___________________________________________________ Principles of Transmission Lines
the line endlessly, the line is infinitely long, and a certain finite value of
impedance across points K and L is finally reached.
3-55. In this discussion of transmission lines, the effect of conductance (G) is
minor compared to that of inductance (L) and capacitance (C), and is
frequently neglected. In figure 3-16, view C, G is omitted and the inductance
and resistance of each line can be considered as one line.
3-56. Let us assume that the sections of figure 3-16, view C continue to the
right with an infinite number of sections. When an infinite number of
sections extends to the right, the impedance appearing across K and L is Z0.
If the line is cut at R and S, an infinite number of sections still extends to the
right because the line is endless in that direction. Therefore, the impedance
now appearing across points R and S is also Z0, as illustrated in view D. You
can see that if only the first three sections are taken and a load impedance of
Z0 is connected across points R and S, the impedance across the input
terminals K and L is still Z0. The line continues to act as an infinite line, as
illustrated in view E.
3-57. Figure 3-17, view A illustrates how the characteristic impedance of an
infinite line can be calculated. Resistors are added in series parallel across
terminals K and L in eight steps, and the resultant impedances are noted. In
step 1 the impedance is infinite; in step 2 the impedance is 110 ohms. In
step 3 the impedance becomes 62.1 ohms, a change of 47.9 ohms. In step 4 the
impedance is 48.5 ohms, a change of only 13.6 ohms. The resultant changes
in impedance from each additional increment become progressively smaller.
Eventually, practically no change in impedance results from further additions
to the line. The total impedance of the line at this point is said to be at its
characteristic impedance; which, in this case, is 37 ohms. This means that an
infinite line constructed as indicated in step 8 could be effectively replaced by
a 37-ohm resistor. View B shows a 37-ohm resistor placed in the line at
various points to replace the infinite line of step 8 in view A. There is no
change in total impedance.
3-58. In figure 3-17, resistors were used to show impedance characteristics
for the sake of simplicity. Figuring the actual impedance of a line having
reactance is very similar, with inductance taking the place of the series
resistors and capacitance taking the place of the shunt resistors. The
characteristic impedance of lines in actual use normally lies between 50 and
600 ohms.
3-17
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