update on its current status and details of the next steps.

    The status of the calculable capacitor project can be summarized as follows:

    • The capacitor has been fully constructed and all the critical components and functions have been tested. The quality and alignment of the main electrode bars is crucial to the performance of the final instrument. The four electrodes (solid stainless steel bars 500 mm long and 50 mm diameter) have been manufactured at NMIA (Australia) using a carefully monitored hand lapping process. The finished bars show deviations from perfect cylinders of less than 100 nm along the entire working length of 400 mm. This remarkable precision of manufacturing should allow an absolute capacitance standard with a relative uncertainty of a few parts in 109. To take advantage of the geometrical perfection of the bars a number of other precision mechanical components are necessary in order to facilitate their installation and alignment in the instrument. Most of these components have been realized by the BIPM workshop.

    • The alignment procedure for the main electrodes has been demonstrated to the required precision, though some further improvements will be made to the adjustment of their skew. The realization of a new specific probe, designed at NMIA, is under way in the BIPM workshop and should help to refine the alignment of the bars.


    • The interferometer required to measure the displacement of a moveable guard electrode producing the measured variation of capacitance (proportional to this displacement) is now installed and successfully tested. It shows a mechanically very stable cavity between the moveable mirrors. Further improvement of the stability of the laser frequency is needed in order to achieve the optimal uncertainty, and this point should be fixed reasonably quickly.

    • The two terminal-pairs coaxial bridge built to link the 0.4 pF capacitance variation produced by the calculable capacitor to a 1 pF capacitance standard has been fully evaluated using the calculable capacitor. The bridge behaves perfectly well and has demonstrated the required accuracy and stability. The uncertainty budget associated with the bridge has been established as well as that due to mechanical imperfection of the calculable capacitor. This latter point is currently the limiting factor in the accuracy of the capacitance measurement; it will be greatly improved once the final adjustment of the electrode bars has been completed, using the new alignment probe currently being machined.

    • Thus far no fundamental flaws have been found that will prevent the whole setup (calculable capacitor associated with its interferometer and bridge) reaching its target uncertainty of better than 1 part in 108.

    The measurement chain for linking the calculable capacitor to the quantum Hall resistance is the same as that used for regular maintenance of capacitance, and is thus in good working order. The extra bridge required for the first step from the calculable capacitor to 1 pF has been fully tested and is now operational. A new resistance bridge dedicated to measuring a pair of 51.6 kΩ resistors (which forms part of the BIPM quadrature bridge) directly against the quantized Hall resistance is also under construction. It will shorten the measurement chain linking the QHR and the BIPM reference capacitors, with the aim of reducing the overall uncertainties, and will form part of the final measurement chain.

    The measurement task will be to relate the capacitance implemented by the new instrument (around 0.4 pF) to the standards maintained by the BIPM in terms of the quantum Hall effect (a quantized resistance of around 13 kΩ). The result can be interpreted in two ways: as a direct SI measurement of the von Klitzing constant, RK, or as a purely electrical determination of the fine structure constant, α.

    Regardless of the interpretation, the aim is the same: to contribute new experimental data on the fundamental constants as part of the effort to ensure any future changes to the SI are based on solid metrology. The completed calculable capacitor should also serve as a practical capacitance standard for the BIPM's calibration services and comparisons work.

    Before starting the first series of measurements linking the calculable capacitor to the QHR (with the expected uncertainty level), the calculable capacitor will be disassembled and the main electrode bars re-aligned with a new improved alignment device currently being fabricated. This step should be completed within the next few months and the measurements started in 2015.