International System of Units

International System of Units

The work to define these standards began in France and England during the 18th and 19th centuries.  The history provides a fascinating glimpse of the way our scientific knowledge has evolved and how scientists in Europe collaborated during tumultuous political times.   
 
In living memory, standards of measurement were chaotic and we benefit from the coherent system that has evolved to replace rods, poles, perches, furlongs, pecks, bushels,shillings and farthings, to name but a few. The complete set are known as Standards International (SI) after the French fashion. It is a metric system of units with a two-tier structure of a core of seven base units;
 Electric Current,Temperature,Time, Length,Mass, Luminosity and Substance. With only current as a base it seems incredible that all metrics used in our hobby can be derived  in this way. Proving this is an exercise for another day.  
 
Apart from the convenience and efficiency of adopting the metric system, SI standard definitions can provide insight into the science behind them. For example consider the  characteristic impedance of transmission lines, designated as Zo and measured in Ohms. By ignoring losses, detailed transmission line mathematics reduce to Zo=(L/C)-2   where L is the inductance of a length of line in microHenries and C is the corresponding capacitance in pico Farads. It is not evident that the ratio of L and C would produce a result in Ohms, reference to the standards for L and C makes this clear. Inductance L is defined as the product of Electro Motive Force (Voltage) and Time (Seconds) divided by Current (Amps)  ie V.S/A. Similarly capacitance is defined as C(Farads) = S.A/ V. It follows that  Zo = (V2//A2)-2and therefor Zo=V/A which by Ohms law has the dimension of Ohms.
 
As a practical example take a few feet of the white jacketted twin conductor cable sold by Santa Cruz Electronics. With an instrument like the ADE Impedance meter measure its capacitance with the far end open and inductance with the far end shorted. Note the values in pF and uH, convert these to Farads and Henries then use the formula to arrive at Zo in Ohms. Measurements on the twin conductor cable were 76.44 pf and 0.41uH. For a Belden 9259 coax cable (nominally 75 Ohms) the measured results were 120.1 pF and 0.825uH.  I leave it up to the reader to find the Zo values, also you may wish to verify that these are independent of the transmission line length.
 
Further discussion likely at our next CAKE meeting on August 12
 
73 Ron
 

Posted in August 2017, cake, current