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Measuring the absolute ohm

The world requires internationally accepted standards for weights and measures which are constantly assessed and refined as new technology emerges. In the area of electrical standards the classical method of calibrating a standard resistor in the first half of the twentieth century was time consuming and finicky.

During the 1950s Keith Clothier, Mel Thompson and Doug Lampard from CSIRO’s National Measurement Laboratory at Sydney University came up with a totally new way of measuring electrical resistance using a calculable capacitor of four parallel brass rods which needed only one length measurement to determine its absolute value. This was done with light waves and resulted in an accuracy of one hundredth of a million, 100 times greater than expected.

From 1964 to 1974, the National Measurement Laboratory gave the world its best value of the absolute ohm, and readings took only 3 hours rather than six months. In 1957 Doug Lampard was awarded the Heaviside Premium by the Institution of Electrical Engineers, London, and in 1965, Doug Lampard and Mel Thompson were jointly awarded the Albert F. Sperry Medal by the Instrument Society of America for their work on calculable standards of capacitance.

The International Bureau of Weights and Measures

In 1875 eighteen countries created an International Bureau of Weights and Measures at Sèvres, near Paris. One of its first tasks was to re-define the metre which was taken to be one ten-millionth of a quadrant of the Earth’s meridian, passing through Dunkirk and a point near Barcelona. The conference agreed that the new definition should be the distance between two engraved lines on a bar of platinum-iridium alloy at zero degrees Celsius.

In 1960 the metre was re-defined, as 1 650 763.73 wavelengths in a vacuum of the radiation of the orange line of the krypton-86 isotope.

The need for electrical measurement standards

So new technology keeps producing new definitions and new standards against which measurements of all physical quantities can be made. A major contribution to new technology was made at the CSIRO National Measurement Laboratory, in the grounds of the University of Sydney, in the infinitely more complex field of electrical measurements.

In electrical engineering there is a constant need to check the values of the standards used to maintain the basic units of electrical measurements – the volt and the ohm. Millions of dollars’ worth of electrical equipment is made in Australia every year. If each manufacturer used even a slightly different value for the volt or the ohm enormous confusion and huge financial losses would follow. The values of such basic building blocks as capacitors and resistors – which go into TV sets, radios, tape recorders etc – must be known accurately to prevent signals from straying into the wrong channels.

The standard for the ohm, the measure of resistance of electric flow

In 1861 the British Association for the Advancement of Science set up a committee on electric units and standards. For the ohm – a measure of resistance to the flow of electric current – they chose the resistance of a column of mercury, one square millimetre in cross-section and 1 063 centimetres long. This mercury ohm has long since been replaced by the so-called absolute ohm which is derived from the units of length and time. It was later found that the mercury ohm differed from the absolute ohm by up to l.5 per cent.

The classical method of relating the ohm to the units of length and time involves the construction of a coil of copper wire of a large number of turns wound onto a very precise former usually nowadays of fused silica. By measuring the position and diameter of each turn of wire the inductance of the coil can be calculated. The inductance is a measure of the magnetic energy generated when a current is passed through the coil and depends only on the geometry of the coil. A complex series of electrical measurements is necessary to relate the resistance of a standard resistor to the inductance of the coil. Once the absolute value of one resistor is determined in this way it is a relatively simple matter to obtain the values of other resistors by comparing them with it. But the measurement of a coil’s many physical dimensions is a finicky and frustrating business which can take up to six months.

CSIRO’s role

By the early 1950s the CSIRO National Measurement Laboratory had developed methods for the precise measurement of small values of electric capacitance and for the comparison of capacitance and resistance. By 1955 scientist Keith Clothier had a well-developed design for a variable capacitor of two metal-coated flat glass plates isolated in a vacuum. But this required measurements of the plates and their spacing to get an accurate value.

Then another scientist, Mel Thompson, was struck by an idea which he was later to describe as ‘pure serendipity’. He realised that the drudgery involved in measuring the exact physical dimensions of a capacitor could be avoided with a device of simpler cylindrical geometry. If the cross-section of the cylinder which was divided into two pairs of electrodes was nominally symmetrical then any imperfections in the symmetry could be taken into account by measuring both ‘cross-capacitors’. His colleague Doug Lampard calculated the capacitance per unit length of a number of different cross-sections and was able to prove that all cross-sections gave the same answer independent of size and shape. This was an unexpected but tremendously useful result.

The results of some of Lampard’s calculations on quite different cross-sectional profiles agreed with each other so closely that the suspicion arose that a general expression for their capacitance existed that was independent of cross-sectional profile. Doug Lampard discovered this identity, and it appeared in a paper entitled ‘A new theorem in electrostatics with applications to calculable standards of capacitance’, published in the Proceedings of the Institution of Electrical Engineers in 1957. This paper described what was probably Doug Lampard’s most important single scientific work.

As a result of these findings Mel Thompson persuaded Keith Clothier to abandon his research and make a new design based on this idea. It resulted in a calculable capacitor of four parallel brass rods which needed only one length measurement to determine its absolute value. This was done with light waves and resulted in an accuracy that surprised even the scientists. As Mel Thompson recalled;

We thought we would get an accuracy of one part per million. Well, it turned out that we did 10 times better than that – and we could now do 10 times better still.

The development of a capacitance standard with an accuracy of about 1 part in 100 million, was more than 100 times more accurate than the best capacitance standard at that time. This allowed the standard ohm to be redefined. In the field of electrical measurements, it was a major advance.

The theorem (which is usually referred to in texts on electrostatics as the Lampard Capacitance Theorem) became the mainstay for establishing the absolute SI unit of resistance in every national standards laboratory for many decades.

International acceptance

From 1964 to 1974, when the Americans confirmed the value with similar equipment based on Thompson’s idea, the National Measurement Laboratory gave the world its best value of the absolute ohm, and readings took not six months, but three hours.

For his work on calculable standards of capacitance Doug Lampard was awarded:

1984

The Centennial Medal, Institute of Electrical and Electronic Engineers (USA)

1977

Doug Lampard was elected a Fellow of the Australian Academy of Science

1965

The Albert F. Sperry Medal (with Mel Thompson) by the Instrument Society of America

1957

The Heaviside Premium by the Institution of Electrical Engineers, London

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