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Characteristic ImpedanceIt was shown by equation 30 that for an infinite uniform line I_{s} = E_{s}/sqrt(z/y), where I_{s} is the sendingend current, E_{s} is the sendingend voltage, z is the linear series line impedance, and y is the linear parallel, or shunt, line admittance (page 198). From this relation,
where Z_{0} is the characteristic impedance, defined^{1} as "the ratio of an applied potential difference to the resultant current at the point where the potential difference is applied, when the line is of infinite length." The term characteristic impedance is applied correctly only to uniform lines with distributed constants (page 192). When an alternating voltage is applied to a uniform infinite line of length L_{∞}, electromagnetic waves are propagated down the line toward infinity and no energy is reflected back to the sending end. The input impedance Z_{i} measured (with an impedance bridge) on this line of length L_{∞}, gives the characteristic impedance Z_{0}. This value is the same for all identical lines. Suppose that some finite length, such as 200 miles, is removed from the infinite line L_{∞}, and that the input impedance Z_{i}' of the remainder of the line (L_{∞}  200} is measured. This impedance Z_{i}' must equal Z_{i} because removing the 200 miles does not appreciably alter the infinite line. But the portion of the line (L_{∞}  200) of impedance Z_{i}' really acts as a termination or load to the 200mile section. It terminates it without reflection, the wave entering it without encountering an impedance discontinuity. Since both the impedances Z_{i }and Z_{i}' equal the characteristic impedance Z_{0} as previously defined, it follows that, when a finite line is terminated with an impedance load equal to its characteristic impedance, then the electromagnetic wave received at the end of the finite line will enter the termination without reflection just as it entered the portion of the infinite line (L_{∞}  200). Hence the characteristic impedance Z_{0} of a finite line is equal to the input impedance of the line when it is terminated in its characteristic impedance Z_{0}. The characteristic impedance of a line is that value of impedance which will terminate a finite length of line so that no wave reflection will occur at the distant end. It should be noted from equation 50 that the characteristic impedance varies with frequency. If it is desired to know the characteristic impedance of a line (pages 221 and 222), this value either can be computed from equation 50 or can be measured. In order to measure the characteristic impedance of a line, the impedance Z_{oc} is first measured with the distant end of the line open, and then Z_{sc} is measured with the distant end shortcircuited. Then, from equations 60 and 64, given on page 207, and the relation
If the resistance and shunt conductance are assumed negligible, the characteristic impedance given by equation 50 becomes
and is sometimes called the natural or surge impedance of the line.


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