International System of Units
The work to define these standards began in France and England during the 18th and 19th centuries and 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 today 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 is 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 electric current as a base it seems incredible that all metrics used in our hobby can be derived in this way but illustrating 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. At radio frequencies we can usually ignore resistive and dielectric losses relative to reactance, in which case the detailed transmission line mathematics reduces to Zo=sq rt(L/C) where L is the inductance of a length of line in Henrys and C is the corresponding capacitance in Farads. Note L and C are our customary designations whereas H and F are the SI equivalents. It is not evident that the ratio of L and C would produce a result in Ohms. Reference to the standards makes this clear. Inductance H(Henries) 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 F(Farads)= S*A/ V. It follows that Zo=V/A which has the dimension of ohms and is independent of frequency.
A few feet of the white jacketed twin stranded 14AWG conductor cable from Santa Cruz Electronics provided a practical example of using the Zo formula. With an ADE Impedance meter, capacitance was measured with the far end open and inductance with the far end shorted. The values in pF and uH were noted then expressed as Farads and Henries for use in the formula to arrive at Zo in ohms. Measurements on the twin conductor cable were 76.44 pf and 0.41uH. For a length of Belden 9259 coax cable (nominally 75 Ohms) the measured results were 120.1pF and 0.825uH. I suggest the reader verify the Zo values that were obtained (73.5 ohms for the cable, 83 ohms for the coax) and may wish to conduct a similar test and verify that Zo is independent of the transmission line length and possibly use a more accurate measuring instrument.
Further discussion is likely at our next CAKE meeting on August 12 come join us !
73 Ron W6WO
Mathematical analysis of the behavior of electrical transmission lines grew out of the work of Clerk Maxwell, Lord Kelvin and Oliver Heavyside. In 1885 Heaviside published the first papers that described propagation in cables and the equations for Zo.
Two important references to the applicability of the simplified equation for Zo are
Antennas J.D. Kraus PhD (W8JK) first Edition 1950 p507.
F.E Terman,Electronic and Radio Engineering 4th Edition 1955 p88