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Chapter 7 Units of Measurement • • • • • • • • Objective of a measurement – to assign a number to the quantity being measured • a magnitude – to assign a unit of measurement to the magnitude The units distinguish one physical quantity from another. Example inch units distinguish a length measurement from a volume measurement using gallon units. The present system of using units originated in ancient times: – Greeks – Chinese – Indians Created to satisfy the need for – quantifying weights and measures – standardization • trade issues Our particular system began in 1790 – The French Academy of Science – Called the ‘Metric System’ In 1875, 18 countries agreed to a treaty called the ‘Convention du Metre’ – A set of weights and measures that would be maintained in Paris By 1960 after years of refining and improving the SI system was agreed upon – Système International d’Unités The SI system • The SI system is a set of definitions • It defines the units that shall be used for reporting all scientific or non scientific measurements. • Other systems exist – mks - meter/kilogram/second •based on artifacts or physical objects – foot/pound/gallon •The SI system defines – 7 Fundamental or Base units – 2 Supplementary units • late additions – 27 Derived units • arrived at by combining the fundamental and supplementary units WITHOUT any numerical factors EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 1 © 2001 7 Base Units • LENGTH – The Metre – The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second – requires that the speed of light is a universal constant ( in vacuum) • 299 792 458 m/s •TIME – The Second The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. • ELECTRIC CURRENT – The Ampere • The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length. • THERMODYNAMIC TEMPERATURE – The Kelvin • The Kelvin, the unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. • LUMINOUS INTENSITY – The Candela • The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 Hz and that has a radiant intensity in that direction of 1/683 watt per steradian. • AMOUNT OF SUBSTANCE – The Mole – The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol." – When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. • MASS – The Kilogram – The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. – The only fundamental unit which is based on an artifact – The other 6 are based on universal constants for example: speed of light, magnetic permeability etc EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 2 © 2001 • • • • • Supplementary Units – The Radian • A measure of plane angle – The Steradian • A measure of solid angle Derived Units – Expressed directly in terms of the fundamental and supplementary units without any numerical quotients – this is called coherence. Examples: – Volume m3 – Density kg m-3 – Frequency s-1 (Hz) – Force kg.m.s-2 Of special interest to us in electrical engineering are: – The VOLT – The OHM – The FARAD – The HENRY The Volt – 1 Volt is the potential difference that exists between 2 points when 1 joule of work is done in moving 1 Coulomb of charge between the two points. 1V 1J 1N m 1kg m s 2 m 1C 1A s 1A s 1V 1kg m 2 s 3 A1 – Note that there are no constants • • COHERENT Resistance – From Ohm’s Law 1 • Capacitance – The Farad 1F • 1V 1kg m 2 s 3 A 2 1A 1C 1kg 1 m 2 s 4 A 2 1V Inductance – The Henry EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 3 © 2001 1H 7.2 • 1Wb 1kg m 2 s 2 A 2 1A Standards The SI system is a set of definitions – Exact statements describing a base unit – Coherent – Uniform • based on presumably unchanging constants of nature • exception the kilogram – Unified • Measurements in dynamics, electrodynamics and thermodynamics can be compared in such a way to observe the laws of conservation of mass and energy • • • • The definition is a set of words Following from this is the realisation – creation of a physical object or physical behavior whose observed attributes closely match the definition For example the definition of time – A clock based on Cs133 is created – the radiation produced has attributes that allow the definition to be realised • creates a Primary Standard Measurement labs around the world conduct experiments to realise the various SI definitions ( via Primary Standards) – National Physical Laboratory (NPL) - UK – National Institute of Standards and Technology (NIST) - USA – National Research Council (NRC) - Canada – Bureau International des Poids et Mesures (BIPM) - France • The values obtained from the realization are transferred to devices which represent • • • the SI definition The representations do not involve continuous recreation of the SI base unit They are: – relatively low cost – easily maintained – stable – rugged – called Secondary Standards The overall picture is thus: EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 4 © 2001 SI Definition International Primary Standard Realisation Secondary Standard Representation Working Standard • We will examine those International Primary Standards related to electrical engineering – The Ampere – The Volt – The Ohm The Ampere • Recall the SI definition • Note the extreme restrictions – infinite length – negligible CSA – Vacuum • In practice the Ampere is realized using a current balance • Experiment is complex • Best Uncertainty about 15ppm • Because of discoveries in Quantum Physics the ampere is now realised by using the ratio of Volt to Resistance • Volt – realised with the Josephson Junction • Ohm – realised using the Quantum Hall Effect EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 5 © 2001 7.3 THE JOSEPHSON JUNCTION • • The Primary standard for voltage is based on the Josephson effect This occurs across 2 semiconductors separated by a thin insulator – A Josephson Junction • When cooled in liquid helium the semiconductors become superconductors – exhibit zero resistance The following diagram illustrates the device. Niobium semiconductor Niobium semiconductor Oxidised Aluminium insulator The Josephson Junction • • • The junction is biased with a DC current The junction is exposed to high frequency microwave radiation (GHz) A DC voltage is produced across the junction – voltage is directly proportional to frequency •It was discovered that the following I-V characteristic was produced Bias Current DC Voltage across junction • • As the bias current was increased the voltage increased in a number of equal steps of constant voltage The voltage at a particular step is given by Vn • f nh 2e where: f = the microwave radiation frequency (Hz) n = the number of the particular step EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 6 © 2001 e = the fundamental charge on an electron h = Plank’s Constant • • • In 1990 the ratio 2e/h, called the Josephson Constant Kj, was agreed internationally to be: Kj = 483 597.9 GHz/V Note that the output is based on constants of nature – Anywhere in the universe Kj should be the same Thus f n Kj Vn • • • • For example if f =75GHz: Vj = 155.1V/step This is an incredibly small voltage Modern systems contain several thousand junctions combined in series Typical Uncertainty is 0.2 ppb – parts per billion – 0.2 parts in 1000 000 000 7.4 • • • • • • The Quantum Hall Effect To realise the ampere we have created half of the story – the volt We now examine the other half – the ohm The primary standard for resistance is based on the Hall effect Recall the principle – A thin semiconductor bar carries a DC current – The bar is subjected to a magnetic field perpendicular to it – a Voltage develops across the bar perpendicular to the direction of the current flow • This is the Hall Voltage – The ratio of the Hall Voltage to the DC current is called the Hall Resistance RH of the bar. In 1980 it was discovered that by: – cooling the bar in liquid helium • semiconductor becomes a superconductor; and – greatly increasing the magnetic field the Hall resistance increased in discrete steps At each step the resistance remained extremely constant EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 7 © 2001 This effect was called the Quantum (Quantized) Hall Effect Hall Resistance RH • Magnetic Field QUANTUM HALL EFFECT • The more remarkable discovery was the equation describing RH RH • h n RK n 2 e • Where: n = the number of the particular step e = the fundamental charge on an electron h = Plank’s Constant Since 1990 it was agreed that the value of RK was: • • • • RK is called the Von Klitzing Constant after the discoverer of the effect Typical uncertainty is ±0.2 ppm Again we have realised a standard based on universal constants The standards for the volt and ohm allow us to realise the ampere to about 0.2 ppm RK 25812 .807 0.005 7.5 • • • • • Secondary and Working Standards The Josephson Junctions and the QHE devices are: – expensive to operate – difficult to use They realize the fundamental units each time – they are primary standards For practical applications, the fundamental units must be readily available for use We need a representation of the primary standard Representation occurs at 2 levels – Secondary standards EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 8 © 2001 – Working standards Secondary Standards • Do not recreate the fundamental units • Produce a value which is compared to the primary standard – called calibration • The value is created by any practical engineering method • Typical Secondary standards in electrical engineering are: – The Zener reference cell; and – The Weston cell • both for voltage – The standard resistor • for resistance • There are no inexpensive secondary current standards – A precision voltage is converted by a device called a transconductance amplifier into a precise current • Secondary standards are still too delicate for everyday use • Typically used only a few times per year and have to be maintained under constant temperature and humidity conditions • For more frequent use – like commercial calibration working standards are used • Typical working standards in Electrical Engineering are: – Multifunction calibrators • Contain precision sources for voltage, current and resistance – Decade boxes or individual devices for: • Resistance • Capacitance • Inductance – Precision power supplies EE11A Handouts: Chapter 7 Prepared by: Mr. Fasil Muddeen 9 © 2001