Monash University, Clayton, Victoria 3168, Australia
This is an absolute standard of the secondary electrical unit of capacitance whose value is determined in terms of the base SI units of length, mass, and time. It is used all over the world and is incorporated into the International System of Units called SI.
Theoretically, the value of capacitance depends on only one length measurement. However, for practical capacitors two or three length measurements are required to calculate the capacitance. These multiple measurements of length increase uncertainty in the calculated value of capacitance and thus reduce its accuracy and precision.
D.G. Lampard and A.M. Thompson of CSIRO Australia, in 1956, discovered that a capacitor with four cylindrical conductors has a cross capacitance (see Fig. 1) which depends on one length measurement in accordance with the theory thus markedly improving the precision of its calculated value. This capacitance is given by the simple expression
Figure 1 Principle of Lampard-Thompson calculable capacitor
(see Reference [1] and [2] for details)
The capacitances C1 and C2 between opposite pairs of conductors (A and C, and B and D in the model) obey the relation
so that if C1 = C2 = C because of symmetry (e.g. symmetrically arranged circular cylinders as in the model), then
In the absolute standard constructed in the Australian National Standards Laboratory (see model), a fifth central cylindrical conductor (called 'the guard') is used to shield a part of the capacitor and to determine the actual length involved in the definition of the capacitance. Two further refinements are added to obtain the best practical absolute standard. These are:
1. metal foil is wrapped around all outer cylinders (the red foil shows this on two cylinders)
2. the end of the guard is fitted with a projecting "spike" to compensate for the end effect while allowing the laser light used for length measurement to pass through the guard conductor.
( NB: In the model, one of the outer cylinders is moved out to clearly show the guard in the centre. In the actual calculable capacitor, the four outer conductors are arranged symmetrically. )
The whole assembly shown in the model is placed in a vacuum and the capacitance is measured with a special impedance bridge detailed in Ref. [1] and [2]. The use of this absolute standard eliminates the dependence on "as maintained" standards of resistance as one of the main secondary units in the measurement of electrical quantities. Unlike absolute standards (defined in terms of the base units with highly precise standards), the "as maintained" standards are subject to a drift in their value due to ageing, physical and chemical changes and environmental influences.
In the last third of the twentieth century, many of the "as maintained" standards for base units have been converted into absolute standards and furthermore they have been redefined in terms of quantum phenomena e.g. standards for meter and second. Similarly, among the electrical units, the standards of volt and ohm have been redefined using quantum effects found in Josephson junction and von Klitzing Hall resistance respectively. Thus the Lampard-Thompson calculable capacitor may be viewed as one of the last macroscopic absolute standard.
References
[1] Thompson, A.M. and Lampard, D.G., A New Theorem in Electrostatics and its Application to Calculable Standards of Capacitance, Nature, vol. 177, p. 888 (1956).
[2] Clothier, W.K., A Calculable Standard of Capacitance, Metrologia, vol. 1, No. 2, pp. 36-55 (1965).
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Pamphlet produced by Dr K. P. Dabke, Honorary Research Associate, Dept. of E & C S Eng. Monash University.
July, 98 CAPCAT.DOC