200-ohm resistor of the section, making a combined resistance of 800 ohms. Combining this resistance with the 800-ohm
shunt resistor of the section gives 400 ohms. Finally, by adding the left-hand 200-ohms resistor to 400 ohms, the input
resistance, ZS, is found to be 600 ohms. Since this is the same value as the terminating or load resistance, the
characteristic impedance of this tee section is said to be 600 ohms. A similar calculation can be made for the pi section
shown in B, the characteristic impedance of which is also 600 ohms. Since a change in the values of the elements of the
network changes its characteristic impedance, the characteristic impedance of a network is a property which depends on
the elements or constants of the network.
a. Long Lines. The characteristic impedance of a long line is determined by its distributed constants.
Depending on the type of line, the characteristic impedance may be nearly a pure resistance, as in the case of low-loss
open-wire lines, or may consist of both resistance and capacitive reactance, as in the case of cables. For example, the
characteristic impedance of a 165-mil, two-wire, open-wire line at a frequency of 1,000 hertz comprises a resistance of
562 ohms and a capacitive reactance of 58 ohms. Note that the resistance is nearly 10 times the capacitive reactance. On
the other hand, the characteristic impedance of a 19-gage cable at the same frequency comprises a resistance of 340 ohms
and a capacitive reactance of 314 ohms. It is this quality of cable that accounts for the low wave-propagation velocity of
signals transmitted over them.
b. Characteristic impedance. Figure 56 aids in understanding the development of the characteristic impedance
of a long line. In order to simplify the calculations, the basic section of the line is represented as a tee section containing
only resistance. If the single section shown in A is open-circuited, the sending end, or input impedance, ES, is 200 ohms
in series with 800 ohms, or 1,000 ohms. If a second section now is connected to the input terminals of the first section, as
in B, the right-hand 200-ohm resistance of this second section adds to the 1,000-ohm input resistance of the first section,
giving a combined resistance of 1,200 ohms. This is combined in parallel with the shunt resistance of 800 ohms, making
the equivalent resistance 480 ohms. Finally, adding this in series with the left-hand 200-ohm resistance, the input
resistance for the two sections is found to be 680 ohms. Using a similar sequence of calculations, the input impedance for
three sections can be shown to be 620 ohms, as in C. As more sections are added, the input impedance decreases slowly,
approaching a steady value of 600 ohms in D. This value is the characteristic impedance of the long line.
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