The unit of electrical capacitance is the farad (abbreviated F), called after the English physicist and also chemist Michael Faraday. The capacitance C of a capacitor is the proportion of the fee Q save on computer in the capacitor to the used dc voltage U:

In the case of alternative current (ac), the capacitance is identified by the alternate current I i beg your pardon flows as soon as an ac voltage U is applied to the impedance Z of the capacitor:

with j together the imagine unit (j2= -1) and ω the angular frequency.

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Hence the holds both for direct and alternate current:

The realisation and also dissemination of the farad is accomplished world-wide with alternative current. Therefore, in the complying with only the ac capacitance is considered. Frequently used capacitance standards space commercial parallel-plate capacitors do of Invar and thermostated fused-silica standards because they, amongst other features, have actually a very small dissipation factor.


1 nF capacitor of the kind "General Radio 1404 A", because that didactic objectives with a cut instance to do the ridge of parallel capacitor key visible.

The realisation the the capacitance unit in ~ through coaxial measuring bridges

The capacitance unit is establish at by means of a so-called quadrature leg which links a 10 nF capacitance standard under calibration to the recognized quantum room resistance. The following figure shows the plan of such a quadrature bridge:


Scheme that a quadrature bridge.

Note the the same alternating current I flows with both standards. Making use of Ohm’s regulation I = U/RH because that the left eight of the bridge and I = ωCU because that the appropriate arm the the leg (which by the method is the definition of resistance and capacitance, respectively), the capacitance of the traditional under calibration have the right to be express in regards to the known quantum hall resistance RH:

C = (1 + Δ)/(ωRH)

with ω = 2πf the angular frequency and also f = 1233,147 Hz the frequency, traced come the frequency typical of (Department 4.4). Δ is the (usually very small) family member deviation that the 10 nF capacitance typical from nominal and also is figured out from a bridge balance system which, for the sake of simplicity, is not shown in the number above.

It is essential to make certain that the ac worth of the quantum hall resistance agrees through the quantised dc value and in certain does no deviate due to parasitic ac dissipation. To stop such unwanted effects, occurred a distinct shielding technique.

According to the reference of the CIPM, the quantum room resistance is described RK-90, come ensure the best feasible agreement through the SI farad. The relative difference in between RK-90 and the present SI worth of RK quantities to much less than 2.10-8, i beg your pardon is nearly not relevant and also will loss away v the brand-new SI.

The accuracy of the quadrature bridge shown above is minimal by one inaccuracy the technical beginning in producing the quadrature voltage jU. Expanding the quadrature leg to a mirror-symmetrical twin bridge allows to eliminating this effect and also to achieving the desired accuracy. Indeed, this boosts the measurement effort. In particular, two ac quantum hall resistances space needed. They space operated in one cryostat v a superconducting solenoid and also are noted with coaxial leads and also shields.


Scheme that a dual quadrature bridge.


Photo the the main part of the quadrature brigde. The broad of the photo synchronizes to around 2.5 m.

In this way, the 10 nF capacitance standards are calibrated. Capacitance criter with nominal worths of 10 pF and also 100 pF (1 pF = 10-12 F) exhibit the finest time stability and transportability. Therefore, they space most suitable for medium-term preservation, in ~ and also for its customers. They are hence the "working horses" the capacitance metrology. To calibrate such a 10 pF or 100 pF capacitance standard, a succession of 10:1 procedures – starting with the currently calibrated 10 nF requirements – is lugged out by way of a coaxial ratio bridge.


Measuring chain from the quantum hall resistance to a 10 pF capacitance standard and also to a dc resistance standard.

The quantum hall resistance is hence a fixed point not only for the resistance scale, but also for the capacitance scale. This is an benefit for the consistency of the device of units. The hesitation achievable for a 10 pF standard quantities to 1.10-8 (k = 2), i m sorry is plainly smaller than the hesitation of the world-beating calculable capacitance artefacts. The reasons for this low apprehension are not only the one-of-a-kind properties the the quantum hall resistance, but likewise the distinct coaxial measurement an approach which permits very an accurate measurements in ~ a short noise level.

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Bottom finish of a coaxial twin holder for two GaAs quantum room resistances for applications at low temperatures and solid magnetic fields. The overlain measured curves show the plateaus of the quantum room resistance.

for the conservation at, 10 pF and also 100 pF working standards of known drift behaviour are traced in this method to the quantum room resistance, around two time a year as and also when required. These capacitance standards room then provided in Working group 2.13 for the calibration of customer standards. There, additionally the capacitance scale with larger nominal values approximately 10 mF is built up.

Back to house AG 2.62


Head of Working group

Dr. Jürgen Schurr


Physikalisch-Technische Bundesanstalt Bundesallee 100 38116 Braunschweig